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A Comparative Analysis of the Effectiveness of Mathematics
Curriculum Taught at GCE (O-Level) and SSC Systems
of Schools in Karachi
A Dissertation
by
MUHAMMAD AKHTAR
In Partial Fulfillment of the Requirements for the Degree of
Doctor of Philosophy (Ph.D.) in Education
Under the Supervision of
DR. AHMAD SAEED
Presented to
Hamdard Institute of Education and Social Sciences
HAMDARD UNIVERSITY KARACHIJanuary, 2014
ABSTRACTA COMPARATIVE ANALYSIS OF THE EFFECTIVENESS OF MATHEMATICS
CURRICULUM TAUGHT AT GCE (O-LEVEL) AND SSC SYSTEMS OF SCHOOLS IN KARACHI
The focus of this study was on the comparison of mathematics curricula of
General Certificate of Education (GCE) Ordinary Level (O-Level) and Secondary
School Certificate (SSC). The purpose of this comparison was to trace out the factors
responsible for the shortcomings in instructional objectives, contents, approaches,
methods of teaching and pattern of assessment in the local (SSC) system of education.
The study was specifically focused on: (1) to compare and analyze the aims and
objectives of teaching mathematics at SSC and GCE (O- Level); (2) to compare the
contents of textbooks and question papers of SSC and GCE mathematics courses;
(3) to critically compare the effectiveness of approaches and teaching methods
applied in both systems; (4) to compare and analyze the assessment patterns in both
systems.The population of the study was comprised of teachers, students, prescribed
text books of mathematics taught at SSC and GCE (O- Level) and question papers of
the examination boards of both systems.
The overall size of the sample was of 300 teachers, 200 students and 20
subject experts. The sample included 180 teachers, 120 students and 10 subject
experts from the SSC system whereas 120 teachers, 80 students and 10 subject
experts from GCE system. An interview protocol and questionnaires were designed
and administered. A content analysis was made to compare the contents of textbooks
and question papers of the last 20 years (1994-2013) of Board of Secondary
Education Karachi (BSEK) and Cambridge International Examinations (CIE). The
quantitative data were analyzed using t-test.
It was concluded that the implementation of mathematics curriculum is
relatively more effectivein GCE (O-Level) than in SSC curriculum although no
significant difference has been found in the methods of teaching in both systems. The
key factors traced out as major contributors in this difference of effectiveness were:
i
GCE teachers were found clear and well-informed about the expected aims and
objectives of their curriculum while SSC teachers were not clear because they did not
have access to the expected aims and objectives of their curriculum; GCE textbooks
were found aligned with the expected aims and objectives of its curriculum while
contents in SSC textbooks were not found in support of some very important expected
outcomes of curriculum such as logical thinking and systematic reasoning; the
approach of GCE teachers regarding organization of the contents for teaching was
found to some extent concentric (spiral) while SSC teachers were found adopting a
topical approach; the focus of GCE system was found on depth in knowledge through
rigorous practice while the focus of SSC system was found on memorization of
factual and procedural knowledge through practice; GCE system was found using
formative assessment (assessment for learning) more systematically than SSC system
where focus was on summative assessment (assessment of learning), during internal
school assessments; GCE system was more focused on application of knowledge
versus dispensation of knowledge however SSC system was focused more on
constant dispensation of knowledge than its application. The foundation of difference
between the two systems was found in their methods of assessment. The question
papers of GCE mathematics were based on the overall expectations of the curriculum
whereas SSC papers coveredthe expectation of factual and procedural knowledge
only. GCE papers consisted of application based questions with no question exactly
the same as the ones in the textbooks whereas SSC papers were comprised of exactly
same as the textbook questions; GCE papers have been found with no sectioning on
the basis of topics whereas SSC papers were sectioned on the basis of different
topics;no pattern of repetition has been found in GCE papers whereas in SSC papers,
a clear pattern of repetition was found; it was found that whole syllabus is required to
be done inorder to attempt the GCE paper completely, whereas the SSC paper could
be completed even after skipping many topics from the syllabus. No discontinuation
of mathematics has been found at school level in GCE system whereas in SSC
system,a suspension of mathematics teaching for one complete year (during grade IX)
ii
has been observed. In the light of these conclusions, concrete recommendations were
made.
CERTIFICATE OF APPROVAL
This is to certify that Muhammad Akhtar has successfully completed his
research study entitled: “A Comparative Analysis of the Effectiveness of
Mathematics Curriculum Taught at GCE (O-Level) and SSC Systems of
Schools in Karachi”, under my supervision. He has completed his study by
his own research and is not a copy of any other thesis on the subject. I have
viewed the dissertation; it meets the standards of Hamdard Institute of
Education and Social Sciences (HIESS), Hamdard University Karachi.
()
Name and Signature of
Date: January,2014 the Research Supervisor
iii
ACKNOWLEDGEMENTS
I thank Almighty Allah for giving me courage and determination, as well as guidance
in conducting this study, despite all difficulties.
I extend my heartiest gratitude to my supervisor professor Dr. Ahmad Saeed. In fact,it
was Dr. Ahmed Seed’s substantial and courteous supervision that has made me able
to undergo this research work. His inspiring and concrete assistance provided me
clarity and showed light when everything was looking vague and dark.
He always remained very tolerant and determined to see me through.
I would like to express my profound thankfulness to the Dean and Director (HIESS),
Dr.Syed Abdul Aziz for extending his moral and academic support and to all my
professors especially to Dr. Zaira Wahab, whose proactive guidance provided me the
hands-on experience of research.
I would like to present my highest gratitude to all participants of the study for their
benevolentcooperation and especially to Anushay Zainab Abbasi for her wonderful
proofreading of the dissertation.
I am obliged to my parents for their enduring and precious prays to Allah for me.
I am grateful to my younger sister Saira Asghar, younger brother Kamran Shahzad
Asghar Kang and my wife Nadia Akhtar for providing me every kind of support and
cooperation during this study.
I am also thankful to my children Nawal Akhtar, Muhammad Areeb Akhtar Kang,
Muhammad Bilal Akhtar Kang, Muhammad Saaim Akhtar Kang and Aaizah Akhtar
for sacrificing their fun moments with me due to my engagement in research work.
iv
TABLE OF CONTENTS
Abstract i
Certificate of Approval iii
Acknowledgments iv
Table of Contents v
List of Tables x
List of Graphs xix
List of Abbreviations xx
CHAPTER 1: INTRODUCTION
1.1 BACKGROUND 1
1.2 OBJECTIVES OF THE STUDY 6
1.3 RESEARCH QUESTIONS 7
1.3.1 Subsidiary Research Questions 7
1.4 SIGNIFICANCE OF THE STUDY 8
1.5 SCOPE OF THE STUDY 9
1.6 DEFINITIONS OF KEY TERMS 9
1.7 BASIC ASSUMPTIONS 10
CHAPTER 2: REVIEW OF RELATED LITERATURE
2.1 IMPORTANCE OF MATHEMATICS11
2.2 AIMS OF TEACHING MATHEMATICS 132.2.1 Objectives of Education 14
2.3 ROLE OF EDUCATIONAL OBJECTIVES 142.4 CHARACTERISTICS OF EDUCATIONAL OBJECTIVES
152.5 TYPES OF EDUCATIONAL OBJECTIVES 15
v
2.5.1 Cognitive Domain 162.5.2 Affective Domain 21
2.5.3 Psychomotor Domain27
2.6 PRINCIPLES OF CURRICULUM CONSTRUCTION 282.6.1 Principle of Utility 282.6.2 Principle of Preparation 292.6.3 Principle of Discipline/Training 292.6.4 Principle of cultural Value292.6.5 Principle of flexibility292.6.6 Principle of suitability302.6.7 Principle of Interest302.6.8 Principle of Correlation 302.6.9 NCTM Guiding Principles 30
2.7 APPROACHES OF ORGANIZING THE CURRICULUM CONTENTS 32
2.7.1 Topical Approach 322.7.2 Spiral or Concentric Approach
322.7.3 Epistemological Approach
322.7.4 Constructivist’s Approach
32
2.8 ROLE OF TEXTBOOKS IN MATHEMATICS EDUCATION 332.9 APPROACHES OF TEACHING MATHEMATICS 35
2.9.1 Learner-Focused Approach 35
2.9.2 Content-Focused Approach, (With emphasis on understanding)35
2.9.3 Content-Focused Approach,(With emphasis on performance)36
vi
2.9.4 Class-Room Focused Approach 37
2.10 METHODS OF TEACHING MATHEMATICS 372.10.1 Lecture Method 372.10.2 Dogmatic Method372.10.3 Inductive-Deductive Method
372.10.4 Heuristic Method382.10.5 Analytic-Synthetic Method
382.10.6 Laboratory Method
382.10.7 Project Method
382.10.8 Topical Method382.10.9 Concentric Method
392.10.10 Problem Solving Method
39
2.11 PRINCIPLES AND STANDARDS FOR INSTRUCTIONAL PROCESS IN MATHEMATICS 39
2.11.1 Principles 39
2.11.2 Standards 40
2.12 ASSESSMENT IN MATHEMATICS41
2.12.1 Purposes of Assessment44
2.12.2 Principles of Assessment442.12.3 Types of Assessment
46
vii
2.13 STRUCTURE OF SCHOOL EDUCATION IN PAKISTAN47
2.13.1 Secondary School Certificate (SSC) Education 48
2.13.2 Mathematics Education in SSC System 492.13.3 Mathematics Education in GCE System 502.13.4 Examination Boards54
2.14 GCE (O-Level) MATHEMATICS (CIE) 552.14.1 Mathematics (Syllabus D) (4024/4029)552.14.2 Additional Mathematics (4037)
562.14.3 IGCSE Mathematics
56
2.15 DFFERENCE IN CONTENTS AND ASSESSMENT BETWEEN GCE & IGCSE MATHEMATICS COURSES
58
2.16 AN OVERVIEW OF MATHEMATICS EDUCATION IN ASIAN COUNTRIES 58
2.16.1 Singapore59
2.16.2 China 61
2.16.3 Japan 63
CHAPTER 3: RESEARCH METHODOLOGY
3.1 RESEARCH STRATEGY 653.2 POPULATION
653.3 SAMPLE
66
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3.3.1 Sample of Schools (SSC / GCE) 663.3.2 Sample of Teachers (SSC / GCE) 673.3.3 Sample of Students (SSC / GCE) 673.3.4 Sample of Subject Experts (SSC / GCE) 68
3.4 RESEARCH INSTRUMENTS68
3.4.1 Pilot Study 69
3.5 DATA COLLECTION 703.5.1 Ethical Consideration 71
3.6 DATA ANALYSIS71
3.7 DELIMITATION OF THE STUDY71
CHAPTER 4: DATA ANALYSIS
SECTION I: COMPOSITION OF THE SAMPLE 73
SECTION II: ITEM BY ITEM ANALYSIS OF DATA 76
4.1 Analysis of the Responses of SSC and GCE Teachers 76
4.2 Analysis of the Responses of SSC and GCE Students 136
4.3 Analysis of the Responses of Experts 194
4.3.1 Summary, Discussion and Conclusions 202
SECTION III: CONTENT ANALYSIS 206
4.4 Analysis of the Contents of Textbooks and Question Papers 206
4.4.1 Summary, Discussion and Conclusions 246
CHAPTER 5: SUMMARY, FINDINGS, CONCLUSIONS AND RECOMMENDATIONS
5.1 SUMMARY 248
5.2 SECTION WISE RESULTS OF DATA ANALYSIS 249
5.3 FINDINGS 271
ix
5.3.1 Section I: (Significance, Aims, Objectives, Curriculum) 271
5.3.2 Section II: (Contents / Textbooks) 276
5.3.3 Section III: (Approaches and Methods) 279
5.3.4 Section IV: (Assessment and Evaluation) 2855.4 CUMULATIVE FINDINGS 289
5.5 CONCLUSIONS 295
5.6 RECOMMENDATIONS 297
5.7 FURTHER RESEARCH 299
REFERENCES 300
APPENDICES 313
Appendix I: Questionnaire for Teachers 313
Appendix II: Questionnaire for Students 319
Appendix III: Interview Protocol for Subject Experts 325
Appendix IV: Interview (Responses of the Subject Experts) 328
Appendix V: Pilot Testing (Computation of Pearson’s ‘r’) 348
Appendix VI: Syllabus SSC Mathematics 352
Appendix VII: Syllabus GCE Mathematics 356
Appendix VIII: Outline of Mathematics Paper (BSEK) 364
Appendix IX: Outline of Mathematics Paper (CIE) 366
Appendix X: List of Schools in the Sample 369
Appendix XI: List of Subject Experts 376
x
LIST OF TABLES
Table Title Page
1 The affective domain in mathematics education 26
2 Comparison of traditional and modern concepts of assessment 43
3 Stages of Matriculation system of school sducation 48
4 Stages of Cambridge system of school education 51
5 Number of schools (SSC/GCE) in the sample from each district of Karachi 66
6 Teachers (SSC/GCE) in the sample from each district of Karachi 67
7 Students (SSC/GCE) in the sample from each district of Karachi 67
8 Subject experts (SSC/GCE) in the sample from each district of Karachi 68
9 Particulars about the teachers 73
10 Particulars about the students 74
11 Particulars about the subject experts 75
12 Mathematics is one of the most important subjects in the school curriculum 76
13(a) Comparison of reasons for giving importance to mathematics 76
14 The aim of mathematics education is to train or discipline the mind 79
15 The aim of mathematics education is to transfer knowledge for its
application in real life 80
16 The aim of mathematics education is to develop problem solving skills 80
17 The aims of mathematics education are convincing 81
18 The aims of mathematics education are achievable 81
19 The aims of mathematics education can be translated into small objectives 82
20 The objectives of current curriculum are derived from real aims of
mathematics education 82
21 The objectives of mathematics education are well defined 83
xi
22 The objectives of mathematics education are clearly transmitted to teachers 83
23 The current curriculum prepares students for practical life 84
24 The curriculum prepares for future vocations 84
25 The focus of curriculum is on the needs of future education 85
26 The curriculum is comparable withother countries of the region 85
27 The curriculum is correlated with other subjects 86
28 The curriculum is flexible 86
29 The curriculum reflects state-of-the-art 87
30 The curriculum leads towards the set aims of mathematics education 87
31 Contents of the textbooks are properly sequenced 88
32 Contents of the textbooks develop interest 88
33 Contents incite the sense of enquiry 89
34 Language of the textbooks is simple 89
35 The contents cover an appropriate proportion of sums on application
of abstract principles of mathematics in real life problems 90
36 Worked examples in the textbooks provide sufficient guidance to solve
all the problems given for exercise on that topic 90
37(a) Comparison of the domains of intellect developed by the contents of
textbooks 91
38 The contents are in accordance with the intellectual level of students 93
39 The contents contain problems that can be solved by personal investigation
without having aprior method to solve them 94
40 The contents include a proper proportion of mathematical representations
(Graphs, diagrams, figures and tables) 94
41 The contents include an appropriate proportion of activities for
mental exercise (puzzles/riddles) 95
42 The contents are balanced in terms of key areas (number operation, geometry,
algebra, measurement, data analysis and probability) 95
43 Pictures and colorful presentations in the textbooks put a positive effect on
conceptual understanding 96
44 The number of problems given on a certain topic affects
xii
conceptual understanding 96
45 Chaining (bit by bit addition of new material in the sums) on a certain
topic in the text books put a positive effect on conceptual understanding 97
46 Contents of the textbooks are properly chained 97
47(a) Comparison of the approaches of mathematics teaching 98
48(a) Comparison of the practices of teachers in their classes 100
49 Students should solve problems by teacher’s explained method only 104
50 Additional material is usually used for deeper understanding of concepts 104
51 Additional material is usually used for rigorous drill of learned material 105
52 Mostly previous exam papersare used as an additional material 105
53 Previous papers are solved as a rehearsal for the actual exam paper 106
54 Past papers are solved because questions of previous papers are
considered important 106
55 Past papers are solved because questions from previous papers often
repeat in the new papers 107
56 Past papers are solved to understand the pattern of questions coming
in the recent papers 107
57 Teacher-constructed problems are presented in the class 108
58 Students are allowed to construct and present their own problems in the class 108
59 Procedures of doing a problem are explained but not the reason for the
selection of that procedure 109
60 There are some topics in the textbooks that are always left untaught as no question
comes in the paper from these topics 109
61 Homework is given in order to complete the syllabus as it cannot be
completed by solving all the sums in class 110
62 Completion of a topic means that the teacher has explained the topic and
students have done the sums in their copies 110
63 Emphasis is given on neat and tidy written work 111
64 Homework is assigned and checked regularly 111
65 Topics are not explored in depth; only the procedure of doing a sum is
explained 112
66 Unexplained short-cuts are told to solve certain problems 112
xiii
67 Derivation of the formula is not clarified, only the method of its
application is explained 113
68 Usually students avoid checking answers 113
69 Usually students try to skip graph questions 114
70 Teachers do not emphasize checking of answers by students 114
71 Teachers do not emphasize checking answers because they have
a fear of getting a wrong answer in front of the class 114
72 Mathematics has a significant application in other subjects 115
73 Teachers’ true role is to generate a question in the mind of a child
before it is answered 116
74 Both posing and answering of questions by a teacher produce
shallow understanding 116
75 Students can communicate mathematical ideas, reasoning and results 117
76 Students take teaching of mathematics as a pleasant activity 117
77 Students exhibit courage in facing unfamiliar problems 118
78 Students express tolerance in solving difficult problems 118
79 Retention of learned material in the memory becomes stronger with repetition 119
80 Repetition of learned material may attach meaningful relationships
among the fragments of knowledge 119
81 Tests/Exams are conducted to assess the level of achievement of the
instructional objectives 120
82 Tests/Exams are conducted to categorize students into successful and
unsuccessful groups 120
83 The verbal/written remark of teacher on the basis of assessment is evaluation 121
84 Assessment helps both teacher and learner in the process of teaching
and learning 121
85 The fear of assessment motivates students to work hard 122
86 The fear of final examinations is actually the fear of being insulted
on its results 122
87 A teacher is always engaged in the process of assessing his/her
students during the class 123
88 The encouraging remarks of a teacher after assessment produce
xiv
positive effect on the performance of students 123
89 The discouraging remark of a teacher produces a negative effect
on the performance of students 124
90 Methods of assessment should enable students to reveal what they know,
rather than what they do not know 124
91 Students take mathematics assessments confidently 125
92 The main purpose of assessment is to improve teaching and
learning of mathematics 125
93 The exam papers assess the objectives of teaching mathematics 126
94 The exam papers are balanced in terms of content areas 126
95 The exam papers (SSC/GCE) assess the actual educational objectives
of teaching mathematics 127
96 The system of checking papers is fair 127
97 Examinations are conducted under strict vigilance 128
98 Use of unfair means in the paper of mathematics is common 128
99 Grading system of SSC/ GCE is appropriate 129
100 Teachers’ assessment during class is as important as the final examination 129
101 Students’ marks of weekly/monthly/terminal tests are added in the marks
of their final exam paper in junior grades 130
102 Final examinations assess the factual and procedural knowledge of
mathematics only 130
103 Questions in the exam papers are given according to a set pattern 131
104 Questions are given from the textbooks in SSC/GCE papers 131
105 Questions are given from past papers in SSC/GCE papers 132
106 Some topics from the syllabus may be dropped on the basis of ample
choice of questions in the exam paper 132
107 On the basis of previous papers some questions can be predicted for the upcoming
paper 133
108 Assessment is done to distinguish students for the improvement of learning 133
109 Test items of SSC/GCE papers cover all objectives of the curriculum 134
110 Sections of SSC/GCE papers are designed in such a way that questions from
particular chapters always come in specific sections 134
xv
111 The entire teaching and learning process in the class is designed and
implemented to pass the final examinations 135
112 Mathematics is an interesting subject 136
113 I feel pleasure in doing mathematics 136
114 I do mathematics because teachers emphasize its importance 137
115 I do mathematics because it is a compulsory subject at school level 137
116 Mathematics demands rigorous practice 138
117 Mathematics requires concentration 138
118 High achievers in mathematics argue strongly 139
119 High achievers in mathematics are good analysts 139
120 High achievers in mathematics raise more questions 140
121 School gives a special emphasis on mathematics over other subjects 140
122(a) Comparison of perspectives of students about mathematics 141
123 High achievers in mathematics also achieve high grades in other
science subjects 143
124 Doing mathematics means doing mental exercise 144
125 Correct solution to a problem gives a feeling of achievement 144
126(a) Comparison of the factors for which students give importance to
mathematics 145
127 Mathematics is a scoring subject 147
128 Textbooks of mathematics have an attractive look 148
129 Language used in the textbooks is clear 148
130 Language of textbooks is difficult because excessive mathematical
terminologies are used 149
131 All topics in the textbooks are taught completely for the preparation
of final examination 149
132 Methods to solve different types of problems are explained through
worked examples in the textbooks 150
133 Textbooks are illustrated with concept-related pictures from real life 150
134 Pictures in the textbooks facilitate in comprehending the concepts 151
135 Diagrams are the frightening element of the textbooks 151
136 I can study a new topic through worked examples provided in the textbook 152
xvi
137 I study the topic from the textbook first before it is explained
by the teacher in class 152
138 I have questions in mind before starting a new lesson 153
139 Only the contents explained by the teacher should be studied 153
140(a) Comparison of components of the contents that have to be learnt in
Mathematics 154
141 Contents of the textbooks are in accordance with the intellectual levels
of students 156
142 Language of the textbooks is in accordance with the language proficiency
of students 157
143 Getting afraid of a problem in the first look makes it very difficult to solve 157
144 Doing important topics is better than doing all the topics in order to get
good marks 158
145 The last questions (star questions) of the exercises are generally
left unsolved 158
146(a) Comparison of the domains of thinking process during the solution
of a problem 159
147 Most of the teachers emphasize solving the sums using their
explained methods only 161
148 There is more than one method to solve a problem 162
149 Most of the teachers emphasize neat and tidy work 162
150(a) Comparison of the remarks of students for questions involving graphs 163
151 Additional material (worksheets/workbooks etc.) is used to get further
practice of the sums 164
152 Teacher-constructed problems are presented in the class 166
153 Separate activities are done for low achievers in the class 166
154 Teachers arrange activities to engage high achiever students to help
their low achiever class fellows 167
155 In a mathematics class of 40 minutes, students normally ask less
than 5 questions 167
156 In a mathematics class of 40 minutes, teachers normally explain for
less than 15 minutes 168
xvii
157 Students mostly ask ‘HOW’ type questions in the class 168
158 ‘WHY’ type questions are rarely posed by students 169
159 Teachers do not encourage ‘WHY’ type questions in the class 169
160 Procedure of solving a problem is explained but not the reason for the
selection of that procedure 170
161 Some topics of the textbooks are never taught 170
162 Homework is assigned in order to complete the syllabus as it cannot be
completed by solving all the sums in class 171
163 Completion of a topic means that teacher has explained the topic and
students have done the sums in their notebooks 171
164 Homework is assigned and checked regularly by the teachers 172
165 Classwork of students is checked regularly by the teachers 172
166 Topics are not explored in depth; only the procedures of solving sums are
explained 173
167 Short cut techniques are explained to solve certain problems but the
logical reasons behind adopting these techniques are not explained 173
168 Derivation of formula is not explained, only the method of its application
is told 174
169 The activities of a mathematics class are largely doing repetition of
similar sums 174
170 Reference books are taken from the library to explore the topics in depth 175
171(a) Comparison of experiences of students in the class about the teaching
of their teachers 175
172(a) Comparison of attributes of a good teacher from students’ perspective 178
173 Assessments help in confidence building 182
174 Assessments help in identifying and reducing mistakes 183
175 Assessments help in the preparation for final examinations 183
176 Quizzes (short tests based on calculations without using calculators)
are conducted regularly in the class 184
177 Speed tests are conducted regularly in the class 184
178 Positive remarks of the teacher on student’s assessment produce better results 185
179 Negative remarks by a teacher on student’s assessment produce
xviii
demoralization 185
180 I am well aware of the pattern of SSC/GCE paper 186
181 Students study seriously under the pressure of tests/examinations 186
182 Teachers leave some topics completely on the basis of their insignificance
in the SSC/GCE paper 187
183 Questions in SSC/GCE papers are given according to a fixed pattern 187
184 Questions are taken from textbooks in SSC/GCE paper 188
185 Questions are taken from past papers in SSC/GCE paper 188
186 Some topics from the syllabus may be dropped on the basis of sufficient
choice of questions in the exam paper 189
187 Some questions can be predicted for the upcoming papers on the basis of previous
papers 189
188(a) Comparison of methods used for revision before taking a test/ examination 190
189 In junior grades (VI – VIII); the final paper is set from the whole syllabus 192
190 In junior grades (VI – VIII); the final paper is set from the topics covered
in the final term only 193
191 In junior grades (VI – VIII); the topics assessed in one terminal
examination do not come in the next term 193
192 Comparison of Responses of the Experts 194
193 Content Analysis 206
193(a) Sets 206
193(b) System of Real Numbers, Indices and Radicals 211
193(c) Algebra 217
193(d) Matrices 232
193(e) Statistics 234
193(f) Geometry 238
194 Section Wise Results of Data Analysis 249
194(a) Aims / Objectives 249
194(b) Contents / Textbooks 252
194(c) Approaches / Methodology 257
194(d) Assessment / Evaluation 263
xix
LIST OF GRAPHS
Graph Title Page
1 Comparison of the reasons for the importance of mathematics 79
2 Comparison of the domains of intellect developed by the contents
of textbooks 93
3 Comparison of the approaches of mathematics teaching 100
4 Comparison of the practices of teachers in their classes 103
5 Comparison of the students' perspectives about mathematics 143
6 Comparison of the factors for which students give importance to
mathematics 147
7 Comparison of components of the contents that are to be learnt in
mathematics 156
8 Comparison of the domains of thinking process in solving a problem 161
9 Comparison of the remarks of students on questions involving graphs 165
10 Comparison of experiences of students in the class about the teaching
methods of their teachers 178
11 Comparison of the attributes of a mathematics teacher from students’
xx
perspective 182
12 Comparison of methods used for revision before taking a test/ examination 192
LIST OF ABBREVIATIONS
ASER Annual Status of Education Report
BSEK Board of Secondary Education Karachi
BTEC Business Technology Education Council
CIE Cambridge International Examinations
EILE Edexcel International London Examination
GCE (A-Level) General Certificate of Education Advanced Level
GCE (O-Level) General Certificate of Education Ordinary Level
GCSE General Certificate of Secondary Education
HSC High School Certificate
HSSC Higher Secondary School Certificate
ICE International Certificate of Education
IGCSE International General Certificate of Secondary Education
NCERT National Council of Educational Training and Research
xxi
NCTM National Council of Teachers of Mathematics
NEP National Education Policy
PISA Programme for International Student Assessment
SSC Secondary School Certificate
TIMSS Trends in International Mathematics and Science Study
TSLN Thinking Schools Learning Nation
UCLES University of Cambridge Local Examination Syndicate
ULEAC University of London Examination and Assessment Council
xxii
CHAPTER ONE
INTRODUCTION
1.1 BACKGROUND
Secondary school education is an important stage in the overall educational
career of students. It provides a strong base for entering into higher secondary
education with appropriate knowledge and skills or act as a terminal stage for those
seeking employment. Quality secondary education is therefore vital for a
successful future.It is a doorway to social and economic development both at an
individual and national level. (OECD, 2011).
Historically, secondary education has been witnessed as a neglected area
especially in developing countries. However, in the 21st century, its worth has
been acknowledged all over the world (World Bank, 2013). In this regard, the
importance of mathematics as a compulsory subject at school level is also well
acknowledged internationally. It is considered as one of the most important
subjects in the secondary school education. It is due to the reason that this subject
fulfills the utilitarian, vocational, disciplinary, intellectual, cultural, and social
objectives of education (Sharma (2008); Ediger & Rao, 2000).
A number of educational authorities in various countries of the world, even in the
developing countries,have been highlighting the importance of this subject at
different times. The reports of these authories have placed a strong emphasis on the
value of mathematics education in the school curriculum. They all recommended
improving the ways of its teaching.
Cockcroft Report (1982) emphasized that mathematics contributes to the
development of human cognitive, affective and psychomotor faculties but the
extent to which it does so, depends on the way it is taught.
In the subcontinent in 1937, Zakir Hussain Committee recommended that
mathematics should be an essential part of school curriculum. The Secondary
Education Commission in India (1952) emphasized the need of teaching
mathematics as a compulsory subject in schools. India’s most outstanding
commission on education (Kothari Commission, 1964) also put an overwhelming
emphasis on the teaching of mathematics (as cited in Rani, 2008; Sharan and
Sharma, 2008; Sidhu, 2008).
Another very prominent government board on education and training in India,
in one of its reports ‘Curriculum for the Ten Year School’, highlighted that
advancement in the fields of science and technology in this century has made it
more essential to give special attention to the study of mathematics (NCERT,
2006).
Sharif Commission (1959) examined the condition of education especially
science and mathematics education in Pakistan andrecommended that teaching of
mathematics should be given special importance at school level (Government of
Pakistan, 1959, p.122).
Asian countries of the region like China, Japan, Korea and Singapore have
acknowledged the worth of teaching this subject. They have been showing a
special interest in mathematics education since the last three decadeds of the 20 th
century. All these countries have developed a centralized national system of
education with extraordinary emphasis on mathematics education (Becker et al.,
1990). Moreover,they are improving the methods of its teaching day by day. One
of the salient features of mathematics education in these countries is the placement
of equal focus on the process of doing (problem solving) and the product (learning
the contents). In addition, theyuse both intrinsic and extrinsic motivation of
students (Leung, 2004; Zhang et al., 2004). As a result of this special attentionto
mathematics, students of these countries have been attaining top positions in the
2
international studies for the last 20 years (TIMSS, 1995, 1999, 2003, 2007 & 2011;
PISA, 2009, 2012).
Singapore has developed acentralized,world-class system of mathematics education.The framework of Singapore’s mathematics education is highly logical with detailed and consistent implementation procedures.
Kaur (2004) reported that in Singapore, the core subject of school curriculum
is mathematics. Singaporean government revolutionized mathematics education in
1997 by taking three initiatives, one of which was the ‘Thinking Skills Initiative’.
They announced their vision to face the challenges of the new century which
was‘Thinking Schools, Learning Nation’. They launched this program in all
schools to ensure that the young generation can think for themselves and can find
solutions to all the problems they face in the future themselves. Thinking Program
entailed teaching eight core thinking skills embedded in mathematics which is a
core subject at both elementary and secondary level in Singapore. As a
result,Singaporean students of grade 4 and grade 8 have outperformed their
counterparts worldwide in successive international studies (TIMSS, 1995, 1999,
2003, 2007 & 2011; PISA, 2009, 2012).
In addition to this outstanding performance in the international studies in
mathematics, their systems of education are contributing in boosting the economies
by producing thinking brains and skilled hands. These countries are now some of
the world's largest and most prosperous economies i.e. China, Japan, Hong Kong,
Taiwan and South Korea (ISR, 2011, p.54).
The studies conducted in Pakistan reveal thatmathematics is not taught properly in
our schools. The students’ achievement level in mathematics is low as compared to
other subjects. Moreover students perform better on those items in which
3
memorization of facts are required whereas their performance is poor on the items
requiring comprehension and skills of problem solving (Das, 2006).
Mostly teachers transfer knowledge of facts and procedures in mathematics.
Textbookcontents are taught to students and theirprecise replication is assessed
throughexaminations taken in a fixed pattern (Amirali & Halai, 2010; Warrick&
Reimers, 1995).
Tayyba (2010) examined the achievement level of lower secondary students in
mathematics. She attempted to study the variation in the achievement level across
students and schools when different curriculum frameworks are applied. The
results of her study reveal that students are able to pass those items which require
simple mathematical skills and low rigor level.
Arif (2010) conducted a research on the analysis of mathematics curriculum for
grade IX in the province of Punjab. He revealed that curriculum does not produce
higher order thinking skills in students and the class activities are not linked with
curriculum objectives. A number of content areas are also skipped by the teachers
(Perveen, 2009). There is dissatisfaction among students, teachers and experts of
the subject about mathematics education in our secondary schools (Arif, 2010;
Naeemullah, 2007).
Sheerazi (2000) in his study found that mathematics is the least understood
subject at school level in Pakistan. He further stated that it is generally taught by
untrained or semi-trained (trained in general pedagogical aspects) but not by
teachers trained for mathematics education. He recommended that comprehensive
subject specific training programs for teachers, especially for mathematics teachers
should be arranged.
Tahir (2005) in his study specified that mathematics education in Pakistan is
lacking in qualitative developments. Textbooks display the contents in a well-
organized and smart way but these textbooks are taught in isolation with the world
4
of work. As a result instead of understanding the concepts and the inquiry process,
students start memorizing the contents.
Secondary School Certificate (SSC) is the local system of education in
Pakistan. There are two boards of examinations for SSC (the local board / federal
board). There is a difference in the schemes of assessment in the local boards and
the Federal Board of Secondary Education. In Karachi, Agha Khan University
Board of Secondary Education also conducts examinations for SSC. The
examination and assessment pattern of this board is remarkably different from
other boards.
General Certificate of Education (GCE) is a prestigious and internationally
recognized qualification. In 1951England abandoned its old School Certificate
(SC) and Higher School Certificate (HSC) system of education and introduced a
new system in Wales and Northern Ireland. The replacements for SC and HSC
levels in GCE system are Ordinary Level (O-Level) and Advanced Level (A-
Level) respectively (Umbreen, 2008). GCEprogram has been functioning in
Pakistan in some institutions since 1959. A number of institutions offer GCE (O-
Level) these days but 432 schools are registered in the British Council, out of
which 130 are located in Karachi (The British Council, 2012).
GCE (O-Level) and SSC systems are running parallel in Pakistan. It is a
common perception thatthe curriculum of GCE mathematics, its teaching and
assessment methods are signicantly different and more effective than the SSC
curriculum. Thus, these two systems are creating a clear discrimination between
the students. The GCE system is expensive and children of privileged class of
society can only opt for it. The SSC system on the other hand, is affordable and
providing education to the children of under-privileged classes of the society.
A number of comparative studies have been conducted in different areas of
teaching and learning of mathematics at the international level. These studies
provide opportunities to share the experiences and to learn from each other
5
(Mundy & Schmidt, 2005). But no substantial research work has been conducted
on the comparative effectiveness of mathematics curriculums of GCE (O-level)
and SSC systems of education in Pakistan.
Arif (2010) in his study also pointed out that comparative studies of SSC and
GCE (O-Level) systems for the physics, chemistry and biology curricula have been
conducted but that of mathematics curriculum has not beentaken up yet. He has
suggested carrying out such kind of comparative study for the curriculum of
mathematics as well.
This study has been conducted toprobe the issue at large.
1.2 OBJECTIVES OF THE STUDY
General Objective
The overall objective of the study was to analyze the effectiveness
of mathematics curriculum taught at General Certificate of Education GCE
(O- Level) and SSC systems of schools in Karachi.
Specific Objective
The study was specifically focused on
1. To compare and analyze the aims and objectives of teaching mathematics
at SSC and GCE (O- Level).
2. To compare the contents of textbooks and Exam papers of SSC and GCE
mathematics courses.
3. To critically compare the effectiveness of approaches and teaching
methods applied in both the systems.
4. To compare and analyze the assessment patterns in both the systems.
6
1.3 RESEARCH QUESTIONS
The following research questions would encompass the statement of the
problem.
1. What are the projected aims of teaching mathematics in SSC and GCE (O-
Level) systems of education?
2. How far are the objectives of teaching mathematics aligned with the
anticipated aims of mathematics education in both the systems?
3. What are the similarities and dissimilarities in the contents of instruction and
assessment in the two systems?
4. What is the difference between the approaches of teaching mathematics in
these systems?
5. What teaching methods are being used to teach mathematics at SSC and
GCE level?
6. What are the patterns of assessments in SSC and GCE systems?
1.3.1 Subsidiary Research Questions
1. What are the similarities and dissimilarities in the learning experiences of
students in both the systems?
2. What are the attitudes of students towards mathematics in these systems?
3. How far are students aware of the patterns of assessment in the two
systems?
4. How far contents of both the courses are suitable for the students in their
concept building?
5. What are the differences and commonalities in the study patterns of
students in these systems?
6. What are the attributes of a good mathematics teacher from the
perspective of students of both the systems?
7
1.4 SIGNIFICANCE OF THE STUDY
The study was expected to yield the following benefits.
1) The findings of the study would provide guidelines to the curriculum
planners, managers and experts in redefining the objectives of the secondary
school mathematics curriculum.
2) It would facilitate the course developers to design the mathematics course
according to the international standards.
3) The educational planners and administrators may consider subject specific
professional training programs for mathematics teachers.
4) The study would provide teachers the view point of students about teaching
and assessment in mathematics.
5) It would help teachers to know about the concerns and difficulties of
students.
6) It may help teachers teach the subject effectively.
7) The study would help improve the prevailing pattern of assessment in
mathematics.
8) The findings of this study may help investigate the shortcomings in the SSC
mathematics course in order to improve itsquality in Pakistan.
9) The study would help in the advancement of knowledge.
10)The study may help the concerned authorities in taking suitable actions to
make the curriculum effective.
8
1.5 SCOPE OF THE STUDY
The study was limited to the comparison of effectiveness of mathematics
curriculumat all educational institutes engaged in teaching of mathematics
curriculum at GCE (O-Level) and SSC (Matriculation) Level in Karachi. The
comparison of the two courses was specifically based on their educational
objectives, contents of the textbooks, question papers, teaching methods and the
patterns of assessment.
1.6 DEFINITIONS OF THE KEY TERMS
Analysis: A comprehensive investigation to distinguish between facts, to
recognize the relationships, to diagnose the organizational principleetc.
Comparative Analysis: Analysis by comparing two or more comparable
alternatives such as contents, methods, approaches etc.
Effectiveness: The level to which something is productive in yielding
anticipated results.
Comparative analysis of the effectiveness: The extent to which two
curricular programs and their implementation is producing productive outcomes
for students in accordance with the expected outcomes of the curriculum.
Mathematics: The study of the measurement, properties, and relationships of
quantities and sets, using numbers and symbols.
Curriculum: A course of study in one subject at a school or college (Oxford
Dictionary).
Mathematics Curriculum: The educational objectives, contents under study,
its ways of instruction and the patterns of its assessment would be considered as
mathematics curriculum.
9
GCE: General Certificate of Education (O-Level).
SSC: Secondary School Certificatecourse of studies also known as
matriculation.
Karachi: It is the largest city of Pakistan with an estimated population of 21
million. It is situated in the South of Pakistan on the coastline of the Arabian
Sea. Due to a high cultural and ethnic diversity in its population, it is often
called as ‘Mini-Pakistan’.
Exam papers: Examinations of mathematics taken at the end of an academic
period. These include both internal school examinations of junior grades and the
final examinations of SSC (BSEK) and GCE (CIE).
Past Papers: Papers of previous years of SSC mathematics course (Board of
Secondary Education Karachi) and GCE mathematics course (Cambridge
International Examinations).
1.7 BASIC ASSUMPTIONS
a) Mathematics is a compulsory subject both at GCE and SSC level.
b) Hundreds of teachers and thousands of students have been engaged in
teaching-learning process of mathematics.
c) Prescribed textbooks of mathematics are used both at GCE and SSC level.
10
CHAPTER TWO
REVIEW OF THE RELATED LITERATURE
2.1 IMPORTANCE OF MATHEMATICS
Although educationists view mathematics from different philosophical standpoints,
yet they have a complete agreement on the significance of its teaching at school
level. It is therefore; taken as a compulsory subject in the school curriculum.The
educational outcomes of mathematics education dependlargely on the ways it is
taught. Several educational bodies in the world have acknowledged its value and
recommended to improve the methods of its teaching.
According to Cockcroft Report (1982) mathematics is an important subject for the
utility of its arithmetic skills at home and work place. It provides basis for
scientific development and modern technology. It is a management tool in
commerce and industry and has a vast application in other fields of knowledge .It
is also a concise, powerful and unambiguous means of communication.
Zakir Hussain Committee in the subcontinent, The Secondary Education
Commission in India , Kothari Commission andIndian National Policy on
Education had all put an overwhelming emphasis on teaching of mathematics in
the school curriculum (as cited in Rani, 2008; Sharan and Sharma, 2008; Sidhu,
2008). India’s most outstanding body on Educational Research and Training also
emphasized that revolution in the fields of science and technology in this century
has made it more essential to pay a special attention to the study of mathematics in
our schools (NCERT, 2006).
Sharif Commission (1959) recommended that an extraordinary devotion
should be given to theteaching of science and mathematics in our schools
(Government of Pakistan, 1959, p.122).
The aim of education is to enable a person lead a valuable life in the society
but simply enabling to function in the society is only a narrow aim of education.
The higher aim of education is to develop an independent personality with all
human potentials (Bruhlmeier, 2010; Sharma, 2007; Taneja, 1990).
According to Sidhu (2008), there is a clear reason for giving mathematics the core
position in the school curriculum all over the world. He declares it the subject that
fulfills both narrow and higher aims of education. Also there is no dispute among
educationists, industrialists and business leaders on the values attached with
mathematics in school education (Sullivan, 2011).
Generally, it is believed that the chief target of mathematics education is to
produce thinking skills among students but there are many ways of thinking.
According to an outstanding Indian government board on education, the primary
goal of mathematics education is to develop thinking habits to tackle abstractions
and to produce problem solving skills (NCERT, 2006).
Although the study of mathematics contribute to the development of human
cognitive, affective and psychomotor faculties but the extent to which it does so
depends on the way in which this subject is taught (Cockcroft, 1982). Many
nations in the world had recognized the educational values connected to the
teaching of mathematics and had taken different measures to improve the
education of this subject. Singapore is the best example in this regard.
Singaporean students of grade 4 and grade 8 outperformed their counterparts
worldwide in successive international studies. The results of last 20 years of
International Studies (TIMSS) and (PISA) reveal the triumph of Singaporean
students in the world (TIMSS, 1995, 1999, 2003, 2007 and 2011; PISA, 2009,
2012). This outstanding performance is due to a strong education system with a
prime focus on the teaching of mathematics. The students of China, Japan, Korea,
Taiwan and Hong Kong have also been attaining top positions in these studies for
last 20 years (TIMSS, 1995, 1999, 2003, 2007 & 2011; PISA, 2009, 2012).
The fundamental thing common in the education systems of these countries is
a strong emphasis on mathematics education in the school curriculum.Theother
important factor common in these countries is also positively corelted with the
system of education and it is a successful economy. These are some of the
12
world's largest and most prosperous economies i.e. China, Japan, Hong Kong, Taiwan and South Korea (ISR, 2011,p.54). Teaching of mathematics as a compulsory subject in the school curriculum has
certain aims. These aims are like ideals and are taken in a broader perspective.
These aims may be common to different subjects. Knowledge of these aims is very
important for a teacher. Aimlessness can harmfully affect the values and the
purposes of teaching. A very well planned and organized educational scheme is
required to acquire these aims (Mishra, 2008; Sharan and Sharma, 2008).
2.2 AIMS OF TEACHING MATHEMATICSThe ideological aims of teaching mathematics are
1. To provide the learner functional knowledge of mathematics inorder to meet
the increasing demands of sophisticated workforce.
2. To train or discipline the mind for overall personality development.
3. To enable the child understand the organization and maintenance of our
social structure as a society, which is the inter-relation of individuals and
various groups.
4. To prepare the child for further studies in different fields like science,
commerce, information technology etc.
5. To develop the cognitive, affective and psychosomatic faculties of child into
powers (Mishra, 2008; Sidhu, 2008; Sharan and Sharma, 2008).
2.2.1 Objectives of Education
To achieve the aims, large educational activities are divided into smaller units
and one by one after the completion of these units, the projected aims are
attained. Therefore to attain an educational aim of teaching a certain subject,
every small thing that we do, is said to be an objective. These are short-term
13
targets that can be achieved within a limited time period under a certain
classroom setting (Ediger et al., 2010).
No subject can be taught properly without clear aims and objectives of its
teaching in the mind. They guide the teachers and learners in the desired
direction. These objectives must be well balanced among cognitive, affective
and psychomotor domains(Rao, 2006).The objectives should be precise, specific
and attainable (Sharan and Sharma, 2008; Cartor, 1982).
2.3 ROLE OF EDUCATIONAL OBJECTIVES
Educational objectives give the framework of our expectations from the students.
Objectives are helpful in the following ways.
a) Instruction can be focused on a particular point.
b) Provide us guidelines for learning and instruction.
c) Enable the teacher to assess students’ performance objectively.
d) Help the teacher evaluate his/her own performance.
e) The most important role of objectives is that they are derived from the actual
aims and goals of a subject. Thus, they are helpful in achieving the true aims
of education (Gronlund and Bookhart, 2009; Sharan and Sharma, 2008,
Sidhu, 2008).
2.4 CHARACTERISTICS OF EDUCATIONAL OBJECTIVES
2.4.1 Specific Performance
An objective always states what a learner is expected to be able to do and/or
produces to be considered competent. For example: to factorize, to construct, to
draw, to prove, to evaluate, etc.
14
2.4.2 Conditions
An objective describes the important conditions under which the behavior is to
occur. For example: after doing this exercise, after doing this activity, etc.
2.4.3 Criterion or Standard
An objective describes the criteria of acceptable performance. For example find
the volume of a cube correct to the nearest litre, find the area correct to three
significant figures etc (Gronlund and Bookhart, 2009; Mager, 1997).
Description of instructional objectives should encompass all the characteristics
of an objective. In this regard, Heinichet al.,(1999) presented a model that is
known as ABCD model. A for Audience, B for Behavior, C for Condition and D is
for Degree. Another model for writing objectives is SMART Model (Drucker,
1954; Doran, 1981) which again characterizes an objective. S for Specific, M for
Measurable, A for Attainable, R for Result-Oriented and T is for Time-Bound.
2.5 TYPES OF EDUCATIONAL OBJECTIVES
A professor of Chicago University, Dr. B.S. Bloom, and his colleagues,
categorized the human behavior into three parts which represent the intended
outcomes of the educational process.
1) Cognitive Domain
2) Affective Domain
3) Psychomotor Domain
2.5.1 Cognitive Domain
This domain is concerned with mental abilities of a learner and it deals largely
with information and knowledge. Most of the educational objectives in the
current practice of teaching belong to this domain (Mustafa, 2011).
15
This domain is further divided into six major categories of which first three are
called lower mental functions and the last three are known as higher mental
functions (Bloom & Krathwohl, 1956).
2.5.1.1 Knowledge
Knowledge objectives emphasize most of the psychological processes of
remembering.
1. Remembering and recalling of basic facts, symbols and specific details
(factual knowledge).
2. Holding of information about classifications and categories, principles
and their relationships (conceptual knowledge).
3. The memorization and retrieval of certain methods and procedures on
demand (procedural Knowledge).
4. Knowledge of his/her own knowledge. This means to know when and
where a particular strategy or technique can produce better results. It is
the knowledge about possible errors and the ways to tackle them in
problem solving (meta-cognitive knowledge) (Anderson et al., 2001).
The instructional objectives in this category are to develop assimilation among
these four types of knowledge. The solution of any problem requires a
background of some factual knowledge. The first step of instructional objectives
is to provide the knowledge about basic facts of mathematics e.g. signs,
symbols, notations, rules, principles etc. This factual knowledge is of a great
importance as it is the basis of mathematical language. A learner cannot
communicate mathematically without this knowledge. The knowledge about
routes is very helpful before starting a journey therefore the knowledge of
16
techniques and methods to solve a problem in advance is of great value. The
procedural knowledge is associated with conceptual knowledge. The
relationships among different ideas or phenomenon are considered to be
developed by procedural knowledge. On the other hand conceptual (relational)
knowledge may direct towards new methods and techniques (Hiebert, 1986;
Leung, 2004). Meta-cognitive knowledge includes knowledge of general
strategies and techniques, the knowledge of appropriate situation where and
when to apply these strettegies and the knowledge of the effectiveness of these
strategies (Pintrich et al., 2000). Meta-cognitive knowledge is considered as the
basis of the problem-solving approach in mathematics (Schoenfeld, 1992).
2.5.1.2 Comprehension
This is the lowest level of understanding i.e. the ability to use the
provided material or the idea being communicated.
1. The ability to examine, understand and draw relative information from a
given situation.
2. The capability to interpret and obtain meanings from the given
information or situation.
3. The competence to translate the obtained meanings to problem solving.
4. The capacity to extrapolate on the basis of certain statistics (Bloom &
Krathwohl, 1956).
The instructional objectives at this level are to enable the students to use
mathematical language appropriately i.e. use the terminologies, symbols,
notations and mathematical vocabulary; read, understand and give meaning to
mathematical representations, graphs, charts, tables, diagrams, geometrical
figures and models; communicate mathematical ideas, reasoning and results
properly and interpret their understanding and can predict a possible solution of
problem at the early stage.
17
2.5.1.3 Application
The ability to use information i.e. to use abstract knowledge in concrete
situations is called application.
1. The ability to apply knowledge to new situations other than those where
the knowledge was gained.
2. The ability to construct one’s own knowledge from the knowledge gained
in a different setting (Bloom & Krathwohl, 1956).
It is the students’ ability to comprehenda problem situation and apply their
abstract mathematical knowledge to solve that problem. If the application of a
formula or procedure isrequired to solve similar problems (sums), this would be
the lowest level of application. If the student applies abstract knowledge to a
real-life situation that is completely new to him/her, this would be the highest
level of application. This activity is always integrated with previous levels of
the cognitive domain. Retrieval of factual and procedural knowledge from
memory and the use of meta-cognitive knowledge at every stage of problem
solving is a part of the application process.
2.5.1.4 Analysis
The ability to break down information into parts in order to clarify the
communicated message or to organize it to express its properties is called
analysis.
1. The ability to divide information into its constituent parts.
2. The ability to distinguish between facts and interpretations.
18
3. The ability to recognize the relationships among the elements of given
information.
4. The ability to diagnose the organizational principles of a given set of data
(Bloom & Krathwohl, 1956).
2.5.1.5 Synthesis
The ability to put pieces together to form a whole i.e. putting together ideas,
arranging and combining them to form a new idea or product that was not clear
before.
1. The ability to generalize from the facts.
2. The ability to deduce, foresee and draw conclusions.
3. The capability to produce new information using old ideas (Bloom &
Krathwohl, 1956).
2.5.1.6 Evaluation
The ability to make judgments about the value of materials and methods is
called evaluation.
1. The ability to compare and contrast information.
2. The ability to assess the value of ideas and procedures.
3. The ability to select on the basis of argument.
4. The ability to prove the worth of certain evidence (Bloom & Krathwohl,
1956).
Analysis of a given situation is always a fundamental part of problem
solving process in mathematics education. It is the basis on which the solution
of a problem depends. Therefore the development of the faculty of analysis as a
domain of overall intellectual development is a major target of mathematics
education. The ability to synthesize scattered data and to produce new
knowledge from it, to infer on the basis of acquired knowledge and arguments
19
and to evaluate the value of certain evidence are also the vital areas of
mathematics education.
Gagne (1977) and Gagne & Briggs (1979) suggested that the most
important area of school learning is the cognitive domain of learning. Gagne
(1985) described five categories of human behavior that can be observed as the
outcomes of learning. These are thinkingskills, communication skills,
cognitiveapproaches, physical faculties and attitudes. Gagne focused his
attention on the cognitive domain (thinking skills, communication skills, and
cognitive approaches) and within the cognitive domain he focused on the
thinking skills (Martin & Briggs, 1986).
2.5.1.7 Instructional Objectives of Cognitive Domain
The major area of instructional objectives of the current practice of teaching
is of cognitive domain. Some of the possible instructional objectives of this
domain are given below.
1. Students comprehend given information and can transform it into
mathematical language.
2. Use mathematical language appropriately i.e. they can use the
terminologies, symbols, notations and mathematical vocabulary.
3. Read, understand and give meaning to mathematical representations, graphs,
charts, tables, diagrams, geometrical figures and models.
4. Communicate mathematical ideas, reasoning and results properly.
5. Hold basic factual information of the procedures and formulae to solve
certain types of problems.
6. Form relationships among different ideas or phenomena.
7. Have knowledge of general strategies and techniques and the appropriate
situation where and when to apply them.
8. Apply abstract knowledge to solve practical life problems.
9. Construct new knowledge from the knowledge gained in a different setting.
20
10. Analyze a set of data by breaking it into parts.
11. Reason, anticipate and draw conclusions.
12. Evaluate the worth of ideas and procedures.
2.5.2 Affective Domain
2.5.2.1 Receiving
This is the level where the learner feels that there is a stimulus that wants
attention. After realization of the presence of stimulus,the learner decides to pay
attention towards it.
a) Consciousness: The mental alertness of the learner towards a certain
thing, phenomenon or issue.
b) Readiness: The inclination of the learner either to pay attentionor to
avoid the stimulus.
c) Selected Attention: The ability to have a control over attention in order
to select the preferred stimulus out of a number of stimulating distractors
(Krathwohl, Bloom & Masia, 1964).
2.5.2.2 Responding
This is the level where the learner actively attends, participates and responds to
a certain phenomenon or activity and enjoys it.
a) Consent in Response: The response of the learner in which the need of
that response is not fully acknowledged by him.
21
b) Readiness to Respond: The inclination of the learner to respond
voluntarily.
c) Gratification in Response: The feeling of satisfaction or pleasure
enjoyed by the learner in that response (Krathwohl, Bloom & Masia,
1964).
2.5.2.3 Valuing
It is the value given by a learner to a particular thing, phenomenon, or behavior.
The range of this level is from simple acceptance to commitment.
a) Acceptance: This is the lowest level of valuing where the learner accepts
a phenomenon, behavior etc. but has a low degree of conviction.
b) Preference: At this level the learner not only accepts a behavior but goes
further and has intent to pursue and attain it.
c) Commitment: This is the highest degree of belief where the learner has a
true commitment for a certain reason and he also tries to convince others
of the same (Krathwohl, Bloom & Masia, 1964).
2.5.2.4 Organization
At this level,the learner who has internalized some values, compare these
values to determine a relationship between them in order to make a personal
value system. The prime focus at this level is on comparing the values, finding
relationships and on the fusion of these values into a system (Krathwohl, Bloom
& Masia, 1964).
22
a) Conceptualization: At this level the learner attain an ability to
conceptualize a value related to those values that have been already
internalized or the new values he or she is going to acquire.
b) Organization of value: This is the level where the learner organizes and
puts in order his or her own value system (Martin & Briggs, 1986).
2.5.2.5 Characterization by a value or by set of values
At this level, the learner’s behavior comes completely under control of
his/her adapted value system and this control persists for a long time. At this
stage, the learner’s personality is characterized by the same behavior
(Krathwohl, Bloom & Masia, 1964).
A number of studies conducted in the recent past have focused on the affective
issues in teaching of mathematics and highlighted the significance of beliefs,
values and attitudes of students towards mathematics and the implications of these
affective issues on performance (Grootenboer, 2007; Leder & Forgasz, 2006; Ma,
2003, McLeod, 1992). Affective issues (beliefs, values, attitudes and emotions)
play a key role in mathematics education. Beliefs are understandings, premises, or
propositions about the world that are felt to be true (Richardson, 1996, p.103).
McLeod (1992) has mentioned four types of beliefs: Beliefs about self, beliefs
about mathematics teaching, beliefs about social context and beliefs about
mathematics. McLeod (1992) is of the view that these beliefs may change with age
but some of them may have a strong anchor and cannot be easily changed by
routine instruction.
Values are often taken in the same meaning as that of beliefs but there is a
clear distinction between them. This distinction has been identified by Clarkson,
Fitzsimons and Seah (1999, p.3). According to this division,“values are only
23
shown in the form of actions whereas beliefs can be expressed through verbal
expressions and it is not necessary that a person expresses his/her beliefs in the
form of observable actions”. Attitudes are observed as either negative or positive.
They are developed in two ways; either by experiencing a repeated emotional
reaction or by attaching a new attitude to an already existing attitude. For example,
if a student has an attitude of dislike towards graphs, he may attach the same
attitude towards geometrical transformations (Grootenboer, 2007; McLeod, 1992).
Research on attitudes suggests that there is no direct relation between attitude and
achievement in mathematics but rather this relation is complex in nature (Ma,
2003, McLeod, 1992).
2.5.2.6 Instructional Objectives of Affective Domain
According to Sharan (2008), the instructional objectives of affective domain of
mathematics education can fall into two categories: appreciation objectives and
interest objectives.
Some of the possible instructional objectives are as suggested below.
2.5.2.6.1 Appreciation Objectives
1. The pupil appreciates the role of mathematics in other disciplines of
science.
2. Appreciates the symmetry and balance in geometrical figures and solids.
3. Enjoys the patterns of relationships among numbers.
4. Appreciates the use of basic knowledge of mathematics in various aspects
of real life.
5. Takes teaching of mathematics as a pleasant activity (Sidhu, 2008).
2.5.2.6.2 Interest Objectives
24
1. The student takes interest in solving problems of mathematics.
2. Pays proper concentration in solving mathematical riddles and puzzles.
3. Pays attention to the teacher during the instruction.
4. Does class activities with enthusiasm and homework with rigor.
5. Checks answers with curiosity after solving every problem.
6. Exhibits neatness in his/her works (Sidhu, 2008).
2.5.2.6.3 Attitude Objectives
1. The student likes his/her mathematics teacher.
2. Enjoys the company of those who are good at mathematics.
3. Helps the weak students in their difficulties willingly.
4. Enjoys taking mathematics assessments.
5. Shows composure during the solution of several similar mathematical
problems for practice.
6. Exhibits courage in facing unfamiliar problems and expresses tolerance
from the start of problem till its result (Sidhu, 2008).
Table 1: The affective domain in mathematics education
Category Examples
Beliefs About
Nature of Mathematics o Mathematics is a study of rules
and procedures
o Mathematics is a mean to
discipline the mind
25
Own Personality
Teaching of Mathematics
Attitudes
Emotions
o I am a good problem solver
o Teaching is dispensation of
knowledge
Reluctance in solving graphical problems
Pleasure in solving geometrical problems
Inclination towards discovery learning
Enjoyment or annoyance in solving non-
routine problems.
Aesthetic responses to mathematics
Adapted from(McLeod (1992, p, 578)
2.5.3 Psychomotor Domain
2.5.3.1 Imitation
The learner observes an activity and attempts to repeat it, or sees a finished
product and attempts to replicate it while attending to a model (Dave, 1967).
2.5.3.2 Manipulation
The learner performs an activity or produces a product by following written
or verbal instructions without observing the model (Dave, 1967).
26
2.5.3.3 Precision
The learner can independently perform the activity or produce the product
without written or oral instructions and without observing a model (Dave,
1967).
2.5.3.4 Articulation
At this stage, the learner attains the ability to perform the activity or produce
the product to new situations with accuracy and speed (Dave, 1967).
2.5.3.5 Naturalization
At this stage, the learner becomes able to perform the activity with ease and
the work becomes a routine (Dave, 1967). The learner can perform the
activity with a less physical and mental vigor (Huitt, 2003; Dave, 1967).
2.5.3.6 Instructional Objectives of Psychomotor Domain
A careful consideration is required for psychomotor objectives in
teaching of mathematics as these objectives provide the opportunity to
practice the learned material. Practice (drill) is very important in mathematics
education as retention of learned material in the memory becomes stronger
with repetition. It has also been observed in studies on mathematics
instruction that using fragments of knowledge that has already been learned
repeatedly may attach meaningful relationships among them but meaningless
repetition is not recommended (Rao, 2006; Leung, 2004). Some of the
possible psychomotor objectives in teaching of mathematics are as under
1. Drawing a locus or a geometrical figure (line segment, circle, triangle
etc.) from the level of imitation to naturalization.
2. Drawing a graph or sketching a diagram by following written or verbal
instructions till drawing diverse geometrical and spatial figures
autonomously.
3. Application of the formulae and procedures of abstract concepts with
accuracy and speed.
27
4. Order, organization and articulation of the solution of a problem.
5. Demonstration of learned concepts through models or charts.
6. Learning and presenting the concepts using technological resources.
7. Efficient use of electronic devices such as calculators, computers etc.
2.6 PRINCIPLES OF CURRICULUM CONSTRUCTION
Mathematics is a very vast subject. It is very difficult to cover all of its areas in the
school curriculum.Thus, selection of suitable contents for its teaching is a very
important issue. The principles of selecting the content for school curriculum are
as follows.
2.6.1 Principle of Utility
There are certain areas of mathematics that are indispensable to learn for every
person. Topic of every day mathematics i.e. profit and loss, ratio and proportion,
simple and compound interest, hire purchase, exchange rate, estimation and
approximation etc. are very important for every educated person. The utilitarian
value of these topics demands that they should be the essential part of
mathematics curriculum at school level (Sidhu, 2008; Mishra, 2008).
2.6.2 Principle of Preparation
The selection of contents should be made in such a way that the learned
contents can provide a preparatory ground to the learner for the future. The
purpose of these contents in the curriculum is to prepare the child for the future.
There are two ways to prepare the children for the future
i. Preparation for future vocations.
ii. Preparation for higher education.(Sidhu, 2008)
2.6.3 Principle of Discipline/Training
28
One of the aims of mathematics education is to discipline or train the mind.
Therefore, a suitable proportion of topics should be consisted of such activities.
The contents of this type sometimes do not have any utilitarian value but in
order to achieve the disciplinary aim of education, this type of content i.e.
puzzles, riddles, crosswords etc. should be a part of the curriculum (Sidhu,
2008; Mishra, 2008; Sharan, 2008).
2.6.4 Principle of cultural Value
Topics that can develop the characteristics of patience, tolerance, consistency,
containment and appreciation are very important along with problem solving.
Therefore, the problems should be posed by incorporating these values in them
(Sidhu, 2008).
2.6.5 Principle of flexibility
The curriculum should be flexible so that old and outdated contents can be
eradicated and new updated contents can be incorporated (Sharan, 2008, Noyes,
2007).
2.6.6 Principle of suitability
According to this principle contents should be selected in accordance with the
age and level of the students. The suitability of the contents for certain age and
level depends primarily on the difficulty level of the contents. It also depends
upon the sequential arrangement of the topics (Noyes, 2007).
2.6.7 Principle of Interest
Thisprinciple focuses on the concerns of the pupils who often seem to complain
about the uninteresting curriculum contents of mathematics. The topic should be
29
selected in such a way that they can catch the interest of students at different
grade levels (Noyes, 2007).
2.6.8 Principle of Correlation
This principle demands that topics in mathematics curriculum should be
correlated with the topics of other subjects especially with physics and
chemistry. Therefore, the curriculum of mathematics will directly or indirectly
support other subjects and this is the inter-disciplinary aim of mathematics
education (Sharan, 2008).
2.6.9 NCTM Guiding Principles
The National Council of Teachers of Mathematics (NCTM) in USA is
concerned with quality in mathematics education. This organization produced a
number of valuable publications regarding mathematics curriculum. The
following guiding principles are adapted from prominent NCTM publications.
(a) Focus on Coherence
There are different areas of mathematics such as arithmetic, algebra and
geometry. All these areas are highly interconnected. The coherence in the
curriculum means to organize and integrate important concepts within these
areas logically and effectively. The purpose of this focus and coherence is to
develop a rich understanding of and proficiency in problem solving.
(b) Focus on Importance
The focus of curriculum should be on those contents and procedures that
are important and are worthy of both teachers’ and students’ time and
attention. The reasons for this importance may be their usefulness in
developing other mathematical concepts, in relating different domains of
30
mathematical knowledge and in making students able for higher education
and asadroit personnel.
(c) Focus on Articulation
Learning mathematics involves integrating the learned concepts to the new
ones in the hierarchy of ideas and to develop a clear understanding of the
relationship among these. A well- articulated mathematics curriculum can
provide the teachers an opportunity to guide students towards gradually
increasing sophistications and depths of knowledge.
(d) Focus on Depth over Breadth
The emphasis of mathematics curriculum should be on depth rather than
breadth. Curriculum must focus on the essential ideas and processes of
mathematics in depth rather than expanding the content areas. But an
important care in this regards is the avoidance of unnecessary repetition of
topics.
2.7 APPROACHES OF ORGANIZING THE CURRICULUM
CONTENTS
There are two basic approaches used to arrange the contents in a sequence.
2.7.1 Topical Approach
The topical approach is a way of organizing the contents topic wise. When one
topic is finished, the next topic starts. This approach is narrower in focus
(Sidhu, 2008; Hurwitz, 2007).
31
2.7.2 Spiral or Concentric Approach
According to the spiral approach, each topic is revisited in a systematic way in a
more detailed and complex manner each time. This means that covering the
same topics several years in a row and advancing them slightly on each pass.
Thus, a child will solve the problems of the same topic in successive years of
his education with an increase in the difficulty level of the problems (Bruner,
1960).
2.7.3 Epistemological Approach
According to this approach, the contents should be differentiated on the basis of
epistemological structure and simple, formal and advanced ways of knowing
mathematics should be the basis of organizing the contents(Noddings, 1985).
2.7.4 Constructivist’s Approach
According to this approach, the contents are organized on the basis of students’
interests and needs. In this approach, the teacher does not have to cover certain
topics in a sequence but the role of teacher is to arouse the interest of the
students and facilitate them in their own construction of knowledge. Therefore,
in this approach, when the teacher succeeds ininciting the curiosity of learners
in a certain area, the learning material related to that area is presented and vice
versa. The order of contents in this approach is completely dependent on
students’ interests and needs (Ball & Kuhs, 1986).
2.8 ROLE OF TEXTBOOKS IN MATHEMATICS EDUCATION
Textbooks are the most important feature of mathematics education all over the
world, especially in developing countries.These are taken as the epicenter of
mathematics teaching. According to Mahmood (2010a), textbooks are the only
available learning material in schools. The availability of additional teaching and
32
learning material like school libraries, audio/video aids, computer, internet etc. is
rare in Pakistan. Textbooks are an important and primary source of teaching and
learning activities (Kajander, 2009; Schmidt et al., 2001; Tanner, 1988). In
mathematics the sequencing and ordering of learning material is very
important.Therefore, teachers mostly use the textbooks as an organized source of
contents and as a curriculum guide (Mahmoodet al., 2009; Freeman & Porter, 1989).
Teachers usually teach the topics which are present in mathematics textbooks and
the topics that are not included in the textbooks are generally not explored (Freeman
& Porter, 1989).
Sheldon (1988) identified three reasons for the extensive use of textbooks in
schools.
a. Designing personal content for teaching is an extremely difficult task for
teacher.
b. Teachers have very limited time available in schools in which they cannot
develop their own teaching material.
c. Due to some external pressures on teachers they cannot do this task.
Teachers use textbooks to achieve a uniformity of instruction among different
classes.They also use them to give students an organized set of problems for further
practice at home (Pepin, 2001).
On the other hand, students use textbooks to revise their conceptual and
procedural knowledge as they believe that solved examples in the textbooks help
them in solving new problems (Reyset al., 2004; Tyson & Woodward, 1989). The
findings of some international studies conducted after the high performance of
students’ of Asian countries in TIMSS, revealed that there is a positive correlation
of high degree between textbooks and achievement of students (Fan & Zhu, 2004;
Haggarty & Pepin, 2002; Li, 2000; Valverde et al., 2002).
33
Yeap (2005) indicated through his study that textbooks having colorful pictures
and presentations put a positive effect on students’ conceptual understandings. He
also argued that the number of problems on a certain topic given in the textbook
affect conceptual understanding positively.
Ginsburg, Leinwand, Anstrom & Pollock (2005) in a comparative study of
textbooks revealed that Singaporean mathematics textbooks contain in-depth
information of mathematical topics compared to American textbooks. He declared it
one of the reasons for the Singaporean students’ deep understanding of concepts. A
number of similar studies have been conducted to analyze the textbooks of school
mathematics in Asian and European countries (Fan, 2007; Pepin, 2001; Schmidtet
al., 2001; Li, 2000; Stevenson et al., 1986).
Mahmood (2010b) found that in Pakistan, there is a serious lack of consistency
in approved textbooks of mathematics by different publishers at elementary levels.
He identified the internal non-linearity and non-integration of topics within a set of
series of books of more than three publishers. He also recognized inconsistency with
respect to contents and identified that some approved textbooks of mathematics do
not cover the required national curriculum content areas. He mentioned that
approved textbooks of mathematics have a reasonable level of vertical integration
but a very little horizontal integration has been found.
2.9 APPROACHES OF TEACHING MATHEMATICS
According to Ball and Kuhs (1986), the following four approaches of teaching
mathematics are used in the classrooms.
2.9.1 Learner-Focused Approach
34
Learner-focused approach (Ball and Kuhs, 1986) emphasizes the need to
focus the entire instructional activities on the interests and needs of the
learner. This is the constructivist’s approach of teaching (Piaget, 1977).
Learning is a process of developing understanding by methods of inquiry
(Cobb & Steffe, 1983).The role of teacher in this approach is to facilitate
the learners’ construction of knowledge by stimulating their thoughts,
administering the learning process by posing thought provoking problems
and asking inciting questions. The role of the teacher is to help the students
and he/she can help them by listening, examining, accommodating,
reaffirming, encouraging and providing counter examples (Dienes, 1972).
The focus of teaching always remains on concept building. The teacher
niether have a sequenced set of activities to donor he/she has to cover an
organized set of topics in the class, instead the teacher has to arouse the
interests of the learners. As this approach focuses on individuals rather than
the contents therefore the organization and presentation of the material
depend on the areas of interests of the students and their needs.
2.9.2 Content-Focused Approach ( with emphasis on understanding)
According to this approach (Ball and Kuhs, 1986), the prime focus of teachers
lies on the content but with a stress on the development of understanding of
concepts and operations. Skemp (1976) stated that it is not enough for students
to understand how to execute different mathematical tasks (relational
understanding). He claimed that for a complete understanding, they should be
aware of why the concepts and their relationships work as they do (instrumental
understanding).
As the focus in this approach is on both content and understanding, the
expectations from the teacher become high. The teacher has a little authority to
organize the learning content in this approach contrary to learner-focused
approach where the organization and presentation of content rests on needs and
35
interests of the learner. The dilemma for teachers with this approach is that on
one hand they want to explore the topic deeply to get a complete understanding
which requires alternate instructional strategies and is quite time consuming but
on the other hand they are given a limited time within which they have to
complete the prescribed contents as well.
2.9.3 Content-Focused Approach (with emphasis on performance)
This approach (Ball and Kuhs, 1986) is taken from a psychological
viewpoint rather than a disciplinary viewpoint. The contents are presented in a
sequence to students and this organization of content is based on a hierarchy of
concepts and skills. The ordering of material is done before presenting it to
students. This sequencing is based on the maxims of content organization. The
material is presented in an expository style with the explanations of difficult
terminologies, concepts and procedures. The teacher asks convergent questions
from the students so that they can draw a conclusion about a certain matter. The
focus of this approach remains on doing the problems from the textbooks and
gaining expertise by practice. The performance of students on these tasks is
taken as learning in the subject.
2.9.4 Class-Room Focused Approach
With a class-room focused approach (Ball and Kuhs, 1986), the teacher is
an active instructor who presents material effectively, explains efficiently
and makes students involve in the teaching-learning process avoiding
36
interruptions from inside or outside of the class. The role of the teacher is a
continuous monitoring of the students’ class-work, home-work and giving
them feedback. The maintenance of continuous flow of planned activities
and students’ interest in the lesson by minimizing the disruptions is the
prime responsibility of the teacher in this approach. Five possible
components especially for the teaching of mathematics in this approach
could be: daily revision, class-work, home-work, weekly revision and
monthly revision of skills and concepts.
2.10 METHODS OF TEACHING MATHEMATICS
Sidhu (2008) described the following methods of teaching for mathematics.
2.10.1 Lecture Method
This is the method of imparting knowledge through speech. In this method,
the teacher delivers a planned lecture in front of students who have to listen to it
attentively. This method is not suitable for teaching mathematics in its purest
form.
2.10.2 Dogmatic Method
In this method, the teacher provides the details of formulae and procedures
to students and they have to follow and practice it. In this method, the emphasis
lies on accuracy.
2.10.3 Inductive-Deductive Method
Inductive method is based on induction which means to generalize or
taking it as a principle after testing its results on a number of occasions. It leads
from concrete to abstract and from examples to formula. Deductive method is
opposite to inductive method in which we have to proceed from abstract to
concrete and from formula to examples.
2.10.4 Heuristic Method
In this method,the learner has to discover knowledge by his/her own effort.
The teacher does not have to impart knowledge in this method. The teacher can
37
guide and assist his/her students in a gradual manner so that they can discover
the knowledge easily.
2.10.5 Analytic-Synthetic Method
Analytic method proceeds from unknown to known. In this method, the
problem is broken into its constituent parts so that a relationship can be found
between these parts and an already known piece of knowledge. Synthetic
method is converse of analytic method in which the learner proceeds from
known to unknown. This is a method of putting isolated bits of knowledge
together to reach the point where one can conclude or get a new piece of
knowledge.
2.10.6 Laboratory Method
It is a method in which students use concrete material (practical equipment) to
develop mathematical concepts. It becomes more interesting when applied in
lower grades with computer games. The construction of geometrical figures
involves the use of geometrical instruments such as protractor, compass, set
squares etc. so it is like laboratory work.
2.10.7 Project Method
This method is based on the fact that knowledge is individual and is a
method of spontaneous and accidental teaching. The students have to work on a
project and as the project progresses, the learner or group of learners start
gathering the bits of knowledge encountered by them on the way.
2.10.8 Topical Method
It is the converse of concentric method. In this method, a topic is taken as a
unified whole or as an unbreakable unit and is taught till its end without any
intervention of any other topic in between.
2.10.9 Concentric Method
In this method, a certain topic is studied over a long period of time, starting
from foundation level of the concept widening its circle and by adding more
contents in it during the subsequent years.
2.10.10 Problem Solving Method
38
This method was first introduced by Polya (1957). In this method students
are provided a problem for which they do not have an immediate answer.
Moreover, they do not know a specific procedure that can be directly applied to
solve it (Rani, 2008; Schoenfeld, 1992). They have to study the problem in
depth and after analyzing the given information, they have to design their own
strategy to solve it. The problems given to students should be interesting, well-
structured and based on completely new situations that are unfamiliar to the
student previously (NCTM, 2000).
2.11 PRINCIPLES ANDSTANDARDS FOR INSTRUCTIONAL
PROCESS IN MATHEMATICS
NCTM in USA published a document ‘Principles and Standards of School
Mathematics’, which provides guidelines for instructional process in mathematics
(NCTM, 2000).
The principles are statements that reflect basic perceptions essential for an effective
instructional process in mathematics.
2.11.1 Principles
Equity: All students can learn mathematics if instructed properly. Therefore
every student should be accommodated in the process, terms of access and
attainment. For this, necessary arrangements should be made.
Curriculum: A curriculum is not a series of activities, it is more than that. It
should be coherent, practical and well planned.
Teaching: Teaching is a task to develop understanding of mathematics by
assimilating factual, procedural and conceptual knowledge under the
umbrella of meta-cognitive knowledge making students competent and
confident to solve problems.
39
Learning: Development of conceptual understanding, procedural fluency,
strategic competence, adaptive reasoning and productive disposition
(Kilpatrick et al., 2001).
Assessment: Assessment should inform about the worth of instruction and
learning. It should guide both teachers and students to improve their
performance.
Technology: The use of technology is very important in mathematics
education because it enhances students’ conceptual learning (NCTM, 2000).
2.11.2 Standards
The standards are metaphors about how instruction should be imparted to
achieve an optimum level of knowledge and understanding in students. These
principles and standards are very helpful to mathematics teachers and educators,
who can take guidance to improve their instruction.
2.11.2.1 Content Standards
A possible national curriculum for a country should include the
following key content areas in mathematics.
Number and Operations
Algebra
Geometry
Measurement
Data Analysis and Probability (NCTM, 2000).
2.11.2.2 Process Standards
Problem Solving: It means to engage the students in those well-
structured problems for which they do not have any direct method to
40
solve. They imply their existing knowledge to design a strategy to solve
these problems and thus construct their own knowledge.
Reasoning and Proof: It is the basic aim of mathematics to reason
logically by evolving thoughts, reconnoitering phenomena,
rationalizingresults, and using mathematical inferences in all content
areas.
Communication: Communication of ideas in mathematical language in
both written and verbal formis very important as it helps build one’s own
understanding and helps others in clearing their concepts.
Connections: Mathematics is an interrelated field where every topic is
connected to some other. The instructional processes in which the
connections within some mathematical ideas or branches are emphasized
become more meaningful for students because in this way, they learn the
practical use of mathematics.
Representations:Mathematical ideas can be represented in a number of
ways such as figures, diagrams, tables, graphs, notations with letter
symbols etc. The proficient use of representations enables students to
translate, interpret and model complex mathematical phenomena (NCTM,
2000).
2.12 ASSESSMENT IN MATHEMATICS
The process of collecting information about the effectiveness of teaching and
learning is called assessment (Hanna & Dettmer, 2004). Evaluation is considered as
the determination of worth of the results of assessment data. The history of formal
assessment on students’ academic achievements is very old (Siu, 2004). There are
two basic concepts of assessment.
a) Traditional Concept
In ancient times the concept of assessment was to judge the knowledge of
the students on certain topics. The traditional concept of assessment is still
41
prevailing in different forms in mathematics. In the traditional method, students
are assessed by routine sums present in their textbooks on certain topics from
their syllabus. The items of these assessments usually assess lower order thinking
skills of the students i.e. mainly factual and procedural knowledge. These tests
are usually time-bound (limited period of time, e.g. 1 period tests /3-hours
exams), instrument-bound (paper-and-pencil and/or with calculators), and venue-
bound (within classrooms/ board level) tests. These tests are of two types;
internal (organized by school) and external (organized by an external examination
board). The fundamental purpose of these assessments is to mark students on the
basis of their performance and to categorize them on the basis of their grades
(Lianghuo, 2004).
b) Modern Concept
According to modern concept of assessment which is much broader,
mathematics education cannot be assessed only on the basis of routine written
tests. It goes beyond it, emphasizing how students are assessed and what, why
and when are they assessed(Lianghuo, 2004).
According to this concept, assessment is the collection of evidence about
students’ knowledge (factual, procedural and conceptual); their skills to use
mathematics and their dispositions towards mathematics. The collection of
evidence is to assist teaching-learning process in multiple ways.
According to Singapore Ministry of Education’s Assessment Guide,
taking tests, devising mark scheme and giving marks is not students’ assessment.
Assessment should be on going, an integral part of teaching-learning process and
its chief purpose should be the improvement of mathematics education
(Lianghuo, 2004, p.3).
42
Table 2: Comparison of traditional and modern concepts of assessment
Mathematics Assessment Traditional Concept Modern Concept
What (Contents)
Cognitive Domain
Knowledge and Lower Order Skills
Focus on product of learning
Both Cognitive and
Affective Domains
Knowledge (Factual, Conceptual, Procedural),
Skills, Aptitudes and dispositions.
Focus on both product and process.
Where (Location) Within Classrooms
Within and/or Outside
Classrooms
When (Time)Summative (at the end of a
term, quarter, year etc.)
Formative (on going
during instruction) and
Summative
How (Method)
Conventional (paper-
pencil) written tests within
a given time duration (one
period test, 3 hours test,
etc.)
Both Conventional and
Alternative (observing
students, annotated
records, student’s work-
folios etc.)
Why (Purpose)
Single purpose (mainly
grading and reporting
students’ level of
learning).
Multiple Purposes
(Principally improvement
of teaching and learning).
43
Adapted from (Lianghuo, 2004, p.4)
2.12.1 Purposes of Assessment
According to NCTM (1995) assessment standard document the four broad purposes for the assessment of mathematics are as follows
1. Monitor students’ progressTo promote progress
2. Making instructional decisionsTo improve instruction
3. Evaluate students’ achievement To recognize achievement
4. Evaluate programs To modify programs
2.12.2 Principles of Assessment
De Lange (1999, p.10) in his report, ‘Framework for Classroom Assessment in
Mathematics’, has made the following list of principles for assessment.
1. The highest purpose of assessment is to distinguish students for the
improvement of learning (Gronlund, 1968; Black & William, 1998).
2. Methods of assessment should disclosethe level of achievement of students
learning rather than quantifying their unlearning (Cockcroft, 1982).
3. A balanced assessment plan includes various formats and it provides
students opportunities to express and document their performance in variety
of ways (Wiggins, 1992).
4. Assessment items should encompass all the expected objectives of the
curriculum.
5. Mark scheme should be accessible to students and should be strictly
followed. It should also provide examples of marking on previous
assessments.
6. The overall process of assessment should be clear to students.
7. A genuine feedback on the performance of students is also an important and
essential part of assessment.
44
8. The quality of a test should not be measured by reliability and validity in the
traditional sense but reliability and validity should be measured in the light
of the above principles (De Lange, 1999, p.10).
According to the Australian association of mathematics teachers, the learning
of mathematics should be measured under the following guidelines.
(a) Practices of assessing mathematical learning should be appropriate
Assessments should match the purposes for which they are conducted, i.e.
either the assessment is for learning opportunities (formative) which should
be conducted on a regular basis or it is an assessment of learning
(summative), which should be conducted on key stages of schooling.
Assessments should encompass the full range of learning objectives. Use of
different strategies (written reports, group presentations, teachers’
observations etc.) should be adopted to ensure this task.
Assessment should match the published national curriculum.
Assessment should be consistent with the educational objectives and aims of
mathematicseducation (The AAMT, 2008).
(b) Assessment should be fair and inclusive
Students should be fully aware of the nature of tasks and criteria for grading
their performances.
Assessment should be inclusive on the basis of gender or culture, and it
should consist of a variety of tasks that gives students the opportunity to
disclosetheir level of achievement of learning. Moreover,assessment should
be conducted in a way that its processes become clear and transparent to
students.
Assessment should be done with planned means (assessment rubrics,
marking schemes etc.) to reduce the chances of subjective judgments.
45
It should be ensured that students at school level mathematics assessment
should be familiar with what (genres of items) might be expected of them
(The AAMT, 2008).
(c) Assessment should inform learning and action
Teachers should give genuine feedback to students on the information
gathered through assessment about their learning and use it to improve their
future instruction.
Teachers should provide constructive feedback to students and their parents
so that they can improve their performance.
Teachers should view the assessment of students as a single event performed
at a particular time only (The AAMT, 2008).
2.12.3 Types of Assessment
There are three types of assessments: diagnostic, formative and summative
(Hanna & Dettmer, 2004).
2.12.3.1 Diagnostic Assessment
Diagnostic assessment helps the teacher to identify the current level of skills
and concepts of students, which in turn helps the teacher plan future teaching
keeping in view the strengths and weaknesses of the students.
Types of Diagnostic Assessments
Small-scale written/oral pre-test.
Oral questioning prior to start instruction.
Brief interviews before starting class.
2.12.3.2 Formative Assessment
46
It is known as assessment for learning; it is an ongoing assessment of
students during the instructional process. Formative assessment also provides
feedback to teachers about the usefulness of instruction and guides the
teacher to improve instruction by highlighting students’ misconceptions. It
helps us improve our teaching by providing feedback day by day throughout
the year (Hanna & Dettmer, 2004).
Types of Formative Assessments:
Observation of students’ work during the lesson.
Unstructured questioning during class.
Blackboard presentations.
Inspection of students’ written home-work.
Small-scale written test during instruction.
Listening to students
2.12.3.3 Summative Assessment
It is known as assessment of learning; it takes place at the end of a
formal teaching and learning program. It provides information and feedback
about the overall effectiveness of the instructional program. Usually it takes
place biannually or at the end of an academic year (Hanna & Dettmer, 2004).
Types of Summative Assessment:
Terminal examinations (monthly, quarterly, half-yearly etc.)
Annual examinations
2.13 STRUCTURE OF SCHOOL EDUCATION IN PAKISTAN
There are two major systems of formal school education in Pakistan (NEP,
2008). Majority of the students attend the national SSC (matriculation) system of
47
education. The GCE system of education is also available and is expanding rapidly.
The structure of school education (SSC) in Pakistan consists of the following stages.
Table 3: Stages of Matriculation system of school education
Pre-School
(3-5 years)Playgroup - Nursery- KG
Primary School
(6-10 years)Class I – V
Middle School
(11-13 years)Class VI – VIII
High School
(14-15 years)
Class IX (SSC part I)
+
Class X (SSC part II)
= (Matriculation)
(ASER, 2012)
2.13.1 Secondary School Certificate (SSC) Education High school education in Pakistan is comprised of grade IX (SSC: part-I) and
grade X (SSC: part-II). The courseincludes a combination of eight subjects
including optionals (such as Biology, Chemistry, Computer Science, Physics,
48
Economics, Geography, Civics, Education etc.) as well as compulsory subjects
(such as Mathematics, English, Urdu, Islamiyat and Pakistani Studies). The
subjects are selected in two groups, Science Group or General Group. In
Science Group students have only one choice; either they have to select biology
or computer science. Chemistry, physics and mathematics are compulsory
science subjects. In General Group, students have to select four optional
subjects from the humanities group of subjects. There are two boards of
examinations for SSC, one is the local board and the other is federal board.
There is a difference in the schemes of assessments in local boards and the
Federal Board of Secondary Education. In Karachi, a third emination board,
Agha Khan University Board of Secondary Education is also available. The
examination and assessment pattern of this board is remarkably different from
other boards.
2.13.1.1 Board of Secondary Education Karachi (BSEK)
The students appearing in SSC Part-I (Science Group) under this board
have to take five exams/subjects (English, Pakistan Studies, Sindhi,
Chemistry and Biology/ Computer Science).In Part-II, they take English,
Islamiyat, Urdu, Mathematics and Physics.General Group candidates take
English, Pakistan Studies, Sindhi, General Mathematics and an optional
subject from humanities group in SSC Part-I. English, Urdu, Islamiyat and
two optional subjects are taken in Part-II.
2.13.1.2 Federal Board of Secondary Education
This board is available to candidates all over Pakistan and even from
UAE and Saudi Arabia. This board, like other boards of the Punjab Province,
takes examinations of all the subjects at both grade IX and grade X levels.
The contents of each subject have been divided into two equal parts and
students are assessed for first part of each subject in grade IX and for the
second part in grade X.
49
2.13.2 Mathematics Education in SSC System Mathematics is a compulsory school subject in SSC system. India (Rani,
2008; Sharan, 2008), China (Li, 2008; Fan, 2004), Singapore (Soh, 2008) and
Japan (Yoshikawa, 2008) are the countries in the region where mathematics is
the focal point of school curriculum. Unfortunately this subject has not yet
attained the required attention of the concerned educational authorities in
Pakistan.
Under Board of Secondary Education Karachi (BSEK), the students of SSC
Part-I (General Group) have to take a compulsory paper of General
Mathematics of 100 marks whereas the students of Science Group do not take
any mathematics paper in SSC Part-I. Science Group students take their
mathematics paper of 100 marks in SSC Part-II. The same book is used by
students in both groups with some topics deleted for general group.
Candidates appearing under Federal Board of Secondary Education take
two papers, one paper in SSC part-I(75 marks) and the other in part-II(75
marks).
2.13.3 Mathematics Education in GCE System GCE mathematics is a compulsory course to be taken for all students of this
system. It consists of two papers, paper-I(80 marks) in which use of calculator is
not allowed and a paper-II (100 marks) in which scientific calculators are
allowed. A very special attention is given to this subject in this system. The
focus of teaching in this system remains on the application of mathematics in
practical situations. The students generally take examination of mathematics in
May/June but they can also appear in October/November for the improvement
of grade if they want. Cambrige International Examination (CIE) is the board
that takes the examination with the help of British Council Pakistan.
50
Table 4: Stages of Cambridge system of school education
Cambridge Primary
(5-11 years)
Cambridge Primary
Cambridge Primary Checkpoint
Cambridge ICT Starters
Cambridge Secondary 1
(11-14 years)
Cambridge Secondary 1
Cambridge Checkpoint
Cambridge ICT Starters
Cambridge Secondary 2
(14-16 years)
Cambridge IGCSE
Cambridge O Level
Cambridge ICE
Cambridge Advanced
(16-19 years)
Cambridge International AS and A Levels
Cambridge AICE
Cambridge Pre–U
(http://www.cie.org.uk)
2.13.3.1 GCE (O-Level)
GCE (O-Level) examination is an international school-leaving
certificate. It is an international qualification equivalent to the UK’s General
Certificate of Secondary Education (GCSE). The GCE (O-Level) has been
replaced by (GCSE) in U.K since 1986 but still it is widely taken all over the
world, especially in the countries that were formerly British colonies
including Pakistan (Umbreen, 2008).
The GCE (O-Level) curriculum is a comprehensive and balanced study
program witha wide range of subjects as a course of study. The curriculum
targets the development of creative thinking, enquiry and problem solving
51
skills of the learners and is organized in sucha way that students attain both
functionaland theoretical knowledge and skills (CIE, 2008). Candidates have
to select their subjects of study from a wide range of options. A candidate
may take as many subjects as he/she wants to take depending on the
availability and qualification of staff for different subjects in the institution
where the candidate is studying.
In Pakistan a candidate has to take 5 compulsory subjects: Mathematics,
English Language, Urdu Language, Pakistan Studies and Islamiyat. Apart
from these compulsory subjects, candidates have to select 4 optional
subjects. Different institutions provide this option in different ways to
students according to their available resources and faculty qualifications.
Usually institutions offer subjects in groups of four such as Commerce
group, Business Studies group or Science group. For example, in science
group, a candidate has to take Physics, Chemistry, and Biology but for the
fourth subject an option is given to select a subject such as Additional
Mathematics/English Literature etc. Those students, who want to take more
subjects than those offered by the institution, can take them privately.
Generally, candidates take their O-Level examinations for 2 subjects,
Islamiyat and Pakistan Studies, in grade-10 (age 15+). The other 7 subjects
are taken in grade-11(age 16+).
There are two sessions for O-Level examination in a year: May/June
and October/November. Results are given out in August and February
respectively (http://www.britishcouncil.pk). Grade A* (A-star) is allotted on
highest performance in O-Level, and grade E is allotted to a minimum
satisfactory performance.
The British Council is an international organization of U.K for
educational and cultural relations with other countries. The GCE (O-Level)
examinations in Pakistan are organized and supervised by the British Council
in Pakistan.
52
2.13.3.2 General Certificate of Secondary Education GCSE
GCSE is a British certificate of education for secondary school students of
an age of fifteen-sixteen in UK, Wales and Northern Ireland. In 1986, the
GCE (O-Level) and CSE were replaced by General Certificate of Secondary
Education (GCSE) in UK. GCSE emphasizes more on course-work and
places less emphasis on final (summative) assessments
(http://www.edexcel.com/international).
2.13.3.3 International General Certificate of Secondary Education (IGCSE)
IGCSE was developed by CIE formerly called UCIE in 1985 for
candidates outside the United Kingdom. The examination board Edexcel has
also developed its own version of ‘Edexcel IGCSE’ since 2009. IGCSE is not
a certificate of education that usually comprises of a combination of some
subjects. It is a program based on distinct subjects of study, i.e. a candidate
of IGCSE can get this qualification in just one subject or as many subjects as
he/she can. For this reason, students of the same school take different number
of IGCSE papers from all over the world. IGCSE is primarily exam-based, it
resembles GCE (O-Level) rather than GCSE. The IGCSEgrades are from A*
to G with a grade "U" (Ungraded). The “U” grade is equivalent to “Failed” in
SSC system. A* grade was not awarded before 1994. GCSE added this
grade to recognize the very top end of achievement
(http://www.edexcel.com/international).
2.13.3.4 Cambridge International Certificate of Education (ICE)
Cambridge ICE is the group award of the International General
Certificate of Secondary Education (IGCSE). To get an ICE, a candidate has
to pass at least seven subjects, selecting from five different groups of
subjects. These groups are comprised of a wide range of subjects from
different curriculum areas. These groups are:
53
Group I: Languages
Group II: Humanities and Social Sciences
Group III: Sciences
Group IV: Mathematics
Group V: Creative, Technical and Vocational
The candidate has to select two languages from group I (First language,
Second language), one subject each from group II, III, IV and V. The seventh
subject may be selected from any group(http://www.cie.org.uk).
2.13.4 Examination Boards
There are mainly two examination boards which conduct O-Level examinations
in Pakistan (http://www.britishcouncil.pk).
a) Cambrige International Examinations (CIE)
b) Edexcel
2.13.4.1 Cambridge International Examinations (CIE)
UCLES is a department of University of Cambridge and Cambridge
International Examination (CIE) is a part of UCLES. CIE is the largest
assessment agency of Europe and is a part of Cambridge Assessment. It is
the brand name of the University of Cambridge Local Examinations
Syndicate (UCLES) which is a non-teaching department of the University of
Cambridge and a nonprofit organization. CIE is responsible for setting and
assessing a large number of examinations within the United Kingdom and on
international level (http://www.cie.org.uk). It was established in 1998 to
provide internationally recognized qualifications to meet the needs of modern
world of employment and education. CIE qualifications are accepted and
recognized all over the world (Brophy, 1999). In Pakistan, O-Level
54
examinations are conducted by UCLES and the process of designing the
question papers and the assessment is done by CIE.
CIE operate in 160 countries across 6 regions: America, Asia Pacific,
Europe, the Middle East and North Africa, South Asia, and Southern Africa.
In some countries, such as Singapore, Cambridge examinations are the state
qualification for students in secondary school. In other parts of the world,
such as Botswana, Namibia and Swaziland, it works with governments to
reform education systems and helps to localize examinations by training
officials, teachers, markers and examiners in curriculum development and
assessment (http://www.cie.org.uk).
2.13.4.2 Edexcel
Edexcel is another board of examinationfor O-level and A-Level. It was
formed in 1996 by the merging two boards of examinations i.e. BTEC and
ULEAC. The Business and Technology Education Council (BTEC) was the
board of examination for vocational qualifications and the University of
London Examination and Assessment Council (ULEAC) was one of the
major examination boards in UK. Edexcel International examinations
provide qualifications at the level of GCE (O-Level and A-Level) and had
started an International General Certificate of Secondary Education (IGCSE),
available outside UK, since
2009(http://www.edexcel.com/international).
2.14 GCE (O-Level) MATHEMATICS (CIE)
2.14.1 Mathematics (Syllabus D) (4024/4029)
Mathematics is a compulsory subject at GCE (O-Level), IGCSE and ICE
levels. The GCE (O-Level) Mathematics is called Syllabus D, and has the
syllabus code 4024/4029. The syllabus code 4029 is specific only for Mauritius.
55
The course 4024 is examined in both May/June and October/November sessions
while 4029 is examined in October/November session only.
The aims of mathematics syllabus‘D’ according to Cambridge International
Examinations (CIE) are to arouse intellectual curiosity, develop mathematical
knowledge and skills for utilitarian value, appreciation and for further studies.
Development of mathematical language for verbal and symbolic communication
and emphasis on problem-solving skill and efficient use of calculators in
computation are some other salient features of this syllabus (CIE, 2008).
GCE mathematics consists of two papers, containing questions on any part
of the syllabus. Moreover, questions are not essentially limited to a single topic.
Paper 1 contains approximately 25 short answer questions. All questions needs
to be attemted without using calculators. Paper 2 has structured questions across
two sections. Section A contains approximately six to seven questions without
any choice. Section B contains five questions from which four questions have to
be attempted, giving students a choice one question (CIE, 2013).
2.14.2 Additional Mathematics (4037)
This course is planned for those students who are good at mathematics and
want to take up mathematics in their higher studies. The O-Level Additional
Mathematics syllabus enables them to extend their mathematical skills,
knowledge and understanding. The syllabus contains most of the contents on
Pure Mathematics which enables learners to acquire a suitable foundation for
further study in mathematics(http://www.cie.org.uk).
2.14.3 IGCSE Mathematics
Cambridge IGCSE Mathematics provides two options; either to select syllabus
codes 0580 (without coursework) or 0581 (with coursework). In both courses,
there are two further choices of Mathematics (core) or Mathematics (extended).
56
In mathematics (core) grades are awarded from C-G whereas in extended
mathematics, grades are from A*-E. All the papers in IGCSE have no choice of
questions and the use of calculators is allowed (http://www.cie.org.uk).2.14.3.1 IGCSE Mathematics (0580-without coursework)
a) Mathematics (core)
Students have to take two papers in mathematics (core): paper 1 and
paper 3. Paper 1 contains short questions with a time limit of 1 hour. Paper 3
consists of structured questions to be done within 2 hours.
b) Mathematics (extended)
Mathematics (extended) consists of paper 2 and paper 4. Time duration for
paper 2 is 1.5 hours and 2.5 hoursfor paper 4 (CIE, 2013).
2.14.3.2 IGCSE Mathematics (0580-with coursework)
a) Mathematics (core)
This includes three papers: paper 1, paper 3 and paper 5 in which the first
two papers are same except for their weightage of marks. Paper 5 is
coursework that carries a weightage of 20%. The first two papers are
weighted as 30% and 50% respectively.
b) Mathematics (extended)
This includes three papers in it as well: paper 2, paper 4 and paper 6
(coursework). The weightage of marks is 30%, 50% and 20% respectively
(CIE, 2013).
2.15 DFFERENCE IN CONTENTS AND ASSESSMENT BETWEEN
GCE & IGCSE MATHEMATICS COURSES
57
For IGCSE mathematics, candidates have an option of doing coursework if
they want whereas for O-Level mathematics there is no coursework.
IGCSE mathematics has two options: core /extended. In Core grades C to G
and in Extended grade A* to E are awarded respectively. GCE (O-Level) has
grades from A* to E.
In O-Level mathematics paper 1, calculators are not allowed whereas in IGCSE
mathematics, calculators are allowed in both papers.
The total time duration for both papers is 4.5 hours for O-Level mathematics
whereas it is 3 hours for IGCSE mathematics (core) and 4 hours for IGCSE
mathematics (extended).
There is no choice in questions in IGCSE mathematics, while in O-Level
mathematics; there is a choice of 1 question in section B of Paper 2
(http://www.cie.org.uk).
2.16 AN OVERVIEW OF MATHEMATICS EDUCATION IN ASIAN
COUNTRIESThe results of some international studies conducted during the last 20 years show
some interesting results. TIMSS is an international study to assess the knowledge
in mathematics and science of fourth and eighth grade students from all over the
world. Singapore, China, Japan, Korea, Taiwan and Hong Kong are among those
Asian countries that have been attaining top positions in international studies on
students’ achievement in mathematics and science.
The outstanding performance of these countries in mathematics is the success
of their education systems. Therefore, it is worthwhileto analyze the ways
mathematics is taught in these countries. A number of international research
studies have been conducted to study the education systems of these countries. A
review of these studies is presented to find some of the common characteristics of
the way mathematics is taught in these countries.
58
2.16.1 Singapore
Singaporean students of 8 th grade got first positions in mathematics in the
first three consecutive studies held during 1995, 1999 and 2003 respectively.
Their position in the fourth study (2007) was third and they have achieved
second position in the fifth study (2011). In the 4 th grade category, Singapore
stood first in the 1995 and 2003 studies (TIMSS, 1995, 1999, 2003, 2007 and
2011).
Program for International Students Assessment (PISA) is another
international study conducted by the Organization for Economic Co-operation and Development (OECD) that evaluates education
systems throughout the world after every three years. Students of 15 years of
age are assessed in key subjects: reading, mathematics and science. In PISA
(2009) assessment out of 65 countries, Singapore again achieved second
position in mathematics (PISA, 2009).
Kaur (2004) reported that in 1997, before the start of 21st century, Singaporeans’
announced their vision to face the challenges of the new century. The vision
consisted of four words: “Thinking Schools, Learning Nation”. Hence, they
launched a thinking program in all schools. The aim of this program was to
ensure that the young generation can think to find solutions of their problems
especially the new problems they will face in the 21st century. Thinking
Program was to teach these eight thinking skills embedded in mathematics
which is a core subject in both elementary and secondary level in Singapore.
Collection of Facts,
Remembering,
Concentrating,
Organizing,
Analyzing,
59
Evaluating,
Creating, and
Assimilating. (Kaur, 2004)
The primary goal of Singaporean school mathematics curriculum is the
intelligent and creative use of mathematics as a means for problem solving
(Soh, 2008). The attainment of this mathematical ability depends on five inter-
related components: concepts, skills, processes, attitudes and metacognition
(Ministry of Education Singapore, 2007).
The most common approach (Stacey, 2005; Lesh & Zawojewski, 2007)
used by the Singaporean teachers is: learning the routine contents thoroughly,
formulating strategies for problem solving and finally applying these strategies
with the development of useful metacognitive skills.
Ginsburg et al., (2005), in an exploratory study conducted by American
Institute of Research, titled, “What the United States can Learn from
Singapore’s World-Class Mathematics System”, admitted that Singaporean
students are more capable than the US in mathematics. The study pointed out
that the following components of Singapore mathematics education make it
superior to the US mathematics education.
Highly logical national mathematics framework
High quality problem-based mathematics textbooks
Strong assessment system
Highly qualified and trained teachers
Alternative framework for weak student
The study identified the weaknesses in the U.S. mathematics program and
indicated that US students never go much beyond learning the mechanics of
applying definitions and formulas to routine, simple, one-step problems. It was
concluded with the recommendation that United States needs in overall, the
sound features of the Singapore mathematics system.
60
2.16.2 China
Li (2008) reported that after the establishment of Peoples Republic of China
in 1949, the Soviet Union model of education was imported and all school
textbooks were adapted from them. In 1952, within three years, a national
unified textbook policy was adopted. After 1958, Chinese curriculum
developers developed their own mathematics curriculum according to their own
conditions. Although the influence of Soviet Union’s system remained in terms
of characteristics like integrity, coherence, focus and rigor, China succeeded in
developing an indigenous national system governed by ministry of education.
Tu (2010) analyzed the system of mathematics education in China and
highlighted the following guiding principles.
Emphasis on ‘The Two Basics’ (Basic Knowledge and Basic Skills).
Focus on development of mathematical thinking skills (Chinese take
mathematics as aerobics of mind).
Preservation of heuristic method of teaching proposed by Confucius (Not to
intervene or answer until and unless the student have made an effort or have
raised a question).
Influence of Dewey’s theory (1910) ‘learning by doing’and Polya’s theory
(1957) of ‘how to solve problems’ on Chinese mathematics teachers.
The salient characteristics of Chinese Mathematics Education are its
explicit learning objectives with four operational levels (knowing,
understanding, grasping and active application). There is a famous Chinese
proverb, “Insight comes out of familiarity”. Chinese believe that until they
know something well, they cannot be able to innovate it. The meaning taken by
this proverb in China is to apply the basic knowledge in problem solving and do
rigorous practice. Similarly, it means to memorize and understand a piece of
knowledge and practice basic skills until efficacy in application is achieved. By
this they don’t mean to practice meaninglessly, in fact they believe in attaining
61
understanding by analogy and comprehension through connections (Tu & Shen,
2010; Zhang et al., 2004).
Lim (2007) studied the characteristics of mathematics teaching in China
and summarized them as follows.
Variation in teaching (use of different kinds of examples).
Revision of previous work before starting new lesson
Summarization of the taught concepts at the end of each lesson.
Regular homework
Serious and orderly discipline in classes
Strict format of writing (precise and unambiguous language).
Use of ICT such as Power Point and multimedia presentations.
A close teacher-student relationship (encouraging in nature).
2.16.3 Japan
Yoshikawa (2008) reported that Japan, after implementing new curriculum
in 2002, reduced the contents so that the topics can be studied in depth. The four
elements in their objectives of teaching mathematics are: knowledge, skills,
ability to think mathematically and interests in mathematics, willingness to learn
mathematics and attitudes towards mathematics.
Mastrull (2002) studied the Japanese system of mathematics education in
comparison with United States. She examined the reasons for outstanding
performance of Japanese students in mathematics and viewed the following
features accountablefor the superiority of Japanese students over US students.
62
Japanese parents especially mothers take in part in the education of their
children.
Japan has a nationally standardized school curriculum and textbooks.
Mathematics is given a special status in the school curriculum and classes of
mathematics are normally held during first periods of the day.
Teachers usually adopt problem-solving approach and involve students in
group work.
A normal Japanese mathematics class starts with the review of previous
work and ends with a summarization of key points by the teacher.
Regular home assignments and their assessment by the teacher in class.
Preference to mental calculation by both teachers and parents. Therefore the
use of calculators in elementary level is prohibited and a minimum use at
secondary level.
Skiba (2001) stated that the Japanese parents give every first grader student
a math set wrapped in a beautiful way like wedding gifts. The gift includes
mathematical instruments and stationery that the student needs during his/her
primary mathematics education. Teachers enjoy a high social status in Japanese
society. They have a higher number of periods per week than the teachers in the
United States yet they are more committed andpersuaded. Professional
development of teachers is extremely important in Japan. The economic status
of teachers in Japan is also very impressive. In addition to salary, they are
rewarded with a variety of allowances including living allowance, housing
allowance and traveling allowance, as well as three bonuses in a year.
There are some common characteristics among the education systems of
these Asian countries: a centralized national system, extraordinary emphasis on
mathematics education (Becker et al., 1990), equal focus on the process of
doing mathematics (problem solving) and learning the contents of mathematics
using both intrinsic and extrinsic motivation of students (Leung, 2004; Zhang et
63
al., 2004). A substantial attention on teacher’s training and provision of
facilities for them is another important common factor.
The reviewed literatureportrays a broader picture of mathematics education in
the school curriculum. Firstly, it exhibits the significance of mathematics teaching on
philosophical grounds, its expected aims and objectives; principles of the content
selection and assessment. Secondly, on an operational level, it reveals the educational
objectives of mathematics within cognitive, affective and psychomotor domains;
approaches of selection and organization of the contents; approaches and methods of
teaching assessment. Thirdly, the literature presents the overall structure of SSC and
GCE systems of education with a focus on the mechanism of mathematics education.
Lastly, the literature displays the key features of mathematics education of those
countries whose students are performingoutstandingly in the international studies
conductedduring the last twenty years. The overall literature review provides a strong
foundation to compare and analyze the effectiveness of the mathematics curriculum
taught at SSC and GCE systems of education in Karachi, Pakistan.
64
CHAPTER THREE
RESEARCH METHODOLOGY
The majorobjective of this study was to analyze the effectiveness of
mathematics curriculum taught at General Certificate of Education GCE (O- Level)
and SSC system of schools in Karachi by comparing the objectives of teaching,
course contents, methods of teaching and the assessment patterns in the two systems.
The study is descriptive in nature in which mixed method approach of research has
been applied. The survey method was used to collect data from a randomly selected
sample. Questionnaires were used to collect data from teachers and students of both
the systems. The data from subject experts were collected through semi-structured
interviews. A criterion of minimum 15 years of experience in teaching mathematics
was developed for the subject experts of both systems.
3.1 RESEARCH STRATEGY
The research was aimed to make a comparative study of the Secondary School
Certificate (SSC) and the General Certificate of Education GCE (O-level),
Mathematics Course in Karachi. The strategy of research was a mixed research
approach.
3.2 POPULATIONThe population of the study was comprised of teachers,
students and prescribed text books of mathematics taught at 5812 (public/private) secondary schools (Board of Secondary Education Karachi, 2012) registered in the SSC systemand 130 schools (The British Council, 2012)registered in the GCE (O-Level) system. The question papers of previous yearsof both SSC (Board of Secondary Education Karachi / BSEK) and O-Level (Cambridge
International Examination / CIE) mathematics course were also part of the population.
3.3SAMPLE
Sudman (1976) suggested that a minimum of 100 elements is needed for each major group or subgroup in the sample and for each minor subgroup, a sample of 20 to 50 elements is necessary. The overall sample size in this study was of 300 teachers, 200 students and 20 subject experts. Karachi city is administratively divided into five districts (District South, District East, District Central, District West and District Malir). Numbers of schools in each district were not evenly distributed. The density of GCE (O-Level) schools in the District South was much higher than the other districts. On the other hand District West and District Malir had a much lower number of GCE (O-Level) schools. To get a fair representation from each district in the sample, stratified random sampling design along with purposive sampling design was adopted. There were 432 registered institutions, offering GCE (O-Level) in Pakistan, out of which 130 were located in Karachi (The British Council, 2012).
3.3.1 Sample of Schools (SSC / GCE)
A detailed summary of SSC and GCE schools in the sample from
each district of Karachi is presented in the following table.
Table 5: Number of schools (SSC/GCE) in the sample from each district of Karachi
Districts Schools (SSC) Schools (GCE) Total
South 60 40 100
East 50 20 70
66
Central 50 10 60
West 10 00 10
Malir 10 00 10
Total 180 70 250
3.3.2 Sample of Teachers (SSC / GCE)
A detailed summary of SSC and GCE teachers in the sample from each
district of Karachi is presented in the following table.
Table 6: Teachers (SSC/GCE) in the Sample from each District of Karachi
DistrictsTeachers (SSC) Teachers (GCE)
TotalMale Female Male Female
South 38 22 45 30 135
East 30 20 25 13 88
Central 30 20 05 02 57
West 06 04 00 00 10
Malir 06 04 00 00 10
Total 110 70 75 45 300
3.3.3 Sample of Students (SSC / GCE)
A detailed summary of SSC and GCE students in the sample from each
district of Karachi is presented in the following table.
Table 7: Students (SSC/GCE) in the sample from each district of Karachi
DistrictsStudents (SSC) Students (GCE)
TotalMale Female Male Female
South 25 15 25 20 85
East 20 15 15 10 60
Central 15 10 05 05 35
West 05 05 00 00 10
67
Malir 05 05 00 00 10
Total 70 50 45 35 200
3.3.4 Sample of Subject Experts (SSC / GCE)
A detailed summary of SSC and GCE subject experts in the sample
from each district of Karachi is presented in the following table.
Table 8: Subject experts (SSC/GCE) in the sample from each district of
Karachi
DistrictsExperts (SSC) Experts (GCE)
TotalMale Female Male Female
South 03 01 05 01 10
East 02 01 02 01 06
Central 01 01 01 00 03
West 00 00 00 00 00
Malir 01 00 00 00 01
Total 07 03 08 02 20
3.4 RESEARCH INSTRUMENTS
Questionnaires were developed on the basis of objectives of study in the light
of related literature and the works of previous researchers (Kiyani (2002, p.291;
Naeemullah, 2007, p.175; Umbreen 2008, p.185 &Naeem, 2011, p.226).
A questionnaire comprising of 100 items was used to collect data from teachers of
both the systems (Appendix I). The data from students were collected through a
questionnaire containing 80 items (Appendix II). An Interview Protocol containing
68
14 open-ended items was designed and administered from the Subject Experts of
both the systems (Appendix III).
3.4.1 Pilot Study
A small sample of 14 teachers and 14 students was drawn from the actual
sample of the study for pilot testing. Questionnaires developed for teachers were
first distributed among 14 teachers, 7 questionnaires were given to the teachers
of SSC system and 7 were given to the teachers of GCE system. Similarly
questionnaires developed for the students were distributed among 14 students,
taking 7 students from each system. The researcher approached each respondent
in person and requested them to enquire about whatever confusion they had in
responding to any item of the questionnaire. The respondents made some
queries about different items. The researcher took the opinion of the
respondents to make those items more clear. The items of the questionnaires
were reexamined on the basis of the opinions of the respondents. Items that
were enquired about due to the use of certain terminology or difficult words
were changed and items were reconstructed using simple terminologies and
words.
The collected data were then analyzed for a measure of the linear
correlation(dependence) between two variables through Pearson product-
moment correlation coefficient (sometimes referred to as the PPMCC or PCC or
Pearson's ‘r’).
The value of Pearson’s ‘r’ found is given below.
Teachers’ Questionnaire = 0.834 (Appendix IV)
Students’ Questionnaire = 0.763 (Appendix IV)
69
3.5 DATA COLLECTION
The prime objective of this study was the comparative analysis of the
effectiveness of mathematics curriculum of SSC and GCE. Data were collected
through questionnaires to get the views of teachers on objectives of teaching, course
contents, approaches/methods of teaching and their stances on prevailing assessment
patterns of both the systems. The views of teachers were supplemented by
administering an interview protocol for the subject experts of both the systems.
Information on students’ outlook about mathematics, their attitude towards the
contents of textbooks, their learning and assessment experiences being studied in
two different systems were obtained by another questionnaire.
Besides data collection through questionnaires, the content analysis of both
curricula was conducted. For this, data were collected from the published records
available as well as through internet resources. To compare the patterns of
assessment, a comparison of annual papers of the last 20 years (1994-2013) of both
SSC and GCE was done. For this purpose published materials as well as internet
resources were used.
After collecting data for the pilot study, data collection was started in
February, 2013. The session of SSC was ending and students of grade X (SSC), after
undergoing their mathematics curriculum, were ready to appear for their annual
examination. These students could answer questions better than those students who
had not completed their course of study. Therefore, data from SSC students and
teachers were collected first. After this, data from GCE teachers and students were
70
collected before the end of their academic session. Finally, interviews from subject
experts were conducted. The whole process of data collection took 4 months and
was completed in May, 2013.
3.5.1 Ethical Consideration
The participants were well informed about the research study. There consent was taken by informing them about the nature of the study. It was confirmed that the data will be kept confidential.To avoid disclosure of personal information, names of the participants are not displayed with the data collected from them.
3.6 DATA ANALYSIS
After the collection of data, it was tabulated, analyzed and interpreted in the
light of the objectives of the study and research questions using the t-test.
The questionnaires developed for teachers and students were analyzed at five-point
rating scale:(i) Strongly Agree (ii) Agree (iii) Undecided (iv) Disagree (v) Strongly
Disagree. The items designed for the interview of the subject experts were all open
ended.
The responses of experts were summarized in the tables mentioning the
frequency of the respondents against each response. The suggestions from the
experts were also included in conclusions and recommendations. The content
analysis of the text books and question papers of GCE and SSC was made.
71
Finally, conclusions were drawn and recommendations were made on the
basis of analyzed responses of teachers, students, experts and in the light of content
analysis.
3.7 DELIMITATION OF THE STUDY
Due to limited time and resources available to the researcher, the study was
delimited to the responses of teachers and students of grade X only from SSC
system and grade XI (O-Level) only from GCE system.
72
CHAPTER FOUR
DATA ANALYSIS
The specific objective of this study was to compare the mathematics curriculum of the
SSC (Matriculation) and GCE (O-Level) in order to find the differences in terms of
strengths and weaknesses of educational objectives, contents of the textbooks,
approaches of teaching, methods of teaching and assessment systems so that the
effectiveness of key factors involved in these courses can be determined. The analysis
of data collected through research instruments is presented in the following pages.
This chapter is divided into following three sections.
SECTION I: COMPOSITION OF THE SAMPLE
SECTION II: ITEM BY ITEM ANALYSIS OF THE DATA
4.1 Analysis of the responses of teachers
4.2 Analysis of the responses of students
4.3 Analysis of the responses of subject experts
SECTION III: CONTENT ANALYSIS
4.4 Analysis of the contents of textbooks and question
papers
SECTION I: COMPOSITION OF THE SAMPLE
Table 9 shows details of particulars about the teachers in the sample.
Table 9: Particulars about the teachers
DetailsFrequency
SSC GCE
GenderMale (110)
Female (70)
Male (75)
Female (45)
Marital StatusMarried (88)
Unmarried (92)
Married (80)
Unmarried (40)
Age
Less than 30 years (74)30 to 34 years (40)35 to 39 years (18)40 to 44 years (18)45 to 49 years (12)
50 years or above (18)
Less than 30 years (36)30 to 34 years (38)35 to 39 years (24)40 to 44 years (10)45 to 49 years (6)
50 years or above (6)
Academic
Qualifications
B.Sc. (38)
B.A / B.Com / B.E (40)
M.Sc. (62)
M.A / M.B.A (40)
B.Sc. (22)
B.A / B.Com / B.E (16)
M.Sc. (70)
M.A / M.B.A (12)
Professional
Qualifications
PTC (2), C.T (2)
B.Ed. (42), M.Ed. (10)
Other Short Courses (4)
B.Ed. (14)
M.Ed. (8)
PGCC (16)
Experience
Less than 5 years (70)5 to 9 years (50)
10 to 14 years (26)15 to 19 years (10)
20 years or above (24)
Less than 5 years (44)5 to 9 years (32)
10 to 14 years (26)15 to 19 years (12)
20 years or above (6)Control of
Institution
Private / Government
Private (165)
Government (15)
Private (120)
Government (0)
(Contd…….)Monthly Income Less than 40 thousands
(147)Less than 40 thousands
(64)
73
40 to 60 thousands (23)60 to 80 thousands (0)80 to 100 thousands (1)100 thousands plus (2)
Did not mention (7)
40 to 60 thousands (32)60 to 80 thousands (8)80 to 100 thousands (2)100 thousands plus (10)
Did not mention (4)
Table 10: Particulars about the students
DetailsFrequency
SSC GCE
GenderMale (70)
Female (50)
Male (45)
Female (35)
GradeX (120)
(Matriculation)
XI (80)
(O-Level-Final year)
Age14 years (11)15 years (25)16 years (68)17 years (16)
15 years (13)16 years (45)17 years (16)18 years (6)
Qualification of Father
Graduate (75)
Undergraduate (39)
Did not mention (6)
Graduate (69)
Undergraduate (7)
Did not mention (4)
Qualification of Mother
Graduate (44)
Undergraduate (70)
Did not mention (6)
Graduate (54)
Undergraduate (22)
Did not mention (4)
Table 11: Particulars about the subject experts
74
DetailsFrequency
SSC GCE
GenderMale (7)
Female (3)
Male (8)
Female (2)
Designations
H.M (3)
HOD (4)
Senior Teachers (3)
H.M (0)
HOD (4)
Senior Teachers (6)
Academic
Qualifications
B.Sc. (2)
M.Sc. (8)
B.Sc. (1)
M.Sc. (9)
Professional
Qualifications
B.Ed. (3)
M.Ed. (6)
Nil (1)
B.Ed. (4)
M.Ed. (1)
PGCC (2), Nil (3)
Experience
(in years)
15-20 (2)
21-25 (2)
26-30 (3)
31-35 (2)
36-40 (0)
41-45 (1)
15-20 (7)
21-25 (2)
26-30 (0)
31-35 (1)
Control of Institution
Private / Government
Private (9)
Government (1)
Private (10)
Government (0)
SECTION II: ITEM BY ITEM ANALYSIS OF DATA
75
4.1 ANALYSIS OF THE RESPONSES OF TEACHERS
Table 12: Mathematics is one of themost important subjects in the school
curriculum
H0:There will be no significant difference between SSC and GCE teachers on the statement that mathematics is one of themost important subjects in the school curriculumRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1= 4.50 0.7360.087 0.345
GCE(O-Level) 120 x2= 4.47 0.766
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table ‘12’we find that the tabulated ‘t’ value = 1.960 is
larger than the computed ‘t’ value = 0.345. Hence H0 is accepted, which leads us to
the conclusion that there is no significant difference between SSC and GCE system
of schools on the statement that mathematics is one of the most important subjects in
the school curriculum.
Table 13(a): Comparison of the reasons for giving importance to mathematics
ReasonsH0:There will be no significant difference between the reasons of SSC and GCE teachers for giving importance to mathematics
1. It is largely
applied in
practical life
Respondents N Mean SD SEx1−x2
t-value
SSC(Matriculation
)180 x1= 4.61 0.648
0.082 2.804
GCE(O-Level) 120 x2= 4.38 0.738
(Contd…….)
2.It is largely
SSC(Matriculation
)
180 x1= 4.30 0.841
0.083 1.325
76
applied in
other subjects GCE(O-Level) 120x2=¿
4.410.591
3.It develops
power of
intellect
SSC(Matriculation
)180 x1= 4.47 0.621
0.071 0.282
GCE(O-Level) 120x2=¿
4.450.594
4.It develops
desirable
habits
SSC(Matriculation
)180 x1= 3.63 0.976
0.111 0.631
GCE(O-Level) 120x2=¿
3.700.907
5.It develops
desirable
attitudes
SSC(Matriculation
)180 x1= 3.48 1.019
0.118 0.593
GCE(O-Level) 120x2=¿
3.550.998
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusions
1. It is largely applied in practical life
Referring to table 13(a), we find that the tabulated ‘t’ value = 1.960 is smaller
than the computed ‘t’ value = 2.804. Hence,H0 is rejected, which leads us to the
conclusion that the two groups of teachers have a significant difference between
them regarding the reason that mathematics is important at school level due to its
practical application.
2. It is largely applied in other subjects
77
Referring to table 13(a), we find that the tabulated ‘t’ value = 1.960 is smaller
than the computed ‘t’ value = 1.325. Hence,H0 is accepted, which leads us to the
conclusion that the two groups of teachers have no significant difference between
them regarding the reason that mathematics is important at school level due to its
application in other subjects.
3. It develops the power of intellect
Referring to table 13(a), we find that the tabulated ‘t’ value = 1.960 is smaller
than the computed ‘t’ value = 0.282. Hence,H0 is accepted, which leads us to the
conclusion that the two groups of teachers have no significant difference between
them regarding the reason that mathematics is important at school level as it
develops intellectual powers.
4. It develops desirable habits
Referring to table 13(a), we find that the tabulated ‘t’ value = 1.960 is smaller
than the computed ‘t’ value = 0.631. Hence,H0 is accepted, which leads us to the
conclusion that the two groups of teachers have no significant difference between
them regarding the reason that mathematics is important at school level as it
develops desirable habits among students.
5. It develops the desirable attitudes
Referring to table 13(a), we find that the tabulated ‘t’ value = 1.960 is smaller
than the computed ‘t’ value = 0.593. Hence,H0 is accepted, which leads us to the
conclusion that the two groups of teachers have no significant difference between
them regarding the reason that mathematics is important at school level as it
develops desirable attitudes among students.
13(b): Graph 1
78
Reason 1 Reason 2 Reason 3 Reason 4 Reason 50%
20%
40%
60%
80%
100%
120%
*Comparison of the reasons for the importance of mathemat-ics
Res
pons
es in
per
cent
*For this comparison SA & A, alternatives of the measurement scale has been collapsed to get the percentage of agreement
Table 14: The aim of mathematics education is to train or discipline the mind
H0:There will be no significant difference between SSC and GCE teachers on the statement that the aim of mathematics education is to train or discipline the mindRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿4.20 0.8350.097 1.546
GCE(O-Level) 120 x2=¿4.05 0.852
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 14, we find that the tabulated ‘t’ value = 1.960 is
larger than the computed ‘t’ value = 1.546. Hence,H0 is accepted, which leads us to
the conclusion that the two groups of teachers have no significant difference between
them regarding the statement that the aim of mathematics education is to train the
mind.
Table 15: The aim of mathematics education is to transfer knowledge for its
application in real life
79
H0:There will be no significant difference between SSC and GCE teachers on the statement that the aim of mathematics education is to transfer knowledge for its application in real lifeRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿4.33 0.8610.091 0.549
GCE(O-Level) 120 x2=¿4.38 0.715
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 15, we find that the tabulated ‘t’ value = 1.960 is
larger than the computed ‘t’ value = 0.549. Hence,H0 is accepted, which leads us to
the conclusion that the two groups of teachers have no significant difference between
them on the statement that the aim of mathematics education is to transfer knowledge
for its application in real life.
Table 16: The aim of mathematics education is to develop problem solving
skills
H0:There will be no significant difference between SSC and GCE teachers
regarding the statement that the aim of mathematics education is to develop
problem solving skills
Respondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿4.35 0.8110.081 1.975
GCE(O-Level) 120 x2=¿4.51 0.596
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 16, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 1.975. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between themregarding the statement that development of problem solving skills is the aim
of mathematics education.
Table 17: The aims of mathematics education are convincing
80
H0:There will be no significant difference between SSC and GCE teachers on the statement that the aims of mathematics education are convincingRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.37 1.1760.112 5.982
GCE(O-Level) 120 x2=¿4.04 0.768
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 17, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 5.982. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the
statement that aims of mathematics education are convincing.
Table 18: The aims of mathematics education are achievable
H0:There will be no significant difference between SSC and GCE teachers on the
statement that the aims of mathematics education are achievable
Respondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿4.02 0.9350.106 0.283
GCE(O-Level) 120 x2=¿4.05 0.890
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 18, we find that the tabulated ‘t’ value = 1.960 is larger than the computed ‘t’ value = 0.283. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on the
statement that aims of mathematics education are achievable.
81
Table 19: The aims of mathematics education can be translated into small
objectives
H0:There will be no significant difference between SSC and GCE teachers on the
statement that the aims of mathematics education can be translated into small
objectives
Respondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.74 0.8150.097 0.618
GCE(O-Level) 120 x2=¿3.80 0.839
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 19, we find that the tabulated ‘t’ value = 1.960 is larger than the computed ‘t’ value = 0.618. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between themon the
statement that the aims of mathematics education can be translated into small
objectives.
Table 20: The objectives of current curriculum are derived from real aims of
mathematics education
H0:There will be no significant difference between SSC and GCE teachers on the statement that objectives of current curriculum are derived from actual aimsRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.82 0.9940.109 1.848
GCE(O-Level) 120 x2=¿3.58 0.892
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 20, we find that the tabulated ‘t’ value = 1.960 is larger than the computed ‘t’ value = 1.848. Hence,
82
H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them in their beliefs
that the objectives of current curriculum are derived from actual aims.
Table 21: The objectives of mathematics education are well defined
H0:There will be no significant difference in the opinions of SSC and GCE teachers that objectives of mathematics teaching are well definedRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.73 0.9570.105 1.428
GCE(O-Level) 120 x2=¿3.88 0.861
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 21, we find that the tabulated ‘t’ value = 1.960 is larger than the computed ‘t’ value = 1.428.Hence, H0 is accepted, which leads us to the conclusion that there is no significant difference in the opinions of SSC and GCE teachers that the
objectives of teaching mathematics are well defined.
Table 22: The objectives of mathematics education are clearly transmitted to
teachers
H0:There will be no significant difference between SSC and GCE teachers regarding the statement that objectives of mathematics education are clearly transmitted to teachersRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.47 1.1100.199 2.261
GCE(O-Level) 120 x2=¿3.92 0.161
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 22, we find that the tabulated ‘t’ value = 1.960 is larger than the computed ‘t’ value = 2.261. Hence,
83
H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between themregarding the
statement that objectives of mathematics education are clearly transmitted to teachers.
Table 23: The current curriculum prepares students for practical life
H0:There will be no significant difference between SSC and GCE teachers on the statement that the current curriculum prepares students for practical lifeRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.84 1.1500.110 2.363
GCE(O-Level) 120 x2=¿4.10 0.764
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 23, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 2.363. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between themon the
statement that the current curriculum prepares students for practical life.
Table 24: The curriculum prepares for future vocations
H0:There will be no significant difference between SSC and GCE teachers regarding the statement that curriculum prepares for future vocationsRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.70 1.0380.099 2.323
GCE(O-Level) 120 x2=¿3.93 0.685
df =298 tabulated ‘t’ value at 0.05 = 1.960
84
Conclusion:Referring to table 24, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 2.323. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them regarding the statement that curriculum prepares for future vocations.
Table 25: The focus of curriculum is on the needs of future education
H0:There will be no significant difference between SSC and GCE teachers for the statement that focus of the curriculum is on the needs of future educationRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.68 1.0660.104 3.846
GCE(O-Level) 120 x2=¿4.08 0.748
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion: Referring to table 25, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 3.846. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them with
respect to the statement that focus of the curriculum is on the needs of future
education.
Table 26: The curriculum is comparable with the curricula of other countries
of the region
H0:There will be no significant difference between SSC and GCE teachers
85
regarding the statement that the curriculum is comparable with the curricula of other countries of the regionRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.14 1.1760.120 6.333
GCE(O-Level) 120 x2=¿3.90 0.915
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion: Referring to table 26, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 6.333. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them regarding the statement that the curriculum is comparable with the curricula of other
countries of the region.
Table 27: The curriculum is correlated with other subjects
H0:There will be no significant difference between SSC and GCE teachers regarding the statement that the curriculum is correlated with other subjectsRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.68 0.9200.102 2.843
GCE(O-Level) 120 x2=¿3.97 0.843
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 27, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 2.843. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them regarding the statement that the curriculum is correlated with other subjects.
Table 28: The curriculum is flexible
86
H0:There will be no significant difference between SSC and GCE teachers in stating the current curriculum flexibleRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.51 1.0410.103 3.981
GCE(O-Level) 120 x2=¿3.92 0.765
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 28, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 3.981. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them in
stating the current curriculum flexible.
Table 29: The curriculum reflects state-of-the-art
H0:There will be no significant difference between SSC and GCE teachers regarding the statement that curriculum reflects state of the artRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.04 1.0370.115 4.869
GCE(O-Level) 120 x2=¿3.60 0.942
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 29, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 4.869. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them regarding the statement that curriculum reflects state-of-the-art.
87
Table 30: The curriculum leads towards the set aims of mathematics
education
H0:There will be no significant difference between SSC and GCE teachers on the statement that the curriculum leads towards the set aims of mathematics educationRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.62 1.1370.113 3.539
GCE(O-Level) 120 x2=¿4.02 0.813
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 30, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 3.539. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between themon the
statement that the curriculum leads towards the set aims of mathematics education.
Table 31: Contents of the textbooks are properly sequenced
H0:There will be no significant difference between SSC and GCE teachers on the statement that contents of the textbooks are properly sequencedRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.66 1.0620.112 1.250
GCE(O-Level) 120 x2=¿3.80 0.879
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 31, we find that the tabulated ‘t’ value = 1.960 is larger than the computed ‘t’ value = 1.250. Hence, H0 is accepted, which leads us to the conclusion that the two groups
88
of teachers have no significant difference between themon the
statement that contents of the textbooks are properly sequenced.
Table 32: Contents of the textbooks develop interest
H0:There will be no significant difference between SSC and GCE teachers on the statement that contents develops interest in studentsRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.55 1.0710.115 0.608
GCE(O-Level) 120 x2=¿3.62 0.922
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 32, we find that the tabulated ‘t’ value = 1.960 is larger than the computed ‘t’ value = 0.608. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between themon the
statement that the content develops interest in students.
Table 33: Contents incite the sense of enquiry
H0:There will be no significant difference between SSC and GCE teachers on the statement that contents incite the sense of enquiryRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.36 1.1240.110 3.090
GCE(O-Level) 120 x2=¿3.70 0.888
89
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 33, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 3.090. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the
statement that contents incite the sense of enquiry.
Table 34: Language of the textbooks is simple
H0:There will be no significant difference between SSC and GCE teachers on the statement that language of the textbooks is simpleRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.90 0.9640.093 1.720
GCE(O-Level) 120 x2=¿4.06 0.642
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 34, we find that the tabulated ‘t’ value = 1.960 is larger than the computed ‘t’ value = 1.720. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between themon the
statement that language of the textbooks is simple.
Table 35: The contents coveran appropriate proportion of sums on
application of abstract principles of mathematics in real life problems
H0:There will be no significant difference between SSC and GCE teachers on the
90
statement that the contents cover application of abstract principles in real life problemsRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.34 1.0920.116 3.275
GCE(O-Level) 120 x2=¿3.72 0.922
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 35, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 3.275. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between themon the
statement that the contents cover application of abstract principles in real life
problems.
Table 36: Worked examples in the textbooks provide sufficient guidance to
solve all the problems given for exercise on that topic
H0:There will be no significant difference between SSC and GCE teachers on the statement that worked examples in the text books provide sufficient guidance to solve all the problems given for exercise on that topicRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.55 1.0610.117 3.846
GCE(O-Level) 120 x2=¿4.00 0.938
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 36, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 3.846. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the
statement that worked examples in the text books provide sufficient guidance to solve
all the problems given for exercise on that topic.
91
Table 37(a): Comparison of the domains of intellect developed by contents of
the textbooks
Domains ofIntellect
H0:There will be no significant difference between SSC and
GCE teachers that contents of the textbooks develop these
domains of intellect
1. Logical
Reasoning
RespondentsN Mean SD
SEx1−x2
t-value
SSC(Matriculation) 180x1=¿
3.611.108
0.104 5.192
GCE(O-Level) 120x2=¿
4.150.685
2.Analytical
and Critical
Thinking
SSC(Matriculation) 180x1=¿
3.461.029
0.104 5.961
GCE(O-Level) 120x2=¿
4.080.766
3.Problem-
Solving Skills
SSC(Matriculation) 180x1=¿
3.860.881
0.093 2.043
GCE(O-Level) 120x2=¿
4.050.723
4.Spirit of
Exploration
and Discovery
SSC(Matriculation) 180x1=¿
3.291.094
0.123 2.764
GCE(O-Level) 120x2=¿
3.631.008
5.Power of
Concentration
SSC(Matriculation) 180x1=¿
3.441.054
0.110 1.636
GCE(O-Level) 120x2=¿
3.620.846
92
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusions
1. Logical reasoning
Referring to table 37(a), we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 5.192. Hence, H0
is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them regarding
the statement that contents of textbooks develop logical reasoning.
2. Analytical and Critical Thinking
Referring to table 37(a), we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 5.961. Hence, H0
is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them regarding
the statement that contents develop analytical and critical thinking.
3. Problem-Solving Skills
Referring to table 37(a), we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 2.043. Hence, H0
is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them regarding
the statement that contents develop problem-solving skills.
4. Spirit of Exploration and Discovery
Referring to table 37(a), we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 2.764. Hence, H0
is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them regarding
the statement that contents develop spirit of exploration and discovery.
93
5. Concentration Power
Referring to table 37(a), we find that the tabulated ‘t’ value = 1.960 is larger than the computed ‘t’ value = 1.636. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them regarding
the reason that contents develop concentration power.
37(b): Graph 2
Domain 1 Domain 2 Domain 3 Domain 4 Domain 50%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
*Comparison of the domains of intellect developed by the contents of textbooks
Res
pons
es in
per
cent
*For this comparison SA & A, alternatives of the measurement scale has been collapsed to get the percentage of agreement
Table 38: The contentsare in accordance with intellectual level of students
H0:There will be no significant difference between SSC and GCE teachers that the contents are in accordance with intellectual level of studentsRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.47 1.0190.115 3.913
GCE(O-Level) 120 x2=¿3.92 0.944
df =298 tabulated ‘t’ value at 0.05 = 1.960
94
Conclusion:Referring to table 38, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 3.913. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between themon the
statement that the contents are in accordance with intellectual level of students.
Table 39: The contents contain problems that can be solved by personal
investigation without having aprior method to solve them
H0:There will be no significant difference between SSC and GCE teachers on the statement that content covers problems whose solutions can be found by personal investigation onlyRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.22 1.0570.103 6.311
GCE(O-Level) 120 x2=¿3.87 0.724
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 39, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 6.311. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between themon the
statement that the content covers problems that can be solved by personal
investigation only.
Table 40: The contents include a proper proportion of mathematical
representations (graphs, diagrams, figures and tables)
H0:There will be no significant difference between SSC and GCE teachers on the statement that content covers a proper proportion of mathematical representationsRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.97 0.8930.091 1.758
GCE(O-Level) 120 x2=¿4.13 0.676
95
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 40, we find that the tabulated ‘t’ value = 1.960 is larger than the computed ‘t’ value = 1.758. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between themon the
statement that the content covers a proper proportion of mathematical representations.
Table 41: The contents include an appropriate proportion of activities for
mental exercise (puzzles/riddles)
H0:There will be no significant difference between SSC and GCE teachers on the statement that the contents include an appropriate proportion of activities to develop the habit of thinking among studentsRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.00 1.2890.130 5.231
GCE(O-Level) 120 x2=¿3.68 0.958
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 41, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 5.231. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the
statement that the contents include an appropriate proportion of activities to develop
the habit of thinking among students.
Table 42: The contents are balanced in terms of key areas (number operation,
geometry, algebra, measurement, data analysis and probability).
H0:There will be no significant difference between SSC and GCE teachers on the statement that the contents are balanced in terms of key areasRespondents N Mean SD SEx1−x2 t-value
96
SSC(Matriculation) 180 x1=¿3.69 0.9790.101 4.752
GCE(O-Level) 120 x2=¿4.17 0.763
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 42, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 4.752. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between themon the
statement that the content is balanced in term of key areas.
Table 43: Pictures and colorful presentations in the textbooks put a positive
effect on conceptual understanding
H0:There will be no significant difference between SSC and GCE teachers on the statement that the pictures and colorful presentations help in conceptual understandingRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.67 1.1610.113 4.071
GCE(O-Level) 120 x2=¿4.13 0.873
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 43, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 4.071. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between themon the
statement that the pictures and colorful presentations help in conceptual
understanding.
Table 44: The number of problems given on a certain topic affects conceptual
understanding
H0:There will be no significant difference between SSC and GCE teachers on the
97
statement that the number of problems given on a certain topic affects conceptual understandingRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.56 1.0180.111 3.963
GCE(O-Level) 120 x2=¿4.00 0.883
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 44, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 3.963. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between themon the
statement that the number of problems given on a certain topic affects conceptual
understanding.
Table 45: Chaining (bit by bit addition of new material in the sums) on a
certain topic in the text books put a positive effect on conceptual
understanding
H0:There will be no significant difference between SSC and GCE teachers on the
statement that chaining of sums put a positive effect on conceptual
understanding
Respondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.61 1.0570.113 3.451
GCE(O-Level) 120 x2=¿4.00 0.883
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 45, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 3.451. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between themon the
statement that chaining of sums put a positive effect on conceptual understanding.
98
Table 46: Contents of the textbooks are properly chained
H0:There will be no significant difference between SSC and GCE teachers with respect to the statement that the content is properly chainedRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.37 1.1660.163 3.987
GCE(O-Level) 120 x2=¿4.02 0.833
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 46, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 3.987. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them with
respect to the statement that the content is properly chained.
Table 47(a): Comparison of the approaches of mathematics teaching
ApproachesH0:There will be no significant difference between the SSC and GCE teachers in the selection of an approach for mathematics teaching
1. Learner-
Focused
Respondents N Mean SDSE
x1−x2
t-value
SSC(Matriculation) 180x1=¿
4.250.591
0.118 1.445
GCE(O-Level) 120x2=¿
4.130.769
2.Content-
Focused
with an
emphasis on
SSC(Matriculation) 180x1=¿
4.100.849
0.086
3.256GCE(O-Level) 120 x2=¿
4.38
0.640
99
conceptual
understanding3.Content-
Focused
with an
emphasis on
performance
SSC(Matriculation) 180x1=¿
3.930.958
0.114 1.140
GCE(O-Level) 120x2=¿
3.800.971
4.Classroom-
Focused
SSC(Matriculation) 180x1=¿
4.080.879
0.116 3.103
GCE(O-Level) 120x2=¿
3.721.043
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusions
1. Learner-Focused
Referring to table 47(a), we find that the tabulated ‘t’ value = 1.960 is larger than the computed ‘t’ value = 1.445. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them in their
choice for learner-focused approach.
2. Content-Focused (with an emphasis on conceptual understanding)
Referring to table 47(a), we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 3.256. Hence, H0
is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between themin their
choice for content-focused approach with an emphasis on understanding.
100
3. Content-Focused (with an emphasis on performance)
Referring to table 47(a), we find that the tabulated ‘t’ value = 1.960 is larger than the computed ‘t’ value = 1.140. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them in their
choice for content-focused approach with an emphasis on performance.
4. Classroom-Focused
Referring to table 47(a), we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 3.103. Hence, H0
is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them in their
choice for classroom-focused approach.
47(b): Graph 3
101
Approach 1 Approach 2 Approach 3 Approach 40%
10%20%30%40%50%60%70%80%90%
100%
*Comparison of the approaches of mathematics teaching
Res
pons
es in
per
cent
Table 48(a): Comparison of the practices of teachers in their classes
PracticesH0:There will be no significant difference between the reasons of SSC and GCE teachers regarding the role of a teacher in the class
1. Solving all
the sums on the
board for
students
RespondentsN Mean SD
SEx1−x2
t-value
SSC(Matriculation) 180x1=¿
2.641.257
0.152 2.434
GCE(O-Level) 120
x2=¿
2.27 1.313
(Contd…….)
102
2.Solving few
sums and
letting students
do the
remaining
SSC(Matriculation) 180x1=¿
4.290.782
0.587 0.443GCE(O-Level) 120
x2=¿
4.031.008
3.Explaining
important
points and
encourage
students to
solve the sums
SSC(Matriculation) 180x1=¿
3.731.188
0.137 1.605GCE(O-Level) 120 x2=¿
3.95
1.141
4.Letting
students solve
the sums
independently
and helping
them on their
demand only
SSC(Matriculation) 180x1=¿
3.641.274
0.144 0.625
GCE(O-Level) 120 x2=¿
3.55
1.185
5. Making
groups of
students and
facilitating
them
findingsolutions
of the given
sums
SSC(Matriculation) 180x1=¿
3.921.104
0.140 2.285
GCE(O-Level) 120x2=¿
3.601.233
df =298 tabulated ‘t’ value at 0.05 = 1.960
103
Conclusions
1. Teacher solves all the sums
Referring to table 48(a), we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 2.434. Hence, H0
is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the
statement that solving all the sums on a topic is teachers’ routine in their classes.
2. Teacher solves some of them and let students to solve the remaining
Referring to table 48(a), we find that the tabulated ‘t’ value = 1.960, at α= 0.05 with df= 298 is smaller than the computed ‘t’ value = 0.443. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on the statement that teachers’ usual class
practice is to solve a few sums on the board and letstudents do the remaining.
3. Teacher explains important points and encourage students to solve the sums
Referring to table 48(a), we find that the tabulated ‘t’ value = 1.960, at α= 0.05 with df= 298 is smaller than the computed ‘t’ value = 1.605. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on the statement that explaining important points
and encouragingstudents to solve the sums is teachers’ normal routine in the
class.
4. Teacher let students solve the sums independently and provide help on
demand only
Referring to table 48(a), we find that the tabulated ‘t’ value = 1.960, at α= 0.05 with df= 298 is smaller than the computed ‘t’
104
value = 0.625. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between themon the statement that letting students solve the
sums independently and providing help on their demand only is teachers’ usual
routine in the class.
5. Teacher facilitates the students working in groups to solve the sums by
mutual understanding
Referring to table 48(a), we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 2.285. Hence, H0
is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the
statement that facilitating students solving sums in groups is teachers’ usual
practice in their classes.
48(b): Graph 4
Routine 1 Routine 2 Routine 3 Routine 4 Routine 50%
10%20%30%40%50%60%70%80%90%
100%
*Comparison of the practices of teachers in their classes
Res
pons
es in
per
cent
105
Table 49: Students should solve problems by teacher’s explained method only
H0:There will be no significant difference between SSC and GCE teachers on the statement that students should solve problems by teacher’s explained method onlyRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿2.76 1.3600.146 2.328
GCE(O-Level) 120 x2=¿2.42 1.154
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 49, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed‘t’=2.328. Hence, H0 is rejected, which leads us to the conclusion that there is a significant difference between SSC and GCE teachers on the statement that students
should solve problems by teacher’s explained method only.
Table 50: Additional material is usually used for deeper understanding of
concepts
H0:There will be no significant difference between SSC and GCE teachers on the statement that additional material is usually used for deeper understanding of concepts.Respondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿4.18 0.856 0.120 1.750
106
GCE(O-Level) 120 x2=¿3.97 1.119
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 50, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.750. Hence, H0 is accepted, which leads us to the conclusion that there is no significant difference between SSC and GCE teachers on the statement
that additional material is usually used for deeper understanding of concepts.
Table 51: Additional material is usually used for rigorous drill of learned
material
H0:There will be no significant difference between SSC and GCE teachers on the statement that additional material is usually used for rigorous drill of learned materialRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.73 0.9460.114 0.088
GCE(O-Level) 120 x2=¿3.72 0.940
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 51, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.088. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on
the statement that additional material is usually used for rigorous drill of learned
material.
Table 52: Mostly previous exam papers are used as an additional material
H0:There will be no significant difference between SSC and GCE teachers on the
107
statement that additional material is mostly previous exam papersRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.38 1.1570.135 1.259
GCE(O-Level) 120 x2=¿3.55 1.411
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion: Referring to table 52, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.259. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on
the statement that additional material is mostly previous exam papers.
Table 53: Previous papers are solved as a rehearsal for the actual exam paper
H0:There will be no significant difference between SSC and GCE teachers on the statement that previous papers are solved as a rehearsal for the actual exam- paperRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.98 0.8610.092 1.630
GCE(O-Level) 120 x2=¿4.13 0.724
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion: Referring to table 53, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.630. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on
the statement that previous papers are solved as a rehearsal for the actual exam paper.
Table 54: Past papers are solved because questions of previous papers are
considered important
108
H0:There will be no significant difference between SSC and GCE teachers on the statement that past papers are solved because questions of previous papers are considered importantRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.36 1.1150.137 0.803
GCE(O-Level) 120 x2=¿3.47 1.199
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 54,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.803. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on
the statement that past papers are solved because questions of previous papers are
considered important.
Table 55: Past papers are solved because questions from previous papers
often repeat in the new papers
H0:There will be no significant difference between SSC and GCE teachers on the statement that past papers are solved because questions from previous papers often repeat in the new papersRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.47 1.1730.147 2.313
GCE(O-Level) 120 x2=¿3.13 1.294
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 55, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 2.313. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the
109
statement that past papers are solved because questions from previous papers often
repeat in the new papers.
Table 56: Past papers are solved to understand the pattern of questions
coming in the recent papers
H0:There will be no significant difference between SSC and GCE teachers on the statement that past papers are solved to understand the pattern of questions coming in the recent papersRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿4.19 0.8190.930 0.108
GCE(O-Level) 120 x2=¿4.18 0.770
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 56, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.108. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on
the statement that past papers are solved to understand the pattern of questions
coming in the recent papers.
Table 57: Teacher-constructed problems are presented in the class
H0:There will be no significant difference between SSC and GCE teachers on the statement that teacher-constructed problems are presented in the classRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.31 1.0260.115 0.957
GCE(O-Level) 120 x2=¿3.20 0.947
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 57, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.957.
110
Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on
the statement that teacher-constructed problems are presented in the class.
Table 58: Students are allowed to construct and present their own problems
in the class
H0:There will be no significant difference between SSC and GCE teachers on the statement that students are allowed to construct and present their own problems in the class Respondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.93 0.9090.119 2.605
GCE(O-Level) 120 x2=¿3.62 1.075
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 58, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 2.605. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the
statement that students are allowed to construct and present their own problems in the
class.
Table 59: Procedures of doing a problem are explained but not the reason for
the selection of that procedure
H0:There will be no significant difference between SSC and GCE teachers on the statement that procedures of doing a problem are explained but not the reason for the selection of that procedureRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.23 1.1320.020 7.500
GCE(O-Level) 120 x2=¿3.08 1.225
111
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 59, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 7.500. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the
statement that procedures of doing a problem are explained but not the reason for the
selection of that procedure.
Table 60: There are some topics in the textbooks that are always left untaught
as no question comes in the paper from these topics
H0:There will be no significant difference between SSC and GCE teachers on the statement that there are some topics in the textbooks that are always left untaught as no question comes in the paper from these topicsRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.17 1.3090.144 3.125
GCE(O-Level) 120 x2=¿3.08 1.165
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 60, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 3.125. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the
statement that there are some topics in the textbooks that are always left untaught as
no question comes in the paper from these topics.
Table 61: Homework is given in order to complete the syllabus as it cannot be
completed by solving all the sums in class
H0:There will be no significant difference between SSC and GCE teachers on the statement that homework is given in order to complete the syllabus as it cannot be completed by solving all the sums in classRespondents N Mean SD SEx1−x2 t-value
112
SSC(Matriculation) 180 x1=¿3.63 1.8460.175 0.914
GCE(O-Level) 120 x2=¿3.47 1.185
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 61, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.914. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on
the statement that homework is given in order to complete the syllabus as it cannot be
completed by solving all the sums in class.
Table 62: Completion of a topic means that the teacher has explained the
topic and students have done the sums in their copies
H0:There will be no significant difference between SSC and GCE teachers on the statement that completion of a topic means that the teacher has explained the topic and students have done the sums in their copiesRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.81 1.1010.141 2.695
GCE(O-Level) 120 x2=¿3.43 1.267
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 62, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 2.695. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the
statement that completion of a topic means that the teacher has explained the topic
and students have done the sums in their copies.
Table 63: Emphasis is given on neat and tidy written work
H0:There will be no significant difference between SSC and GCE teachers on the
113
statement that emphasis is given on neat and tidy written workRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿4.22 0.6990.098 4.796
GCE(O-Level) 120 x2=¿3.75 0.914
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 63, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 4.796. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the
statement that Emphasis is placed on neat and tidy written work.
Table 64: Homework is assigned and checked regularly
H0:There will be no significant difference between SSC and GCE teachers on the statement that homework is assigned and checked regularlyRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿4.25 0.9060.118 3.220
GCE(O-Level) 120 x2=¿3.87 1.049
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 64, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 3.220. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the
statement that homework is assigned and checked regularly.
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Table 65: Topics are not explored in depth; only the procedure of doing a
sum is explained
H0:There will be no significant difference between SSC and GCE teachers on the statement that topics are not explored in depth; only the procedure of doing a sum is explainedRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.19 1.2070.140 4.000
GCE(O-Level) 120 x2=¿2.63 1.178
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 65, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 4.000. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the
statement that topics are not explored in depth; only the procedure of doing a sum is
explained.
Table 66: Unexplained short-cuts are told to solve certain problems
H0:There will be no significant difference between SSC and GCE teachers on the statement that unexplained short-cuts are told to solve certain problemsRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.23 1.1710.134 1.268
GCE(O-Level) 120 x2=¿3.06 1.118
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 66, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.268. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on
the statement that unexplained short-cuts are told to solve certain problems.
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Table 67: Derivation of the formula is not clarified, only the method of its
application is explained
H0:There will be no significant difference between SSC and GCE teachers on the statement that derivation of the formula is not clarified, only the method of its application is explainedRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿2.67 1.0810.140 0.214
GCE(O-Level) 120 x2=¿2.70 1.253
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 67, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.214. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on
the statement that derivation of the formula is not clarified, only the method of its
application is explained.
Table 68: Usually students avoid checking answers
H0:There will be no significant difference between SSC and GCE teachers on the statement that generally students avoid checking answersRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.14 1.1760.142 0.070
GCE(O-Level) 120 x2=¿3.15 1.218
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 68, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.070. Hence, H0 is accepted, which leads us to the conclusion that the two
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groups of teachers have no significant difference between them on
the statement that Usually students avoid checking answers.
Table 69: Usually students try to skip graph questions
H0:There will be no significant difference between SSC and GCE teachers on the statement that generally students try to skip graph questionsRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.37 1.0960.129 0.930
GCE(O-Level) 120 x2=¿3.25 1.187
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 69, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.930. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on
the statement that usually students try to skip graph questions.
Table 70: Teachers do not emphasize checking of answers by students
H0:There will be no significant difference between SSC and GCE teachers on the statement that teachers do not emphasize checking of answers by studentsRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.11 1.2230.129 2.774
GCE(O-Level) 120 x2=¿2.73 1.118
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 70, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 2.774.
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Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the
statement that teachers do not emphasize checking of answers by students.
Table 71: Teachers do not emphasize checking answers because they have a
fear of getting a wrong answer in front of the class
H0:There will be no significant difference between SSC and GCE teachers on the statement that teachers do not emphasize checking answers because they have a fear of getting a wrong answer in front of the classRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿2.56 1.2730.142 0.563
GCE(O-Level) 120 x2=¿2.48 1.157
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 71, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.563. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on
the statement that teachers do not emphasize checking answers because they have a
fear of getting a wrong answer in front of the class.
Table 72: Mathematics has a significant application in other subjects
H0:There will be no significant difference between SSC and GCE teachers on the statement that mathematics have a significant application in other subjectsRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿4.17 0.8380.080 1.375
GCE(O-Level) 120 x2=¿4.28 0.555
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df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 72, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.375. Hence, H0 is accepted which leads us to the conclusion that there is no significant difference between SSC and GCE teachers on the statement that
mathematics has a significant application in other subjects.
Table 73: Teachers’ true role is to generate a question in the mind of a child
before it is answered
H0:There will be no significant difference between SSC and GCE teachers on the statement that teachers’ true role is to generate a question in the mind of a child before it is answeredRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿4.29 0.7230.088 3.750
GCE(O-Level) 120 x2=¿3.96 0.758
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 73, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 3.750. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the
statement that teachers’ true role is to generate a question in the mind of a child
before it is answered.
Table 74: Both posing and answering of questions by a teacher produce
shallow understanding
H0:There will be no significant difference between SSC and GCE teachers on the
statement that both posing and answering of questions by a teacher produce
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shallow understanding
Respondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.79 0.8670.110 0.091
GCE(O-Level) 120 x2=¿3.80 0.971
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 74, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.091. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on
the statement that both posing and answering of questions by a teacher produce
shallow understanding.
Table 75: Students can communicate mathematical ideas, reasoning and
results
H0:There will be no significant difference between SSC and GCE teachers on the statement that students can communicate mathematical ideas, reasoning and resultsRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.84 o.8060.087 3.218
GCE(O-Level) 120 x2=¿4.12 0.690
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 75, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 3.218. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the
statement that students can communicate mathematical ideas, reasoning and results.
Table 76: Students take teaching of mathematics as a pleasant activity
H0:There will be no significant difference between SSC and GCE teachers on the
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statement that students take teaching of mathematics as a pleasant activityRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.73 0.9690.118 1.780
GCE(O-Level) 120 x2=¿3.52 1.033
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 76, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.780. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on
the statement that students take teaching of mathematics as a pleasant activity.
Table 77: Students exhibit courage in facing unfamiliar problems
H0:There will be no significant difference between SSC and GCE teachers on the statement that students exhibit courage in facing unfamiliar problemsRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.59 0.9350.096 2.917
GCE(O-Level) 120 x2=¿3.87 0.724
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 77, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 2.917. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the
statement that students exhibit courage in facing unfamiliar problems.
Table 78: Students express tolerance in solving difficult problems
H0:There will be no significant difference between SSC and GCE teachers on the statement that students express tolerance in solving difficult problems
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Respondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.69 0.9670.108 1.296
GCE(O-Level) 120 x2=¿3.55 0.872
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 78, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.296. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on
the statement that students express tolerance in solving difficult problems.
Table 79: Retention of learned material in the memory becomes stronger with
repetition
H0:There will be no significant difference between SSC and GCE teachers on the statement that retention of learned material in the memory becomes stronger with repetitionRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿4.07 0.6490.092 0.109
GCE(O-Level) 120 x2=¿4.08 0.849
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 79, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.109. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on
the statement that retention of learned material in the memory becomes stronger with
repetition.
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Table 80: Repetition of learned material may attach meaningful relationships
among the fragments of knowledge
H0:There will be no significant difference between SSC and GCE teachers on the statement that repetition of learned material may attach meaningful relationships among the fragments of knowledgeRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿4.16 0.7170.084 0.476
GCE(O-Level) 120 x2=¿4.12 0.715
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 80, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.476. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on
the statement that repetition of learned material may attach meaningful relationships
among the fragments of knowledge.
Table 81: Tests/Exams are conducted to assess the level of achievement of the
instructional objectives
H0:There will be no significant difference between SSC and GCE teachers on the statement that tests/exams are conducted to assess the level of achievement of the instructional objectivesRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿4.37 0.4840.079 2.532
GCE(O-Level) 120 x2=¿4.17 0.763
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 81, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 2.532. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the
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statement that tests/exams are conducted to assess the level of achievement of the
instructional objectives.
Table 82: Tests/Exams are conducted to categorize students into successful
and unsuccessful groups
H0:There will be no significant difference between SSC and GCE teachers on the statement that tests/exams are conducted to categorize students into successful and unsuccessful groupsRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.73 1.1680.144 4.035
GCE(O-Level) 120 x2=¿3.27 1.260
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 82, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 4.035. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the
statement that tests/exams are conducted to categorize students into successful and
unsuccessful groups.
Table 83: The verbal/written remark of a teacher on the basis of assessment is
evaluation
H0:There will be no significant difference between SSC and GCE teachers on the statement that the verbal/written remark of a teacher on the basis of assessment is evaluationRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.87 0.9260.107 0.654
GCE(O-Level) 120 x2=¿3.80 0.898
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 83, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.654.
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Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on
the statement that the verbal/written remark of a teacher on the basis of assessment is
evaluation.
Table 84: Assessment helps both teacher and learner in the process of
teaching and learning
H0:There will be no significant difference between SSC and GCE teachers on the statement that assessment helps both teacher and learner in the process of teaching and learningRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿4.36 0.6410.084 1.071
GCE(O-Level) 120 x2=¿4.27 0.756
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 84, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.071. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on
the statement that assessment helps both teacher and learner in the process of teaching
and learning.
Table 85: The fear of assessment motivates students to work hard
H0:There will be no significant difference between SSC and GCE teachers on the statement that the fear of assessment motivates students to work hardRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿4.28 0.6870.086 4.318
GCE(O-Level) 120 x2=¿3.90 0.752
df =298 tabulated ‘t’ value at 0.05 = 1.960
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Conclusion:Referring to table 85, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 4.318. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the
statement that the fear of assessment motivates students to work hard.
Table 86: The fear of final examinations is actually the fear of being insulted
on its results
H0:There will be no significant difference between SSC and GCE teachers on the statement that the fear of final examinations is actually the fear of being insulted on its resultsRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.77 1.0710.129 3.798
GCE(O-Level) 120 x2=¿3.28 1.106
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 86, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 3.798. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the
statement that the fear of final examinations is actually the fear of being insulted on
its results.
Table 87: A teacher is always engaged in the process of assessing his/her
students during the class
H0:There will be no significant difference between SSC and GCE teachers on the statement that a teacher is always engaged in the process of assessing his/her students during the classRespondents N Mean SD SEx1−x2 t-value
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SSC(Matriculation) 180 x1=¿4.01 0.9770.103 0.583
GCE(O-Level) 120 x2=¿4.07 0.799
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 87, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.583. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on
the statement that a teacher is always engaged in the process of assessing his/her
students during the class.
Table 88: The encouraging remarks of a teacher after assessment produce
positive effect on the performance of students
H0:There will be no significant difference between SSC and GCE teachers on the statement that the encouraging remarks of a teacher after assessment produce positive effect on the performance of studentsRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿4.43 0.7040.070 0.000
GCE(O-Level) 120 x2=¿4.43 0.647
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 88, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.000. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on
the statement that the encouraging remarks of a teacher after assessment produce
positive effect on the performance of students.
Table 89: The discouraging remark of a teacher produces a negative effect on
the performance of students
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H0:There will be no significant difference between SSC and GCE teachers on the statement that the discouraging remark of a teacher produces a negative effect on the performance of studentsRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿4.00 0.8480.096 0.729
GCE(O-Level) 120 x2=¿4.07 0.799
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 89, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.729. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on
the statement that the discouraging remark of a teacher produces a negative effect on
the performance of students.
Table 90: Methods of assessment should enable students to reveal what they
know, rather than what they do not know
H0:There will be no significant difference between SSC and GCE teachers on the statement that methods of assessment should enable students to reveal what they know, rather than what they do not knowRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.81 0.9700.104 2.115
GCE(O-Level) 120 x2=¿4.03 0.822
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 90, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 2.115. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the
statement that methods of assessment should enable students to reveal what they
know, rather than what they do not know.
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Table 91: Students take mathematics assessments confidently
H0:There will be no significant difference between SSC and GCE teachers on the statement that students take mathematics assessments confidentlyRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.51 1.1140.128 0.469
GCE(O-Level) 120 x2=¿3.45 1.064
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 91, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.469. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on
the statement that students take mathematics assessments confidently.
Table 92: The main purpose of assessment is to improve teaching and
learning of mathematics
H0:There will be no significant difference between SSC and GCE teachers on the statement that the main purpose of assessment is to improve teaching and learning of mathematicsRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿4.27 0.6990.087 1.609
GCE(O-Level) 120 x2=¿4.13 0.769
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 92, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.609. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on
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the statement that the main purpose of assessment is to improve teaching and learning
of mathematics.
Table 93: The exam papers assess the objectives of teaching mathematics
H0:There will be no significant difference between SSC and GCE teachers on the statement that the exam papers assess the objectives of teaching mathematicsRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.99 0.8680.088 1.364
GCE(O-Level) 120 x2=¿3.87 0.650
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 93, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.364. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on
the statement that the exam papers assess the objectives of teaching mathematics.
Table 94: The exam papers are balanced in terms of content areas
H0:There will be no significant difference between SSC and GCE teachers on the statement that the exam papers are balanced in terms of content areasRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿4.06 0.8260.079 0.127
GCE(O-Level) 120 x2=¿4.05 0.539
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 94, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.127.
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Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on
the statement that the exam papers are balanced in terms of content areas.
Table 95: The exam papers (SSC/GCE) assess the actual educational
objectives of teaching mathematics
H0:There will be no significant difference between SSC and GCE teachers on the statement that the exam papers assess the actual educational objectives of teaching mathematicsRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.90 0.8350.087 0.230
GCE(O-Level) 120 x2=¿3.92 0.671
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 95, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.230. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on
the statement that the exam papers assess the actual educational objectives of teaching
mathematics.
Table 96: The system of checking papers is fair
H0:There will be no significant difference between SSC and GCE teachers on the statement that the system of checking papers is fairRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.64 1.301 0.116 5.259
GCE(O-Level) 120 x2=¿4.25 0.704
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df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 96, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 5.259. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the
statement that the system of checking papers is fair.
Table 97: Examinations are conducted under strict vigilance
H0:There will be no significant difference between SSC and GCE teachers on the statement that examinations are conducted under strict vigilanceRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.63 1.3450.117 6.752
GCE(O-Level) 120 x2=¿4.42 0.671
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 97, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 6.752. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the
statement that examinations are conducted under strict vigilance.
Table 98: Use of unfair means in the paper of mathematics is common
H0:There will be no significant difference between SSC and GCE teachers on the statement that use of unfair means in the paper of mathematics is common
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Respondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.53 1.2400.146 6.712
GCE(O-Level) 120 x2=¿2.55 1.241
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 98, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 6.712. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the
statement that use of unfair means in the paper of mathematics is common.
Table 99: Grading system of SSC/ GCE is appropriate
H0:There will be no significant difference between SSC and GCE teachers on the statement that grading system of SSC/ GCE is appropriateRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.52 0.8510.095 4.737
GCE(O-Level) 120 x2=¿3.97 0.780
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 99, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 4.737. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the
statement that grading system of SSC/ GCE is appropriate.
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Table 100: Teachers’ assessment during class is as important as the final
examination
H0:There will be no significant difference between SSC and GCE teachers on the statement that teachers’ assessment during class is as important as the final examinationRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿4.09 0.8380.086 1.860
GCE(O-Level) 120 x2=¿4.25 0.654
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 100, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.860. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on
the statement that teachers’ assessment during class is as important as the final
examination.
Table 101: Students’ marks of weekly/monthly/terminal tests are added in the
marks of their final exam paper in junior grades
H0:There will be no significant difference between SSC and GCE teachers on the statement that students’ marks of weekly/monthly/terminal tests are added in the marks of their final exam paper in junior gradesRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿4.08 0.8760.089 2.359
GCE(O-Level) 120 x2=¿4.25 0.676
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 101, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 2.359. Hence, H0 is rejected, which leads us to the conclusion that the two
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groups of teachers have a significant difference between them on the
statement that students’ marks of weekly/monthly/terminal tests are added in the
marks of their final exam paper in junior grades.
Table 102: Final examinations assess the factual and procedural knowledge of
mathematics only
H0:There will be no significant difference between SSC and GCE teachers on the statement that final examinations assess the factual and procedural knowledge of mathematics onlyRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.83 0.9030.118 4.237
GCE(O-Level) 120 x2=¿3.33 1.068
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 102, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 4.237. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the
statement that final examinations assess the factual and procedural knowledge of
mathematics only.
Table 103: Questions in the exam papers are given according to a set pattern
H0:There will be no significant difference between SSC and GCE teachers on the statement that questions in the exam papers are given according to a set patternRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.80 1.0750.130 2.077
GCE(O-Level) 120 x2=¿3.53 1.125
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 103, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 2.077.
135
Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the
statement that questions in the exam papers are given according to a set pattern.
Table 104: Questions are given from the textbooks in SSC/GCE papers
H0:There will be no significant difference between SSC and GCE teachers on the statement that questions are given from the textbooks in SSC/GCE papersRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.38 1.2320.135 7.259
GCE(O-Level) 120 x2=¿2.40 1.092
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 104, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 7.259. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the
statement that questions are given from the textbooks in SSC/GCE papers.
Table 105: Questions in SSC/GCE papers are given from the past papers
H0:There will be no significant difference between SSC and GCE teachers on the statement that questions in SSC/GCE papers are given from the past papers Respondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.62 1.2540.145 5.448
GCE(O-Level) 120 x2=¿2.83 1.264
df =298 tabulated ‘t’ value at 0.05 = 1.960
136
Conclusion:Referring to table 105, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 5.448. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the
statement that questions in SSC/GCE papers are given from the past papers.
Table 106: Some topics from the syllabus may be dropped on the basis of
ample choice of questions in the exam paper
H0:There will be no significant difference between SSC and GCE teachers on the statement that some topics from the syllabus may be dropped on the basis of ample choice of questions in the exam paperRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.56 1.1620.139 3.813
GCE(O-Level) 120 x2=¿3.03 1.178
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 106, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 3.813. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the
statement that some topics from the syllabus may be dropped on the basis of ample
choice of questions in the exam paper.
Table 107: On the basis of previous papers some questions can be predicted
for the upcoming paper
H0:There will be no significant difference between SSC and GCE teachers on the statement that on the basis of previous papers some questions can be predicted for the upcoming paperRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.78 0.969 0.128 5.547
137
GCE(O-Level) 120 x2=¿3.07 1.163
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 107, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 5.547. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the
statement that on the basis of previous papers some questions can be predicted for the
upcoming paper.
Table 108: Assessment is done to distinguish students for the improvement of
learning
H0:There will be no significant difference between SSC and GCE teachers on the statement that assessment is done to distinguish students for the improvement of learningRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿4.08 0.5850.062 0.484
GCE(O-Level) 120 x2=¿4.05 0.467
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 108, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.484. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on
the statement that assessment is done to distinguish students for the improvement of
learning.
Table 109: Test items of SSC/GCE papers cover all objectives of the
curriculum
H0:There will be no significant difference between SSC and GCE teachers on the
138
statement that test items of SSC/GCE papers cover all objectives of the curriculumRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.89 0.8920.121 0.248
GCE(O-Level) 120 x2=¿3.92 0.743
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 109, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.248. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on
the statement that test items of SSC/GCE papers cover all objectives of the
curriculum.
Table 110: Sections of SSC/GCE papers are designed in such a way that
questions from particular chapters always come in specific sections
H0:There will be no significant difference between SSC and GCE teachers on the statement that sections of SSC/GCE papers are designed in such a way that questions from particular chapters always come in specific sectionsRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.99 0.8000.117 4.872
GCE(O-Level) 120 x2=¿3.42 1.109
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 110, we find that the tabulated ‘t’ value = 1.960 is smaller than the computed ‘t’ value = 4.872. Hence, H0 is rejected, which leads us to the conclusion that the two groups of teachers have a significant difference between them on the
statement that sections of SSC/GCE papers are designed in such a way that questions
from particular chapters always come in specific sections.
139
Table 111: The entire teaching and learning process in the class is designed
and implemented to pass the final examinations
H0:There will be no significant difference between SSC and GCE teachers on the statement that the entire teaching and learning process in the class is designed and implemented to pass the final examinationsRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 180 x1=¿3.87 1.0830.119 1.261
GCE(O-Level) 120 x2=¿3.72 0.958
df =298 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 111, we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.261. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between them on
the statement that the entire teaching and learning process in the class is designed and
implemented to pass the final examinations.
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4.2 ANALYSIS OF THE RESPONSES OF STUDENTS
Table 112: Mathematics is an interesting subject
H0:There will be no significant difference between SSC and GCE students on the statement that mathematics is an interesting subjectRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿4.43 0.7600.119 1.008
GCE(O-Level) 80 x2=¿4.31 0.880
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 112,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.008. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on
the statement that mathematics is an interesting subject.
Table 113: I feel pleasure in doing mathematics
H0:There will be no significant difference between SSC and GCE students on the statement that I feel pleasure in doing mathematicsRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿3.97 1.0600.157 0.892
GCE(O-Level) 80 x2=¿3.83 1.009
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 113,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.892. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on
the statement that I feel pleasure in doing mathematics.
141
Table 114: I do mathematics because teachers emphasizeits importance
H0:There will be no significant difference between SSC and GCE students on the statement that I do mathematics because teachers emphasizeits importanceRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿2.96 1.1410.162 1.728
GCE(O-Level) 80 x2=¿2.68 1.111
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 114,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.728. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on
the statement that I do mathematics because teachers emphasizeits importance.
Table 115: I do mathematics because it is a compulsory subject at school level
H0:There will be no significant difference between SSC and GCE students on the statement that I do mathematics because it is a compulsory subject at schoolRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿4.16 1.0770.175 4.689
GCE(O-Level) 80 x2=¿3.34 1.302
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 115,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 4.689. Hence, H0 is rejected, which leads us to the conclusion that the two groups
142
of students have a significant difference between them on the statement
that I do mathematics because it is a compulsory subject at school level.
Table 116: Mathematics demands rigorous practice
H0:There will be no significant difference between SSC and GCE students on the statement that mathematics demands rigorous practiceRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿4.43 0.7630.106 0.943
GCE(O-Level) 80 x2=¿4.33 0.725
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 116,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.943. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on
the statement that mathematics demands rigorous practice.
Table 117: Mathematics requires concentration
H0:There will be no significant difference between SSC and GCE students on the statement that mathematics requires concentrationRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿4.63 0.6600.086 0.581
GCE(O-Level) 80 x2=¿4.68 0.546
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 117,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.581. Hence, H0 is accepted, which leads us to the conclusion that the two
143
groups of students have no significant difference between them on
the statement that mathematics requires concentration.
Table 118: High achievers in mathematics argue strongly
H0:There will be no significant difference between SSC and GCE students on the statement that high achievers in mathematics argue stronglyRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿3.53 1.1440.162 1.728
GCE(O-Level) 80 x2=¿3.25 1.108
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 118,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.728. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on
the statement that high achievers in mathematics argue strongly.
Table 119: High achievers in mathematics are good analysts
H0:There will be no significant difference between SSC and GCE students on the statement that high achievers in mathematics are good analystsRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿3.72 1.0470.131 1.221
GCE(O-Level) 80 x2=¿3.88 0.802
df =198 tabulated ‘t’ value at 0.05 = 1.960
144
Conclusion:Referring to table 119,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.221. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on
the statement that high achievers in mathematics are good analysts.
Table 120: High achievers in mathematics raise more questions
H0:There will be no significant difference between SSC and GCE students on the statement that high achievers in mathematics raise more questionsRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿4.20 0.8940.144 3.958
GCE(O-Level) 80 x2=¿3.63 1.059
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 120,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 3.958. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement
that high achievers in mathematics raise more questions.
Table 121: School gives a special emphasis on mathematics over other
subjects
H0:There will be no significant difference between SSC and GCE students on the statement that school gives a special emphasis on mathematics over other subjects
145
Respondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿3.64 1.2820.176 0.682
GCE(O-Level) 80 x2=¿3.76 1.172
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 121,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.682. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on
the statement that school gives a special emphasis on mathematics over other
subjects.
Table 122(a): Comparison of the perspectives of students about mathematics
StandpointsH0:There will be no significant difference between the SSC and GCE students on their perspectives towards mathematics
1. Its contents
are useless in
daily life
Respondents N Mean SDSE
x1−x2
t-value
SSC(Matriculation) 120x1=¿
2.421.185
0.166 0.723
GCE(O-Level) 80x2=¿
2.301.130
2. It is
difficult to
memorize the
formulae/
procedures
SSC(Matriculation) 120x1=¿
3.021.375
0.180 3.000
GCE(O-Level) 80x2=¿
2.491.158
3. There is
useless
repetition of
SSC(Matriculation) 120x1=¿
2.881.164
0.157 4.459
GCE(O-Level) 80 x2=¿ 1.041
146
similar sums2.18
4. It requires a
lot of time for
practice
SSC(Matriculation) 120x1=¿
3.911.188
0.165 0.121
GCE(O-Level) 80x2=¿
3.801.114
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusions
1. Its contents are useless in daily life
Referring to table 122(a),we find that the tabulated ‘t’ value = 1.960 is larger than the computed‘t’=0.723. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the
statement that mathematics is boring because its contents are useless in daily life.
2. It is difficult to memorize the formulae/procedures
Referring to table 122(a),we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 3.000. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement
that mathematics is boring because it is difficult to memorize formulae.
3. There is useless repetition of similar sums
147
Referring to table 122(a),we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 4.459. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement
that mathematics is boring because there is useless repetition of similar sums.
4. It requires a lot of time for practice
Referring to table 122(a),we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.121. Hence, H0 is accepted, which leads us to the conclusion that the two groups of teachers have no significant difference between themon the
statement that it requires a lot of time for practice.
122(b): Graph 5
Perspective 1 Perspective 2 Perspective 3 Perspective 40%
10%20%30%40%50%60%70%80%90%
*Comparison of the perspectives of students about mathematics
Res
pons
es in
per
cent
148
*For this comparison SA & A, alternatives of the measurement scale has been collapsed to get the percentage of agreement
Table 123: High achievers in mathematics also achieve highgrades in other
science subjects
H0:There will be no significant difference between SSC and GCE students on the statement that high achievers in mathematics also achieve highgrades in other science subjectsRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿3.63 1.1440.154 0.779
GCE(O-Level) 80 x2=¿3.51 1.169
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 123,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.779. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on
the statement that high achievers in mathematics also achieve highgrades in other
science subjects.
Table 124: Doing mathematics means doing mental exercise
H0:There will be no significant difference between SSC and GCE students on the statement that doing mathematics means doing mental exerciseRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿4.35 0.8850.102 1.275
GCE(O-Level) 80 x2=¿4.48 0.551
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 124,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.275. Hence, H0 is accepted, which leads us to the conclusion that the two
149
groups of students have no significant difference between them on
the statement that doing mathematics means doing mental exercise.
Table 125: Correct solution to a problem gives a feeling of achievement
H0:There will be no significant difference between SSC and GCE students on the statement that correct solution to a problem gives a feeling of achievementRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿4.45 0.7380.093 1.720
GCE(O-Level) 80 x2=¿4.61 0.582
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 125,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.720. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on
the statement that correct solution to a problem gives a feeling of achievement.
Table 126(a): Comparison of the factors for which students give importance to mathematics
FactorsH0:There will be no significant difference between the SSC and GCE students on the factors for the importance of mathematics
1.It trains the
mind
Respondents N Mean SDSE
x1−x2
t-value
SSC(Matriculation) 120 x1=¿
4.47
0.685 0.096 0.0729
150
GCE(O-Level) 80x2=¿
4.540.655
2. It is a
compulsory
subject in
school
curriculum
SSC(Matriculation) 120x1=¿
4.081.000
0.149 1.208
GCE(O-Level) 80x2=¿
3.901.051
3.It is
an essential
part of entry
tests for
higher
education
SSC(Matriculation) 120x1=¿
3.631.201
0.164 1.219
GCE(O-Level) 80x2=¿
3.891.102
4.It is applied
in many other
subjects
SSC(Matriculation) 120x1=¿
4.170.792
0.098 2.041
GCE(O-Level) 80x2=¿
4.370.597
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusions
1. It trains the mind
Referring to table 126(a),we find that the tabulated ‘t’ value = 1.960 is larger than the computed ‘t’ value = 0.729. Hence, H0 is accepted, which leads us to the conclusion that the two groups
151
of students have no significant difference between them on the
statement that mathematics is important because it trains the mind.
2. It is a compulsory subject in school curriculum
Referring to table 126(a),we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.208. Hence, H0
is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the
statement that mathematics is important because it is a compulsory subject in
school curriculum.
3. It is an essential part of entry tests at the higher education level
Referring to table 126(a),we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.219. Hence, H0
is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the
statement that mathematics is important because it is an essential part of entry
tests at the higher education level.
4. It is applied in many other subjects
Referring to table 126(a),we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 2.041. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the
statement that mathematics is important because it is applied in many other
subjects.
126(b): Graph 6
152
Factor 1 Factor 2 Factor 3 Factor 40%
20%
40%
60%
80%
100%
120%
*Comparison of the factors for which students give importance to mathematics
Res
pons
es in
per
cent
*For this comparison SA & A, alternatives of the measurement scale has been collapsed to get the percentage of agreement
Table 127: Mathematics is a scoring subject
H0:There will be no significant difference between SSC and GCE students on the statement that mathematics is a scoring subjectRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿4.57 0.7070.102 1.176
GCE(O-Level) 80 x2=¿4.45 0.709
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 127,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.176. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on
the statement that mathematics is a scoring subject.
153
Table 128: Textbooks of mathematics have an attractive look
H0:There will be no significant difference between SSC and GCE students on the statement that textbooks of mathematics have an attractive lookRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿2.63 1.2760.197 0.355
GCE(O-Level) 80 x2=¿2.56 1.421
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 128,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.355. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on
the statement that mathematics textbooks have an attractive look.
Table 129: Language used in the textbooks is clear
H0:There will be no significant difference between SSC and GCE students on the statement that language used in the textbooks is clearRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿3.63 0.9340.144 1.111
GCE(O-Level) 80 x2=¿3.79 1.039
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 129,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.111. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on
the statement that language used in the textbooks is clear.
154
Table 130: Language of textbooks is difficult because excessive mathematical
terminologies are used
H0:There will be no significant difference between SSC and GCE students on the statement that language of textbooks is difficult because excessive mathematical terminologies are usedRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿3.12 1.1320.159 4.779
GCE(O-Level) 80 x2=¿2.36 1.082
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 130,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 4.779. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement
that language of textbooks is difficult because excessive mathematical terminologies
are used.
Table 131: All topics in the textbooks are taught completely for the
preparation of final examination
H0:There will be no significant difference between SSC and GCE students on the statement that all topics in the textbooks are taught completely for the preparation of final examinationRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿3.36 1.3850.159 5.238
GCE(O-Level) 80 x2=¿4.20 0.892
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 131,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 5.238. Hence, H0 is rejected, which leads us to the conclusion that the two groups
155
of students have a significant difference between them on the statement
that all topics in the textbooks are taught completely for the preparation of final
examination.
Table 132: Methods to solve different types of problems are explained
through worked examples in the textbooks
H0:There will be no significant difference between SSC and GCE students on the statement that methods to solve different types of problems are explained through worked examples in the textbooksRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿3.64 0.9060.128 2.734
GCE(O-Level) 80 x2=¿3.99 0.864
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 132,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 2.734. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement
that methods to solve different types of problems are explained through worked
examples in the textbooks.
Table 133: Textbooks are illustrated with concept-related pictures from real
life
H0:There will be no significant difference between SSC and GCE students on the statement that textbooks are illustrated with concept-related pictures from real lifeRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿2.70 1.1990.167 3.832
GCE(O-Level) 80 x2=¿3.34 1.136
df =198 tabulated ‘t’ value at 0.05 = 1.960
156
Conclusion:Referring to table 133,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 3.832. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement
that textbooks are illustrated with concept-related pictures from real life.
Table 134: Pictures in the textbooks facilitate in comprehending the concepts
H0:There will be no significant difference between SSC and GCE students on the statement that the pictures facilitate in comprehending the conceptsRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿3.61 1.0230.153 0.392
GCE(O-Level) 80 x2=¿3.55 1.089
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 134,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.392. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on
the statement that the pictures facilitate in comprehending the concepts.
Table 135: Diagrams are the frightening element of the textbooks
H0:There will be no significant difference between SSC and GCE students on the statement that diagrams are the frightening element of the textbooksRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿2.59 1.2260.156 2.821
GCE(O-Level) 80 x2=¿2.15 0.982
df =198 tabulated ‘t’ value at 0.05 = 1.960
157
Conclusion:Referring to table 135,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 2.821. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement
that diagrams are the frightening element of the textbooks.
Table 136: I can study a new topic through worked examples provided in the
textbook
H0:There will be no significant difference between SSC and GCE students on the statement, “I can study a new topic through worked examples provided in the textbook”.Respondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿3.52 1.2830.168 5.774
GCE(O-Level) 80 x2=¿2.55 1.078
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 136,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 5.774. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the
statement,“I can study a new topic through worked examples provided in the
textbook”.
Table 137: I study the topic from the textbook first before it is explained by
the teacher in class
H0:There will be no significant difference between SSC and GCE students on the statement, “I study the topic from the textbook first before it is explained by the teacher in class”.Respondents N Mean SD SEx1−x2 t-value
158
SSC(Matriculation) 120 x1=¿3.83 1.1280.165 1.818
GCE(O-Level) 80 x2=¿3.53 1.158
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 137,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.818. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on
the statement, “I study the topic from the textbook first before it is explained by the
teacher in class”.
Table 138: I have questions in mind before starting a new lesson
H0:There will be no significant difference between SSC and GCE students on the statement,“I have questions in mind before starting a new lesson”.Respondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿3.78 1.1170.156 1.795
GCE(O-Level) 80 x2=¿3.50 1.055
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 138,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.795. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on
the statement, “I have questions in mind before starting a new lesson”.
Table 139: Only the contents explained by the teacher should be studied
H0:There will be no significant difference between SSC and GCE students on the statement that only the contents explained by the teacher should be studied
159
Respondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿2.95 1.3400.176 5.114
GCE(O-Level) 80 x2=¿2.05 1.135
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 139,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 5.114. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement
that only the contents explained by the teacher should be studied.
Table 140(a): Comparison of components of the contents that have to be learnt in mathematics
ComponentsH0:There will be no significant difference between the SSC and GCE students on memorization of these components of the contents
1. Formulae
Respondents N Mean SDSE
x1−x2
t-value
SSC(Matriculation) 120x1=¿
4.051.028
0.156 0.897
GCE(O-Level) 80x2=¿
3.911.116
2.Steps of
long
procedures
SSC(Matriculation) 120x1=¿
3.581.135
0.161 0.124
GCE(O-Level) 80x2=¿
3.601.098
3.Definitions SSC(Matriculation) 120 x1=¿ 1.119 0.173 7.514
160
3.58
GCE(O-Level) 80x2=¿
2.281.253
4.Proofs of
geometrical
theorems
SSC(Matriculation) 120x1=¿
4.031.195
0.188 9.148
GCE(O-Level) 80x2=¿
2.311.365
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusions
1. Formulae
Referring to table 140(a),we find that the tabulated ‘t’ value = 1.960 is larger than the computed ‘t’ value = 0.897. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the
statement that formulae are to be memorized in mathematics.
2. Steps of long procedures
Referring to table 140(a),we find that the tabulated ‘t’ value = 1.960 is larger than the computed ‘t’ value = 0.124. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the
statement that steps of long procedures are to be memorized in mathematics.
3. Definitions
161
Referring to table 140(a),we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 7.514. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the
statement that definitions are to be memorized in mathematics.
4. Proofs of theorems
Referring to table 140(a),we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 9.148. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the
statement that proofs of geometrical theorems are to be memorized in
mathematics.
140(b): Graph 7*For this comparison, SA & A alternatives of the measurement scale has been collapsed to get the percentage of agreement
Table 141: Contents of the textbooks are in accordance with the intellectual
levels of students
H0:There will be no significant difference between SSC and GCE students on the statement that the contents of textbooks are in accordance with the intellectual levels of studentsRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿3.48 1.1150.148 0.203
GCE(O-Level) 80 x2=¿3.51 0.955
162
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table141,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.203. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on
the statement that the contents of textbooks are in accordance with the intellectual
levels of students.
Table 142: Language of the textbooks is in accordance with the language
proficiency of students
H0:There will be no significant difference between SSC and GCE students on the statement that the language of textbooks is in accordance with the language proficiency of studentsRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿3.55 0.8970.132 1.016
GCE(O-Level) 80 x2=¿3.69 0.922
df =198 tabulated ‘t’ value at 0.05 = 1.960
163
Formulae Steps of long procedures Definitions Proofs of theorems0%
10%20%30%40%50%60%70%80%90%
*Comparison of components of the contents that have to be learnt in mathematics
R
espo
nses
in p
erce
nt
Conclusion:Referring to table 142,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.016. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on
the statement that the language of textbooks is in accordance with the language
proficiency of students.
Table 143: Getting afraid of a problem in the first look makes it very difficult
to solve
H0:There will be no significant difference between SSC and GCE students on the statement that getting afraid of a problem in the first look makes it very difficult to solveRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿4.09 0.9610.182 4.945
GCE(O-Level) 80 x2=¿3.19 1.424
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 143,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 4.945. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement
that getting afraid of a problem in the first look makes it very difficult to solve.
Table 144: Doing important topics is better than doing all the topics in order
to get good marks
H0:There will be no significant difference between SSC and GCE students on the statement that doing important topics is better than doing all the topics in order to get good marksRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿3.48 1.3020.171 5.673
GCE(O-Level) 80 x2=¿2.51 1.102
164
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 144,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 5.673. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement
that doing important topics is better than doing all the topics in order to get good
marks.
Table 145: The last questions (star questions) of the exercises are generally
left unsolved
H0:There will be no significant difference between SSC and GCE students on the statement that the last questions (star questions) of the exercises are generally left unsolvedRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿3.48 1.2090.172 0.581
GCE(O-Level) 80 x2=¿3.58 1.178
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 145,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.581. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between themon
the statement that the last questions (star questions) of the exercises are generally left
unsolved.
Table 146(a): Comparison of the domains of thinking process during the
solution of a problem
DomainsH0:There will be no significant difference between the SSC and GCE students on the domains of thinking process during the solution of a problem
1.Retrieval of Respondents N Mean SD SE t-value
165
formula and
method from
memory
x1−x2
SSC(Matriculation) 120x1=¿
4.061.162
0.134 1.045
GCE(O-Level) 80x2=¿
4.200.736
2.Developmen
t of one’s own
strategy to
solve the
problem
SSC(Matriculation) 120x1=¿
3.371.296
0.167 2.515
GCE(O-Level) 80x2=¿
3.791.052
3.Thinking to
get an insight
SSC(Matriculation) 120x1=¿
3.621.109
0.149 2.215
GCE(O-Level) 80x2=¿
3.950.979
4.Effort to
recall the
chapter and
exercise of the
problem
SSC(Matriculation) 120x1=¿
4.070.950
0.175 5.943
GCE(O-Level) 80
x2=¿
3.03 1.359
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusions
1. Retrieval of formula and method from memory
166
Referring to table 146(a),we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.045. Hence, H0
is rejected which leads us to the conclusion that the two groups of students have no significant difference between them on the
statement that during the solution of a problem they think to retrieve the formula
and method from memory.
2. Development of our own strategy to solve the problem
Referring to table 146(a),we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 2.515. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the
statement that during the solution of a problem they think to develop their own
strategy to solve the problem.
3. Thinking to get an insight
Referring to table ‘146(a)’ we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 2.215. Hence H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the
statement that during the solution of a problem they think to get an insight for its
solution.
4. Effort to remember the chapter and exercise number of the problem
Referring to table ‘146(a)’ we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 5.943. Hence H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the
statement that during the solution of a problem they try to remember from which
chapter and exercise number the problem is.
167
146(b): Graph 8
Domain 1 Domain 2 Domain 3 Domain 40%
10%20%30%40%50%60%70%80%90%
100%
*Comparison of the domains of thinking process dur-ing the solution of a problem
Res
pons
es in
per
cent
*For this comparison SA & A, alternatives of the measurement scale has been collapsed to get the percentage of agreement
Table 147: Most of the teachers emphasize solving the sums using their
explained methods only
H0:There will be no significant difference between SSC and GCE students on the statement that most of the teachers emphasize solving the sums using their explained methods onlyRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿3.48 1.1880.166 1.386
GCE(O-Level) 80 x2=¿3.71 1.127
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 147,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.386. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on
168
the statement that most of the teachers emphasize solving the sums using their
explained methods only.
Table 148: There is more than one method to solve a problem
H0:There will be no significant difference between SSC and GCE students on the statement that there is more than one method to solve a problemRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿4.33 0.7900.101 1.485
GCE(O-Level) 80 x2=¿4.48 0.636
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 148,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.485. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on
the statement that there is more than one method to solve a problem.
Table 149: Most of the teachers emphasize neat and tidy work
H0:There will be no significant difference between SSC and GCE students on the statement that most of the teachers emphasize neat and tidy workRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿4.16 1.0370.163 4.172
GCE(O-Level) 80 x2=¿3.48 1.190
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 149,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 4.172. Hence, H0 is rejected, which leads us to the conclusion that the two groups
169
of students have a significant difference between them on the statement
that most of the teachers emphasize neat and tidy work.
Table 150(a): Comparison of the remarks of students for questions involving
graphs
RemarksH0:There will be no significant difference between the SSC and GCE students on their remarks for graph questions
1.Difficult
Respondents N Mean SDSE
x1−x2
t-value
SSC(Matriculation) 120x1=¿
3.401.337
0.186 3.889
GCE(O-Level) 80x2=¿
2.401.186
2.Boring
SSC(Matriculation) 120x1=¿
3.141.368
0.198 0.202
GCE(O-Level) 80x2=¿
3.101.374
3.Time
Consuming
SSC(Matriculation) 120x1=¿
3.671.218
0.191 1.885
GCE(O-Level) 80x2=¿
3.311.383
4.Annoying
SSC(Matriculation) 120x1=¿
3.041.246
0.192 1.875
GCE(O-Level) 80x2=¿
3.401.383
170
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusions
1. Difficult
Referring to table 150(a),we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 3.889. Hence, H0
is rejected which leads us to the conclusion that the two groups of students have no significant difference between them on the
statement that graph question are difficult.
2. Boring
Referring to table 150(a),we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.202. Hence, H0
is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the
statement that graph questions are boring.
3. Time Consuming
Referring to table 150(a),we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.885. Hence, H0
is accepted, which leads us to the conclusion that the two groups
171
of students have no significant difference between them on the
statement that graph questions are time consuming.
4. Annoying
Referring to table 150(a),we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.875. Hence, H0
is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on the
statement that graph questions are annoying.
150(b): Graph 9
Difficult Boring Time Consuming Annoying0%
10%
20%
30%
40%
50%
60%
70%
80%
*Comparison of the remarks of students for questions involving graphs
Res
pons
es in
per
cent
*For this comparison SA & A, alternatives of the measurement scale has been collapsed to get the percentage of agreement
Table 151: Additional material (worksheets/workbooks etc.) is used to get
further practice of the sums
172
H0:There will be no significant difference between SSC and GCE students on the statement that additional material (worksheets/workbooks etc.) is used to get further practice of the sumsRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿3.63 1.2170.159 1.069
GCE(O-Level) 80 x2=¿3.80 1.024
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 151,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.069. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on
the statement that additional material (worksheets/workbooks etc.) is used for further
practice of the sums.
Table 152: Teacher-constructed problems are presented in the class
H0:There will be no significant difference between SSC and GCE students on the statement that teacher-constructed problems are presented in the classRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿3.60 1.0950.159 4.717
GCE(O-Level) 80 x2=¿2.85 1.115
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 152,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 4.717. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement
that teacher-constructed problems are presented in the class.
173
Table 153: Separate activities are done for low achievers in the class
H0:There will be no significant difference between SSC and GCE students on the statement that separate activities are done for low achievers in the classRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿3.13 1.1420.157 5.668
GCE(O-Level) 80 x2=¿2.24 1.058
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 153,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 5.668. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement
that separate activities are done for low achievers in the class.
Table 154: Teachers arrange activities to engage high achiever students to
help their low achiever class fellows
H0:There will be no significant difference between SSC and GCE students on the statement that teachers arrange activities to engage high achiever students to help their low achiever class fellowsRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿3.25 1.3170.185 2.054
GCE(O-Level) 80 x2=¿2.87 1.257
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 154,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 2.054. Hence, H0 is rejected, which leads us to the conclusion that the two groups
174
of students have a significant difference between them on the statement
that teachers arrange activities to engage high achiever students to help their low
achiever class fellows.
Table 155: In a mathematics class of 40 minutes, students normally ask less
than 5 questions
H0:There will be no significant difference between SSC and GCE student on the statement that in a mathematics class of 40 minutes students normally ask less than 5 questionsRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿3.08 1.1960.166 2.892
GCE(O-Level) 80 x2=¿2.60 1.121
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 155,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 2.892. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement
that in a mathematics class of 40 minutes students normally ask less than 5 questions.
Table 156: In a mathematics class of 40 minutes, teachers normally explain
for less than 15 minutes
H0:There will be no significant difference between SSC and GCE students on the statement that in a mathematics class of 40 minutes teachers normally explain for less than 15 minutesRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿2.54 1.1590.172 0.402
GCE(O-Level) 80 x2=¿2.83 1.209
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 156,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.402.
175
Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on
the statement that in a mathematics class of 40 minutes teachers normally explain for
less than 15 minutes.
Table 157: Students mostly ask ‘HOW’ type questions in the class
H0:There will be no significant difference between SSC and GCE students on the statement that Students mostly ask ‘HOW’ type questions in the classRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿ 4.23 0.8770.110 0.091
GCE(O-Level) 80 x2=¿4.24 0.679
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 157,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.091. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on
the statement that students mostly ask ‘HOW’ type questions in the class.
Table 158: ‘WHY’ type questions are rarely posed by students
H0:There will be no significant difference between SSC and GCE students on the statement that ‘WHY’ type questions are rarely posed by studentsRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿3.86 1.1250.157 0.637
GCE(O-Level) 80 x2=¿3.76 1.070
df =198 tabulated ‘t’ value at 0.05 = 1.960
176
Conclusion:Referring to table 158,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.637. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on
the statement that ‘WHY’ type questions are rarely posed by students.
Table 159: Teachers do not encourage ‘WHY’ type questions in the class
H0:There will be no significant difference between SSC and GCE student on the statement that teachers do not encourage ‘WHY’ type questions in the classRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿3.25 1.1760.161 2.112
GCE(O-Level) 80 x2=¿3.59 1.076
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 159,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 2.112. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement
that teachers do not encourage ‘WHY’ type questions in the class.
Table 160: Procedure of solving a problem is explained but not the reason for
the selection of that procedure
H0:There will be no significant difference between SSC and GCE students on the statement that procedure of solving a problem is explained but not the reason for the selection of that procedureRespondents N Mean SD SEx1−x2 t-value
177
SSC(Matriculation) 120 x1=¿3.48 1.0840.159 1.258
GCE(O-Level) 80 x2=¿3.68 1.122
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 160,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.258. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on
the statement that procedure of solving a problem is explained but not the reason for
the selection of that procedure.
Table 161: Some topics of the textbooks are never taught
H0:There will be no significant difference between SSC and GCE student on the statement that some topics of the textbooks are never taughtRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿3.78 1.0570.172 6.221
GCE(O-Level) 80 x2=¿2.71 1.275
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 161,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 6.221. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement
that some topics of the textbooks are never taught.
Table 162: Homework is assigned in order to complete the syllabus as it
cannot be completed by solving all the sums in class
H0:There will be no significant difference between SSC and GCE students on the
178
statement that homework is assigned in order to complete the syllabus as it cannot be completed by solving all the sums in classRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿4.02 1.0040.137 1.168
GCE(O-Level) 80 x2=¿3.86 0.910
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 162,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.168. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on
the statement that homework is assigned in order to complete the syllabus as it cannot
be completed by solving all the sums in class.
Table 163: Completion of a topic means that teacher has explained the topic
and students have done the sums in their notebooks
H0:There will be no significant difference between SSC and GCE student on the statement that completion of a topic means that teacher has explained the topic and students have done the sums in their notebooksRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1= 3.52 1.2430.157 2.357
GCE(O-Level) 80 x2=¿3.89 0.981
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 163,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 2.357. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement
that completion of a topic means that teacher has explained the topic and students
have done the sums in their notebooks.
179
Table 164: Homework is assigned and checked regularly by the teachers
H0:There will be no significant difference between SSC and GCE student on the statement that homework is assigned and checked regularly by the teachersRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿3.69 1.2680.178 9.438
GCE(O-Level) 80 x2=¿2.01 1.183
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 164,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 9.438. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement
that homework is assigned and checked regularly by the teachers.
Table 165: Classwork of students is checked regularly by the teachers
H0:There will be no significant difference between SSC and GCE student on the statement that classwork of students is checked regularly by the teachersRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿3.19 1.3430.182 6.319
GCE(O-Level) 80 x2=¿2.04 1.195
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 165,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 6.319. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement
that classwork of students is checked regularly by the teachers.
180
Table 166: Topics are not explored in depth; only the procedure of solving a
sum is explained
H0:There will be no significant difference between SSC and GCE students on the statement that topics are not explored in depth; only the procedure of solving a sum is explainedRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿3.10 1.2300.179 0.223
GCE(O-Level) 80 x2=¿3.06 1.246
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 166,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.223. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on
the statement that topics are not explored in depth; only the procedure of solving a
sum is explained.
Table 167: Short cut techniques are explained to solve certain problems but
the logical reasons behind adopting these techniques are not explained
H0:There will be no significant difference between SSC and GCE students on the statement that short cut techniques are explained to solve certain problems but the logical reasons behind adopting these techniques are not explainedRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿3.33 1.1910.182 1.374
GCE(O-Level) 80 x2=¿3.08 1.309
df =198 tabulated ‘t’ value at 0.05 = 1.960
181
Conclusion:Referring to table 167,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.374. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on
the statement that short cut techniques are explained to solve certain problems but the
logical reasons behind adopting these techniques are not explained.
Table 168: Derivation of formula is not explained, only the method of its
application is told
H0:There will be no significant difference between SSC and GCE students on the statement that derivation of formula is not explained, only the method of its application is toldRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿3.26 1.3190.177 0.452
GCE(O-Level) 80 x2=¿3.18 1.167
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 168,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.452. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on
the statement that derivation of formula is not explained, only the method of its
application is told.
Table 169: The activities of a mathematics class are largely doing repetition of
similar sums
H0:There will be no significant difference between SSC and GCE students on the statement that the activities of a mathematics class are largely doing repetition of similar sumsRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿3.70 1.033 0.143 0.279
182
GCE(O-Level) 80 x2=¿3.66 0.967
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion: Referring to table 169,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.279. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on
the statement that the activities of a mathematics class are largely doing repetition of
similar sums.
Table 170: Reference books are taken from the library to explore the topics in
depth
H0:There will be no significant difference between SSC and GCE students on the statement that reference books are taken from the library to explore the topics in depthRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿2.37 1.2840.185 0.160
GCE(O-Level) 80 x2=¿2.53 1.281
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion: Referring to table 170,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.160. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on
the statement that reference books are taken from the library to explore the topics in
depth.
Table 171(a): Comparison of experiences of students in the class about the
teaching methods of their teachers
183
Methods
H0:There will be no significant difference between the SSC andGCE students regarding their observations of teaching
methods of their teachers
1.Teachers
explain some
problems on a
topic from the
textbook on the
board
Respondents N Mean SDSE
x1−x2
t-value
SSC(Matriculation) 120x1=¿
4.180.774
0.094 0.426
GCE(O-Level) 80x2=¿
4.140.545
(Contd…….)2.Explain all the
problems on a
topic from the
textbook on the
board
SSC(Matriculation) 120x1=¿
2.831.179
0.167 2.874
GCE(O-Level) 80x2=¿
2.351.137
3.
Explainimportant
points and
procedures and
help students in
solving the sums
SSC(Matriculation) 120x1=¿
3.881.070
0.144 2.083
GCE(O-Level) 80x2=¿
4.18
0.952
4.Give sums
directly and
facilitate
students in
finding their
solutions
SSC(Matriculation) 120x1=¿
2.591.280
0.183 0.328
GCE(O-Level) 80x2=¿
2.651.264
df =198 tabulated ‘t’ value at 0.05 = 1.960
184
Conclusions
1. Teachers explain some problems on a topic from the textbook on the board
Referring to table 171(a),we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.426. Hence, H0
is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them regarding
their experience in the class of mathematics that teachers explain some problems
on a topic from the textbooks on the board.
2. Explain all the problems on a topic from the textbook on the board
Referring to table 171(a),we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 2.874. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between themregarding their
experience in the class of mathematics that teachers explain all the problems on a
topic from the textbooks on the board.
3. Explain important points and procedures and help students in solving the
sums
Referring to table 171(a),we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 2.083. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between themregarding their
experience in the class of mathematics that teachers explain important points and
procedures and help students in solving the sums.
4. Give sums directly and facilitate students in finding their solutions
Referring to table 171(a),we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.328. Hence, H0
185
is accepted, which leads us to the conclusion that the two groups of students have no significant difference between themregarding
their experience in the class of mathematics that teachers give sums directly and
facilitate students in finding their solutions.
171(b): Graph 10
Method 1 Method 2 Method 3 Method 40%
10%20%30%40%50%60%70%80%90%
100%
*Comparison of experiences of students in the class about the teaching methods of their teachers
Res
pons
es in
per
cent
*For this comparison SA & A, alternatives of the measurement scale has been collapsed to get the percentage of agreement
Table 172(a): Comparison of attributes of a good teacher from students’
perspective
186
AttributesH0:There will be no significant difference between the SSC and GCE students regarding the attributes of a good teacher
1.Starting
a new lesson
with
recapitulation
Respondents N Mean SDSE
x1−x2
t-value
SSC(Matriculation) 120x1=¿
4.041.095
0.143 0.979
GCE(O-Level) 80x2=¿
4.180.925
2.Presenting
uninteresting
matter in an
interesting
way
SSC(Matriculation) 120x1=¿
4.120.954
0.119 2.689
GCE(O-Level) 80x2=¿
4.440.726
(Continued from the previous page…….)
3.Presenting
difficult
concepts in a
simple way
SSC(Matriculation) 120x1=¿
4.400.726
0.093 1.827
GCE(O-Level) 80x2=¿
4.570.588
4.Explaining
lengthy
concepts very
concisely
SSC(Matriculation) 120x1=¿
4.000.970
0.163 1.349
GCE(O-Level) 80x2=¿
3.781.219
5.Keeping
students alert
and attentive
by creating
humor
SSC(Matriculation) 120x1=¿
4.081.017
0.131 2.784
GCE(O-Level) 80x2=¿
4.440.824
6.Giving
encouraging
SSC(Matriculation) 120 x1=¿
4.19
0.823 0.106 3.679
187
remarks GCE(O-Level) 80x2=¿
4.580.671
7.Engaging
the entire
class in
productive
activities
SSC(Matriculation) 120x1=¿
3.041.021
0.153 2.810
GCE(O-Level) 80x2=¿
3.821.085
8.Finishing a
lesson with a
summary of
the class
activities
SSC(Matriculation) 120x1=¿
4.120.972
0.155 0.194
GCE(O-Level) 80x2=¿
4.151.137
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusions
1. Starting a new lesson with recapitulation
Referring to table 172(a),we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.979. Hence, H0
is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them regarding
the attribute of a good teacher that he/she starts a new lesson with recapitulation.
2. Presenting uninteresting matter in an interesting way
Referring to table 172(a),we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 2.689. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them regarding the
attribute of a good teacher that he/she presents uninteresting matter in an
interesting way.
188
3. Presenting difficult concepts in a simple way
Referring to table 172(a),we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.827. Hence, H0
is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them regarding
the attribute of a good teacher that he/she presents difficult concepts in a simple
way.
4. Explaining lengthy concepts very concisely
Referring to table 172(a),we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.349. Hence, H0
is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them regarding
the attribute of a good teacher that he/she explains lengthy concepts very
concisely.
5. Keeping students alert and attentive by creating humor
Referring to table 172(a),we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 2.748. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them regarding the
attribute of a good teacher that he/she keeps students alert and attentive by
creating humor.
6. Giving encouraging remarks
Referring to table 172(a),we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 3.679. Hence, H0 is rejected, which leads us to the conclusion that the two groups of
189
students have a significant difference between them regarding the
attribute of a good teacher that he/she gives encouraging remarks.
7. Engaging the entire class in productive activities
Referring to table 172(a),we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 2.810. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them regarding the
attribute of a good teacher that he/she engages all class in productive activities.
8. Finishing a lesson with a summary of the class activities
Referring to table 172(a),we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.194. Hence, H0
is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them regarding
the attribute of a good teacher that he/she finishes a lesson with a summary of
who the class activities.
172(b): Graph 11
190
Attribute 1
Attribute 2
Attribute 3
Attribute 4
Attribute 5
Attribute 6
Attribute 7
Attribute 8
0%
20%
40%
60%
80%
100%
120%
*Comparison of the attributes of a mathematics teacher from students' perspective
Res
pons
es in
per
cent
*For this comparison SA & A, alternatives of the measurement scale has been collapsed to get the percentage of agreement
Table 173: Assessments help in confidence building
H0:There will be no significant difference between SSC and GCE students on the statement that assessments help in confidence buildingRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿4.24 0.8300.126 1.984
GCE(O-Level) 80 x2=¿3.99 0.893
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 173,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 1.984. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement
that assessments help in confidence building.
191
Table 174: Assessments help in identifying and reducing mistakes
H0:There will be no significant difference between SSC and GCE students on the statement that assessments help in identifying and reducing mistakesRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿4.34 0.7390.095 0.316
GCE(O-Level) 80 x2=¿4.31 0.608
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 174,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.316. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on
the statement that assessments help in identifying and reducing mistakes.
Table 175: Assessments help in the preparation for final examinations
H0:There will be no significant difference between SSC and GCE students on the statement that assessments help in the preparation for final examinationsRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿4.44 0.8070.092 0.217
GCE(O-Level) 80 x2=¿4.46 0.594
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 175,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.217. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on
the statement that assessments help in the preparation for final examinations.
192
Table 176: Quizzes (short tests based on calculations without using
calculators) are conducted regularly in the class
H0:There will be no significant difference between SSC and GCE student on the statement that quizzes (short tests based on calculations without using calculators) are conducted regularly in the classRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿2.88 1.3480.192 2.135
GCE(O-Level) 80 x2=¿3.29 1.323
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 176,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 2.135. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement
that quizzes (short tests based on calculations without using calculators) are
conducted regularly in the class.
Table 177: Speed tests are conducted regularly in the class
H0:There will be no significant difference between SSC and GCE students on the statement that speed tests are conducted regularly in the classRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿2.43 1.2550.189 1.746
GCE(O-Level) 80 x2=¿2.76 1.343
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 177,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 1.746.
193
Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on
the statement that speed tests are conducted regularly in the class.
Table 178: Positive remarks of the teacher on student’s assessment produce
better results
H0:There will be no significant difference between SSC and GCE students on the statement that positive remarks of the teacher on student’s assessment produce better resultsRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿4.09 0.9260.172 0.349
GCE(O-Level) 80 x2=¿4.03 1.343
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 178,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.349. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on
the statement that positive remarks of the teacher on student’s assessment produce
better results.
Table 179: Negative remarks by a teacher on student’s assessment produce
demoralization
H0:There will be no significant difference between SSC and GCE students on the statement that negative remarks by a teacher on student’s assessment produce demoralizationRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿3.77 0.932 0.141 0.851
GCE(O-Level) 80 x2=¿3.89 1.006
194
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 179,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.851. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on
the statement that negative remarks by a teacher on student’s assessment produce
demoralization.
Table 180: I am wellaware of the pattern of SSC/GCE paper
H0:There will be no significant difference between SSC and GCE student on the statement, “I am well aware of the pattern of SSC/GCE paper”Respondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿4.26 0.8350.133 2.105
GCE(O-Level) 80 x2=¿3.98 0.981
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table ‘180’ we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 2.105. Hence H0
is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement, “I
am well aware of the pattern of SSC/GCE paper”.
Table 181: Students study seriously under the pressure of tests/examinations
H0:There will be no significant difference between SSC and GCE students on the statement that students study seriously under the pressure of tests/examinationsRespondents N Mean SD SEx1−x2 t-value
195
SSC(Matriculation) 120 x1=¿3.96 1.1030.149 0.939
GCE(O-Level) 80 x2=¿4.10 0.976
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 181,we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.939. Hence, H0 is accepted, which leads us to the conclusion that the two groups of students have no significant difference between them on
the statement that students study seriously under the pressure of tests/examinations.
Table 182: Teachers leave some topics completely on the basis of their
insignificance in the SSC/GCE paper
H0:There will be no significant difference between SSC and GCE student on the statement that teachers leave some topics completely on the basis of their insignificance in the SSC/GCE paperRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿3.64 1.0830.189 4.974
GCE(O-Level) 80 x2=¿2.70 1.444
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 182,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 4.974. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement
that teachers leave some topics completely on the basis of their insignificance in the
SSC/GCE paper.
196
Table 183: Questions in SSC/GCE papers are given according to a fixed
pattern
H0:There will be no significant difference between SSC and GCE student on the statement that questions in SSC/GCE papers are given according to a fixed patternRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿4.11 0.9510.173 7.688
GCE(O-Level) 80 x2=¿2.78 1.340
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 183,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 7.688. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement
that questions in SSC/GCE papers are given according to a fixed pattern.
Table 184: Questions are taken from the textbooks in SSC/GCE paper
H0:There will be no significant difference between SSC and GCE student on the statement that questions are taken from the textbooks in SSC/GCE paperRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿3.89 1.0270.153 11.503
GCE(O-Level) 80 x2=¿2.13 1.084
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 184,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 11.503. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement
that questions are taken from the textbooks in SSC/GCE paper.
197
Table 185: Questions are taken from past papers in SSC/GCE paper
H0:There will be no significant difference between SSC and GCE student on the statement that questions are taken from past papers in SSC/GCE paperRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿3.88 0.9540.163 8.282
GCE(O-Level) 80 x2=¿2.53 1.232
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 185,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 8.282. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement
that questions are taken from past papers in SSC/GCE paper.
Table 186: Some topics from the syllabus may be dropped on the basis of
sufficient choice of questions in the exam paper
H0:There will be no significant difference between SSC and GCE student on the statement that some topics from the syllabus may be dropped on the basis of sufficient choice of questions in the exam paperRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿3.72 1.1240.171 8.070
GCE(O-Level) 80 x2=¿2.34 1.222
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 186,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 8.070. Hence, H0 is rejected, which leads us to the conclusion that the two groups
198
of students have a significant difference between them on the statement
that some topics from the syllabus may be dropped on the basis of sufficient choice of
questions in the exam paper.
Table 187: Some questions can be predicted for the upcoming papers on the
basis of previous papers
H0:There will be no significant difference between SSC and GCE student on the statement that some questions can be predicted for the upcoming papers on the basis of previous papersRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿4.17 0.7810.154 7.532
GCE(O-Level) 80 x2=¿3.01 1.227
df =198 tabulated ‘t’ value at 0.05 = 1.960Conclusion:Referring to table 187,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 7.532. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement
that on the basis of previous papers some questions can be predicted for the upcoming
paper.
Table 188(a): Comparison of methods used for revision before taking a test/
examination
MethodsH0:There will be no significant difference between the SSC and GCE students on the methods used for revision
1.Solving all
the sums from
the textbooks
Respondents N Mean SDSE
x1−x2
t-value
SSC(Matriculation) 120x1=¿
3.831.198
0.177 4.972
GCE(O-Level) 80x2=¿
2.951.242
199
2.Solving
different types
of sums from
the textbooks
SSC(Matriculation) 120x1=¿
4.240.809
0.1302.308
GCE(O-Level) 80x2=¿
3.940.959
3. Solving
sums from the
past papers
(five years)
SSC(Matriculation) 120x1=¿
4.180.967
0.124 0.806
GCE(O-Level) 80x2=¿
4.280.779
4.Reading
solved sums
from the
copies
SSC(Matriculation) 120 x1=¿
3.571.275
0.183 5.355
GCE(O-Level) 80x2=¿
2.591.269
5. Reading
worked
examples from
the textbooks
SSC(Matriculation) 120x1=¿
3.571.214
0.177 4.915
GCE(O-Level) 80x2=¿
2.701.237
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusions
1. Solving all the sums from the exercises
Referring to table 188(a),we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 4.972. Hence, H0
is rejected which leads us to the conclusion that the two groups of students have no significant difference between them on the
statement that all sums should be solved from the exercises.
200
2. Solving different types of sums from the exercises
Referring to table 188(a),we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 2.308. Hence, H0
is rejected which leads us to the conclusion that the two groups of students have no significant difference between them on the
statement that different types of sums should be solved on a topic from the
textbook for revision.
3. Solving sums from the past papers (five years)
Referring to table 188(a),we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 0.806. Hence, H0
is accepted, which leads us to the conclusion that the two groups of students have no significant difference between themon the
statement that sums should be solved from past papers for revision.
4. Reading solved sums from the notebooks (notes maintained in the form of
solutions of sums from the textbooks)
Referring to table 188(a),we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 3.889. Hence, H0
is rejected which leads us to the conclusion that the two groups of students have no significant difference between themon the
statement that sums should be read from the notebooks for revision.
5. Reading worked examples from the textbooks
Referring to table 188(a),we find that the tabulated ‘t’ value = 1.960 is greater than the computed ‘t’ value = 3.889. Hence, H0
is rejected which leads us to the conclusion that the two groups of students have no significant difference between themon the
statement that worked examples from the textbooks should be read for revision.
188 (b): Graph 12
201
Method 1 Method 2 Method 3 Method 4 Method 50%
10%20%30%40%50%60%70%80%90%
100%
*Comparison of methods used for revision before taking a test/ examination
Res
pons
es in
per
cent
*For this comparison SA & A, alternatives of the measurement scale has been collapsed to get the percentage of agreement
Table 189: In junior grades (VI – VIII); the final paper is set from the whole
syllabus
H0:There will be no significant difference between SSC and GCE student on the statement that in junior grades (VI – VIII); the final paper is set from the whole syllabusRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿3.01 1.4050.167 5.569
GCE(O-Level) 80 x2=¿3.94 0.959
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 189,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 5.569. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement
that in junior grades (VI – VIII); the final paper is set from the whole syllabus.
202
Table 190: In junior grades (VI – VIII); the final paper is set from the topics
covered in the final term only
H0:There will be no significant difference between SSC and GCE student on the statement that in junior grades (VI – VIII); the final paper is set from the topics covered in the final term onlyRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿3.48 1.3280.174 7.356
GCE(O-Level) 80 x2=¿2.20 1.118
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 190,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 7.356. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement
that in junior grades (VI – VIII); the final paper is set from the topics covered in the
final term only.
Table 191: In junior grades (VI – VIII); the topics assessed in one terminal
examination do not come in the next term
H0:There will be no significant difference between SSC and GCE student on the statement that in junior grades (VI – VIII); the topics assessed in one terminal examination do not come in the next termRespondents N Mean SD SEx1−x2 t-value
SSC(Matriculation) 120 x1=¿3.08 1.2470.164 5.976
GCE(O-Level) 80 x2=¿2.10 1.051
df =198 tabulated ‘t’ value at 0.05 = 1.960
Conclusion:Referring to table 191,we find that the tabulated ‘t’ value = 1.960 is less than the computed ‘t’ value = 5.976. Hence, H0 is rejected, which leads us to the conclusion that the two groups of students have a significant difference between them on the statement
203
that in junior grades (VI – VIII); the topics assessed in one terminal examination do
not come in the next term.
4.3 ANALYSIS OF THE RESPONSES OF SUBJECT EXPERTSThe responses of experts of both the systems, for each question asked from
them, have been compared and presented in the following table.
Table 192: Comparison of the Responses of Subject Experts
Q1. Are you satisfied with the current routine of teaching mathematics at school
level? If not, what are your reservations?
Responses of Experts (SSC-System) Responses of Experts (GCE-System)
Satisfied (3)
Unsatisfied (7)
Undecided (0)
Reservations
-There is shortage of resources. (3)
-Teachers are untrained. (2)
-The objectives of teaching are not
coherent with the needs of students and
society. (1)
-There is a discontinuation of one year, as
mathematics is not taught in grade IX. (1)
Satisfied (8)
Unsatisfied (2)
Undecided (0)
Reservations
-The syllabus is very lengthy. (1)
-Increasing trend of private tuitions of
this subject is decreasing the interest of
students in the class. (1)
Q.2 Is teaching of mathematics according to some clear objectives? If yes, then
according to your observation, what is the major objective?
Responses of Experts (SSC-System) Responses of Experts (GCE-System)
Agreed (7)
Disagreed (2)
Undecided (1)
-Syllabus is designed to continue this
subject in higher grades. (3)
Agreed (10)
Disagreed (0)
Undecided (0)
-Objectives are to enhance thinking skills
of students. (2)
204
-Enable the students to do basic
operations and calculations. (1)
(Contd…….)-Objectives are to make students learn the
formulae and procedures of solving
different kinds of problems. (2)
-Objectives are not clear to teachers but
in my opinion the only objective is to
make student’s memorize the contents
and procedures so that they can get good
marks by reproducing them in the final
examination. (1)
-Prepare students for GCE-Exam. (4)
-Prepare students for higher learning
giving them first-hand knowledge. (2)
-Enable students to think within the
horizon before thinking beyond horizon.
(1)
-Making students able to think and
making them good problem solvers. (1)
Q.3 Do you agree that these objectives can fulfill the true aims of mathematics
education?
Responses of Experts (SSC-System) Responses of Experts (GCE-System)
Agreed (3)
Disagreed (5)
Undecided (2)
Agreed (9)
Disagreed (0)
Undecided (1)
Q.4 Do you agree that mathematics education in Pakistan is comparable with the
other countries of Asia?
Responses of Experts (SSC-System) Responses of Experts (GCE-System)Agreed (4)
Disagreed (5)
Undecided (1)
Agreed (7)
Disagreed (3)
Undecided (0)
Q.5 Do you agree that mathematics should be the prime focus of school
curriculum as it develops cognitive, affective and psychomotor faculties of an
individual
Responses of Experts (SSC-System) Responses of Experts (GCE-System)
Agreed (9)
Disagreed (0)
Agreed (10)
Disagreed (0)
205
Undecided (0)
(Contd…….)-Agreed,butif our teaching touches these
domains then, the current focus of
teaching is on the contents only. (1)
Undecided (0)
-------
Q.6 Are you satisfied with the contents of textbooks of mathematics used at
secondary level?
Responses of Experts (SSC-System) Responses of Experts (GCE-System)
Satisfied (4)
Unsatisfied (4)
Undecided (0)
-Yes, but problem is not with the
contents. It is with the methods of
teaching and assessment. (1)
-Yes, but some topics like number
sequence, probability, etc. should be
included. (1)
Satisfied (5)
Unsatisfied (3)
Undecided (0)
-Yes, books are not written locally. They
serve the needs in terms of contents but it
will be better if books are written by local
authors. (1)
-Yes but the names of persons and places
are not familiar to our students. If these
are familiar, students can mentally
visualize the context of that problem and
learning of the concept becomes more
concrete. (1)
Q.7 What changes would you like to suggest improving these textbooks?
Responses of Experts (SSC-System) Responses of Experts (GCE-System)
-New topics should be added. (3)
-Word problems designed to apply
mathematical concepts in real life
situations should be increased. (4)
-Textbooks should be updated on
regularly and periodically. (3)
-To cover all the topics of O-Level
mathematics syllabus the books have an
addendum at the end of each book. It will
be better if all the contents given in the
addendum are incorporated into the main
part of the books. (2)
206
(Contd…….)-Worked examples in the textbooks
should be improved. (1)
-Textbooks should be activity-based that
can develop interest among students. (2)
-In lower grades, too many books of
different publishers are used and schools
frequently change these books. If a series
of textbooks is used in one year and next
year is replaced by another series, it will
affect the logical sequence of contents
and vertical integration of concepts. (2)
-It is better if the books are written by
local authors. (3)
-Reference books should be used instead
of textbooks keeping in view the needs of
students. (4)
-Content on number sequence and
problem solving should be increased. (1)
-Answers of graph and loci questions
should be given in the form of
constructed graphs and geometrical
figures respectively. (1)
-A teachers’ manual should be published
with each book for their guidance. (2)
Q.8 Are you satisfied with the current methods of selection and sequencing of
contents? If not, please give your opinion.
Responses of Experts (SSC-System) Responses of Experts (GCE-System)
Satisfied (2)
Dissatisfied (7)
Undecided (1)
-Sequence of contents is not proper at
lower secondary and secondary level. (2)
-Selection of contents should be made
accordingly with the sequence of the
textbooks. (3)
-Selection is made taking topics from the
three key areas (arithmetic, algebra,
geometry) but the prime concern of this
selection is to ensure making a balanced
question paper for terminal/half-yearly
Satisfied (7)
Dissatisfied (3)
Undecided (0)
-It should be done on logical grounds. (4)
-The selection of content should be done
on the basis of educational needs of
students. (5)
-In the process of selection and its
sequencing, no special consideration is
made on the prerequisites, interests and
needs of students. (3)
207
examination. (4)
(Contd…….)-It is done in a sitting of teachers where
the selection, elimination and sequence of
contents are made according to their
choice and feasibility of completing it
within the available time. (3)
-------
Q.9 In your opinion, what changes should be made in the approaches and
methods of teaching mathematics?
Responses of Experts (SSC-System) Responses of Experts (GCE-System)
-Activity-based teaching. (4)
-Project-based teaching. (2)
-Taking the aid of technology (audio-
video aides, internet etc.). (4)
-Mathematics should be taught just like a
language. (1)
-Emphasis is mostly given on the product
but the process is also as important as the
product. (1)
-Teachers should have to address all the
cognitive levels in their teaching
(knowledge, comprehension, application,
analysis, synthesis and evaluation). (1)
-Step by step instructions should be given
instead of giving the key to open the lock
(a method to solve the problem). (2)
-Activity based teaching. (2)
-Spend maximum time on basic concepts.
(4)
-Prefer mental calculations and avoid
calculators as much as possible. (3)
-Computer Assisted Instruction (CAI)
should be introduced. (1)
-Instead of teaching a large number of
chapters, teach a chapter in depth. (2)
-Teach the students to use the (FFF)
approach in solving a problem i.e. face
it, fight it and finish it. (1)
-Make the students confident by rigorous
practice. (6)
208
(Contd…….)Q.10 Are you satisfied with current system of assessment in mathematics at
school level? If not, please suggest some changes.
Responses of Experts (SSC-System) Responses of Experts (GCE-System)
Satisfied (4)
Dissatisfied (6)
Undecided (0)
-Use formative assessment system. (2)
-Discourage rote memorization of
contents by giving application based
problems as much as possible. (3)
-Check understanding of students rather
than checking that the student can solve a
sum or not. (2)
-Don’t give sums directly from the
textbook or five year (previous papers).
(4)
Satisfied (7)
Dissatisfied (3)
Undecided (0)
-Agreed but tests should be held more
frequently. (3)
-More quizzes and mental maths tests
should be administered. (2)
-Teachers should construct their own
problems rather than taking them from
past papers. (3)
Q.11 Are you satisfied with the current pattern of the mathematics paper
(GCE/SSC)? In your opinion, what improvements should be made in it?
Responses of Experts (SSC-System) Responses of Experts (GCE-System)
Satisfied (2)
Dissatisfied (8)
Undecided (0)
-Questions should not be taken from
textbooks / previous papers. (3)
-Pattern of the paper should be such that
it discourages guess work and selected
study habits. (2)
Satisfied (7)
Dissatisfied (2)
Undecided (1)
-Agreed but selective learning should be
discouraged. (3)
-More application based questions should
be included. (2)
-It should test deep understanding instead
209
(Contd…….)
-Pattern of questions should be such that
students can use their skills to solve them
(2).
-Vigilance system during examination
should be improved. (4)
-Workshops/Refresher-Courses for
papers setters and checkers should be
organized.(3)
-System of assessing the papers should be
improved. (2)
of basic knowledge. (1)
-------
Q.12 What are the major strengths of the current system of teaching and
learning mathematics in your opinion?
Responses of Experts (SSC-System) Responses of Experts (GCE-System)
-It provides strong factual and procedural
knowledge of different operations in
mathematics. (1)
-Enables the students to do computation
with knowledge of long procedures and
formulae. (1)
-Provides strong content knowledge for
further studies. (3)
-Develops among students, a skill of
presenting their learned material in a
well-organized and orderly manner. (1)
-It develops a habit of doing neat and tidy
work in students. (1)
-Fair and unbiased. (1)
-It is internationally recognized. (2)
-No choice of leaving any topic from the
prescribed syllabus. (1)
-There is room to incorporate different
methods of teaching in this system. (1)
-Flexibility of appearing for CIE paper
either in May or November, twice a year.
-Examinations are conducted under strict
vigilance. No chance of using unfair
means. (3)
- Paper is balanced in terms of
calculations done mentally (Paper-I) and
using calculators (Paper-II). (1)
210
(Contd…….)- A sense of responsibility by maintaining
the notes (solution of problem in the
textbooks) and getting them checked
from the teachers regularly. (1)
- A standardized system of assessing the
papers. (1)
Q.13 What are the major weaknesses in your opinion in the current system of
mathematics education?
Responses of Experts (SSC-System) Responses of Experts (GCE-System)-There is a discontinuation of one complete year for the study of mathematics in the system. Students after class VIII study mathematics in class X. The suspension of mathematics in grade IX is the biggest weakness of the current system. (2)-Syllabus is too lengthy for a 9-month session. (1)-System of current examinations encourage cramming. (1)- System encourages selected study of some topics, leaving some of the topics completely untouched. (2)-There is a wide gap of standards between SSC and HSC. (1)-Massive use of unfair means. (3)
-This system is very expensive. (4)-Not for majority of the students. (1)
-It is based on (2 + 212 ) hour’s
performance of students. Learning of students in previous 4 years is to be incorporated. (1)-Excessive use of private tuitions. (2)-Very lengthy syllabus. (2)
-------
211
(Contd…….)Q.14 What changes would you like to suggest for the overall improvement of
mathematics education?
Responses of Experts (SSC-System) Responses of Experts (GCE-System)
-Training sessions for teachers. (8)
-Revision of curriculum. (6)
-Eliminating the one year suspension of
mathematics during class IX. (2)
-Improving the assessment system. (6)
-Improving the textbooks. (4)
-Making neutral places as centers of
examination to curb the problem of
cheating. (1)
-Coursework should be included along
with the final paper. (3)
-Increasing the contents that produce
thinking skills. (8)
-Discouraging the trends of tuitions
especially shortcuts (crash-courses) at
different private tuition centers. (4)
-Increasing the role of school. (5)
-Discouraging the increasing trend of the
practice of only selected contents at
tuition centers. (2)
-This system should be in the range of as
many students as possible. (2)
4.3.1 Summary, Discussion and Conclusions
The comparative analysis of the responses of the subject experts revealed that
in both systems, there is a complete agreement on the significance of mathematics
in the school curriculum, but GCE experts showed a comparatively higher
satisfaction level than the SSC experts with the current practice of teaching.
212
The issues highlighted by SSC / GCE experts may be summarized and
concluded as follows.
The clarity of aims and objectives of teaching mathematics, as expected in
their corresponding curricula, was found much higher in GCE subject experts
than the SSC experts. The aims and objectives of GCE curriculum and its
assessment were defined in their curriculum and were easily available on the
internet. Moreover, teachers were informed of the aims and objectives in this
system. On the SSC side, neither were these easily approachable nor was there
a trend of informing teachers of them by school managements.
A suspension of mathematics at grade IX level was found on SSC side but no
such discontinuity of mathematics educationwas found in GCE system at
school level.
GCE curriculum was found to be relatively much broader in terms of key areas
of the content than that of SSC curriculum.
The contents of GCE curriculum were more logically sequenced than the SSC
curriculum contents.
There was relatively more drill (practice) of the learned material in GCE than
SSC system.
There was no significant difference in the selection and organization of the
contents for instruction but GCE teachers were more inclined towards the
concentric approach which was missing on the SSC side.
GCE system was focused on ‘depth versus breadth’, while SSC system have
focus on ‘breadth versus depth’. It means that teachers of GCE system
emphasize proficiency in basic knowledge and skills while on the other side,
there is a focus on furthering content knowledge.
213
There was a wide gap of standards in terms of different areas of contents of
SSC and HSC, while there wasn’t such a big difference between the course
contents of O-Level and A-Level mathematics.
Textbooks on GCE side have an internal coherence which is comparatively
lower on SSC side. GCE schools use a series of 4 books as the syllabus of O-
Level. Almost all schools use these four books from grade VI till XI (O-
Level). Students therefore do not face trouble in changing schools. On the
other side, schools in the SSC system do not use the same series of books from
grade VI till VIII. Moreover, there is a suspension of mathematics for one year
in grade IX, after which all the schools have to use the same book of Sindh
Textbook Board in grade X.
The principle of cultural value has been found in the textbooks of SSC system
which is missing on the GCE side because the books used by GCE schools are
not written by local authors. GCE students face problems in conceptualizing a
given situation when names of persons, places, and objects etc. do not
resemble their surroundings.
The contents for the development of problem solving skills were quite large in
number in GCE course compared to SSC course.
The worked examples in the textbooks of GCE system are more self-
explanatory and encompass all the procedures that are to be used in the
solution of problems on a certain topic.
Formative assessment was more systematic on GCE side than SSC system.
Formative assessments are done systematically on regular intervals and
students’ performance is accumulated in their final exam’s performance. As a
result, students take these assessments seriously. SSC system relies only on
summative assessments. Moreover, in most SSC schools, there is a terminal
system (semester system). They move forward on topical bases. Once a topic
is taught and assessed in a term, it does not come in the next term or even in
the final examination.
214
There was no difference in the methods of SSC and GCE systems for the
preparation of final examination. Both systems emphasize their students to
solve previous exam papers for the preparation of final examination.
There was a significant difference in the approaches used by GCE and SSC
systems to solve previous papers. GCE system emphasizes on providing
students with an experience of putting a problem on a topic in different
situations in various ways. Moreover, the solution of papers is also done for
extra practice and rehearsal of the examination. On the other hand, SSC
system does this with the approach of prediction of questions for the upcoming
papers.
There was a higher trend for selected study on SSC side than GCE side.
The pattern of SSC papers is fixed. Questions are taken as they are in
textbooks. Questions from certain chapters are always given in specific
sections. An ample amount of choice is given to select questions from
different sections. As a result, there is a trend of selected study in this system.
On GCE side, neither are questions taken from textbooks, nor is there a fixed
pattern of questions in specific sections. Moreover, there is a minor choice of
just one question in GCE paper. As a result, students have to prepare the entire
syllabus.
GCE examinations were found to be held under strict vigilance while there is a
common observation of the use of unfair means in SSC examinations.
There was more flexibility of taking examination on GCE side. Students can
appear for the examination twice in a year either in May or in November. On
SSC side, there is only one annual examination a student can appear in.
However, a supplementary examination is held for those candidates who have
not passed their annual examination.
The approach of teaching mathematics of GCE teachers was ‘content-
focused’but with an emphasis on understanding and performance. The
approach of SSC teachers, on the other hand, was also ‘content-focused’ but
emphasis is simply on performance.
215
SECTION III: CONTENT ANALYSIS
4.4 Analysis of the Contents of Textbooks and Question Papers
A comparison of the contents of textbooks as well as the patterns of
assessment in both systems has been presented in the following tables.
Table 193(a): SetsSSC GCE
SetsBasic operations on Sets
Union, intersection, difference,
complement
Symmetric difference ( A∆B)
Use of Venn Diagram
Power Set
DE Morgan’s Laws
Cartesian Product & its Graphs
Function and its Types
(Sindh Textbook Board Mathematics
for IX-X,2012,Ch.1)
SetsBasic operation on Sets
Union,intersection,difference,complemen
t
-------
Use of Venn diagrams
-------
DE Morgan’s Laws
-------
-------
(New Syllabus Oxford Mathematics
Book2,Ch.10), (Book3; Addendum,Ch.I)
Nature of the Contents
General Objectives
-Cognitive
*Understand and use set language.
General Objectives
-Cognitive
*Same
216
*Solve problems involving basic
operations on sets.
------- (Contd…….)
-Psychomotor
* Enable students to draw Venn diagrams
of given sets
*Same
*Use of Venn diagrams in solving daily
life problems.
-Psychomotor
* Enable students to draw Venn diagrams
from the given information in any form.
Ingredients of the contents
*Methods to operate on sets were
explained through worked examples and
sets of Real numbers or letters of English
alphabet were mostly used.
Similar sums were given in further
exercises.
-------
Ingredients of the contents
* Methods to operate on sets were
explained through worked examples and
sets of concrete objects were mostly used.
Similar problems were given for further
exercises.
*Word problems were given, where
application of basic operations of sets was
required as well as the proper use of Venn
diagrams, for their solution.
Presentation
*Black& white color was used to
differentiate among parts of Venn
diagrams.
Presentation
*Different colors were used to
differentiate among different parts of
Venn diagrams.
Sequencing: Appropriate Sequencing: Appropriate
Integration with other Topics
-------
Integration with other Topics
Problems were given in which Venn
diagrams were required using properties
of different types of triangles and
quadrilaterals. It has also been linked
with dimensions and area of rectangle.
Language: Simple English language was
used but with a rich use of symbols and
Language:Mostly simple English
language was used with a mild use of
217
notations.
(Contd…….)
Symbols and notations where necessary.
Comparison of the Contents of Question Papers
(Comparison is based on the last 20 years of papers of SSCand GCE)
Questions taken from the Textbooks
(2013,Q2 from Ex 1.3,Q5);
(2011,Q2 from Ex1.2,Q17)
Questions taken from the Textbooks
-------
Questions taken from Previous
Papers(2007,Q2a&b from 2004,Q2a&b);
(2008,Q2b from 2000,Q2b);
(2002,Q2b from 2000,Q2b);
(1997,Q2b from 1995,Q2a)
(Global’s Papers:2013-2004)
(Global’s Papers: 2003-1994)
Questions taken from Previous Papers
-------
(O-Level Classified Mathematics,
Unit,10)
Repetition of Similar Questions:In the
following questions exactly same
operation was repeated except some
minor changes of numbers in the given
sets.
1.Cartesian Product
(2013,Q2); (2009,Q2b); (2006,Q2b);
(2003,Q2b); (2001,Q2b); (1999,Q2b);
(1996,Q2b)
2.Power Set
(2008,Q2b); (2007,Q2a); (2004,Q2a);
(2002,Q2b); (2000,Q2b); (1998,Q2b);
Repetition of Similar Questions
No pattern of repetition of similar
questions has been found.
-------
218
(1997,Q2b); (1995,Q2b)
(Contd…….)3.Proof of De Morgan’s Laws
(2012,Q2); (2008,Q2a); (2007,Q2b);
(2006,Q2a); (2005,Q2a); (2004,Q2b);
(2003,Q2a); (2002,Q2a); (2001,Q2a);
(2000,Q2a); (1999,Q2a); (1998,Q2a);
(1997,Q2a)
4.Symmetric Difference (A∆B)
(2011, Q2); (2010, Q2).
(Global’s Papers:2013-2004)
(Global’s Papers: 2003-1994)
(O-Level Classified Mathematics,
Unit,10)
-------
(O-Level Classified Mathematics,
Unit,10)
Questions in a Particular Section of
Paper
The question on Sets is always given as
the first question in Section A of the
paper.
Questions in a Particular Section of
Paper
-------
Topics Never Assessed
*Use of venn diagrams in Sets.
*Graphical representation of Cartesian
Product.
*Function and its types
Topics Never Assessed
-------
Choice to Leave the Question in Paper
Always
Choice to Leave the Question in Paper
Never
Questions on Application of Concepts in
Real Life Problems
Questions on Application of Concepts in
Real Life Problems
A clear majority of questions entail a
219
-------
(Contd…….)
problem from practical life is given.
Sample Questions from SSC and GCE Paper
Q1
U={x/x∈N, x≤ 10}A={2,4,6,8,10}B={3,6,9,10}Prove that (A ∪ B)ʹ = Aʹ ∩ Bʹ
(Annual,2012, Q2)
Q2.
If A = {1,2,3,4} and B = {2,4,6,8}, Show that( A ∪ B )−(A∩B) = A ∆ B
Q1
B H
3
15 16 5 2 p
9
S q
In a survey, 60 students are asked
which of the subjects Biology (B),
History (H ) and Spanish (S) they
are studying.
The Venn diagram shows the results.
27 students study History.(a) Find the values of p and q. (b) Find n (H ʹ). (c)Find n(B∪H ) ∩S’
(N2012, p1,Q14)
Q2.
Mary has 50 counters. Some of the
counters are square, the remainders are
round.
There are 11 square counters that are
green. There are 15 square counters that
220
(Annual,2011,Q.2)
(Contd…….)
*No question has been found in the previous 20 years of papers where a Venn diagram is required.
are not green.
Of the round counters, the numbers that
are not green is double the numbers that
are green.
By drawing a Venn diagram, or
otherwise, find the number of counters
that are
(i) round,
(ii) round and green,
(iii) not green
(J2008,p2,Q5a)
Table 193(b): System of Real Numbers, Indices and RadicalsSSC GCE
System of Real Numbers Exponents and
Radicals
Properties of Rational Numbers
Decimal Fractions as Rational and
Irrational Numbers.
Properties of Real Numbers
Exponents and Laws of Exponents
Rational Exponents
The nth Root of a Positive Real Number
Surds
-------
Rational Numbers, Integers,
Indices and Standard Form
Rational Numbers.
Terminating and Recurring Decimals
Properties of Real Numbers
Indices and Laws of Indices
Fractional Indices
Radical and Index Form
-------
Standard Form
221
(Sindh Textbook Board Mathematics
for IX-X, 2012, Ch., 2).
(Contd…….)
(New Syllabus Oxford Mathematics
Book1, Ch., 2, 3 & Book3, Ch., 2).
Nature of the Contents
General Objectives
-Cognitive
*Identification of the properties satisfied by
Rational Numbers
*Recognition of the property used in a given
equation on Real Numbers.
*Differentiate between Rational and
Irrational Fractions.
*Solve problems involving exponents using
laws of Exponents.
*Same
*Use of the method of Rationalization in
solving Surds.
-------
General Objectives
-Cognitive
*Use of the properties satisfied by
Rational Numbers on Integers.
*Use of the properties of Real
Numbers on Integers.
*Differentiate between Rational and
Irrational Fractions and to covert
fractions in recurring decimals.
*Same
*Enable students to solve sums
having fractions as indices.
-------
*Solve simple equations involving
indices.
Ingredients of the Contents
*Which property is used in the following
example?
i) 0.4+9=9+0.4 {Ans: (Commutative)}
ii) x(y+z)=xy+xz {Ans: Distributive property
Ingredients of the Contents
* Complete by appropriate operation
symbol
i) (-5) □ (3) = (3) □ (-5) = -2 { Ans:
+}
* Replace each □ by an appropriate
222
of multiplication w.r.t addition}
(Contd…….)iii) -5 < -4 0 < 1 {Ans: Additive
property}
*Contents to learn properties of Rational
Numbers were given.
*Contents on Laws of Exponents (similar)
integer
ii) (-3)×(□+8) = (-3)×(-28) + (-
3)×(8)= □
{Ans:-28 & 60}
*Fill in □ by < or >
iii) 3√−27□ -√16
*Contents on Arithmetical Operations on Rational Numbers & Problem Solving Involving Rational Numbers were given.
For Example: James uses 13 of
his land for growing durians, 14 for bananas, 3
8 for guavas
and the remaining 9 hectares for mangoes. What is the total area of his land?* Contents on Laws of Indices (similar)
Presentation
*Contents regarding properties of Real
Numbers were presented in a way to name of
property used.
*Problems to practice the Laws of Exponents
were presented.
Presentation
*Contents on properties of Real
Numbers Reveals that use of
properties was required instead the
name of property.
*Problems to practice the Laws of
Indices were there with an addition of
223
*Detailed sums on Rational Exponents were
given.
e.g.: Simplify
( x l
xm )l+m
× ( xm
xn )m+ n
× ( xn
x l )n+l
(Ex,2.7,Q8)
simple equations involving indices.
e.g.: Solve 5x = 1
*Simple sums on Fractional Indices
were given.
e.g.: Simplify
3√ a5 b6
c4 (Book3,Ex,2e,Q2g)
Sequencing: Appropriate Sequencing: Appropriate
Language:Simple
(Contd…….)
Language: Simple
Comparison of the Contents of Question Papers
(Comparison is based on the last 20 years of papers of SSC and GCE)
Questions taken from the Textbooks
(2013,Q3 from Ex 2.7,Q7);
(2012,Q3,Q4fromEx2.7,Q8 & Ex2.8,Q2);
(2011,Q7 from Misc. II,Q8(i);
(2010,Q3 from Ex2.7,Q8);
(2008,Q3a from Misc.ExII,Q8(i); (2004,Q3a
from Ex2.7,Q10);
(2000,Q3a from Misc.ExII,Q8(ii); (1998,Q3a
from Ex2.7,Q10);
(1997,Q3a from Misc.ExII,Q8(iii)
(Global’s Papers:2013-2004)
(Global’s Papers: 2003-1994)
Questions taken from the Textbooks
-------
(O-Level Classified Mathematics,
Unit,1A-1D)
Questions taken from Previous
Papers(2009,Q3a, from 2006,Q3a);
(2008,Q3a from 2007,Q8b;
Questions taken from Previous
Papers
224
(2007,Q3a from 2003,Q3a);
(2005,Q8a from 2004,Q3a)
-------
(O-Level Classified Mathematics,
Unit,1A-1D)
Repetition of Similar Questions:In these
questions, exactly same operation was
repeatedly required without any minor
change in numbers.
(Contd…….)1.Ex.2.7
Q7: (2013; 2012; 2010)
Q10 :(2005; 2004; 1998).
2.Ex2.7(Old Syllabus)
Q8: (2002),
Q19: (2009; 2006; 1999)
In the following10
years(1998,1999,2002,2004,2005.2006,2009,
2010, 2012, 2013), question on this topic has
been given from just 5 questions i.e. Q7, 8,
10, 8(Old Syllabus), 19(Old Syllabus).
2.Misc.ExII
Q8(i): (2011; 2008; 2007)
Q8 (ii): (2003; 2000),
Q8 (iii): (1997).
*Question on this topic has been given from
overall 6 questions in last 17 years.
(Global’s Papers:2013-2004)
Repetition of Similar Questions
Addition, subtraction, multiplication
and division of fractions have been
found in pattern of repetition.
(J1999,p1,Q1;J19997,p1,Q12;
1998,p1,Q2; J2001,p1,Q4;
J2002,p1,Q2; J2006,p1,Q2;
J2007,p2,Q4; J2008,p1,Q1;
J2009,p1,Q2; J2010,p1,Q2;
J2011,p1,Q3).
*These questions carry just one mark
and were presented in the beginning
of paper1.
*No other pattern of repetition has
been found. A variety of ways have
been found in which questions were
given for the application of the learnt
concepts.
(O-Level Classified Mathematics,
Unit 1A – 1D).
225
(Global’s Papers: 2003-1994)
Questions in a Particular Section of Paper
The question on this topic has always been
found in Section B of the paper.
Questions in a Particular Section of
Paper
Questions on this topic have always
been found in paper1.
Topics Never Assessed
*Besides some fill in the blanks no other
question except the above said 6 questions
has been given in major section of the paper.
(Contd…….)
Topics Never Assessed
-------
Choice to Leave the Question in Paper
Always
Choice to Leave the Question in
Paper
Never
Questions on Application of Concepts in
Real Life Problems
-------
Questions on Application of
Concepts in Real Life Problems
-------
Sample QuestionsQ1.
( x2a
xa+b )( x2 b
xb+c )( x2 c
xc +a )(Annual, 2011, Q7)
Q2.
Q1.
a) ( 14 )
−2|b) 64
23|
c) Simplify ( 4 x2 y 9
x4 y )12
(J2011,p1,
Q21)
226
Simplify ( 1252× 8642 )
13
(June,2005,Q8a)
(Contd…….)
Q2.
It is given that N= 87 × 132
a) Complete the statements.
88×132=N+ -------
87×131=N − ------
b) Hence evaluate this
88×132 − 87×131
(June,2005,p,1,Q15)
Table 193(c) AlgebraSSC GCE
Algebraa)Algebraic Expressions-Variables and Constants, Coefficient, Algebraic expressions and their kinds.-Polynomials and their Classification. - Order of Algebraic Expressions- Value of Algebraic Expressions-Fundamental Operations on Algebraic Expressions.- Remainder Theorem.- Formulae and Their Applications.
Algebraa)Fundamental AlgebraWriting an Algebraic Expression.Use of Brackets in Simplifications.-------SameSameSameSame--------------Construction of Formula.
{New Syllabus Oxford
227
-------
{Sindh Textbook Board Mathematics for IX-X, 2012, Ch., 4}
b) Factorization, HCF, LCM, Simplification and Square Root
- Factorization of the Form;a2−b2.- Factorization of the Form; x2+bx+c.- Factorization of the Form; a3+b3
and a3−b3 .
- Factorization of the Form; a3+b3
+c3−3 abc .
- Factorization of the Form; a2 (b−c )+b2 (c−a )+c2 ( a−b ) .
(Contd…….)- Factorization using Remainder Theorem.- H.C.F. and L.C.M.- Simplification of Algebraic Fractions.- Square Root by Factor/Division Method.-------
{Sindh Textbook Board
Mathematics Book1, Ch., 5}
b) Expansion and Factorization of Algebraic Expressions.Algebraic Manipulation and FormulaeSameSame-------
-------
-------
-------
L.C.MSame-------Problem Solving involving Algebraic Fractions.
{New Syllabus Oxford Mathematics Book2, Ch., 3,4}
c)Algebraic Equations and Simple InequalitiesSolution to Quadratic
228
Mathematics for IX-X, 2012, Ch., 5}
c)Algebraic Sentences
- Solution of Simple Linear Equations in One or Two Variables.- Graphical solution of two simultaneous Linear Equations.- Solution of Equation Involving Radicals in One Variable.- Solution of Equation Involving Absolute Value in One Variable.- Inequalities.- Solution of Quadratic Equations by Factorization, Completing Square Method or by Quadratic Formula.--------------
(Contd…….){Sindh Textbook Board Mathematics for IX-X, 2012, Ch., 1, PartII}
Equations-Same
-Same
-Same
-------
-Same-Same
Problem Solving with AlgebraProblem Solving Involving Quadratic Equations.
{New Syllabus Oxford Mathematics Book1, Ch., 7; Book 2, Ch., 5 & Book3, Ch., 1}
Nature of the ContentsGeneral Objectives General Objectives
229
-Cognitive *Name different kinds of Algebraic Expressions and Classify Polynomials.
-------
-------
*Do fundamental operations (+, −, × and ÷) on Algebraic Expressions.
*Find remainder by means of Remainder Theorem.*Apply formulae on simplifying and factorizing Algebraic Expressions.
-------
*Factorize an Algebraic Expression by means of Remainder Theorem.*find L.C.M, H.C.F and Square Root of an Algebraic Expression. (Contd…….)*Solve a pair of simultaneous
-Cognitive-------
*writing of an Algebraic Expression
*Translate a problem into a mathematical formula/equation choosing letters to represent quantities from given information.*Same
-------
*Same but application of only three formulae is required.
*Solve word problems using Algebra.
-------
* L.C.M only
*Same
230
equations graphically.
*Solve equations involving Radicals/Absolute Value.*Solve a quadratic equation using quadratic formula.
-------
*Equations involving Radicals only
*Solve a quadratic equation by factorization, completing square method or by applying quadratic formula.
*Translate a given word problem into a quadratic equation and solve it.
Ingredients of the Contenta)*Find the type (w.r.t.terms) and degree of the given polynomialx4y + y2 +y3
*Write the given Algebraic Expression in ascending and descending order w.r.t ‘a’2a3y+ 4a y2 + 5a2y3
*Find the value of 4a2−3ab +bc when a=0, b=4 and c=1*Addition, Subtraction, Product and Division of Polynomials.*Find the remainder by means of Remainder Theorem whenx3+x−1 is divided by x+1
Ingredients of the Contenta)*Write an algebraic expression from the given information(i)Add 2x to twice 3y.(ii)Subtract 5x from half of y. (Book1, Ex, 5a)*Translate the given word expression into an algebraic expression(i)Eight more than half of a number.(ii)One quarter of a number which is 4 less than m? (Book1,Ex, 5a)*Addition, Subtraction and Product of algebraic expressions.*Simplify algebraic expressions
231
*Application of the Formulae:1. a(c+d)=ac+ad2. (x+a)(x+b)=x2+(a+b)x+ab3. (a+b)2=a2+2ab+b2
4. (a−b)2=a2−2ab+b2
5. (a+b)(a−b)=a2−b2
6. (a+b)2=(a−b)2+4ab7. (a−b)2=(a+b)2−4ab8. (a+b)2−(a−b)2=4ab9. (a+b)2+(a−b)2=2(a2+b2)10. (a+b+c)2=a2+b2+c2+2ab+2bc+2ca11. (a+b)3=a3+3a2b+3ab2+b3
12. (a−b)3=a3−3a2b+3ab2−b3
13. a3+b3=(a+b)(a2−ab+b2)14. a3−b3=(a−b)(a2+ab+b2)15. (a+b+c)( a2+b2+c2−ab−bc−ca) = a3+b3+c3−3abc
with fractional coefficients.
Simplify 2x7 + x+1
5 (Book,Ex, 5f)
(Contd…….)*Factorization(i)By taking common i.e. expressions of the type 4x + 12, 4m −6my −18mz(ii)By grouping first and then taking common.e.g.: 14cx + 10dy – 4cy – 35xd (Book1,Ex, 5g)*Solving simple equations(i) 5(7x-3) = 14(2x-2)
(ii)5+4 x9
=−1
*Evaluation of an Algebraic Formula
If 1a = 1
b + 1c +1
d , find ‘c’ when
a=2, b=3 and d=5. (Book1,Ex, 7d)*Construction of Formula(i)The vertical angle (xo) of an isosceles triangle whose base angle is yo
(ii)A boy is b years old and his father is 6 times as old as him. Find the father’s age. Find also sum of their ages in y years’ time. (Book1,Ex, 7f,g)
232
(Contd…….)b)*Factorization of the Expressions of the types1. a2±2ab+b2=(a±b)2
2. a2−b2=(a+b)(a−b)3. a3±b3
4. a3+b3+c3−3abc
5. a2 (b−c )+b2 (c−a )+c2 ( a−b )
*Factorization by means of Remainder Theoremx3+x2−2*Find H.C.F & L.C.M by Factor/Division methodx3−y3 , x4−y4
*Simplification of Algebraic FractionsSimplify
a2+aba2−ab
÷ a2+ab+b2
a3−b3
(Ex.5.11,Q11)*Find the Square Root by Factor/Division Method
*Solution of Word Problems through Algebrae.g.: Tom, Dick and Harry share $256. Dick’s share is four times as much as Tom’s and Toms’ share is one-third of Harry’s. How much is each of their shares?(Book1,Ex, 7h)
b)*Expansion and factorization using Formulae(i) a2±2ab+b2=(a±b)2
(ii) a2−b2=(a+b)(a−b)*Factorization of quadratic expressions by breaking the middle term/trial and error method.*Simplification of Algebraic Fractions
(i) m2−9m2−7m+12
(ii) 12b a3
3a b2 ÷ 4 abc3 ad
× 14 d2
7bc
(iii) y2−4 y+42−6 y
× 2 y+43 y2−12
(Book2,Ex,4b,c,d)*Addition and Subtraction of Algebraic Fractions by taking L.C.M.
233
For what value of ‘p’, 4a4+4a3−3a2−pa+1 will be a perfect square? (Ex.5.14, Q 11).
(Contd…….)
c)*Solution of a pair of linear equations simultaneously by graphical method. (PartII, Ex, 1.2)*Solution of equations(i) √4 x−5=√3 x+7
(ii) −6+|5x−3|=3
*Solution of inequalities3(x+5) > 2(x+2)+8
Simplify 12 a−3
− 23−2a + 18
9−4 a2
*Changing the subject of a formulaMake (h) the subject of the given
formula: pq=
13n √ h+2 k
3 h+k
(Book2,Ex.4j)*Problem Solving Involving Algebraic Fractions.
A piece of wood is 5cm longer
than a second piece and 34 of the
second piece is equal to 35 of the
first, what is the length of the second piece? (Book2, Ex, 4h).
c)*Same (Book2, Ex, 8d)
*Changing the subject of a formula(i) Make ‘a’ the subject of the
given formula √3 a−2=√ ab
(ii) Find the value of ‘c’ when b=9 and a=4
234
*Solution of quadratic equation by factorization, completing square method and by quadratic formula. (PartII, Ex, 1.6,1.7,1.8)
(Contd…….)
a=√ 3 b+cb−c
(Book2, Ex, 4j,k)
*Find the largest and smallest values of (i) x2+y2
(ii) x2−y2 if −10 ≤ x ≤ 10 and −5 ≤ x ≤ 5* Show, unshaded, the region satisfied by the following inequalities.x ≥ 0 , y ≥ 0 , x+y < 7 , y > 2x(Book3, Ex,3d; Book4, Addendum,Ch,III)*Solution of word problems by forming an equation that reduces to quadratic and then solving it using any method.
(Book2, Ex, 3h)
Presentation*Contents have a number of operations on Algebraic Expressions. *A rich use of formulae in simplification/factorization has been found.*Content appeared to make the learners a good user of
Presentation*Contents have only basic use of operations on Algebraic Expressions.*Minimum Use of formulae has been observed. *Content appeared to make the learners able to use algebra in problem solving.
235
mathematical formulae.-------
*Content presents a rich use of algebra in solving word problems.
Sequencing*Content on Algebra has been presented in a logical sequence. *Content proceeds from simple to complex.
Sequencing*Same
*Content flow was very natural. First, the content relates word expressions to algebraic expressions, then it moves to arithmetical operations and in the end, its purpose was that the learner should be able to set up an equation from a given situation and use the learned algebraic operations to solve a daily life problem.
Integration with other Topics
Observed
Integration with other Topics
Observed(relatively more)
Language:Simple
(Contd…….)
Language: Simple
Comparison of the Contents of Question Papers(Comparison is based on the last 20 years of papers of SSC and
GCE)Questions taken from the Questions taken from the
236
TextbooksThese questions are found either taken exactly from the textbook or in a few cases, with minor changes in signs or numbers.
*Finding the value using formulaeEx,4.7, 4.8 and 4.9(2011,Q4 from Ex 4.9,Q2); (2010,Q5,from example4 of Ex4.7);(2009,Q3b from Ex, 4.7,Q1);(2008,Q5a from Ex4.8,Q2(vi); (2007,Q3b from Ex4.7,Q1); (2006,Q3b from Ex,4.9,Q2(v); (2005,Q3a from Ex4.7,Q1,2); (2004,Q3b from Ex,4.7,Q1); (2003,Q3a from Ex4.7,Q1); (2002,Q3b from Ex,4.9,Q2(v)(2000,Q7b from Ex,4.7,Q5);(1999,Q6b from Ex4.7,Q1);(1998,Q6b from Ex4.7,Q4);(1997,Q6b from Ex4.7,Q1);(1996,Q3b from Ex4.7,Q1);(1995,Q9a from Ex4.7,Q1);{Ex,4.7,Q1 has been taken 10 times in 20 years papers}
Textbooks
-------
-------
-------
(O-Level Classified Mathematics,
Unit,2A-2D)
(Contd…….)
-------
237
*Factorization of the typea2 (b−c )+b2 (c−a )+c2 ( a−b )
Ex, 5.6(New exercise added in 2009)(2013,Q6 from Example1 of Ex,5.6);(2012,Q6 from Ex,5.6,Q2);(2011,Q5 from Ex,5.6,Q1);(2010,Q6 from Ex,5.6,Q1);*Factorization by means of Remainder TheoremEx,5.7 (New Syllabus) which was Ex,4.7(Old Syllabus)(2013,Q20b from Ex,5.7,Q6);(2012,Q20b from Ex,5.7,Q3);(2011,Q20b from Ex 5.7,Q2); (2010,Q20b from Ex,5.7,Q9);(2009,Q8a from Ex, 4.7,Q5);(2008,Q5b from Ex5.7,Q3); (2007,Q8a from Ex4.7,Q8); (2006,Q8a from Ex,4.7,Q11); (2005,Q6b from Ex4.7,Q13); (2004,Q7a from Ex,4.7,Q5); (2003,Q8a from Ex4.7,Q8); (2002,Q6b from Ex,4.7,Q12);(2001,Q6b from Ex,4.7,Q5);(2000,Q7a from Ex,4.7,Q3);(1999,Q7b from Ex4.7,Q7);
-------
-------
-------
(O-Level Classified Mathematics,
Unit,2A-2D)
(Contd…….)
238
(1998,Q7b from Ex4.7,Q5);(1997,Q3b from Ex4.7,Q3);(1996,Q9b from Ex4.7,Q3);(1995,Q3b from Ex4.7,Q8);{Q5(3 times), Q5(4 times), Q8(3 times)}
*Square RootEx,5.14(New Syllabus) which was Ex,4.11(Old Syllabus)(2013,Q8 from Ex,5.14,Q9);(2012,Q8 from example,4 of Ex,5.14);(2011,Q8 from Ex 5.14,Q12); (2010,Q16 from example,4 of Ex,5.14);(2009,Q5b from Ex, 5.14,Q10);(2008,Q3b from Ex4.11,Q33;)(2007,Q5a from Ex4.11,Q31;)(2006,Q7a from Ex,4.11,Q33); (2005,Q9b from Ex4.11,Q31); (2004,Q5b from Ex,4.11Q31); (2003,Q5a from Ex4.11,Q31); (2002,Q7a from Ex,4.11,Q33)(2001,Q6a from Ex,4.11,Q30);(1999,Q3b from Ex4.11,Q35);(1998,Q3b from Ex4.11,Q14);(1997,Q7a from Ex4.11,Q13);
-------
-------
-------
(O-Level Classified Mathematics,
Unit,2A-2D)
239
(Global’s Papers:2013-2004)(Global’s Papers: 2003-1994)
(Contd…….)FactorizationOne question having four expressions of the following types(i) a4 + b4
(ii) ax2 + bx + c(iii) a3±b3
(iv)a3+b3+c3−3abcTaken from Ex, 5.5, 5.3, 5.4 and 5.5 respectively.
Graphical Solution of Simultaneous EquationsThe question has always been taken from the textbook.Solution of Quadratic Equation using Quadratic FormulaThe question has always been taken from the textbook.Solution of Equations involving Radical/Absolute ValueThe question has always been
-------
-------
(O-Level Classified Mathematics,
Unit,2A-2D)
240
taken from the textbook except in 2013 and 2012. In these two years, the question on this topic has not been given in the main section of the paper.Instead, it has been given in Section A as an MCQ.(Global’s Papers:2013-2004)(Global’s Papers: 2003-1994)
(Contd…….)Questions taken from Previous PapersThe above list shows the number of times a question has been taken from the textbook. It is clear from the list that the same question has been taken many times.
Questions taken from Previous Papers
------
Repetition of Similar Questions:In these questions, the same operation is repeated without any minor change in numbers. Finding the value using formulae(Ex,4.7 new syllabus){Ex,4.7,Q1 has been taken 10 times in 20 years papers}Remainder Theorem (Ex,4.7
Repetition of Similar Questions
-------
241
old syllabus){Repetition:Q5(3 times),Q5(4 times),Q8(3 times)}Square Root (Ex,4.11 old syllabus){Repetition:Q31(4 times),Q33(3 times)}(Global’s Papers:2013-2004)(Global’s Papers: 2003-1994)
(O-Level Classified Mathematics, Unit 1A – 1D).
Questions in a Particular Section of PaperThe question on this topic has always been always given in Section A of the paper.
(Contd…….)
Questions in a Particular Section of PaperQuestions on this topic have always been found in paper1.
Topics Never Assessed*No other question besides the 6 mentioned questions has been found in the major section of the paper.
Topics Never Assessed
-------
Choice to Leave the Question in Paper
Always
Choice to Leave the Question in Paper
Never
Questions on Application of Questions on Application of
242
Concepts in Real life Problems
-------
Concepts in Real life ProblemsQuestions on application of algebra in real life problems have been observed in both paper 1 and paper 2.
Sample QuestionsQ.1Factorize any four of the following:
(i) x2 – yz + xy – xz(ii) 4x2 +5x – 21(iii) a4 + 4(iv) 1 +2ab – (a2 + b2)(v) x3 – x – 2y + 8y3
(vi) a3 – b3 – 27c3 – 9abc(Annual,2008,Q4)
(Contd…….)Q.2Find the solution set of the following equations graphically;
5x +7y =137x + 6y =3
(Annual,2010,Q18)Q.3Find the factors of x3 – x2 −14x + 24 with the help of remainder
Q.1(a) Factorize completely(i) 15x2 + 10x,(ii) t2 – 2t – 15.(b) Solve 4(x – 0.3) = 3(x – 0.2)
(June,2008,paper1,Q19)
Q.2Ahmed throws a ball to John. The ball travels 10 meters at an average speed of x meters per second.(a) Write an expression, in terms of x, for the time taken, in seconds, for the ball to travel from Ahmed to John.
(b) John then throws the ball to Pierre.The ball travels 15 meters.The ball’s average speed is 0.5
243
theorem.(Annual,2012,Q20b)
meters per second greater than the ball’s average speed from Ahmed to John.
Write an expression, in terms of x, for the time taken, in seconds, for the ball to travel from John to Pierre.
(c) The time taken between John catching the ball and then throwing it to Pierre is 2 seconds.
The total time taken for the ball to travel from Ahmed to Pierre is 7 seconds.Write down an equation in x, and show that it simplifies to 2x2 – 9x – 2 = 0.
(d) Solve the equation 2x2 – 9x – 2 = 0, giving each answer correct to 2 decimal places.
(e) (i) Find the average speed, in meters per second, of the ball as it travels from John to Pierre. (ii) How much longer does it take for the ball to travel from John to Pierre than fromAhmed to John?
Give your answer in seconds.
(June,2010,paper2,Q8)Give your answer in seconds.
Table 193(d): MatricesSSC GCE
Matrices Matrices
244
*Introduction
*Addition, subtraction and product of
Matrices
*Inverse of a Matrix
*Solution of Simultaneous Linear
Equations by Cramer’s Rule
-------
(Sindh Textbook Board Mathematics
for IX-X, 2012, Unit, 6, Part-I).
Same
Same
Same
*Solution of simultaneous equations by
Matrix method
*Use of Matrices in Solving Everyday
Life Problems
New Syllabus Oxford Mathematics
Book3, Ch., 5).
Sequencing: Appropriate Sequencing: Appropriate
Integration with other Topics
-------
Integration with other Topics
The contents are integrated with the
solution of every day mathematics
problems of sale, purchase, profit and
loss.
Language:Simple Language: Simple
Comparison of the Contents of Question Papers
(Comparison is based on the last 20 years of papers of SSC and GCE)
Questions taken from the Textbooks
New Edition Sindh Text Book
Ex 6.4(Multiplicative Inverse of a
Matrix) & Ex 6.5(Cramer’s Rule)
(2013,Q9 from Ex 6.5,Q7);
(2012, Q9 from Ex6.5, Q1);
(2011, Q9 from Ex6.4, Q5a);
(2010, Q7 from Ex6.5, Q3).
(Global’s Papers:2013-2004)
Questions taken from the Textbooks
-------
(Contd…….)
-------
(O-Level Classified Mathematics,
245
(Global’s Papers: 2003-1994) Unit,12)
Questions taken from Previous
Papers(2009,Q5a, from 2008,Q8a);
(2007,Q5b from 2003,Q5b);
( 2007,Q3a from 2006,Q6a);
( 2002,Q6a from 1999,Q7a)
(Global’s Papers:2013-2004)
(Global’s Papers: 2003-1994)
Questions taken from Previous Papers
-------
(O-Level Classified Mathematics,
Unit,12)
Repetition of Similar Questions:
Solution of simultaneous equations by
Cramer’s Rule
2013,2012,2010 (new exercise added in
2009)(3 times)
Multiplicative Inverse
2011,2009,2008,2007,2006,2003,2002,
2001,19991,1998,1997)(11 times)
(Contd……..)(Global’s Papers:2013-2004)
(Global’s Papers: 2003-1994)
Repetition of Similar Questions
Addition, subtraction, multiplication and
division of fractions have been found in
pattern of repetition.
(J1999,p1,Q1); (J19997,p1,Q12);
(1998,p1,Q2); (J2001,p1,Q4);
(J2002,p1,Q2); (J2006,p1,Q2);
(J2007,p2,Q4); (J2008,p1,Q1);
(J2009,p1,Q2); (J2010,p1,Q2);
(J2011,p1,Q3).
*These questions are just 1 mark
questions that are presented in the
beginning of paper1.
*No other pattern of repetition has been
found. A variety of ways have been found
in which questions are given for the
application of the learned concepts.
(O-Level Classified Mathematics, Unit,
12).
Questions in a Particular Section of
Paper
The question on this topic has been seen
Questions in a Particular Section of
Paper
Questions on this topic have always been
246
in Section B of the new pattern of paper;
previously it has been given in Section A.
found in paper1.
Topics Never Assessed
-------
Topics Never Assessed
-------
Choice to Leave the Question in Paper
Always
Choice to Leave the Question in Paper
Never
Questions on Application of Concepts in
Real Life Problems
-------
Questions on Application of Concepts in
real Life Problems
Questions on practical application of
Matrices in real life problems were
included.
Table 193(e): StatisticsSSC GCE
Information Handling*Introduction, Key Terms, Types of Variables, Types of Data*Collection and Presentation of Data*Frequency Distribution, Graphs (Histogram and Frequency Polygon)-*Bar Graphs, Pie Diagrams--------*Measures of Central Tendency (Mean, Median and Mode)
(Contd…….)*Dispersion and its Measures (Variance and Standard Deviation), Their Merits &
StatisticsSame
Same
Same
Same
*Stem and Leaf Diagram, Dot Diagram
Same
--------
*Cumulative Frequency Distribution
New Syllabus Oxford Mathematics
Book1, Ch13; Book2, Ch11& Book4,
247
Demerits--------
(Sindh Textbook Board Mathematics
for IX-X, 2012, Unit, 4, Part-II).
Ch5).
Sequencing: Appropriate Sequencing: Appropriate
Integration with other Topics
-------
Integration with other Topics
The contentswere integrated mostly with
problems related to probability.
Language:Simple Language: Simple
Comparison of the Contents of Question Papers
(Comparison is based on the last 20 years of papers of SSC and GCE)
Questions taken from the Textbooks
(2013,Q20a from Ex4.4,Q4);
(2012,Q20a from Misc. Ex,Q3);
(2011,Q20a from Ex4.3,Q7);
( 2010 from Ex4.3,Q7)
(Global’s Papers:2013-2004)
(Global’s Papers: 2003-1994)
(Contd…….)
Questions taken from the Textbooks
-------
(O-Level Classified Mathematics, Unit,9)
Questions taken from Previous
Papers(2011,Q20a from 2010,Q20a);
Questions taken from Previous Papers
248
(2009,Q16b, from 2000,Q16b);
(2009,Q15a from 2002,Q15b from
1998,Q15b);
(2008, Q15b from 1998, Q16b); (2004,
Q16a from 1999, Q16b); (2003, Q15b
from 2001, Q15b).
-------
Repetition of Similar Questions:
Variance/S.D
(2013,Q20a); (2009,Q15a); (2008,Q15b);
(2007,Q16b); (2006,Q16b); (2005,Q15b);
(2004,Q15b);(2003,Q16b);
(2002,Q15b); (2001,Q16b); (200015a);
(1999, Q15b); (1998, Q15b).
Median (Grouped Data)
(2012,Q20a);
(2010,Q20a); (2008,Q16b);
(2002,Q16a);
(1998, Q16b).
Mean (Grouped Data)
(2011,Q20a); (2006,Q15b);
(2003,Q15b); (2001,Q15b);
(2000Q16b)
Mode (Grouped Data)
(2007,Q15b;
2004,Q16a; 1999,Q16b)
(Contd…….)Median (Ungrouped Data)
(2007,Q16b);(2005,Q16b);
Repetition of Similar Questions
*No pattern of repetition has been found.
A variety of ways have been found in
which questions were given for the
application of the learned concepts.
-------
(O-Level Classified Mathematics, 2012,
Unit 1A – 1D).
249
( 2002,Q16a); (1998,Q16b)
(Global’s Papers:2013-2004)
(Global’s Papers: 2003-1994)
-------
Questions in a particular section of
paper
The question on this topic has Always
been seen in Section C of the paper.
Questions in a particular section of
paper
Questions on this topic have been found
in both paper1 and paper 2.
Topics Never Assessed
--------
Topics Never Assessed
--------
Choice to Leave the Question in Paper
Always
Choice to Leave the Question in Paper
Never
Questions on Application of Concepts in
Real Life Problems
-------
Questions on Application of Concepts in
Real Life Situations
A significant number of questions have
been observed on the application of
statistical concepts in real life problems.
Table 193(f): GeometrySSC GCE
Geometry Geometry
250
The geometry section has been found
divided into three parts
(i) Fundamental Concepts of geometry
(ii) Demonstrative Geometry
(iii) Practical Geometry
(Sindh Textbook Board Mathematics
for IX-X, 2012, Unit,7,8,9, Part-I
& Unit, 5, 6, 7, Part II).
This section was found subdivided into
the following parts
(i) Properties of Angles, Angle Properties
of Polygons
(ii) Similarity, Congruency and
Symmetry
(iii) Circle Theorems
(iv) Loci and Simple Constructions
{New Syllabus Oxford Mathematics
Book1, Ch14 & 15; Book2, Ch1; Book3,
Ch. 8 & 9 & Book4, Addendum, Ch.
IV)}
Contents:
(i) Fundamental Concepts of Geometry
- Inductive and Deductive Reasoning- Characteristics of Deductive Reasoning- Basic Concepts Definitions and Postulates- Basic Concepts of Circle (Circumference, Chord, Secant, Tangent)- Circumscribed circle, Inscribed Circle and Escribed Circle of a Triangle- Theorems on Circles(ii) Demonstrative Geometry
-Deductive Method of proving a Geometrical Theorem along with related steps-Theorems on Parallel Lines, Triangles, Parallelograms and Quadrilaterals
(Contd…….)(iii) Practical Geometry
- Construction of Triangles,
Contents:
(i) Properties of Angles, Angle
Properties of Polygons
- Complementary & Supplementary Angles- Alternate, Vertically Opposite, Interior & Corresponding Angles- Angle Properties of triangles, Quadrilaterals and Polygons- Sum of Interior and Exterior Angles of Polygons(ii) Similarity, Congruency and Symmetry- Similar Figures and Objects- Similarity and Enlargement- Similarity and Scale Drawings- Area and Volume of Similar Figures- Area and Volume of Similar Solids
(iii) Circle Theorems
- Geometrical Properties of Circles- Angle Properties of Circles
251
- Constructions of Right Bisectors of Sides of a Triangle-Construction of Angle Bisectors, Median and Altitudes in a Triangle- Constructions (Circum-circle, Inscribed circle and Escribed Circle) of a triangle- Tangent to a Given Circle from a Point outside the Circle- Direct Common Tangents to Two Given Circles and Transverse Common Tangents to Two Given Circles
- Angles in Opposite Segments of Circles- Problems on Angle Properties of Circles- Problems on Tangents from an External Point on a Circle
(iv) Loci and Simple Constructions
- Construction of triangle, Square, Rectangle, Parallelogram, Rhombus and any other Quadrilateral- Bisection of a line segment and an angle- Loci in two dimensions- Intersection of Loci- Loci in three dimensions
Presentation & Objectives of the
Contents
(i) Fundamental Concepts of Geometry
The fundamental concepts of geometry
were explained through figures. In the
exercises, students were expected to
define and draw figures of particular
terms of geometry or differentiate
between two terms (Ex7.1,PartI;
Ex5.1,PartII)
Presentation & Objectives of the
Contents
(i) Basic Geometrical Concepts
The basic concepts of geometry about
types of angles and triangles, properties
of angles formed when a transversal cuts
two parallel lines, angle properties of
polygons and finding the sum of interior
angles of polygons were explained
through worked examples. Students were
expected to apply their learned properties
about angles to find the unknown angles
in the figures given as sums in the
exercises. Neither the definition of a term
was required nor was the drawing of
figure expected.
(Book 3,Ch14 & 15)
252
(ii) Demonstrations of the Proofs of
Geometrical Theorems
The methods with all its steps of proving
a geometrical theorem were explained.
Students were expected to prove a
theorem deductively showing all the
instructed steps. After each theorem an
exercise was given in which statements
are given to be proved by applying the
same method as explained in the proof of
theorem.
Prove that
* If two lines intersect, the vertically
opposite angles so formed are congruent.
* If a transversal intersect two parallel
lines, the alternate angles so formed are
congruent.
* The sum of the measure of the angles of
a triangle is 180o.
* If a perpendicular is drawn from the
center to a chord of a circle, it bisects the
chord.
* The measure of central angle of a minor
arc of a circle is double that of the
inscribed angle of the corresponding
major arc.
(ii) Use of Geometrical Theorems in the
given Figures
The proofs of theorems were not
required; instead the use of theorems has
been focused to solve a geometrical
problem. Exercises provide a numbers of
geometrical figures in which the missing
angles are required to be found using
theorems and all the reasons are rquired.
Find the unknown angles
*
*
*
253
(Contd…….)* If a line is drawn perpendicular to the
radial segment of a circle at its outer end,
it is tangent to the circle at that point.
* The two tangents, drawn to a circle
from a point outside it, are equal in
length.
* Theorems on Locus are required to be
proved by deductive method as well.
- The locus of a point equidistant from
two fixed points is the right bisector of
the line joining the fixed points.
- The locus of a point equidistant from
the arms of an angle is the bisector of the
angle.
(i)Calculate angle BOC. (ii) Calculate angle OCA.* A and C are points on the circumference of a circle center B. AD and CD are tangents. Angle ADB = 40°.
Explain why angle ABC is 100°.
* Locus theorems are required to be demonstrated by accurate scale drawings.- Construct triangle ABC in which AB = 8cm , BC = 7.5 cm & AC = 6 cmOn the diagram Construct(i) Locus of a point P on the same side of AB as the point C and such that area of ∆APB = area of ∆ACP(ii) (a) Locus of a point equidistant from A and B (b) Locus of a point equidistant from A and C (c) The circle through A, B and C(Book4, Ex IVc,Q3)
Language:More mathematical language
has been used.
Language: Less mathematical language
has been used.
254
(Contd…….)Comparison of the Contents of Question Papers
(Comparison is based on the last 20 years of papers of SSC and GCE)
Questions taken from the Textbooks
Demonstrative Geometry
The proofs of theoremsrequired in the
papers have always been taken from the
textbooks.
Practical Geometry
One of the following type of questions
has been observed each year
(i) To draw the circumscribed circle after
drawing a triangle
This question has been found 8 times
(2013; 2008; 2007; 2003; 2001; 1999;
1997; 1995)
(ii) To draw the direct common tangent
after drawing two circles
This question has been found 8 times
(2011; 2010; 2009; 2005; 2004; 2000;
1998; 1994)
(iii) To draw the transverse common
tangent to two circles
This question has been found 4 times
(2012; 2006; 2002; 1996)
Questions taken from the Textbooks
-------
-------
-------
255
(Global’s Papers:2013-2004)
(Global’s Papers: 2003-1994)
(Contd…….)
(O-Level Classified Mathematics,
Unit,7A-7D)
Repetition of Similar Questions:
A pattern of repetition of similar
questions has been observed. There were
some theorems that have been found
repeatedly in the subsequent papers.
For instance:
* If a perpendicular is drawn from the
center to the chord of a circle, prove that
it bisects the chord.
The above question has been found 15
times in the last 20 year’s papers.
(2013; 2011; 2009; 2007; 2006; 2005;
2004; 2003; 2002; 2001; 2000; 1999;
1997; 1999; 1995)
* If two angles of a triangle are
congruent, prove that the sides opposite
to them are also congruent.
The above question has been repeated 8
times.
(2013; 2011; 2009; 2008; 2007; 2005;
2004; 1995)
* If a transversal intersect two parallel
lines, the alternate angles thus formed are
congruent.
The above question has been repeated 8
times.
(2012; 2007; 2006; 2005; 2003; 2001;
Repetition of Similar Questions
No definite pattern of repeated questions
from successive years has been observed.
-------
-------
(O-Level Classified Mathematics, 2012,
256
1997; 1995)
(Global’s Papers:2013-2004)
(Global’s Papers: 2003-1994)
Unit 7A – 7D).
(Contd…….)Questions in a Particular Section of
Paper
The questions on Demonstrative and
Practical Geometry have always been
found in section B till 2009. In the new
pattern of the paper (2010 onwards), 2 or
3 questions on theorems were found in
section B and 1 question,Q.19
(compulsory) was found in Section C.
Question on Practical Geometry is
coming in Section C in the new pattern of
paper.
Questions in a Particular Section of
Paper
Questions on this topic have been found
in both paper1 and paper 2.
Topics Never Assessed
* In demonstrative geometry, after every
theorem, an exercise was given. Not even
a single question has been found from
these exercises in any of the past 20 years
papers. Only the theorems were given in
the papers.
* In practical geometry, questions on the
construction of triangles (the ambiguous
case), drawing medians of triangles,
drawing altitudes of a triangles and
drawing inscribed circle of triangles have
never been found.
Topics Never Assessed
-------
257
(Contd…….)
Choice to Leave the Question in Paper
In the old pattern of paper (till 2009),
section B was reserved for both
demonstrative and practical geometry.
Three out of five questions were required.
In these 5 questions, 4 were always given
on theorems and 1 on practical geometry.
Therefore, this section always had a
choice of leaving the question on
practical geometry but there was a
compulsion to select a minimum of two
questions on theorems.
In the new pattern (2010 onwards), 2 or 3
short answer questions on theorems are
given in section B, where 10 questions
out of 15 are required to be attempted.
Therefore, there is a complete choice to
leave all the questions on theorems in this
section.
In section C, 3 out of 5, questions were
required to be selected including Q.19
which was on theorems and was
compulsory in this section. Therefore, in
this section there is a choice of leaving
two of the following topics completly:
factorization, information handling and
Choice to Leave the Question in Paper
-------
-------
-------
-------
258
practical geometry.
4.4.1 Summary, Discussion and Conclusions
The comparative analysis of the contents of the textbooks and question papers
of the past twenty years of both systems reveal that although there are other
differences in the contents of textbooks of two systems, a significant difference is
in the approach of teaching the contents. This difference of approach in the two
systems is due to the difference in the approaches and methods of assessment.
The key issuesrevealed during the record analysis may be summarized and
concluded as:
Contents of SSC textbooks were leaned towards the provision of mathematical
knowledge of procedures and operations while in GCE, there was a clear
inclination found towards the application of mathematical procedures and
operations in everyday problems.
GCE textbooks and question papers were consisted of a majority of word
problems while SSC textbooks and question papers constituted a very small
number of word problems.
SSC textbooks were found with a black and white illustrations and a
discernible use of mathematical language while GCE textbooks had colourful
presentation of pictures and diagrams with an indiscernible use of
mathematical language embedded in common language.
Objectives of SSC and GCE contentswere not very different except, less
material on problem solving and application of concepts in word problems was
found on SSC side.
The use of contents of textbooks on SSC side was not aligned with the
objectives mentioned in the books. This was due to the pattern of assessment
259
where exact same questions from the textbooks were given. As a result, both
teachers and students do not try to go beyond factual and procedural
knowledge. Rather, students try to memorize certain areas of the content so
that they can reproduce it with precision and get good marks in the
examination.
SSC question papers contained exactly the questions as the textbook questions
but in GCE, no such evidence was found.
SSC papers contained a number of repeated questions from the successive
years while on GCE side, no clear pattern of repetition was observed.
SSC papers have been found with a fixed pattern. Questions from certain
chapters are always given in specific sections. An ample amount of choice is
always given to select questions from different sections. As a result of this
fixed pattern and ample choice, there is a high trend of selected study and
leaving some areas of the syllabus untaught, in SSC system. GCE on the other
hand neither has such a pattern nor such plenteous choice in the paper.
Therefore, students in this system have to study all the topics in the syllabus.
SSC papers were predictable due to a fixed pattern and repetition of questions.
Therefore, a trend of guessing questions for the upcoming paper by analyzing
the pattern of questions in the previous papers is present in this system. GCE
papers were not predictable.
SSC paper did not have any content on everyday mathematics (percentage,
rate/sale/purchase/interest /money etc.) while on the GCE side, there are a
substantial proportion of these topics in the paper.
GCE textbooks were found relatively more internally coherent within different
content areas than the SSC textbook.
GCE textbooks contained contents for further exploration and discovery of a
concept beyond the requirements of syllabus which was not present in the SSC
textbook.
260
GCE textbooks contained material for mental exercise (discipline of mind) that
is not a requirement of the syllabus, but no such material was found in SSC
textbooks.
261
CHAPTER FIVE
SUMMARY, FINDINGS, CONCLUSIONS AND RECOMMENDATIONS
5.1 SUMMARYThe focus of this study was on the comparative effectiveness of the
SSC and the GCE (Ordinary Level)mathematics curriculum. The purpose was to trace
out the factors involved in the problems and shortcomings of the curriculum
objectives, contents, approaches and methods of teaching and examination system in
the SSC system. The study’s specific focus was: (1) to compare and analyze the aims
and objectives of teaching mathematics at SSC and GCE (O- Level); (2) to compare
the contents of textbooks and exam papers of SSC and GCE mathematics courses; (3)
to critically compare the effectiveness of approaches and teaching methods applied in
both systems; (4) to compare and analyze the assessment patterns in both systems.
The population of study comprised teachers, students, prescribed text books of
mathematics taught at SSC and GCE (O- Level) and the question papers of the
Examination Boardsof the two systems. The sample included the mathematics
teachers teaching grade X (SSC) and O-Level final year (GCE). The students
studying in 10th class (SSC) and O-Level final year (GCE). Textbook of mathematics
for IX and X , published by Sindh Textbook Board and a set of four textbooks used in
GCE (O-level) system, published by Oxford University Press; question papers of the
past 20 years of Board of Secondary Education Karachi (BSEK) and Cambridge
International Examinations (CIE) were also a part of the sample.As many as 10
subject experts, 180 teachers and 120 students were selected from the SSC system.
From the GCE system, 10 subject experts, 120 teachers and 80 students were selected.
Questionnaires designed with a five-point rating scale were administered to the
sample. A semi-structured interview was conducted to the subject experts.A content
analysis was done to compare the contents of textbooks and question papers of both
SSC and O-Level mathematics course. The quantitative data collected were tabulated
and analyzed using t-test.
5.2 SECTION WISE RESULTS OF DATA ANALYSISThe results of data analysis for each section have been
summarized in the following four tables.
Table 194(a): (Significance of Mathematics / Aims / Objectives)KEY: A = Accepted, R = Rejected, A = Agree, DA = Disagree, U = Undecided; *{U = 100% − (A% + DA %)}*(SA & SDA alternatives of the measurement scale have been collapsed in A & DA respectively)
Sr.No
H0
Aims / ObjectivesA/R
t-Value
A(Percentage)
DA(Percentage)
(A)Teachers SSC GCE SSC GCE
1
There will be no significant difference between SSC and GCE teachers on the statement that mathematics is one of the most important subjects in the school curriculum.
A 0.345 96.7% 95% 2.2% 3.2%
2
There will be no significant difference between SSC and GCE teachers on the statement that the aim of mathematics education is to train or discipline the mind.
A 1.546 87.8% 80% 4.4% 6.7%
3
There will be no significant difference between SSC and GCE teachers to take the practical value of mathematics as an aim of its education.
A 0.549 92.3% 93.4% 5.5% 3.3%
4
There will be no significant difference between SSC and GCE teachers regarding the development of problem solving skills as an aim of its education.
R 1.975 92.8% 95% 6.1% 5%
5 There will be no significant difference between SSC and GCE teachers on the statement that the aims of mathematics education are convincing.
R 5.98255.6% 80% 25% 3.3%
249
(Contd…….)
6
There will be no significant difference between SSC and GCE teachers on the statement that aims of mathematics education are achievable.
A 0.283 85.6% 81.6% 9.4% 6.7%
7
There will be no significant difference between SSC and GCE teachers that the aims of mathematics education can be translated into small educational objectives.
A 0.618 65.5% 70.9% 8.9% 8.3%
8
There will be no significant difference between SSC and GCE teachers on the statement that the objectives of current teaching are derived from actual aims.
R 2.202 62.2% 71.7% 16% 8.3%
9
There will be no significant difference between SSC and GCE teachers on the statement that objectives of mathematics teaching are well defined.
A 1.428 75.6% 76.7% 15% 10%
10
There will be no significant difference between SSC and GCE teachers on the statement that objectives of mathematics education are clearly transmitted to teachers.
R 2.261 57.8% 76.7% 29% 15%
H0
Aims / ObjectivesA/R
t-Value
A(Percentage)
DA(Percentage)
(B)Students SSC GCE SSC GCE
11
There will be no significant difference between SSC and GCE students on the statement that I do mathematics because teachers emphasize its importance.
A 1.728 41.6% 58.8% 37% 29%
12 There will be no significant difference between SSC and GCE students on the statement that I do mathematics because it is compulsory to take this subject at school level.
R 4.689 84.2% 36.3% 4.2% 56%
250
(Contd…….)
13
There will be no significant difference between SSC and GCE students on the statement that school places a special emphasis on mathematics than the other subjects.
A 0.682 67% 65% 25% 8.8%
14
There is no significant difference between SSC and GCE students on the statement that mathematics is important because it trains the mind.
A 0.729 90.8% 96.3% 0.8% 2.55
15
There is no significant difference between SSC and GCE students on the statement that mathematics is important because it is a compulsory subject in school curriculum.
A 1.208 79.2% 75% 10% 18%
16
There is no significant difference between SSC and O-Level students on the statement that mathematics is important because it is largely applied at the higher education level.
A 1.219 67.5% 67.5% 21% 15%
17
There is a significant difference between SSC and O-Level students on the statement that mathematics is important because it is applied in many other subjects.
R 2.041 85.8% 93.8% 5% 1.6%
18
There is no significant difference between SSC and O-Level students on the statement that mathematics is a scoring subject.
A 1.176 93.3% 96.3% 1.6% 2.5%
(C)Responses of Experts on Aims / Objectives of MathematicsQ1
Is teaching of mathematics according to some clear objectives? If yes, then according to your observation, what is the major objective?
SSC Agreed70%
Disagreed20%
Undecided10%
Responses *Percentage of each Response*To meet the needs of further education of this subject. 30%
*To enable students to do basic operations of mathematics. 10%
*To enable students to solve different types of problems by applying mathematical rules and procedures.
20%
*Aims and objectives are not clear to teachers; the only objective is to make students pass the examination with good marks.
10%
251
(Contd…….)
GCE Agreed100%
Disagreed0%
Undecided0%
Responses *Percentage of each Response*Enhancement of thinking skills. 20%*Preparation of students for GCE Exam. 40%*Prepare students for future education. 20%*Enable students to think within horizon before thinking beyond horizon. 10%
*Making students good problem solvers. 10%*Percentage of each Response = (Frequency of that response ÷Total number of Responses on that question) × 100%
Table 194(b): Contents / TextbooksKEY: A = Accepted, R = Rejected, A = Agree, DA = Disagree, U = Undecided; *{U = 100% − (A% + DA %)}*(SA & SDA alternatives of the measurement scale have been collapsed in A & DA respectively)
Sr.No
H0
Contents / TextbooksA/R
t-Value
A(Percentage)
DA(Percentage)
(A)Teachers SSC GCE SSC GCE
1
There will be no significant difference between SSC and GCE teachers that contents of the textbooks are properly sequenced.
A 1.250 74.6% 84.1% 21% 8.9%
2
There will be no significant difference between SSC and GCE teachers on the statement that contents develop interest in students.
A 0.608 62.7% 65.3% 23% 17%
3
There will be no significant difference between SSC and GCE teachers that contents incits the sense of enquiry.
R 3.090 58.9% 70.3% 28% 12%
4
There will be no significant difference between SSC and GCE teachers that language of the textbooks is simple.
A 1.720 84.5% 90% 13% 1.7%
5
There will be no significant difference between SSC and GCE teachers that the contents cover application of abstract principles in real life problems.
R 3.275 54.4% 73.3% 29% 12%
6 There will be no significant difference between SSC and GCE teachers on the statement that worked examples in the text books provide sufficient guidance.
R3.846
67.9% 80% 24% 12%
252
(Contd…….)
7
There will be no significant difference between SSC and GCE teachers on the statement that the contents are in accordance with intellectual level of students.
R 3.913 63.4% 78.4% 24% 13%
8
There will be no significant difference between SSC and GCE teachers that contents covers problems whose solutions can be found by personal investigation.
R 6.311 51.1% 80% 32% 6.7%
9
There will be no significant difference between SSC and GCE teachers that contents covers a proper proportion of mathematical representations.
A 1.758 81.2% 91.7% 11% 3.3%
10
There will be no significant difference between SSC and GCE teachers that the contents include an appropriate proportion of activities to develop the habit of thinking.
R 5.231 42.2% 71.7% 49% 15%
11
There will be no significant difference between SSC and GCE teachers that the contents are balanced in terms of key areas.
R 4.752 73.4% 91.6% 19% 6.7%
12
There will be no significant difference between SSC and GCE teachers that the pictures and colorful presentations help in conceptual understanding.
R 4.071 66.7% 85% 21% 8.3%
H0
Contents / TextbooksA/R
t-Value
A(Percentage)
DA(Percentage)
(B)Students SSC GCE SSC GCE
13
There will be no significant difference between SSC and GCE students on the statement that mathematics textbooks have an attractive look.
A 0.355 31.6% 27.5% 44% 60%
14 There will be no significant difference between SSC and GCE students on the statement that language used in the textbooks is clear.
A 1.111 71.6% 75% 18% 15%
253
(Contd…….)
15
There will be no significant difference between SSC and GCE students on the statement that language of mathematics textbooks is difficult to understand.
R 4.779 43.3% 18.8% 40% 70%
16
There will be no significant difference between SSC and GCE students on the statement that all the topics in the textbooks are taught completely for the preparation of final examination.
R 5.238 59.2% 83.8% 29% 7.5%
17
There will be no significant difference between SSC and GCE students on the statement that methods to solve different types of problems are explained through worked examples in the textbooks.
R 2.734 70.8% 88.8% 14% 7.5%
18
There will be no significant difference between SSC and GCE students on the statement that textbooks are illustrated with concept-related pictures from real life.
R 3.832 33.3% 55% 53% 28%
19
There will be no significant difference between SSC and GCE students on the statement that the pictures facilitate in comprehending the concepts.
A 0.392 64.2% 65% 17% 23%
20
There will be no significant difference between SSC and GCE students on the statement that diagrams are the frightening element of the textbooks.
R 2.821 29.2% 12.5% 57% 80%
21
There will be no significant difference between SSC and GCE students on the statement that I can study a new topic through worked examples provided in the textbook.
R 5.774 64.2% 27.5% 26% 63%
22 There will be no significant difference between SSC and GCE students on the statement that the contents explained by teacher only should be studied.
R 5.114 41.6% 15% 44% 75%
254
(Contd…….)
23
There will be no significant difference between SSC and GCE students on the statement that the contents of textbooks is in accordance with the intellectual level of students
A 0.203 53.8% 55.8% 14% 18%
24
There will be no significant difference between SSC and GCE students on the statement that the language of textbooks is in accordance with the language proficiency of students
A 1.016 60% 60% 13% 11%
(C)Responses of Experts on Contents / Textbooks of Mathematics
Q1 Are you satisfied with the contents of textbooks of mathematics used at secondary level?
SSC Agreed40%
Disagreed40%
Undecided00%
Responses *Percentage of each Response* Problem is not with the contents; it is with the methods of teaching and assessment
10%
* Some topics like number sequence, probability etc. should be included. 10%
GCE Agreed50%
Disagreed30%
Undecided0%
Responses *Percentage of each Response*Books are not written locally, they serve the needs in terms of contents but book of local authors will be better.
20%
Q2 What changes would you like to suggest improving these textbooks?SSC *Percentage of each ResponseSuggestions
* New topics should be added. 30%*World problems should be increased. 40%*Contents should be updated. 30%*Worked examples should be improved. 10%*Textbooks should be activity based. 20%* In lower grades, schools frequently change books. It affects the logical sequence of contents and vertical integration of concepts.
20%
255
(Contd…….)GCE *Percentage of each ResponseSuggestions
*Books should be written by local authors. 30%*Reference books should be used instead of textbooks. 40%
*Contents on problem solving should be increased. 20%
* A teachers’ manual should be published with each book for their guidance. 20%
* Answers of graph and loci questions should be given in the form of constructed graphs and geometrical figures respectively.
10%
Q3 Are you satisfied with the current methods of selection and sequencing of contents? If not, please give your opinion.
SSC Agreed20%
Disagreed70%
Undecided10%
Responses *Percentage of each Response*Sequence is not appropriate between the contents taught at lower secondary and secondary level.
20%
*Selection of contents should be made accordingly with the sequence of the textbooks.
30%
*Selection is made to incorporate (arithmetic, algebra, geometry) but the prime concern of this selection is to ensure a balanced exam paper.
40%
*Selection, elimination and sequence of contents are made according to the choice of concerned teachers and feasibility of completing it within the available time
30%
GCE Agreed70%
Disagreed30%
Undecided0%
Responses *Percentage of each Response*It should be done on logical grounds 40%*The selection of contents should be done on the basis of educational needs of students
50%
*In the process of selection and its sequencing, no special consideration is made on the prerequisites, interests and needs of students.
30%
256
*Percentage of each Response = (Frequency of that response ÷Total number of Responses on that question) × 100%
Table 194 (c): Approaches / Methodology KEY: A = Accepted, R = Rejected, A = Agree, DA = Disagree, U = Undecided; *{U = 100% − (A% + DA %)}*(SA & SDA alternatives of the measurement scale have been collapsed in A & DA respectively)
Sr.No
H0
Approaches / MethodologyA/R
t-Value
A(Percentage)
DA(Percentage)
(A)Teachers SSC GCE SSC GCE
1
There will be no significant difference between SSC and GCE teachers on the statement that students should solve problems by teachers’ explained method only.
R 2.328 61.1% 26.7% 61% 27%
2
There will be no significant difference between SSC and GCE teachers on the statement that additional material is usually used for rigorous drill of learned material.
A 0.088 73.4% 68.4% 16% 15%
3
There will be no significant difference between SSC and GCE teachers on the statement that additional material used is mostly previous exam papers.
A 1.259 54.5% 66.7% 32% 28%
4
There will be no significant difference between SSC and GCE teachers on the statement that previous papers are solved as a rehearsal for the actual exam paper.
A 1.630 83.5% 86.7% 8.8% 3.3%
5
There will be no significant difference between SSC and GCE teachers on the statement that past papers are solved because questions of previous papers are considered important.
A 0.803 54.5% 65% 34% 28%
6
There will be no significant difference between SSC and GCE teachers on the statement that past papers are solved because questions from previous papers often repeat in the new papers.
R 2.313 67.2% 41.4% 25% 48%
7 There will be no significant difference between SSC and GCE teachers on the statement that past papers are solved to understand the pattern of questions coming in the recent papers.
A 0.108 91% 90.1% 5.5% 3.3%
257
(Contd…….)
8
There will be no significant difference between SSC and GCE teachers on the statement that teacher-constructed problems are presented in the class.
A 0.957 81.2% 81.7% 11% 13%
9
There will be no significant difference between SSC and GCE teachers on the statement that students are allowed to construct and present their own problems in the class.
R 2.605 81% 66.4% 11% 18%
10
There will be no significant difference between SSC and GCE teachers on the statement that procedures of solving a problem are explained but not the reason for the selection of that procedure.
R 7.500 51.4% 46.8% 32% 41%
11
There will be no significant difference between SSC and GCE teachers on the statement that there are some topics in the textbooks that are always left as no question comes in the paper from these topics.
R 3.125 54.6% 30.7% 36% 65%
12
There will be no significant difference between SSC and GCE teachers on the statement that homework is given in order to complete the syllabus as it cannot be completed by solving all sums in the class.
A 0.914 70% 66.7% 26% 28%
13
There will be no significant difference between SSC and GCE teachers on the statement that emphasis is given on neat and tidy written work.
R 4.796 94.5% 66.7% 3.3% 16%
14
There will be no significant difference between SSC and GCE teachers on the statement that homework is assigned and checked regularly.
R 3.220 88% 68% 7.7% 25%
15 There will be no significant difference between SSC and GCE teachers on the statement that topics are not explored in depth; only the
R 4.000 54.2% 33% 37% 57%
258
procedure of solving a sum is explained. (Contd…….)
16
There will be no significant difference between SSC and GCE teachers on the statement that unexplained short-cuts are told to solve certain problems.
A 1.268 54% 54% 37% 38%
17
There will be no significant difference between SSC and GCE teachers on the statement that derivation of the formula is not clarified; only the method of its application is explained.
A 0.214 33% 30% 57% 60%
18
There will be no significant difference between SSC and GCE teachers on the statement that teachers do not emphasize students to check answers.
R 2.774 52.2% 31.6% 40% 58%
19
There will be no significant difference between SSC and GCE teachers on the statement that teachers true role is to generate a question in the mind of a child before it is answered.
R 3.750 83.3% 94.4% 6.6% 3.3%
20
There will be no significant difference between SSC and GCE teachers on the statement that both posing and answering questions by teachers produce shallow understanding.
A 0.091 72.2% 70% 11% 12%
21
There will be no significant difference between SSC and GCE teachers on the statement that retention of learned material in the memory becomes stronger with repetition.
A 0.109 88.8% 86.6% 3.3% 6.6%
22 There will be no significant difference between SSC and GCE teachers on the statement that repetition of a learned material may attach meaningful relationships among the fragments of knowledge.
A 0.476 90% 88.3% 4.4% 1.6%
259
(Contd…….)H0
Approaches / MethodologyA/R
t-Value
A(Percentage)
DA(Percentage)
(B)Students SSC GCE SSC GCE
23
There will be no significant difference between SSC and GCE students on the statement that doing important topics is better than doing all the topics to get good marks.
R 5.673 62.5% 27.5% 31% 64%
24
There will be no significant difference between SSC and GCE students on the statement that generally the last questions (star questions) of the exercises are usually left unsolved.
A 0.581 59.2% 67.5% 29% 28%
25
There will be no significant difference between SSC and GCE students on the statement that most of the teachers emphasize students to solve the sums using only their explained methods.
A 1.386 71.3% 65.8% 19% 28%
26
There will be no significant difference between SSC and GCE students on the statement that there is more than one method to solve a problem.
A 1.485 86.6% 95% 3.3% 1.3%
27
There will be no significant difference between SSC and GCE students on the statement that most of the teachers emphasize neat and tidy work.
R 4.712 84.2% 63.8% 12% 35%
28
There will be no significant difference between SSC and GCE students on the statement that additional material is used to get further practice of the sums.
A 1.069 69.2% 73.8% 24% 15%
29
There will be no significant difference between SSC and GCE students on the statement that teacher-constructed problems are presented in the class.
R 4.717 67.5% 38.8% 20% 53%
30 There will be no significant difference between SSC and GCE students on the statement that separate activities are done for low
R 5.668 51.6% 16.3% 37% 78%
260
achievers in the class.(Contd…….)
31
There will be no significant difference between SSC and GCE students on the statement that teachers arrange activities to engage high achiever students to help their low achiever class fellows.
R 2.054 52.5% 42.5% 36% 51%
32
There will be no significant difference between SSC and GCE student on the statement that in mathematics class of 40 minutes students normally ask less than 5 questions.
R 2.892 46.65 25% 23% 63%
33
There will be no significant difference between SSC and GCE students on the statement that in mathematics class of 40 minutes teachers normally explain for less than 15 minutes.
A 0.402 22.5% 35% 57% 56%
34
There will be no significant difference between SSC and GCE students on the statement that students mostly ask ‘HOW’ type questions in the class.
A 0.091 90.8% 93.8% 7.5% 3.8%
35
There will be no significant difference between SSC and GCE student on the statement that teachers do not encourage ‘WHY’ type questions in the class.
R 2.112 50% 66.3% 33% 19%
36
There will be no significant difference between SSC and GCE students on the statement that procedure of solving a problem is explained but not the reason for the selection of that procedure.
A 1.258 57.5% 68.8% 24% 23%
37
There will be no significant difference between SSC and GCE student on the statement that some topics of the textbooks are never taught.
R 6.221 73.3% 30% 15% 53%
38 There will be no significant difference between SSC and GCE students on the statement that homework is assigned in order to complete the syllabus as it cannot be
A 1.168 80% 78.8% 11% 14%
261
completed by solving all the sums in class. (Contd……..)
39
There will be no significant difference between SSC and GCE student on the statement that homework is assigned and checked regularly by the teachers.
R 9.438 68.3% 18.8% 24% 75%
40
There will be no significant difference between SSC and GCE students on the statement that topics are not explored in depth; only the procedure of solving a sum is explained.
A 0.223 49.2% 42.5% 38% 44%
41
There will be no significant difference between SSC and GCE students on the statement that the activities of mathematics class are largely a repetition of similar sums.
A 0.279 69.2% 72.5% 21% 19%
42
There will be no significant difference between SSC and GCE students on the statement that reference books are taken from the library to explore the topics in depth.
A 0.160 25.8% 31.3% 65% 64%
(C)Responses of Experts on Approaches / Methodology
Q1 In your opinion what changes should be made in approaches and methods of teaching mathematics?
SSC Agreed70%
Disagreed20%
Undecided10%
Responses *Percentage of each Response*Activity based teaching. 40%*Project based teaching. 20%*Taking the aid of technology (audio-video aides, internet etc.). 40%
*Mathematics should be taught just like a language. 10%
*Mostly emphasis is given on product but the process is also as important as the product.
10%
*Teachers should have to address all the cognitive levels in their teaching (knowledge, comprehension, application, analysis, synthesis and evaluation).
10%
*Step by step instructions should be given instead of giving the key to open the lock (a method to solve the problem).
20%
262
(Contd…….)
GCE Agreed100%
Disagreed0%
Undecided0%
Responses *Percentage of each Response*Activity based teaching. 20%*Use maximum time on basic concepts. 40%*Preference should be given to mental calculations and calculators should be avoided as much as possible.
30%
*Instead of teaching a large number of chapters, teach a chapter in depth. 20%
*Computer Assisted Instruction (CAI)
should be increased. 10%
*Make the students confident by rigorous
practice. 60%
*Percentage of each Response = (Frequency of that response ÷Total number of Responses on that question) × 100%
Table 194 (d): Assessment / EvaluationKEY: A = Accepted, R = Rejected, A = Agree, DA = Disagree, U = Undecided; *{U = 100% − (A% + DA %)}*(SA & SDA alternatives of the measurement scale have been collapsed in A & DA respectively)
Sr.No
H0
Assessment / EvaluationA / R
t-Value
A(Percentage)
DA(Percentage)
(A)Teachers SSC GCE SSC GCE
1
There will be no significant difference between SSC and GCE teachers on the statement that tests/exams are conducted to assess the level of achievement of the instructional objectives.
R 2.532 100% 91.6% 0% 6.6%
2
There will be no significant difference between SSC and GCE teachers on the statement that tests/exams are conducted to categorize students into successful and unsuccessful groups.
R 4.035 72.2% 56.6% 23% 32%
3 There will be no significant difference between SSC and GCE teachers on the statement that the verbal/written remark of teacher on
A 0.654 76.6% 81.6% 13% 12%
263
the basis of assessment is evaluation.(Contd…….)
4
There will be no significant difference between SSC and GCE teachers on the statement that assessment helps both teacher and learner in the process of teaching and learning.
A 1.071 95.5% 90% 2.2% 1.6%
5
There will be no significant difference between SSC and GCE teachers on the statement that the fear of assessment motivates students for hard work.
R 4.318 93.3% 80% 3.3% 6.6%
6
There will be no significant difference between SSC and GCE teachers on the statement that a teacher is always engaged in the process of assessing his/her students during the class.
A 0.583 81.1% 85% 12% 6.6%
7
There will be no significant difference between SSC and GCE teachers on the statement that the encouraging remarks of a teacher after assessment produce positive effect on the performance of students.
A 0.000 94.4% 90% 3.3% 1.6%
8
There will be no significant difference between SSC and GCE teachers on the statement that methods of assessment should enable students to reveal what they know, rather than what they do not know.
R 2.115 78.8% 85% 13% 8.3%
9
There will be no significant difference between SSC and GCE teachers on the statement that the main purpose of assessment is to improve teaching and learning of mathematics.
A 1.609 90% 91.6% 2.2% 5%
10 There will be no significant difference between SSC and GCE teachers on the statement that the exam papers assess the objectives of teaching mathematics.
A 1.364 80% 81.6% 8.8% 5%
264
(Contd……)
11
There will be no significant difference between SSC and GCE teachers on the statement that the exam papers are balanced in terms of content areas.
A 0.127 87.7% 90% 7.7% 1.6%
12
There will be no significant difference between SSC and GCE teachers on the statement that the exam papers assess the actual educational objectives of teaching mathematics.
A 0.230 80% 80% 15% 3.3%
13
There will be no significant difference between SSC and GCE teachers on the statement that the system of checking papers is fair.
R 5.259 66.6% 88.3% 25% 1.6%
14
There will be no significant difference between SSC and GCE teachers on the statement that examinations are conducted under strict vigilance.
R 6.752 71.1% 93.3% 24% 1.6%
15
There will be no significant difference between SSC and GCE teachers on the statement that use of unfair means in the paper of mathematics is common.
R 6.712 42.2% 30% 40% 62%
16
There will be no significant difference between SSC and GCE teachers on the statement that grading system of (SSC/ GCE) is appropriate.
R 4.737 68.8% 81.6% 20% 6.6%
17
There will be no significant difference between SSC and GCE teachers on the statement that teachers’ assessment during class is as important as the final examination.
A 1.860 87.7% 91.6% 7.7% 1.6%
18 There will be no significant difference between SSC and GCE teachers on the statement that students’ weekly/monthly/terminal test scores are added in the marks of their final exam paper in junior grades.
R 2.359 87.7% 70% 8.8% 3.3%
265
(Contd…….)
19
There will be no significant difference between SSC and GCE teachers on the statement that final examinations assess the factual and procedural knowledge only.
R 4.237 82.2% 56.6% 11% 32%
20
There will be no significant difference between SSC and GCE teachers on the statement that questions in the exam papers are given according to a set pattern.
R 2.077 75.55 71.6% 18% 20%
21
There will be no significant difference between SSC and GCE teachers on the statement that questions are taken from the textbooks in (SSC/GCE) papers.
R 7.259 60% 23.3% 34% 65%
22
There will be no significant difference between SSC and GCE teachers on the statement that questions are taken from past papers in (SSC/GCE) papers.
R 5.448 43.3% 40% 46% 45%
23
There will be no significant difference between SSC and GCE teachers on the statement that some topics from the syllabus may be dropped due to ample choice of in the paper.
R 3.813 68.8% 53.3% 26% 38%
24
There will be no significant difference between SSC and GCE teachers on the statement that on the basis of previous papers, some questions can be predicted for the upcoming paper.
R 5.547 80% 53.3% 17% 35%
25
There will be no significant difference between SSC and GCE teachers on the statement that sections of exam paper are made in such a way that questions from some particular chapters always come in a specific section.
R 4.872 83.3% 65% 7.7% 23%
26 There will be no significant difference between SSC and GCE teachers on the statement that all the teaching and learning process in the class is designed and implemented to
A 1.261 77.7% 73.3% 20% 18%
266
pass the final examinations.(Contd…….)
H0
Assessment / EvaluationA /R
t-Value
A(Percentage)
DA(Percentage)
(B) Students SSC GCE SSC GCE
27
There will be no significant difference between SSC and GCE students on the statement that assessments help in confidence building.
R 1.984 87.5% 85% 5% 8.8%
28
There will be no significant difference between SSC and GCE students on the statement that assessments help in identifying and reducing mistakes.
A 0.316 93.3% 95% 3.3% 1.3%
29
There will be no significant difference between SSC and GCE students on the statement that assessments help in the preparation of final examinations.
A 0.217 86.6% 97.5% 3.3% 1.3%
30
There will be no significant difference between SSC and GCE student on the statement that quizzes (short tests based on calculations without using calculators) are conducted regularly in the class.
R 2.135 39.2% 55% 53% 40%
31
There will be no significant difference between SSC and GCE students on the statement that speed tests are conducted regularly.
A 1.746 24.2% 35% 68% 59%
32
There will be no significant difference between SSC and GCE students on the statement that positive remarks of the teacher on student’s assessment produce better result.s
A 0.349 81.6% 82.5% 7.5% 8.8%
33
There will be no significant difference between SSC and GCE student on the statement that I am well aware of the pattern of (GCE/SSC) paper.
R 2.105 87.5% 82.5% 5% 14%
34 There will be no significant difference between SSC and GCE students on the statement that students study seriously under the
A 0.939 77.5% 87.5% 15% 11%
267
pressure of tests/examinations.(Contd…….)
35
There will be no significant difference between SSC and GCE student on the statement that teachers leave some topics completely on the basis of their insignificance in the SSC/GCE paper.
R 4.974 69.2% 37.5% 21% 54%
36
There will be no significant difference between SSC and GCE student on the statement that questions in SSC/GCE papers are given according to a fixed pattern.
R 7.688 86.6% 40% 8.3% 49%
37
There will be no significant difference between SSC and GCE student on the statement that questions are taken from the textbooks in SSC/GCE paper.
R 11.503 78.3% 16.3% 13% 71%
38
There will be no significant difference between SSC and GCE student on the statement that questions are taken from past papers in SSC/GCE paper.
R 8.282 76.6% 30% 14% 60%
39
There will be no significant difference between SSC and GCE student on the statement that some topics from the syllabus may be dropped on the basis of sufficient choice of questions in the exam paper.
R 8.070 73.3% 22.5% 21% 60%
40
There will be no significant difference between SSC and GCE student on the statement that on the basis of previous papers, some questions can be predicted for the upcoming paper.
R 7.532 90% 50% 4.2% 43%
41
There will be no significant difference between SSC and GCE student on the statement that in junior grades (VI – VIII); the final paper is set from the whole syllabus.
R 5.569 44.2% 80% 49% 13%
42 There will be no significant difference between SSC and GCE student on the statement that in junior grades (VI – VIII); the final
R 7.356 61.6% 15% 32% 71%
268
paper is set from the topics covered in the final term only. (Contd……)
43
There will be no significant difference between SSC and GCE student on the statement that in junior grades (VI – VIII); the topics assessed in one terminal examination do not come in the next term.
R 5.976 48.3% 12.5% 44% 73%
(C)Responses of Experts on Assessment / Evaluation of Mathematics
Q1 Are you satisfied with current system of assessment in mathematics at school level? If not, please suggest some changes.
SSC Agreed40%
Disagreed60%
Undecided10%
Suggestions *Percentage of each Response* Formative assessments should be increased. 20%
* Rote memorization of contents should be discouraged by giving application based problems as much as possible.
30%
* Understanding of students is to be checked rather than checking that the student can solve a sum or not.
20%
* Sums should not be given directly from the textbook or previous exam papers. 40%
GCE Agreed70%
Disagreed30%
Undecided0%
Suggestions *Percentage of each Response* Tests should be held more frequently 30%* More quizzes and mental math’s tests should be administered 20%
* Teachers should construct their own sums instead of taking them from past papers
30%
Q2Are you satisfied with the current pattern of mathematics paper (GCE/SSC)? What improvement should be made in it according to your opinion?
SSC Agreed20%
Disagreed80%
Undecided0%
Opinions *Percentage of each Response* Questions should not be taken from textbooks / previous papers. 40%
* Pattern of paper should be such that it discourages guess work and selected study
30%
269
habits.(Contd……)
* Pattern of questions should be such that students can use their skills to solve them. 20%
* Vigilance system during examination should be improved. 40%
Workshops/Refresher-Courses for papers setters and checkers should be organized. 30%
System of assessing the papers should be improved. 20%
GCE Agreed70%
Disagreed20%
Undecided10%
Opinions *Percentage of each Response* Selective learning should be discouraged. 30%
* More application based questions should be included. 20%
* It should test deep understanding instead of basic knowledge. 10%*Percentage of each Response = (Frequency of that response ÷Total number of Responses on that question) × 100%
270
5.3FINDINGS
5.3.1 SECTION I: (Significance / Aims / Objectives)
5.3.1.1 Significance of Mathematics
a) Teachers
1. No significant difference has been found between SSC and GCE teachers
on the importance of mathematics in the school curriculum, an extremely
high trend for agreement; SSC (97%) and GCE (95%) have been found for
it (Table 194a. no.1).
2. No significant difference between SSC and GCE teachers has been found
regarding the statement that mathematics course is important atthe school
level due to its application in practical life. An extremely high trend for
agreement in both groups; SSC (92%) and GCE (93%), have been found
for the statement (Table 194a, no.3).
3. A decreasing trend of agreement for the following statements (given in an
order from highest to least) has been found in both groups of teachers for
the importance to mathematics (Table 13b, graph 1).
(i) It is largely applied in practical life (Agreed: SSC 96%; GCE
95%).
(ii) It is largely applied in other subjects (Agreed: SSC 90%; GCE
98%).
(iii) It develops the power of intellect (Agreed: SSC 95%; GCE 93%).
(iv) It develops desirable habits (Agreed: SSC 58%; GCE 67%).
(v) It develops desirable attitudes (Agreed: SSC 57%; GCE 56%).
271
b) Students
4. No significant difference has been found between SSC and GCE students
regarding the following statements.
(i) Mathematics is important because it trains the mind(Agreed: SSC
91%; GCE 96%).
(ii) Mathematics is important because it is compulsory to pass this subject
in order to succeed (Agreed: SSC 79%; GCE 75%).
(iii) Mathematics is important because it is largely applied at the higher
education level (Agreed: SSC 68%; GCE 67%).
(Table 194a, no.14, 15, 16)
5. A decreasing trend of agreement for the following statements (given in an
order from highest to least) has been found in both groups of students for
the importance to mathematics (Table 126b, graph 6).
(i) It trains the mind (Agreed: SSC 91%; GCE 96%).
(ii) It is applied in many other subjects (Agreed: SSC 88%; GCE 94%).
(iii) It is compulsory to pass this subject to get promoted to the next grade
at school level (Agreed: SSC 79%; GCE 75%).
(iv) It is largely applied in admission tests at higher education level
(Agreed: SSC 68%; GCE 67%).
6. There is a significant difference between SSC and GCE students on the
statement,“I do mathematics to get good marks as it is a scoring subject”.
A high trend for agreement (84%) on SSC side while a low trend for
agreement (36%) on GCE side have been found for this statement (Table
194a, no. 12).
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5.3.1.2 Aims
a) Teachers
7. No significant difference has been found between SSC and GCE teachers
on the following aims of mathematics (Table.194a, no. 2, 3).
(i) Disciplinary aim (training of mind) (Agreed: SSC 88%; GCE 80%).
(ii) Utilitarian aim (practical value in real life) (Agreed: SSC 92%; GCE
93%).
Moreover, there is no significant difference between the two groups
regarding the following statements.
(i) Aims of mathematics education are achievable (Agreed: SSC 86%;
GCE 82%).
(ii) Aims of mathematics education can be translated into small
educational objectives(Agreed: SSC 66%; GCE 71%).
(Table 194a, no. 6, 7)
8. There is a significant difference between the teachers of two groups on
the following statements.
(i) Development of problem solving skills is an aim of education
(Agreed: SSC 93%; GCE 95%).
(ii) Aims of education are convincing (Agreed: SSC 56%; GCE 80%).
(Table194a, no. 4, 5)
b) Students
9. There is no significant difference between SSC and GCE students on the
disciplinary aim of mathematics education with an agreement of 91% on
SSC side and 96% on GCE side (Table.199a, no. 14).
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5.3.1.3 Objectives
a) Teachers
10. There is no significant difference between SSC and GCE teachers on the
statement that objectives of mathematics teaching are well defined
(Agreed: SSC 92%; GCE 93%).
(Table.194a, no. 9)
11. There is a significant difference between SSC and GCE teachers on the
following statements.
(i) Objectives of current teaching are derived from real aims (Agreed:
SSC 62%; GCE 72%).
(ii) Objectives are transmitted clearly to teachers(Agreed: SSC 58%; GCE
77%) (Table.194a, no. 8, 10).
b) Students
12. There is no significant difference of opinion between SSC and GCE
students on the following statements.
(i) I have to do mathematics because of teachers’ emphasis on its
importance (Agreed: SSC 42%; GCE 59%).
(ii) School gives a special emphasis on mathematics over the other
subjects (Agreed: SSC 67%; GCE 65%) (Table.194a, no. 11, 13).
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5.3.1.4 Curriculum
13. A significance difference has been found between the teachers of SSC
and GCE system on the following statements about curriculum.
(i) The curriculum prepares the students to apply mathematical
knowledge in their daily lives (Agreed: SSC 73%; GCE 85%).
(ii) The curriculum prepares the students for future vocations (Agreed:
SSC 72%; GCE 83%).
(iii) The focus of curriculum is on the needs of future education (Agreed:
SSC 68%; GCE 87%).
(iv) The curriculum is comparable with other countries of the region
(Agreed: SSC 44%; GCE 72%).
(v) The curriculum is correlated with topics of other subjects (Agreed:
SSC 73%; GCE 83%).
(vi) The curriculum is flexible (Agreed: SSC 63%; GCE 77%).
(vii) The curriculum reflects state-of-the-art (Agreed: SSC 54%; GCE
83%).
(viii) The curriculum leads the students to achieve the set aims of
mathematics education (Agreed: SSC 59%; GCE 85%).
(Table 23, 24, 25, 26, 27, 28, 29 30)
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5.3.2 SECTION II: (Contents / Textbooks)
a) Teachers
14. No significant difference of opinion has been found between SSC and
GCE teachers on the following statements about contents.
(i) The language of contents is simple (Agreed: SSC 85%; GCE 90%).
(ii) Contents cover a proper proportion of mathematical representations
(Agreed: SSC 81%; GCE 92%).
(iii) It is properly sequenced (Agreed: SSC 75%; GCE 84%).
(iv) It develops interest among students (Agreed: SSC 63%; GCE 65%).
(Table 194b, no. 1, 2, 4, 9)
15. A significant difference has been found on the opinions of teachers in the
two groups on the following statements about contents.
(i) The pictures and colorful presentations in the textbooks help in
conceptual understanding (Agreed: SSC 67%; GCE 85%).
(ii) The content is balanced in terms of key areas of mathematics
(Agreed: SSC 73%; GCE 92%).
(iii) It contains worked examples that provide sufficient guidance to solve
given problems on a topic easily (Agreed: SSC 68%; GCE 80%).
(iv) It is according to the intellectual level of students (Agreed: SSC 63%;
GCE 78%).
(v) It constitutes a proper proportion of activities to develop the habit of
thinking (Agreed: SSC 42%; GCE 72%).
(vi) It constitutes an appropriate proportion of problems on application of
abstract principles of mathematics in real life situations (Agreed: SSC
54%; GCE 73%).
(vii) It incites the sense of enquiry (Agreed: SSC 59%; GCE 70%).
(Table 194b, no 3, 5, 6, 7, 8, 10, 11, 12)
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16. A significant difference has been found between SSC and GCE teachers
on the following statements about the contents of text books (Table 37b,
Graph 2)
(i) It develops logical reasoning (Agreed: SSC 69%; GCE 93%).
(ii) It develops analytical and critical thinking (Agreed: SSC 60%; GCE
85%).
(iii) It develops problem-solving skills (Agreed: SSC 67%; GCE 88%).
(iv) It develops a spirit of exploration and discovery (Agreed: SSC 50%;
GCE 63%).
(v) It develops the power of concentration (Agreed: SSC 54%; GCE
78%).
b) Students
17. There is no significance difference between the students of SSC and GCE
system regarding the following statements.
(i) Textbooks have an attractive look (Agreed: SSC 32%; GCE 28%).
(ii) Language of textbooks is clear and according to the proficiency of
students (Agreed: SSC 72%; GCE 75%).
(iii) The difficulty level of problems in the content is in accordance with
the intellectual level of students (Agreed: SSC 54%; GCE 56%).
(iv) Pictures facilitate in comprehending the concepts (Agreed: SSC 64%;
GCE 65%).
(Table 194b, no.13, 14, 19, 23)
18. A significant difference has been found between the two groups of
students on the following statements.
(i) Language of textbooks is difficult (Agreed: SSC 43%; GCE 19%).
(ii) Content is illustrated with concept-related pictures from daily life
(Agreed: SSC 33%; GCE 55%).
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(iii) Methods to solve different types of problems are explained through
worked examples in the textbooks (Agreed: SSC 71%; GCE 89%).
(iv) Diagrams are the frightening element of the textbooks (Agreed: SSC
29%; GCE 13%).
(v) I can study a new topic through worked examples provided in the
textbook (Agreed: SSC 64%; GCE 28%).
(vi) Only the contents explained by teacher should be studied (Agreed:
SSC 42%; GCE 15%).
(vii) All the topics in the textbooks are taught completely for the
preparation of final exam (Agreed: SSC 59%; GCE 84%).
(Table 194b, no.15, 16, 17, 18, 20, 21, 22)
19. No significant difference between SSC and GCE students has been found
for the statement (i) & (ii) while a significant difference has been found
for the statement (iii) & (iv) about the components of the contents that are
to be memorized (Table 143b, Graph7)
(i) Formulae should be memorized (Agreed: SSC 83%; GCE 80%).
(ii) Steps of long procedures should be memorized (Agreed: SSC 70%;
GCE 70%).
(iii) Definitions should be memorized (Agreed: SSC 67%; GCE 23%).
(iv) Proofs of geometrical theorems should be memorized (Agreed: SSC
82%; GCE 26%).
20. A significant difference has been found between SSC and GCE students
on the following remark about questions involving graphs (Table 150b,
no. 1, Graph 9).
(i) Graphs are difficult (Agreed: SSC 49%; GCE 23%).
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5.3.3 SECTION III: (Approaches / Methods)
a) Teachers
Approaches 21. No significant difference has been found between the teachers of SSC
and GCE system on approach (i) and (iii) while a significant difference
has been found on approach (ii) and (iv) (Table 47b, Graph 3).
(i) The selection, sequence and focus of entire instructional activities
remain on the needs and interests of the learner (Agreed: SSC 95%;
GCE 87%).
(ii) The focus remains on the contents but with an emphasis placed on the
development of understanding of concepts among the learners
(Agreed: SSC 87%; GCE 93%).
(iii) The focus remains on contents but with an emphasis on solving
problems from textbooks and becoming expert in them (Agreed: SSC
80%; GCE 78%).
(iv) The focus remains on the maintenance and continuous flow of
planned activities in the class with an emphasis of class discipline
(Agreed: SSC 85%; GCE 68%).
The highest trend of agreement (95%) for approach (i) but a relatively
low trend of agreement (80%) for approach (iii) has been observed in SSC
group of teachers.
On the other hand, the highest trend of agreement (93%) was for
approach (ii) and a relatively low trend of agreement (68%) for approach (iv)
has been observed in GCE group of teachers.
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Methods
22. No significant difference has been found between the teachers of SSC
and GCE system on method (ii), (iii) and (iv) while a significant
difference has been found on method (i) and (v).
(i) All the sums from an exercise should be solved on the black/white
board (Agreed: SSC 39%; GCE 25%).
(ii) Some questions should be solved on the board and students should
have to do the remaining sums in class (Agreed: SSC 93%; GCE
80%).
(iii) Only important points should be explained on the board and students
should be encouraged to solve problems with teacher’s help (Agreed:
SSC 69%; GCE 77%).
(iv) Problems should be given to solve and teacher should help students
only when they ask for it (Agreed: SSC 66%; GCE 65%).
(v) Problems should be given to students in groups to find their solutions
with the cooperation of teacher and other members of the group
(Agreed: SSC 77%; GCE 72%).
The highest trend of agreement (93%) for method (ii) while the least
trend of agreement (39%) for approach (i), has been found in SSC group of
teachers.
On the other hand, the highest trend of agreement (80%) was for
approach (ii) and the least trend of agreement (25%) for approach (i) has
been found in GCE group of teachers.
It shows that there is no difference of opinions on the role of a teacher in
both groups.
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23. No significant difference has been found between SSC and GCE teachers
on the following statements.
(i) Repetition of a learned material may attach meaningful relationships
among the fragments of knowledge(Agreed: SSC 90%; GCE 88%).
(ii) Retention of learned material in the memory becomes stronger with
repetition (Agreed: SSC 89%; GCE 87%).
(iii) For rigorous drill, additional material is used (Agreed: SSC 73%;
GCE 68%).
(iv) Additional material used for drill is mostly previous exam papers
(Agreed: SSC 55%; GCE 67%).
(v) Previous exam papers are solved to understand the pattern of paper
(Agreed: SSC 91%; GCE 90%).
(Table 194c, no. 2, 3, 7, 21, 22)
24. A significant difference has been found between SSC and GCE teachers
on the following statements.
(i) Sums should be solved by the teacher’s explained method only
(Agreed: SSC 61%; GCE 27%).
(ii) Questions of previous papers often repeat (Agreed: SSC 67%; GCE
42%).
(iii) Some topics are always left untaught (Agreed: SSC 55%; GCE 31%).
(iv) Homework is assigned and checked regularly (Agreed: SSC 88%;
GCE 68%).
(v) Emphasis is placed on neat and tidy written work (Agreed: SSC 95%;
GCE 67%).
(vi) Emphasis is not placed on checking answers (Agreed: SSC 52%; GCE
32%).
(vii) Topics are not explored in depth; only the procedures of solving the
sums are explained (Agreed: SSC 54%; GCE 33%).
(Table 194c, no. 1, 6, 11, 13, 14, 15, 18)
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b) Students
Learning Experiences
25. No significant difference has been found between SSC and GCE students
on the following statements
(i) Usually, the last questions (star questions) of the exercises are left
unsolved (Agreed: SSC 59%; GCE 68%).
(ii) There is more than one method to solve a problem (Agreed: SSC
87%; GCE 95%).
(iii) Emphasis is given by teachers to solve problems by their explained
methods only (Agreed: SSC 71%; GCE 66%).
(iv) Additional material (worksheets/workbooks etc.) is used to get further
practice of the sums (Agreed: SSC 62%; GCE 74%).
(v) Teachers normally explain for less than 15 minutes in a class (Agreed:
SSC 23%; GCE 35%).
(vi) Homework is assigned in order to complete the syllabus (Agreed:
SSC 80%; GCE 79%).
(vii) Topics are not explored in depth; only the procedure of doing a sum is
explained (Agreed: SSC 49%; GCE 43%).
(viii) The activities of mathematics class are largely a repetition of similar
sums (Agreed: SSC 62%; GCE 73%).
(ix) Students mostly ask ‘HOW’ type questions in the class (Agreed: SSC
91%; GCE 94%).
(Table 194c, no. 24, 25, 26, 28, 33, 38, 40, 40, 42)
26. A significant difference has been found between SSC and GCE students
on the following statements.
(i) Doing important topics is better than doing all the topics for getting
good marks (Agreed: SSC 63%; GCE 28%).
(ii) Most of the teachers emphasize neat and tidy work (Agreed: SSC
84%; GCE 64%).
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(iii) Teacher-constructed problems are presented in the class (Agreed: SSC
68%; GCE 39%).
(iv) Separate activities are done for low achievers in the class (Agreed:
SSC 52%; GCE 16%).
(v) Teachers arrange activities to engage high achiever students to help
their low achiever class fellows (Agreed: SSC 53%; GCE 43%).
(vi) Students normally ask less than 5 questions in a period (Agreed: SSC
47%; GCE 25%).
(vii) ‘WHY’ type questions are not encouraged by teachers in the class
(Agreed: SSC 50%; GCE 66%).
(viii) Some topics of the textbooks are never taught (Agreed: SSC 73%;
GCE 30%).
(ix) Homework is assigned and checked regularly by the teachers
(Agreed: SSC 68%; GCE 19%).
(Table 194c, no. 23, 27, 29, 30, 31, 32, 33, 37, 39)
27. No significant difference has been found between the students of SSC
and GCE system on method (i) and (iv) while a significant difference has
been found on method (ii) and (iii). (Table 171b, Graph 10)
(i) Teachers explain some problems from an exercise in the textbook on
the board (Agreed: SSC 91%; GCE 94%).
(ii) Teachers explain all the problems from an exercise in the textbook on
the board (Agreed: SSC 37%; GCE 24%).
(iii) Teachers explain the important procedures and points on the board
and helping us in solving sums individually (Agreed: SSC 72%; GCE
86%).
(iv) Teachers give us problems and facilitate us in finding their solutions
(Agreed: SSC 30%; GCE 34%).
The highest trend of agreement (91%) for method (i) while the least
trend of agreement (30%) for approach (iv), has been found in SSC group of
students.
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On the other hand, the highest trend of agreement (94%) was for
approach (i) and the least trend of agreement (24%) for approach (ii) has
been found in GCE group of teachers.
It shows that there is no difference of opinion on the methods
experienced by them. In both groups of students the commonly experienced
methods are found (i) & (iii) i.e. teachers solve some questions on the board
by explaining important procedures and help students to solve the other.
28. No significant difference of opinion between SSC and GCE students has
been found on attribute (iii). Moreover, a high trend of agreement, SSC
93%&GCE 98% has been found in both groups for it. It means that
students of both groups like those teachers who present difficult things in
an easy manner.
(Table 172b, Graph 11)
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5.3.4SECTION IV: (Assessment / Evaluation)
a) Teachers
29. No significant difference has been found between SSC and GCE teachers
on the following statements.
(i) The verbal/written remark of teacher on the basis of assessment is
evaluation (Agreed: SSC 77%; GCE 82%).
(ii) Assessment helps both teacher and learner in the process of teaching
and learning (Agreed: SSC 96%; GCE 90%).
(iii) A teacher is always engaged in the process of assessing his/her
students during the class (Agreed: SSC 81%; GCE 85%).
(iv) The encouraging remarks of a teacher after assessment produce
positive effect on the performance of students (Agreed: SSC 94%;
GCE 90%).
(v) The main purpose of assessment is to improve teaching and learning
of mathematics (Agreed: SSC 90%; GCE 92%).
(vi) The exam papers are balanced in terms of content areas (Agreed: SSC
88%; GCE 90%).
(vii) Teachers’ assessment during class is as important as the final
examination (Agreed: SSC 88%; GCE 92%).
(viii) All the teaching and learning process in the class is designed and
implemented to pass the final examinations (Agreed: SSC 78%; GCE
73%) (Table 194d, no. 3, 4, 6, 7, 9, 11, 17, 26).
30. A significant difference has been found between SSC and GCE teachers
on the following statements.
(i) Tests/Exams are conducted to assess the level of achievement of the
instructional objectives (Agreed: SSC 100%; GCE 92%).
(ii) Tests/exams are conducted to categorize students into successful and
unsuccessful groups (Agreed: SSC 72%; GCE 57%).
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(iii) The fear of assessment motivates students to work hard work
(Agreed: SSC 93%; GCE 80%).
(iv) Assessment should enable students to reveal what they know rather
than what they do not know (Agreed: SSC 79%; GCE 85%).
(v) The system of checking papers is fair (Agreed: SSC 67%; GCE 88%).
(vi) Examinations are conducted under strict vigilance (Agreed: SSC 71%;
GCE 93%).
(vii) Use of unfair means in the paper of mathematics is common (Agreed:
SSC 42%; GCE 30%).
(viii) Grading system of (GCE/SSC) is appropriate (Agreed: SSC 69%;
GCE 82%).
(ix) Students’ marks of weekly/monthly/terminal tests are added in the
marks of their final exam paper in junior grades (Agreed: SSC 88%;
GCE 70%).
(x) Final examinations assess the factual and procedural knowledge of
mathematics only (Agreed: SSC 82%; GCE 57%).
(xi) Questions in the exam papers are given according to a set pattern
(Agreed: SSC 76%; GCE 72%).
(xii) Questions are taken from the textbooks in (GCE/SSC) papers
(Agreed: SSC 60%; GCE 23%).
(xiii) Questions are taken from past papers in (GCE/SSC) papers (Agreed:
SSC 43%; GCE 40%).
(xiv) Some topics from the syllabus may be dropped on the basis of ample
choice of question in the exam paper (Agreed: SSC 69%; GCE 53%).
(xv) On the basis of previous papers some questions can be predicted for
the upcoming paper (Agreed: SSC 80%; GCE 53%).
(xvi) Sections of exam papers are made in such a way that questions from
some particular chapters always appear in a specific section (Agreed:
SSC 83%; GCE 65%).
(Table 194d, no. 1,2,5,8,13,14,15,16,18,19,20,21,22,23,24,25)
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b) Students
31. No significant difference has been found between SSC and GCE students
on the following statements.
(i) Assessments help in identifying and reducing mistakes (Agreed: SSC
93%; GCE 95%).
(ii) Assessments help in the preparation of final examinations (Agreed:
SSC 87%; GCE 98%).
(iii) Speed tests are conducted regularly in the class (Agreed: SSC 24%;
GCE 35%).
(iv) Positive remarks of the teacher on student’s assessment produce better
results (Agreed: SSC 82%; GCE 83%).
(v) Students study seriously under the pressure of tests/examinations
(Agreed: SSC 78%; GCE 88%).
(Table 194d, no. 28, 29, 31, 32, 34)
32. A significant difference has been found between SSC and GCE students
on the following statements.
(i) Assessments help in confidence building (Agreed: SSC 88%; GCE
85%).
(ii) Quizzes (short tests based on calculations without using calculators)
are conducted regularly in the class (Agreed: SSC 39%; GCE 55%).
(iii) I am well aware of the pattern of (GCE/SSC) paper (Agreed: SSC
88%; GCE 83%).
(iv) Teachers leave some topics completely on the basis of their
insignificance in the (GCE/SSC) paper (Agreed: SSC 69%; GCE
38%).
(v) Questions in (GCE/SSC) papers are given according to a fixed pattern
(Agreed: SSC 87%; GCE 40%).
(vi) Questions come from the textbooks in (GCE/SSC) papers (Agreed:
SSC 78%; GCE 16%).
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(vii) Questions are taken from past papers in SSC/GCE paper (Agreed:
SSC 77%; GCE 30%).
(viii) Some topics from the syllabus may be dropped on the basis of
sufficient choice of questions in the exam paper (Agreed: SSC 73%;
GCE 23%).
(ix) On the basis of previous papers some questions can be predicted for
the upcoming paper (Agreed: SSC 90%; GCE 50%).
(x) In junior grades (VI – VIII); the final paper is set from the whole
syllabus (Agreed: SSC 44%; GCE 80%).
(xi) In junior grades (VI – VIII); the final paper is set from the topics
covered in the final term only (Agreed: SSC 62%; GCE 15%).
(xii) In junior grades (VI – VIII); the topics assessed in one terminal
examination do not come in the next term (Agreed: SSC 48%; GCE
13%).
33. A significant difference has been found between SSC and GCE students
on the methods of revision (i), (ii), (iv) and (v). Only method (iii) is one
on which no significant difference has been found (Table 188b, Graph
12).
An extremely high trend for agreement SSC 88% & GCE 94% has
been found in both groups of students for method (iii).
It means that there is no significant difference between the two groups
of students on solving sums from past papers (five years) as a method of
revision.
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5.4 CUMULATIVE FINDINGS
a) General1. SSC and GCE systems were in a complete agreement on the significance
of mathematics in the school curriculum but in GCE system, a higher
satisfaction level has been found in the current practice of teaching.
2. The clarity of aims and objectives of teaching mathematics, as expected
in their corresponding curricula, was much higher among teachers of the
GCE system than the teachers of the SSCsystem.
3. Teachers and students of both systems gave importance to mathematics
due to its practical and disciplinary value.
4. There was a ‘one year’s suspension’ of mathematics during grade IX on
the SSC side but no such discontinuity of mathematics educationwas
found in GCE system at school level.
5. GCE students were found completing their course in five years while
SSC students complete their course in one year. GCE system was using a
series of four textbooks, Book1 – Book 4. From grade VII - XI; they
study selected contents of these four books. On the other hand, schools in
SSC system were found using different series of textbooks till grade VIII,
after which they all use the same textbook published by Sindh Textbook
Board (in grade X).
6. GCE system has been found with a focus on ‘depth versus breadth’,
while SSC system has a focus on ‘breadth versus depth’. It means that
teachers of GCE system emphasize more on proficiency in knowledge
and skills while on the other hand there is a focus on furthering subject’s
knowledge in SSC system.
7. There was a relatively higher chance of drill (practice) of learned material
found on GCE side than on the SSC side. This is because GCE system
gives more time to complete the syllabus and has a policy of revisiting
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the topics in the exams successively at different grade levels to refresh
the learning.
b) Curriculum8. The mathematics curriculum ofthe GCE system was found state-of-the-
art and comparable with the curricula of other countries of the region
while the SSC curriculum was not found such.
9. The curriculum of GCE system was foundto be based on the principles of
‘utility’ and ‘preparation’. It prepares students for practical life and
further studies. On the other hand, SSC curriculum’s prime focus has
been on the principle of preparation for further studies.
10. GCE curriculum has been found relatively more inclusive in terms of
key content areas than the SSC curriculum.
11. The focus of GCE curriculum was on coherence within different areas
of the contents but SSC curriculum was relatively less coherent.
12. The focus of GCE curriculum on coherence was on both, linear and
upward integration and on the integrated application of learned
concepts of one topic into other topics. The coherence within different
areas of content was found only on the basic operational level in the
SSC curriculum.
13. The focus on articulation in GCE curriculum was also more than the
SSC curriculum.
c) Contents14. The logical sequence of the contents of GCE curriculum was more than
the SSC curriculum.15. The contents for the development of problem solving skills in the
students were found quite large in number in GCE course as compared
to SSC course.
16. SSC textbook did not have any content on everyday mathematics
(percentage, rate/sale/purchase/interest /money etc.) while on the GCE
side, there were a substantial proportion of these topics in the textbooks.
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17. The worked examples found in the textbooks of GCE system were more
self-explanatory than the examples found in SSC textbooks.
18. There was a wide gap of standards in terms of different areas of
contents of SSC and HSC, while the difference between the course
contents of O-Level and A-Level was not as much.
19. Contents of SSC textbooks were found leaning towards the provision of
mathematical knowledge of procedures and operations while on the
GCE side there was a clear inclination towards the application of
mathematical procedures and operations in everyday problems. GCE
textbooks and question papers comprised of word problems in excess
while SSC textbooks and question papers constituted a very small
number of word problems.
20. Textbooks of SSC system were not colourful, and had a discernible use
of mathematical language while GCE textbooks were found having
colourful presentation of pictures and diagrams with an indiscernible
use of mathematical language embedded in common language.
21. GCE textbooks were found containing contents for further exploration
and discovery of a concept beyond the requirements of syllabus which
were not present on SSC side.
22. Textbooks of GCE system were found containing material for mental
exercise (discipline of mind) beyond the requirement of syllabus but no
such material was found in the SSC textbook.
d) Approaches23. The approach of SSC teachers in selecting the contents for teaching was
found significantly different from GCE teachers. SSC teachers select
contents on the basis of three content areas i.e. arithmetic, algebra and
geometry. It was found that this is done in order to set a paper for
internal assessments with three sections, each containing questions from
the above stated three areas. GCE teachers were found selecting
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contents in a logical sequence; mostly sequence of textbooks was used
without a consideration to incorporate different areas of content.
24. The approach of GCE system in organizing the contents for instruction
was found to some extent spiral (concentric), while SSC system was
applying a topical approach.
25. The approach of teaching mathematics of GCE teachers was found
‘Content-Focused’ with an emphasis on understanding and
performance. The approach of SSC teachers, on the other side was also
‘Content-Focused’ but emphasis was simply on performance.
26. Students of SSC system were observed with an approach of selective
study and prediction of questions for the upcoming paper. Students of
GCE system on the other hand were found usingan approach of
comprehensive study to have an experience of various ways of setting a
problem on a topic in different situations.
27. SSC students were found with an approach towards rote memorization
especially in the geometrical theorems. GCE students did not show the
approach of memorizing the mathematical contents except learning the
formulae and procedures for solving the sums.
28. GCE students were found to solve maximum of problems with an
approach having the following steps: comprehending the problem,
analyzing and evaluating the given situation, selecting a method of its
solution, retrieving the procedure and/or formula from memory same or
similar to given situation, applying it and finding its solution. On the
other hand, SSC students were usually recognizing the problem by
linking it with the textbook where they had previously solved it,
retrieving from memory the method and/or formula, and using it to find
the solution.
e) Methods29. There was no significant difference found in the methods of teaching in
both systems. Teachers of both systems were found to solve some
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problems of different types on the blackboards/whiteboards by
explaining important points, procedures and formulae. Some problems
were given to be solved in the class and some as homework.
30. SSC teachers ensure that students keep proper notes of the solution of
textbook problems. Regular checking of these notes has been observed
on this side. GCE teachers were not found following this procedure.
31. Homework is regularly and more properly checked on the SSC side
than on the GCE side.
32. SSC system emphasizes on neatness and tidiness of work which has
been observed relatively less on GCE side.
33. Teachers on SSC side mostly assert students to use the method
explained by them, but on GCE side, relatively less teachers stress on it.
34. GCE and SSC systems prepare their students for examination in the
same manner. Both systems emphasize the solving of previous papers
of CIE and BSEK respectively.
35. There was no significant difference in the construction of tests in both
systems. Teachers of both systems did not have a trend of constructing
their own problems. SSC teachers were found usually taking these
problems from textbooks and previous papers. GCE teachers were
found taking them from workbooks, internet and previous papers.
36. There was a significant difference in the method of assessment in both
systems. Formative assessment was found more systematic on GCE
side than SSCsystem. Formative assessments are done systematically
on regular intervals and students’ performance is accumulated in their
final exam’s performance. As a result, students use to take these
assessments seriously. SSC system was found relying only on
summative assessments. Moreover, in most of the SSC schools, there is
a terminal system (semester system). They move forward on topical
bases. Once a topic has been taught and assessed in a termdoes not
come in the next term or even in the final examination.
293
f) Assessment37. Question papers of SSC system contain textbook questions but O-Level
papers contain problems entirely different from those in textbooks.
38. There is a pattern of repetition of the same questions in successive years
in SSC papers while on GCE side, no clear pattern of repetition has
been observed.
39. There is a fixed outline of SSC papers in the sense that questions from
certain chapters are always given in specific sections. An ample and
consistent choice is always given to select questions from different
sections. As a result of this fixed design and ample choice, a high trend
of selected study and deletion of topics from the syllabus has been
observed to be prevailing in this system. GCE papers on the other hand
neither have a fixed design nor plenteous choice in the paper. Students
of this system have to study all the topics from their syllabus.
40. SSC papers were found predictable to a large extent, due to a fixed
design and repetition of questions. Therefore, a trend of guessing
questions for the upcoming papers by analyzing the pattern of questions
in the previous year’s papers has been found in this system. GCE papers
were neither easily predictable nor did they follow a pattern.
41. GCE examinations were found to be held under strict vigilance while
there was a common observation of the use of unfair means in the SSC
examinations.
42. There is more flexibility of taking examinations on GCE side. Students
can appear for the examination twice in a year either in May or in
November. On the SSC side, there is only one annual examination to
appear in. However, a supplementary examination is held for those
candidates who have not passed their annual examination.
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5.5 CONCLUSIONS
On the basis of analysis of data and findings of the study, the following conclusions were drawn.
1. The GCE (O-Level) mathematics curriculum has been found being more
effectively implementedas compared to the SSC curriculum.
2. The first major factor found accountable for the effectiveness of GCE
curriculum was the clarity of aims and objectives of this curriculum among
GCE teachers which was not found, to that extent, among SSC teachers.
Two important reasons are found of irrelevance of SSC system from the
expected aims and objectives of their curriculum. The first reason is that the
aims and objectives are neither easily approachable to teachers nor is there a
movement in school managements to make them available. The second and
most important reason is the worthlessness of these objectives for teachers
as the method of examination was found to be fulfilling only shallow
expectations of the curriculum.
3. The second key factor found responsible for the effectiveness of GCE
curriculum was the contents of their textbooks. These contents provide
support in attaining the expected aims and objectives of their curriculum.
These contents were found well balanced according to different domains of
knowledge and they were found to promote problem solving, critical
thinking and reasoning skills among students which is the requirement of the
curriculum. Moreover, additional material such as workbooks and previous
papers also found supportive to their textbooks in serving this cause.
Textbooks on SSC side were not incorporated with additional resources
including teacher’s manual, workbook and electronic resources according to
the recommendations and guidelines of the national curriculum. Also, the
contents of the textbooks were not found to be according to the standards
and benchmarks by the National Curriculum of Mathematics (Government
of Pakistan, 2006).
295
4. The third prime factor found for the effectiveness of GCE curriculum was
the difference in their approaches regarding: concentric organization of the
contents for teaching; focus on depth versus breadth; systematics formative
assessment and focus on investigation and application of knowledge versus
dispensation of knowledge. SSC system has a topical approach of
sequencing the contents for instruction. With this approach, a topic once
taught does not appear in the next term or in the final internal school
examinations at VI – VIII levels. SSC system focuses on breadth versus
depth (expansion of content knowledge), dispensing information versus
investigation and assessment of learning (summative) versus assessment for
learning (formative). The aforementioned approaches were found to be the
key reasons of relatively lower effectiveness of the SSC curriculum in
achieving its aims.
5. Methods of teaching were not that different but methods of assessment were
found to be entirely different in the two systems, which is the fourth major
factor of difference in the effectiveness of theses curricula. Method of
assessment of GCE was based on its curriculum expectations. GCE papers
have been observed neither with a fixed pattern of repetition of questions
nor with a plenteous choice. Moreover, examinations of this system were
found to be held under strict vigilance.
6. The fifth and most damaging factor found in the assessment system of SSC
was that in this system, questions from textbooks are given in both internal
school examinations and in the papers of BSEK. As a result, students who
feel some difficulty in grasping the concept start drifting towards
memorizing the contents. Besides this, a fixed pattern of papers, with an
ample choice in different sections and repetition of same questions
successively was found. Moreover, a deviation towards selective study i.e.
leaving some topics completely and guessing the contents of the upcoming
papers has been observed. Also, the exams are not found to be conducted
under such strict vigilance as was found in the GCE system.
296
7. The sixth dominant factor found for the difference in the effectiveness was
the suspension of mathematics education in grade IX in the SSC system.
This suspension has been found to be another negative contributor because
after such a long interruption, students who fail to recall their previous
knowledge, a prerequisite for furthering on that topic, suffer problems in
concept building because they cannot attach the new information with their
previously learned knowledge. No such discontinuation of mathematics at
school level has been found in the GCE system, which is another contributor
in making curriculum more effective.
5.6RECOMMENDATIONS
In the light of drawn conclusions, the following recommendations are made.
1. It is recommended that the expected aims and objectives of teaching
mathematics at SSC level are transmitted to teachers. This document should
be made public on the internet and should also be provided in schools.
2. There is an urgent need to divert the focus of our schools towards enhancing
thinking skills among students, especially higher order thinking skills
(analysis, synthesis and evaluation). These thinking skills can be produced
through proper teaching and assessment of mathematics in our schools. For
this, two steps are suggested. The first step is motivation and counseling of
school heads. To achieve this, it is recommended that a ‘Focus Program’
with a possible motto, “work for learning via work on thinking”, should be
started for the school heads. Ministry of Education can conduct this program
in collaboration with Board of Secondary Education Karachi (BSEK), to
ensure the participation of heads of all registered schools in BSEK. In this
program, school heads can be guided and counseled to focus on students’
thinking skills in their schools. They may be directed to ensure the teaching
of mathematics according to the expected aims and objectives of SSC
curriculum, in their institutions.
297
3. It is recommended that the contents of the SSC textbook be revised.
Contents on everyday application of mathematics (profit / loss / sale /
purchase / hire-purchase / percentage / interest / money etc.) may be
incorporated. Topics involving geometrical figures such as mensuration
(area and volume of 2D / 3D figures) and trigonometry should be included.
Topics that enhance logical reasoning such as number sequence and
geometrical patterns should also be included. It is also recommended to
increase the coherence within different areas of content by integrating them
through word problems. Student’s monotonous outlook towards textbook
should be changed by including material on the solution of real life
problems through mathematical concepts; reducing excessive use of
mathematical language with simple language and including colorful pictures
and illustrations related to topic may be used to enhance conceptual
understanding.
4. It is strongly recommended that approaches of mathematics teachers should
be changed. For this, the earlier recommended“Focus Program” may also
be helpful. There is a dire need of proper training for mathematics teachers,
at least basic training of teaching mathematics with proper approaches
should be provided to all teachers. This may be done by organizing short
training sessions under the supervision of school heads within the umbrella
of “Focus Program”. Moreover, it is also recommended that separate
professional degree programs from Bachelor to Ph.D. level for mathematics
education should be started.
5. There is an urgent need to change the method of assessment in the SSC
system, both in internal school examinations and in BSEK examinations.
There is an urgent need of changing the routine of giving textbook questions
in the papers. To solve the problem of rote memorization in mathematics, it
is recommended not to include any material in the paper in the same
framework as is given in the textbooks. To discourage the approaches of
selective study and prediction of papers, it is recommended that the pattern
298
of sectioning papers on the basis of topics be changed and the choice of
selection among questions should be minimized.
6. It is strongly recommended that nature of questions in the SSC papers
should be changed. Items of the question papers should assess application of knowledge rather than assessing theprecision in replication of content knowledge (facts, principles and algorithms). Word problems that assess higher order thinking skills
should be included and increased gradually. The quality of questions can be
improved by constructing those items in which figures, diagrams and graphs
are involved.Moreover, problems that require insight solutions (problem-solving strategies) may also be included gradually.
7. There is a dire need of continuation of mathematics as a subject at all levels
in school curriculum. It is therefore recommended that the suspension of
mathematics for a whole year during grade IX should be stopped. The
textbook of mathematics consists of two merged parts: part I & part II. The
part wise examination of each subject i.e. part I in grade IX and part II in
grade X may be adopted, to ensure continuation of mathematics and
naturally other subjects in addition.
5.7 FUTURE RESEARCH
Areas for further research may be. Comparison of Assessment and Evaluation System of SSC
and GCE Comparative Analysis of the Contents of Textbooks of SSC
and GCE
299
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Stevenson, H. W., Lee, S-Y., & Stigler, J. W. (1986). Mathematics achievement
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316
Appendix: I
Hamdard Institute of Education and Social Sciences
HAMDARD UNIVERSITY KARACHI
A Comparative Analysis of the Effectiveness of Mathematics Curriculum Taught at GCE (O-Level) and SSC System of Schools in Karachi
QUESTIONNAIRE FOR TEACHERS
SECTION I: PARTICULARS ABOUT THE RESPONDENT.
DIRECTIONS: Please fill in the given spaces or tick (√) mark as appropriate from the following
i) Name (Optional):-------------------------------------------------------------------------------------------
ii) Gender: a) Male:----------- b) Female:-----------iii) Marital Status: a) Married:--------- b) Unmarried:--------- iv) Age: i) Less than 30 years: ------------ ii) 30 to 34 years: -----------iii) 35 to 39 years: -------- iv) 40 to 44 years: ---------- v) 45 to 49 years: ---------- vi) 50 years and above: -------
v) Area of Residence:-----------------------------------------------------------------------------------------
6. Qualification:
a) Academic: -----------------------------------------------------------------------
b) Professional: --------------------------------------------------------------------
7. Teaching Experience:
a) SSC (Matric): i) Less than 5 years----------- ii) 5 to 9 years--------
iii) 10 to 14 years--------- iv) 15 to 19 years------------ v) 20 years and above----
b) GCE (O-Level): i) Less than 5 years----------- ii) 5 to 9 years--------
iii) 10 to 14 years--------- iv) 15 to 19 years------------ v) 20 years and above----
8. Please specify the system (GCE/SSC), for which you are responding: ------------------------------
9. Name & Address of Institution: ---------------------------------------------------------------------------
10. Control of Institution: a) Public: --------------------------- b) Private: -----------------------------
11. System of Education in the Institution (GCE/SSC/Both):--------------------------------------------
12. Location of Institution: a) Town--------------------------------- b) District: --------------------------
13. Monthly Income: i) Less than 40 thousands: -------------- ii) 40 to 60 thousands: ---------------
313
Appendix: I
iii) 60 to 80 thousands: ---------- iv) 80 to 100 thousands: --------- v) 100 thousands plus: ---------
SECTION II: CURRICULUM-EFFECTIVENESS SCALE
DIRECTIONS: Please tick (√) mark as appropriate from the following columns:SA=Strongly Agree, A=Agree, UD=Undecided, DA=Disagree, SD=Strongly Disagree.
S.# ItemsAims/Objectives
1 Mathematics is one of themost important subjects in the school curriculum. SA A UD D SD
2
Mathematics is an important subject because:-i) it is used largely in practical life SA A UD D SD
ii) it is largely applied in other subjects SA A UD D SDiii) it develops powers of intellect SA A UD D SDiv) it develops desirable habits SA A UD D SDv) it develops desirable attitudes SA A UD D SD
3 The aim of mathematics education is to train or discipline the mind. SA A UD D SD
4 The aim of mathematics education is to transfer mathematical knowledge in order to apply it in real life. SA A UD D SD
5 The aim of mathematics education is to develop problem solving skills. SA A UD D SD
6 The aims of mathematics education are convincing. SA A UD D SD7 The aims of mathematics education are achievable. SA A UD D SD
8 The aims of mathematics education can be translated into small educational objectives. SA A UD D SD
9The educational objectives of the current curriculum of mathematics are derived from the real aims of mathematics education.
SA A UD D SD
10 The objectives of mathematics education are well defined. SA A UD D SD
11 The objectives of mathematics education are clearly transmitted to teachers. SA A UD D SD
Curriculum
12 The curriculum prepares the students to apply mathematical knowledge in their daily lives. SA A UD D SD
13 The curriculum prepares the students for future vocations. SA A UD D SD
14 The focus of curriculum is on the needs of future education. SA A UD D SD
15 The curriculum is comparable with the curricula of other countries of the region. SA A UD D SD
16 The curriculum is correlated with topics of other subjects. SA A UD D SD17 The curriculum is flexible. SA A UD D SD18 The curriculum reflects state-of-the-art. SA A UD D SD19 The curriculum leads the students to achieve the set aims SA A UD D SD
314
Appendix: I
of mathematics education.
Contents20 Contents of the textbooks are properly sequenced. SA A UD D SD21 Contents of the textbooks develop interest in students. SA A UD D SD22 Contents incite the sense of enquiry in students. SA A UD D SD23 Language of the textbooks is simple. SA A UD D SD
24 Contents have a proper proportion of sums on application of abstract principles of mathematics in real life situations. SA A UD D SD
25Worked examples in the textbooks provide sufficient guidance to solve all the sums given for exercise on that topic.
SA A UD D SD
26
Contents of the textbooks develops:-i) logical reasoning SA A UD D SDii) analytical and critical thinking SA A UD D SDiii) problem-solving skills SA A UD D SDiv) spirit of exploration and discovery SA A UD D SDv) power of concentration SA A UD D SD
27 Contents are in accordance with intellectual level of students. SA A UD D SD
28 Contents cover problems that can be solved by personal investigation without having any method to solve them. SA A UD D SD
29 The contents include a proper proportion of mathematical representations (graphs, figures, diagrams, tables). SA A UD D SD
30 The contents include an appropriate proportion of activities for mental exercise (puzzles/riddles etc.). SA A UD D SD
31The contents are balanced in terms of key areas (number operation, geometry, algebra, measurement, data analysis and probability).
SA A UD D SD
32 Pictures and colorful presentations in the textbooks put a positive effect on students’ conceptual understandings. SA A UD D SD
33 The number of problems on a certain topic given in the textbook affects conceptual understanding positively. SA A UD D SD
34Chaining (bit by bit addition of new material in the sums) on a certain topic in the text booksput a positive effect on conceptual understanding.
SA A UD D SD
35 Contents of the textbooks are properly chained. SA A UD D SDApproaches/Methods
36 The approach of a mathematics teacher should be:-i) The selection, sequence and focus of entire
instructional activities remain on the needs and interests of learner.
SA A UD D SD
ii) The focus remains on content but with an emphasis on the development of understanding of concepts among the learners.
SA A UD D SD
iii) The focus remains on content but with an SA A UD D SD
315
Appendix: I
emphasis on solving problems from textbooks and becoming expert in them.
iv) The focus remains on the maintenance and continuous flow of planned activities in the class with an emphasis of class discipline.
SA A UD D SD
37
I as a mathematics teacher like to: i) solve all the sums from an exercise on the
board SA A UD D SD
ii) solve some questions on the board and let the students do remaining sums in the class SA A UD D SD
iii) explain only important points on the board and encourage students to solve problems with my help
SA A UD D SD
iv) give them problems to solve by their own and help them only when they ask for it SA A UD D SD
v) give problems to groups of students in the class to discussand find solutions SA A UD D SD
38 Sums should be solved usingthe method explained by the teacher only. SA A UD D SD
39 Additional material is usually used for deeper understanding of concepts. SA A UD D SD
40 Additional material is usually used for rigorous drill of learned material. SA A UD D SD
41 Mostly previous exam papers are used as an additional material SA A UD D SD
42 Past papers are solved as a rehearsal for the actual exam papers. SA A UD D SD
43 Past papers are solved because questions of previous papers are considered important. SA A UD D SD
44 Past papers are solved because questions from previous papers often repeat in the new papers. SA A UD D SD
45 Past papers are solved to understand the pattern of questions coming in the recent papers. SA A UD D SD
46 Teacher-constructed problems are presented in the class. SA A UD D SD
47 Students are allowed to construct and present their own problems in the class. SA A UD D SD
48 Procedures of doing a problem are explained but not the reason for the selection of that procedure. SA A UD D SD
49There are some topics in the textbooks that are always left untaught as no question comes in the paper from these topics.
SA A UD D SD
50 Homework is given in order to complete the syllabus as it cannot be completed by solving all the sums in class. SA A UD D SD
51 Completion of a topic means that teacher has explained the topic and students have done the sums in their copies. SA A UD D SD
52 Emphasis is placed on neat and tidy written work. SA A UD D SD
316
Appendix: I
53 Homework is assigned and checked regularly. SA A UD D SD
54 Topics are not explored in depth; only the procedure of doing a sum is explained. SA A UD D SD
55 Unexplained short-cuts are told to solve certain problems. SA A UD D SD
56 Derivation of the formula is not clarified, only the method of its application is explained. SA A UD D SD
57 Usually students avoid checking answers. SA A UD D SD58 Usually students try to skip graph questions. SA A UD D SD
59 Teachers do not emphasize checking of answers by students. SA A UD D SD
60 Teachers do not emphasize checking answers because they have a fear of getting a wrong answer in front of class SA A UD D SD
61 Mathematics has a significant application in other subjects SA A UD D SD
62 Teachers’ true role is to generate a question in the mind of a child before it is answered. SA A UD D SD
63 Both posing questions and giving their answers by teacher himself/herself produce shallow understanding. SA A UD D SD
64 Students can communicate mathematical ideas, reasoning and results. SA A UD D SD
65 Students take teaching of mathematics as a pleasant activity. SA A UD D SD
66 Students exhibit courage in facing unfamiliar problems. SA A UD D SD
67 Students express tolerance in solving difficult problems. SA A UD D SD
68 Retention of learned material in the memory becomes stronger with repetition. SA A UD D SD
69 Repetition of learned material may attach meaningful relationships among the fragments of knowledge. SA A UD D SD
Assessment/Evaluation
70 Tests/Exams are conducted to assess the level of achievement of the instructional objectives. SA A UD D SD
71 Tests/exams are conducted to categorize students into successful and unsuccessful groups. SA A UD D SD
72 The verbal/written remark of a teacher on the basis of assessment is evaluation. SA A UD D SD
73 Assessment helps both teacher and learner in the process of teaching and learning. SA A UD D SD
74 The fear of assessment motivates students to work hard. SA A UD D SD
75 The fear of final examinations is actually the fear of being insulted on its results. SA A UD D SD
76 A teacher is always engaged in the process of assessing his/her students during the class. SA A UD D SD
77 The encouraging remarks of a teacher after assessment produce a positive effect on the performance of students. SA A UD D SD
78 The discouraging remark of a teacher produces a negative SA A UD D SD
317
Appendix: I
effect on the performance of students.
79 Methods of assessment should enable students to reveal what they know, rather than what they do not know. SA A UD D SD
80 Students take mathematics assessments confidently. SA A UD D SD
81 The main purpose of assessment is to improve teaching and learning of mathematics. SA A UD D SD
82 The exam papers assess the objectives of teaching mathematics. SA A UD D SD
83 The exam papers are balanced in terms of content areas. SA A UD D SD
84 The exam papers assess the actual educational objectives of teaching mathematics. SA A UD D SD
85 The system of checking papers is fair. SA A UD D SD86 Examinations are conducted under strict vigilance. SA A UD D SD
87 Use of unfair means in the paper of mathematics is common. SA A UD D SD
88 Grading system of SSC/GCE is appropriate. SA A UD D SD
89 Teachers’ assessment during class is as important as the final examination. SA A UD D SD
90Students’ marks of weekly/monthly/terminal tests are added in the marks of their final exam paper in junior grades.
SA A UD D SD
91 Final examinations assess the factual and procedural knowledge of mathematics only. SA A UD D SD
92 Questions in the exam papers are given according to a set pattern. SA A UD D SD
93 Questions are given from the textbooks in SSC/GCE papers. SA A UD D SD
94 Questions are given from past papers in SSC/GCE papers. SA A UD D SD
95 Some topics from the syllabus may be dropped on the basis of ample choice of questions in the exam paper. SA A UD D SD
96 On the basis of previous papers some questions can be predicted for the upcoming paper. SA A UD D SD
97 Assessment is done to distinguish students for the improvement of learning. SA A UD D SD
98 Test items of SSC/GCE papers cover all objectives of the curriculum. SA A UD D SD
99Sections of exam paper are designed in such a way that questions from particular chapters always come in a specific section.
SA A UD D SD
100 The entire teaching and learning process in the class is designed and implemented to pass the final examinations. SA A UD D SD
318
Appendix: II
Hamdard Institute of Education and Social Sciences
HAMDARD UNIVERSITY KARACHI
A Comparative Analysis of the Effectiveness of Mathematics Curriculum Taught at GCE (O-Level) and SSC System of Schools in Karachi
QUESTIONNAIRE FOR STUDENTS
SECTION I: PARTICULARS ABOUT THE RESPONDENT.
DIRECTIONS: Please fill in the given spaces or tick (√) mark as appropriate from the following:
1. Name(Optional):-----------------------------------------------------------------------------------
2. Class: ----------------------- GCE (O-Level): -------------------- SSC (Matric) -------
3. Name of Institution: -------------------------------------------------------------------------------
4. Location of Institution: ----------------------------------------------------------------------------
5. System of Education in the Institution (GCE/SSC/Both):------------------
vi) Age: ---------------------years.
7. Gender: a) Male: ---------- b) Female: ----------
8. Qualification of Parents: a) Father: i) Graduate: ------------- ii) Undergraduate: --------
b) Mother: i) Graduate: ------------- ii) Undergraduate: --------
9. Area of Residence: -----------------------------------------------------------------------------------------
10. District: -----------------------------
319
Appendix: II
SECTION II: CURRICULUM-EFFECTIVENESSSCALE
DIRECTIONS: Please tick (√) mark as appropriate from the following columns:SA=Strongly Agree, A=Agree, UD=Undecided, DA=Disagree, SD=Strongly Disagree.
Sr.# ItemsGeneral
1 Mathematics is an interesting subject. SA A UD D SD2 I feel pleasure in doing mathematics. SA A UD D SD
3 I do mathematics because teachers emphasize its importance. SA A UD D SD
4 I do mathematics because it is a compulsory subject at school level. SA A UD D SD
5 Mathematics demands rigorous practice. SA A UD D SD6 Mathematics requires concentration. SA A UD D SD7 High achievers in mathematics argue strongly. SA A UD D SD8 High achievers in mathematics are good analysts. SA A UD D SD9 High achievers in mathematics raise more questions. SA A UD D SD
10 School gives a special emphasis on mathematics over the other subjects. SA A UD D SD
11
What is your view about mathematics as a subjecti) its contents are useless in daily life SA A UD D SD
ii) it is difficult to memorize the formulae SA A UD D SDiii) there is useless repetition of similar sums SA A UD D SDiv) it requires a lot of time for practice SA A UD D SD
12 High achievers in mathematics also achieve high grades in other science subjects. SA A UD D SD
13 Doing mathematics means doing mental exercise. SA A UD D SD
14 Correct solution of a problem gives a feeling of achievement. SA A UD D SD
15
Mathematics is very important subject becausei) it trains the mind SA A UD D SD
ii) it is compulsory to pass this subject for getting promotion in next grade at school level SA A UD D SD
iii) it is largely applied in admission tests at higher education level SA A UD D SD
iv) it is applied in many other subjects SA A UD D SD16 Mathematics is a scoring subject. SA A UD D SD
Textbooks/Contents17 Textbooks of mathematics have an attractive look. SA A UD D SD
18 Language used in the textbooks is clear. SA A UD D SD
320
Appendix: II
19 Language of mathematics textbooks is difficult because excessive mathematical terminologies are used. SA A UD D SD
20 All the topics in the textbooks are taught completely for the preparation of final examination. SA A UD D SD
21 Methods to solve different types of problems are explained through worked examples in the textbooks. SA A UD D SD
22 Textbooks are illustrated with concept-related pictures from real life. SA A UD D SD
23 The pictures facilitate in comprehending the concepts. SA A UD D SD24 Diagrams are the frightening element of the textbooks. SA A UD D SD
25 I can study a new topic through worked examples provided in the textbook. SA A UD D SD
26 I study the topic from the textbook first before it is explained by the teacher in class. SA A UD D SD
27 I have questions in mind before starting a new lesson. SA A UD D SD28 Only the contents explained by teacher should be studied. SA A UD D SD
29
It is to memorize in mathematicsi) formulae SA A UD D SD
ii) steps of long procedures SA A UD D SDiii) definitions SA A UD D SDiv) proofs of geometrical theorems SA A UD D SD
30 Contents of the textbooks are in accordance with intellectual level of students. SA A UD D SD
31 Language of the textbooks is in accordance with language proficiency of students SA A UD D SD
Learning Experiences
32 Getting afraid of a problem in the first look makes it very difficult to solve. SA A UD D SD
33 Doing important topics is better than doing all the topics in order to get good marks. SA A UD D SD
34 The last questions (star questions) of the exercises are generally left unsolved. SA A UD D SD
35
To solve a mathematics problem we think i) to retrieve formula and method from memory SA A UD D SD
ii) to develop our own strategy to solve the problem SA A UD D SD
iii) to get an insight(idea/clue) for solution SA A UD D SDiv) to recall from which chapter and exercise
number the problem belongs SA A UD D SD
36 Most of the teachers emphasize solving the sums using their explained methods only. SA A UD D SD
37 There is more than one method to solve a problem. SA A UD D SD
38 Most of the teachers emphasize neat and tidy work. SA A UD D SD
321
Appendix: II
39
Drawing graphs isi) difficult SA A UD D SD
ii) boring SA A UD D SDiii) time consuming SA A UD D SDiv) annoying SA A UD D SD
40 Additional material (worksheets/workbooks etc.) is used to get further practice of the sums. SA A UD D SD
41 Teacher-constructed problems are presented in the class. SA A UD D SD42 Separate activities are done for low achievers in the class. SA A UD D SD
43 Teachers arrange activities to engage high achiever students to help their low achiever class fellows. SA A UD D SD
44 In a mathematics class of 40 minutes, students normally ask less than 5 questions. SA A UD D SD
45 In a mathematics class of 40 minutes, teachers normally explain for less than 15 minutes. SA A UD D SD
46 Students mostly ask ‘HOW’ type questions (How to solve it? / How to use it?) in the class. SA A UD D SD
47 ‘WHY’ type questions (Why this method is used?) are rarely posed by students. SA A UD D SD
48 Teachers do not encourage ‘WHY’ type questions in the class. SA A UD D SD
49 Procedure of doing a problem is explained but not the reason for the selection of that procedure. SA A UD D SD
50 Some topics of the textbooks are never taught. SA A UD D SD
51 Homework is assigned in order to complete the syllabus as it cannot be completed by solving all the sums in class. SA A UD D SD
52Completion of a topic means that teacher has explained the topic and students have done the sums in their notebooks.
SA A UD D SD
53 Homework is assigned and checked regularly by the teachers. SA A UD D SD
54 Classwork of students is checked regularly by the teachers. SA A UD D SD
55 Topics are not explored in depth; only the procedure of doing a sum is explained. SA A UD D SD
56Short cut techniques are explained to solve certain problems but the logical reasons behind adopting these techniques are not explained.
SA A UD D SD
57 Derivation of formula is not explained only the method of its application is told. SA A UD D SD
58 The activities of mathematics class are largely doing repetition of similar sums. SA A UD D SD
59 Reference books are taken from the library to explore the topics in depth. SA A UD D SD
322
Appendix: II
60
Teachers teach mathematicsi) by explaining some problems from an exercise
in the textbook on the boardSA A UD D SD
ii) by explaining all the problems from an exercise in the textbook on the board SA A UD D SD
iii) by explaining the important procedures and points on the board and helping students in solving sums individually
SA A UD D SD
iv) by giving students well-structured problems and facilitating them in finding their solutions by their own methods
SA A UD D SD
61
A good teacher of mathematics is that who:i) Starts a lesson with the revision of previous
workSA A UD D SD
ii) Presents an uninteresting thing in an interesting way SA A UD D SD
iii) Makes difficult things easy SA A UD D SDiv) Explains a lengthy topic very concisely SA A UD D SDv) Keeps the students alert and attentive by
creating humor or by interesting stories SA A UD D SD
vi) Gives encouraging feedback to students SA A UD D SDvii) Engages all the class in work SA A UD D SDviii) Ends a lesson with summarization SA A UD D SD
Tests/ Examinations62 Assessments help in confidence building. SA A UD D SD63 Assessments help in identifying and reducing mistakes. SA A UD D SD64 Assessments help in the preparation of final examinations. SA A UD D SD
65 Quizzes (short tests based on calculations without using calculators) are conducted regularly in the class. SA A UD D SD
66 Speed tests are conducted regularly in the class. SA A UD D SD
67 Positive remarks of the teacher on student’s assessment produce better results. SA A UD D SD
68 Negative remarks by a teacher on student’s assessment produce demoralization. SA A UD D SD
69 I am well aware of the pattern of SSC/GCE paper. SA A UD D SD
70 Students study seriously under the pressure of tests/examinations. SA A UD D SD
71 Teachers leave some topics completely on the basis of their insignificance in the SSC/GCE paper. SA A UD D SD
72 Questions in SSC/GCE papers are given according to a fixed pattern. SA A UD D SD
73 Questions are taken from the textbooks in SSC/GCE papers. SA A UD D SD
74 Questions are taken from past papers in SSC/GCE papers. SA A UD D SD
323
Appendix: II
75 Some topics from the syllabus may be dropped on the basis of sufficient choice of questions in the exam paper. SA A UD D SD
76 Some questions can be predicted for the upcoming paper on the basis of previous. SA A UD D SD
77
Revision for mathematics test/ examination is done byi) solving all sums on the topic from the textbook SA A UD D SD
ii) solving different types of sums from the exercises in the textbooks SA A UD D SD
iii) solving sums from the past papers (five years) SA A UD D SDiv) reading solved sums from the notebooks (notes
maintained in the form of solution of sums) SA A UD D SD
v) reading worked examples from the textbooks SA A UD D SD
78 In junior grades (VI – VIII); the final paper is set from the whole syllabus. SA A UD D SD
79 In junior grades (VI – VIII); the final paper is set from the topics covered in the final term only. SA A UD D SD
80 In junior grades (VI – VIII); the topics assessed in one terminal examination do not come in the next term. SA A UD D SD
324
Appendix: III
INTERVIEW PROTOCOL
FOR EXPERTS OF THE SUBJECT
1. Name (optional):-----------------------------------------------------------------------------------
2. Qualifications: a) Academic: ---------------------------------
b) Professional: ------------------------------
3. Designation: --------------------------------------------
4. Name of Institution: -------------------------------------------------------------------------------
5. Control of Institution: a) Government: ------------------------
b) Private: -------------------------------
6. Experience (in years): a) Teaching: --------------------------------------------------------
b) Other (Please mention): ---------------------------------------
7. Please specify the system (GCE/SSC) for which you are responding: -------------------
Q.1 Are you satisfied with the current routine of teaching mathematics at school level? If not, what are your reservations?---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Q.2 Is teaching of mathematics according to some clear objectives? If yes, then according to your observation, what is themajor objective?-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
325
Appendix: III
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Q.3 Do you agree that these objectives can fulfill the true aims of mathematics education?-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Q.4 Do you agree that mathematics education in Pakistan is competitive with the other countries of Asia?--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Q.5 Do you agree that mathematics should be the prime focus of school curriculum as it develops cognitive, affective and psychomotor faculties of an individual ?-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Q.6 Are you satisfied with the contents of textbooks of mathematics used at secondary level?--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Q.7 What changes would you like to suggest to improve these textbooks?-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
326
Appendix: III
Q.8 Are you satisfied with the current methods of selection and sequencing of contents? If not, please give your opinion.---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Q.9 In your opinion, what changes should be made in the approaches and methods of teaching mathematics?--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Q.10 Are you satisfied with current system of assessment in mathematics at school level? If not, please suggest some changes.----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Q.11 Are you satisfied with the current pattern of mathematics paper (GCE/SSC)? In your opinion, what improvements should be made in it?----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Q.12 What are the major strengths of the current system of teaching and learning mathematics in your opinion?------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
327
Appendix: III
Q.13 What are the major weaknesses in your opinion in the current system of mathematics education?-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Q.14 What changes would you like to suggest for the overall improvement of mathematics education?-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
328
Appendix: IV
INTERVIEW PROTOCOLResponses of the Subject Experts
Interview: 1 System: SSC Institution: Private Designation: HM
Qualification: B.Sc. M.EdTeaching Experience: 45 years Gender: Male
Q. Nos. Responses
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
Unsatisfied because objectives of teaching are not coherent with the needs of students and
society.
Agreed, objective is to provide basic knowledge to study this subject in higher classes.
Disagreed.
Disagreed.
Agreed.
Unsatisfied.
New topics should be added on everyday mathematics. Word problems sould be increased and
examples in the textbooks should be improved.
Sequence of contents is not proper at lower secondary and secondary level.
Teaching should be activity-based
Unsatisfied. We mostly rely on final examinations. It will be better to use forrmative
assessment system.
Pattern of paper should be such that it discourages guess work and selected-content study
habit.
It provides strong factual and procedural knowledge of different operations in mathematics.
Syllabus is too lengthy for a 9-month session.
Curriculum should be revised and its expected learning outcomes should
be transmitted to teachers. Moreover, pattern of SSC paper should be
changed to assess the level of attainment of true objectives of the
curriculum. Refresher courses should be conducted for teachers.
329
Appendix: IV
INTERVIEW PROTOCOLResponses of the Subject Experts
Interview: 2 System: SSC Institution: Private Designation: HM
Qualification: B.Sc. MEdTeaching Experience: 35 years Gender: Male
Q. Nos. Responses
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
Unsatisfied because mostly untrained teachers are teaching mathematics in most of the schools
Agreed.
Disagreed.
Disagreed.
Agreed.
Satisfied.
Word problems on everyday mathematics should be included and increased.
Sequence of contents needs improvement.
Activity-based teaching willbe more productive than the routine teaching.
Discourage rote memorization of contents by giving application based problems as much as
possible.
Vigilance system during SSC examinations should be improved.
The system develops among students, a skill of presenting their learned material in a well-
organized and orderly manner.
There is a discontinuation of one complete year for the study of
mathematics in the system. Students after class VIII study mathematics in
class X. The suspension of mathematics in grade IX is the biggest weakness
of the current system.
Teaching of mathematics should be made uninterrupted by eliminating the one year suspension
of mathematics during class IX. Refresher courses should be organized.
330
Appendix: IV
INTERVIEW PROTOCOLResponses of the Subject Experts
Interview: 3 System: SSC Institution: Private Designation: HM
Qualification: M.ScM.EdTeaching Experience: 21 years Gender: Male
Q. Nos. Responses
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
Unsatisfied because there is a discontinuation of one year in its teaching. This subject is not
taught in grade IX which creates problems in the conceptual understanding of students.
Agreed, objective is to continue this subject in higher grades.
Disagreed.
Disagreed.
Agreed.
Unsatisfied.
Textbooks should be updated regularly. Worked examples in the textbooks should be
improved.
Improvement in the sequence of contents of the textbook is required.
Teaching with the aid of technology (audio-video aides, internet etc.) is required.
Understanding of students should be checked rather than checking that the student can solve a
sum or not.
System of assessing papers should be improved. Examinations should be conducted under
strict care to control the increasing trend of cheating.
It provides strong content knowledge for further studies.
Discontinuation of mathematics in grade IX is the major weakness.
Textbooks should be revised. Mathematics should be taught without a break during school
education. It should be taught in Karachi Board during grade IX like Federal Board and all the
Boards of the province Punjab.
331
Appendix: IV
INTERVIEW PROTOCOLResponses of the Subject Experts
Interview: 4 System: SSC Institution: Private Designation: HOD
Qualification: M.ScTeaching Experience: 15 years Gender: Male
Q. Nos. Responses
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
Satisfied
Undecided
Agreed
Agreed
Other subjects should also be given equal importance.
Satisfied.
New topic should be included in the textbook.Textbooks should be activity-based that can
develop interest among students.
Selection and sequencing of content should be made according to educational needs of the
students.
Mathematics should be taught just like a language.
Textbooks sums should not be given in the papers.
Satisfied, but exams should be conducted under proper supervision and use of unfair means
should be controlled.
It provides basic knowledge of mathematical procedures and formulae.
Use of unfair means in the examination is the biggest problem of this
system.
Curriculum and textbooks should be revised.
332
Appendix: IV
INTERVIEW PROTOCOLResponses of the Subject Experts
Interview: 5 System: SSC Institution: Private Designation: HOD
Qualification: M.Sc M.EdTeaching Experience: 27 years Gender: Male
Q. Nos. Responses
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
Not satisfied, as there is a shortage of trained teachers who can teach mathematics in a
professional manner.
Disagreed, objective is to make students learn formulae and procedures to solve different kinds
of problems.
Disagreed.
Disagreed.
Agreed.
Unsatisfied.
Word problems designed to apply mathematical concepts in real life situations should be
increased.
Selection of contents should be made accordingly with the sequence of the textbooks.
Emphasis is mostly given on the product but the process is also as important as the product.
Rote memorization should be discouraged by increasing word problems in the textbooks.
Workshops and refresher-courses should be organized for paper setters and checkers.
It develops a habit of doing neat and tidy work in students. It develops a sense of responsibility
by maintaining notes (solution of problems) and making them checked from their teachers
regularly.
System of current examination encourages cramming.
Improving the assessment system and improving the contents of the textbook.
333
Appendix: IV
INTERVIEW PROTOCOLResponses of the Subject Experts
Interview: 6 System: SSC Institution: Private Designation: HOD
Qualification: M.Sc B.Ed Teaching Experience: 23 years Gender: Male
Q. Nos. Responses
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
Schools lack in educational resources required to teach students properly.
Agreed.
Disagreed.
Disagreed.
Agreed.
Satisfied.
Word problems in the texbooks should be increased. Textbooks’ worked examples should be
improved.
Sequence of the textbook should be used.
Teaching of mathematics should be activity based.
Don’t give textbook sums in the asssessments. Assessment items should be made with a great
care.
Questions should neither be taken from textbooks nor from the previous year’s papers.
It provides enough knowledge required to continue this subject in higher classes.
Examinations are not conducted under proper vigilance. System of paper setting and its
assessment also needs improvement. Taking textbook questions in the internal school papers as
well as in SSC papers is the major weakness.
Making neutral places as centers of examination to curb the problem of cheating.
334
Appendix: IV
INTERVIEW PROTOCOLResponses of the Subject Experts
Interview: 7 System: SSC Institution: Private Designation: Sn. Teacher
Qualification: M.Sc B.EdTeaching Experience: 30 years Gender: Female
Q. Nos. Responses
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
Not satisfied, there is a need of computer assisted instruction (CAI) to teach mathematics
effectively.
Agreed, syllabus is designed to further this subject in higher grades.
Undecided.
Disagreed.
Agreed.
Satisfied
Word problems designed to apply mathematical concepts in real life situations should be
increased.
Not satisfied, textbook sequence is better to use.
Project-based teaching should also be introduced in the current practice of teaching.
Assessment should check the understanding of concepts rather than checking the memorization
of contents.
Pattern of the paper should be such that it promotes comprehensive study habit.
Provides knowledge of basic operations and procedures.
System encourages rote learning and promotes an approach of studying
important topics rather than the entire syllabus.
Improvement should be made in the textbooks and in the examination system.
335
Appendix: IV
INTERVIEW PROTOCOLResponses of the Subject Experts
Interview: 8 System: SSC Institution: Private Designation: HOD
Qualification: M.Sc B.EdTeaching Experience: 28 years Gender: Male
Q. Nos. Responses
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
Satisfied
Agreed, enable students to do basic operations and calculations of mathematics.
Agreed.
Agreed.
Agreed.
Yes, but some topics like number sequence, probability, etc. should be included.
In lower grades, too many books of different publishers are used and schools frequently
change these books. If a series of textbooks is used in one year and next year is replaced by
another series, it will affect the logical sequence of contents and vertical integration of
concepts
Selection is made taking topics from the three key areas (arithmetic, algebra, geometry) but the
prime concern of this selection is to ensure making a balanced question paper for terminal/half-
yearly examination.
Step by step instructions should be given instead of giving the key to open the lock (a method
to solve the problem).
Sums should not be taken from textbooks or previous papers. Teacher should construct their
own problems to give in assessments.
Pattern of paper should be such that students use their skills to solve problems rather than
learning and reproducing them.
It provides a rich knowledge of mathmatical language, terminologies, symbols, formulae and
procedures.
System encourages selected study of some topics, leaving some of the topics completely untouched.Assessment system should be improved.
336
Appendix: IV
INTERVIEW PROTOCOLResponses of the Subject Experts
Interview: 9 System: SSC Institution: Designation: Sn. Teacher
Qualification: M.Sc M.EdTeaching Experience: 16 years Gender: Female
Q. Nos. Responses
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
Satisfied
Agreed.
Agreed.
Agreed.
Agreed.
Yes, but problem is not with the contents. It is with the methods of teaching and assessment.
Textbooks should be revised.
Teachers select contents from three areas arithmetic, algebra and geometry to make a balanced
paper.
Activity based and project based teaching should be started with the routine teaching methods.
Satisfied, but the habit of using unfair means during examination sould be controlled.
Vigilance during examinations should be made better.
------------
Massive use of unfair means is the major problem.
Revision of curriculum, improvement in the textbooks and strict
examination system.
337
Appendix: IV
INTERVIEW PROTOCOLResponses of the Subject Experts
Interview: 10 System: SSC Institution: Private Designation: Sn. Teacher
Qualification: M.Sc M.EdTeaching Experience: 35 years Gender: Male
Q. Nos. Responses
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
Not fully satisfied because there is shortage of resources in schools
Disagreed, objectives are not clear to teachers. The only objective in my opinion is to make
students memorize the contents and procedures to get good marks in the SSC examination.
Undecided.
Undecided.
Agreed but only if our teaching touches theses domains. The current focus is on contents only.
Unsatisfied.
Books of same publisher should be used. It is better to use the books of Sindh Textbook Board
in lower grades also.
Not fully satisfied, it is done in a sitting of teachers where the selection, elimination and
sequence of contents are made according to their choice and feasibility of completing it within
the available time.
Teachers should have to address all the cognitive levels in their teaching (knowledge,
comprehension, application, analysis, synthesis and evaluation).
Formative assessment should be used. Application based sums should be increased. The
present routine of taking problems from textbooks is increasing the trend of rolte learning.
Teachers should be trained and their knowledge about test construction and assessment should
be updated.
Enables the students to do computation with knowledge of long procedures and formulae.
There is a wide gap of standards between SSC and HSC.
338
Appendix: IV
14. Without a fair and vigilant examination and consistent assessment system no improvement can
be made in the standards of education.
INTERVIEW PROTOCOLResponses of the Subject Experts
Interview: 1 System: GCE Institution: Private Designation: HOD
Qualification: M.Sc Teaching Experience: 15 years Gender: Male
Q. Nos. Responses
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
The syllabus is too lengthy
Agreed, objective is to prepare students for CIE.
Agreed.
Not fully agreed.
Agreed.
Unsatisfied.
To cover all the topics of O-Level mathematics syllabus the books have an addendum at the
end of each book. It will be better if all the contents given in the addendum are incorporated
into the main part of the books.
It should be done on logical grounds.
Spend maximum time of your teaching in building basic concepts. Emphasize mental
calculations and practice of learned concepts.
Agreed, but tests should be held more frequently.
Agreed, but selective study habit should be discouraged.
A standardized, fair and unbiased system of assessment.
It is not for majority of students.
This system should be made available to as many students students as possible.Coursework
should be included because syllabus is too lengthy.
339
Appendix: IV
INTERVIEW PROTOCOL
Responses of the Subject Experts
Interview: 2 System: GCE Institution: Private Designation: HOD
Qualification: M.Sc Teaching Experience: 17 years Gender: Male
Q. Nos. Responses
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
Unsatisfied because increasing trend of private tutions of this subject is reducing the interest of
students in the class.
Agreed, making students able to think and making them good problem solvers.
Agreed.
Mathematics education is much better in Singapure and other Asian countries like China,
Japan etc.
Agreed.
Yes, books are not written locally. They serve the needs in terms of contents but it will be
better if books are written by local authors.
Reference books should be used instead of textbooks keeping in view the needs of students.
In the process of selection and its sequencing, no special consideration is made on the
prerequisites, interests and needs of students.
Activities in the class should be increased and made more interesting. Practice is very
important in mathematics.
More quizzes and mental maths tests should be administered.
It should test deeper understanding instead of basic knowledge.
It is internationally recognized.
Excessive use of private tuitions is the major problem in this system.
Discouraging the increasing trend of selective studyand private tuitions.
340
Appendix: IV
INTERVIEW PROTOCOLResponses of the Subject Experts
Interview: 3 System: GCE Institution: Private Designation: Sn. Teacher
Qualification: M.Sc B.Ed. Teaching Experience: 15 years Gender: Male
Q. Nos. Responses
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
Satisfied.
Agreed, enable students to think within the horizon before thinking beyond the horizon.
Agreed.
Agreed.
Agreed.
Satisfied.
Books of local authors should be used. Moreover, reference books should be used instead of
textbooks keeping in view the needs of students.
Selection and sequencing of contents should be based on interests and needs of students.
Preference should be given to mental calculations and use of calculators be minimized. Basic
operations and procedures should be taught properly.
Satisfied.
Satisfied.
Paper is balanced in terms of calculations done mentally (Paper-I) and using calculators
(Paper-II).
It is very expensive and not for masses.
Schools should play their role to discourage the trend of private tutions.
341
Appendix: IV
INTERVIEW PROTOCOLResponses of the Subject Experts
Interview: 4 System: GCE Institution: Private Designation: HOD
Qualification: M.ScTeaching Experience: 35 years Gender: Female
Q. Nos. Responses
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
Satisfied.
Agreed, objective is to prepare students for GCE exam
Undecided.
Agreed.
Agreed.
Satisfied.
Topic given in the addendum separately should be incorporated in the textbooks.
The organization of contents should be coherent.
Computer Assisted Instruction (CAI) should be introduced. Practice should be maximized.
Teachers should construct their own problems rather than taking them from past papers.
More application based questions should be included.
It is internationally recognized.
It is very expensive.
Trend of crash-courses at different private tuition centers should be discouraged.
342
Appendix: IV
INTERVIEW PROTOCOLResponses of the Subject Experts
Interview: 5 System: GCE Institution: Private Designation: Sn. Teacher
Qualification: M.Sc PGCCTeaching Experience: 17 years Gender: Male
Q. Nos. Responses
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
Satisfied.
Agreed, provision of basic mathematical knowledge a prerequisite for higher studies.
Agreed.
Agreed.
Agreed.
Satisfied.
Use of referencebooks is better than using textbooks according to the needs of students.
The selection and arrangement of contents should be logical based on the needs of students.
It is better to teach a small content in depth than teaching a large number of topics
superficially.
Satisfied.
Satisfied.
A strict and vigilant examination with a fair assessment system is its major strength.
Very lengthy syllabus.
A coursework should be incorporated in the curriculum.
343
Appendix: IV
INTERVIEW PROTOCOLResponses of the Subject Experts
Interview: 6 System: GCE Institution: Private Designation: Sn. Teacher
Qualification: M.Sc B.Ed Teaching Experience: 25 years Gender: Male
Q. Nos. Responses
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
Satisfied.
Agreed, objective is to make students able to pass GCE exam with excellent grades.
Agreed.
Agreed.
Agreed.
Satisfied.
Books should be written by local authors. Refernce books should be used according to the
needs of students.
It should be done sensibly with the need of the learners.
Students should be made confident by rigorous practice of sums. Calculators should be used
but not unnecessarily.
Satisfied, but number of tests/assessmentsshould be increased.
Satisfied, but application based problems should be increased.
There is room to incorporate different methods of teaching in this system.
Private tutions are taken excessively in this system and this trend is increasing day by day.
Discouraging the trends of tuitions especially shortcuts (crash-courses) at different private
tuition centers. Contents that produce thinking skills should be increased.
344
Appendix: IV
INTERVIEW PROTOCOLResponses of the Subject Experts
Interview: 7 System: GCE Institution: Private Designation: Sn. Teacher
Qualification: B.Sc M.Ed. Teaching Experience: 15 years Gender: Female
Q. Nos. Responses
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
Satisfied.
Agreed, objective is to develop thinking skills.
Agreed.
In my opinion, mathematics education in Pakistan needs improvement.
Agreed.
Unsatisfied.
Content on number sequence and problem solving should be increased.
Contents should be organized on the basis of interests and needs of students.
Basic concepts should be taught and revised periodically. Practice and application of basic
concepts repeatedly makes students confident.
Small-scale asssessments should be organized regularly and periodically.
Satisfied.
Examinations are conducted under strict vigilance. There is no chance of using unfair means.
It is based on (2+ 2.5) hour’s performance of students. Learning of
students in previous 4 years should to be incorporated.
Discouraging the trend of selectivestudy andincreasing the contents that enhance critical
thinking skills.
345
Appendix: IV
INTERVIEW PROTOCOLResponses of the Subject Experts
Interview: 8 System: GCE Institution: Private Designation: Sn. Teacher
Qualification: M.Sc B.Ed Teaching Experience: 16 years Gender: Male
Q. Nos. Responses
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
Satisfied.
Agreed, prepare students for higher learning giving them first-hand knowledge.
Agreed.
Agreed.
Agreed.
Satisfied.
A teachers’ manual should be published with each book for their guidance.
The selection of content should be done on the basis of needs of students.
Activities in classes should be increased.
Satisfied.
Satisfied.
A standaradrized system of assessing papers is the major strength of this system.
Syllabus is too lengthy.
This system should be within reach of common people.
346
Appendix: IV
INTERVIEW PROTOCOLResponses of the Subject Experts
Interview: 9 System: GCE Institution: Private Designation: HOD
Qualification: M.Sc B.Ed Teaching Experience: 16 years Gender: Male
Q. Nos. Responses
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
Satisfied.
Agreed, objective is to prepare students for CIE
Agreed.
Agreed.
Agreed.
Unsatisfied.
Answers of graph and loci questions should be given in the form of constructed graphs and
geometrical figures respectively.
It should focus the need of students.
Practice of learned concepts should beincreased.Calculations should be done mentally
avoiding calculators as much as possible.
Satisfied.
Satisfied.
Flexibility of appearing for CIE paper is its strength. Students can appear in the examination
either in May or November, twice in a year.
The system is expensive.
Increasing the contents that improve thinking skills.
347
Appendix: IV
INTERVIEW PROTOCOLResponses of the Subject Experts
Interview: 10 System: GCE Institution: Private Designation: Sn. Teacher
Qualification: M.Sc PGCC Teaching Experience: 22 years Gender: Male
Q. Nos. Responses
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
Satisfied.
Agreed, objectives are to enhance thinking skills of students.
Agreed.
Agreed.
Agreed.
Yes but the names of persons and places are not familiar to our students. If these are familiar,
students can mentally visualize the context of that problem and learning of the concept
becomes more concrete.
It is better if the books are written by local authors.
The method of selection and sequencing of contents should be based on needs of students.
Teach the students to use the (FFF) approach in solving a problem i.e. face it, fight it and
finish it.
Satisfied, but the number of quizzes and class tests should be increased.
Satisfied, but selective learning should be discouraged.
It requires a comprehensive study and does not allow leaving atopic from the entire prescribed
syllabus.
Syllabus is very lengthy.
Coursework should be included along with the final paper.Contents that developreasoning
348
Appendix: IV
skills should be increased.
349
Appendix: V
PILOT TESTING
COMPUTATION OF PEARSON’S ‘ r ’
a) Computation of Pearson’s ‘r’ for Teachers’ Questionnaire
X (SSC) Y (GCE) X2 Y2 XY
417 410 173889 168100 149720
380 433 144400 173889 136524
500 464 250000 215296 156364
507 455 257049 207025 156348
519 473 269361 223729 155769
429 441 184041 194421 165505
471 450 221841 202500 180188
ƩX=3223 ƩY=3126 ƩX2=1500581 ƩY2=1398620 ƩXY=1444821
Formula
r = NƩxy−(Ʃx)(Ʃy)
√[ NƩ x2−(Ʃx )2 ] [ NƩ y2−( Ʃy )2 ]
Calculations
350
Appendix: V
r = 7(1444821)−(3223)(3126)
√[7 (1500581)−(3223 )2 ] [7(1398620)−(3126 )2 ]
r = 10113747−10075098√ [10504067−10387729 ] [ 9790340−9771876 ]
r = 38649√ [116338 ] [ 18464 ]
r = 38649√2148064832
r = 3864946347.220
r = 0.834
b) Computation of Pearson’s ‘r’ for Students’ Questionnaire
351
Appendix: V
X (SSC) Y (GCE) X2 Y2 XY
403 388 162409 150544 149720
372 367 138384 134689 136524
419 395 175561 156025 156364
421 428 177241 183184 156348
394 380 155236 144400 155769
404 387 163216 149769 165505
411 379 168921 143641 180188
ƩX=2824 ƩY=2724 ƩX2=1140968 ƩY2=1062252 ƩXY=1100418
Formula
r = NƩxy−(Ʃx)(Ʃy)
√[ NƩ x2−(Ʃx )2 ] [ NƩ y2−( Ʃy )2 ]
Calculations
r = 7(1100418)−(2824)(2724 )
√[7 (1140968)−(2824 )2 ] [7(10622520)−(2724 )2 ]
r = 7702926−7692576√ [7986776−7974976 ] [74357640−7420176 ]
r = 10350√ [11800 ] [ 15588 ]
352
Appendix: V
r = 10350√183938400
r = 1035013562.389
r = 0.763
353
Appendix: VI
SYLLABUS (SSC)MATHEMATICS
Part-I
1. Sets
- Revision of the work done in the previous classes.- Notation of Sets, subset and its types, power set, Exercises.- Operations on Sets; their properties and Venn-Diagram, Exercises.- Cartesian product, Exercises.- Binary Relations; domain and range. - Functions, types of functions, Exercises.- Cartesian coordinate system for a plane, Exercises.- Graphical representation of Cartesian product, Exercises.
2. System of Real Numbers, Exponents and Radicals
- Properties of Rational Numbers, Decimal fractions as Rational and Irrational Numbers - Properties of Real Numbers- Properties of equality and inequality of Real Numbers, Exercises- Exponent, Laws of exponents, Exercises- Concept of Radicals and Square Root of a Positive Real Number, Exercises- The nth Root of a Positive Real Number, Exercises- Rational Exponents, Exercises- Surds, Exercises
3. Logarithms
- Scientific Notation, Exercises- Definition of Logarithm, Exercises- Laws of Logarithms, Exercises- Common Logarithms, Exercises- Anti Logarithms, Exercise- Application of Logarithms in Computations, Exercises
4. Algebraic Expressions
- Variables and Constants, Coefficient, Algebraic expressions and their kinds, Exercises- Polynomials, Classification of polynomials, Exercises- Order of Algebraic Expressions, Exercises- Value of Algebraic Expressions, Exercises
354
Appendix: VI
- Fundamental Operations on Algebraic Expressions, Exercises- Remainder Theorem, Exercise- Formulae and Their Applications, Exercise
5. Factorization, H.C.F, L.C.M, Simplification and Square Roots
- Revision of the work done in the previous classes, Exercises- Factorization of the Form;a2−b2, Exercises- Factorization of the Form; x2+bx+c, Exercises- Factorization of the Form; a3+b3and a3−b3 ,Exercises- Factorization of the Form; a3+b3+c3−3 abc ,Exercises- Factorization of the Form; a2 (b−c )+b2 (c−a )+c2 ( a−b ) ,Exercises- Factorization using Remainder Theorem, Exercises- H.C.F. and L.C.M., Exercises- Simplification of Algebraic Fractions, Exercises- Square Root by Division method, Exercise
5. Matrices
- Introduction, Notation, Order of a Matrix, Exercises- Types of Matrices, Exercises- Transpose, Addition and Subtraction of Matrices, additive Inverse, Exercises- Multiplication of Matrices, Exercises- Determinant, Adjoint and Multiplicative Inverse of a Matrix, Exercises- Solution of two Simultaneous Linear Equations using Matrices, Exercises- Cramer’s rule, Exercises
6. Fundamental Concepts of Geometry
- Inductive and Deductive Reasoning- Characteristics of Deductive Reasoning- Basic Concepts Definitions and Postulates, Exercise
7. Demonstrative Geometry
- Theorems on Lines and Polygons- Methods of proofs of Theorems-Theorems their Proofs and an Exercise after each theorem
8. Practical Geometry
- Revision of Construction of Triangles, Exercises-The Ambiguous Case of Construction of a Triangle, Exercise- Constructions of Right Bisectors of Sides of a Triangle, Exercises-Construction of Angle Bisectors, Median and Altitudes in a Triangle, Exercises
355
Appendix: VI
SYLLABUS (SSC)MATHEMATICS
Part-II
1. Algebraic Sentences
- Solution of Simple Linear Equations in One or Two Variables, Exercises- Graphical solution of two simultaneous Linear Equations, Exercises- Solution of Equation Involving Radicals in One Variable, Exercises- Solution of Equation Involving Absolute Value in One Variable, Exercises- In equations, Exercises- Solution of Quadratic Equations by Factorization, Completing Square Method or by Quadratic Formula, Exercises
2. Elimination
- Concepts- Elimination of One Variable from Two Equations, Exercises
3. Variations
- Basic Concepts of Ratio, Proportion and Variation, Exercises- K-Method and Theorems on Proportion, Exercises- Properties of Proportions, Exercises- Word Problems, Exercises
4. Information Handling
- Introduction, Definitions of Key Terms, Types of Variables, Types of Data- Collection and Presentation of Data- Frequency Distribution, Graphs (Histogram and Frequency Polygon), Exercises- Bar Graphs, Pie Diagrams, Exercises- Measures of Central Tendency (Mean, Median and Mode), Their Merits &Demerits, Exercises- Dispersion and its Measures (Variance and Standard Deviation), Their Merits &Demerits, Exercises
356
Appendix: VI5. Fundamental Concepts of Geometry
- Basic Concepts of Circle (Circumference, Chord, Secant, Tangent, Exercises- Circum-circle, Inscribed Circle and Escribed Circle of a Triangle, Exercises- Theorems on Circles, Exercises
6. Demonstrative Geometry
- Introduction- Theorems, Exercises after every Theorem
7. Practical Geometry
- Constructions (Circum-circle, Inscribed circle and Escribed Circle), Exercises- Tangent to a Given Circle from a Point outside the Circle, Direct Common Tangents to Two Given Circles and Transverse Common Tangents to Two Given Circles, Exercises
8. Trigonometry
- Introduction- Trigonometric Ratios of Acute Angles - Values of Trigonometric Ratios of Angles of (300 ,450 ,600 ¿ ,Exercises- Trigonometric Identities, Exercises- Solution of a Right Triangle, Exercises- Finding Heights and Distances using Trigonometric Ratios, Exercises
357
Appendix: VII
SYLLABUS (GCE)O-LEVEL
MATHEMATICS
(4024)1. Number
• use natural numbers, integers (positive, negative and zero), prime numbers, common factors and common multiples, rational and irrational numbers, real numbers;• continue given number sequences, recognize patterns within and across different sequences and generalize to simple algebraic statements (including expressions for the nth term) relating to such sequences.
2. Set language and notation
• use set language and set notation, and Venn diagrams, to describe sets and represent relationships between sets as follows:
a) Definition of sets, e.g. A = {x : x is a natural number}B = {(x, y): y = mx + c}C = {x : a ≤ x ≤ b}D = {a, b, c... }
b) Notation:Union of A and B A ∪BIntersection of A and B A ∩ BNumber of elements in set A n(A)“ . . . is an element of . . . ” ∈“ . . . is not an element of . . . ” ∉ of set A A’The empty set ØUniversal set εA is a subset of B A ⊆BA is a proper subset of B A ⊂BA is not a subset of B A ⊄BA is not a proper subset of B A ⊄B
3. Function notation
use function notation, e.g. f(x) = 3x − 5, f: x →3x − 5 to describe simple functions,
and the notationf-1(x) = x+5
3 and f-1(x) = x+5
3 to describe their inverses.
358
Appendix: VII4. Squares, square roots, cubes and cube roots
• calculate squares, square roots, cubes and cube roots of numbers.4. llabus content
5. Directed numbers
• use directed numbers in practical situations (e.g. temperature change, tide levels).
6. Vulgar and decimal fractions and percentages
• use the language and notation of simple vulgar and decimal fractions and percentages in appropriate contexts; • recognise equivalence and convert between these forms.
7. Ordering • order quantities by magnitude and demonstrate familiarity with the
Symbols =, ≠, >, <, ≤, ≥
8. Standard form
• use the standard form A × 10nwhere n is a positive or negative integer,and 1 ≤ A < 10.
9. The four operations
• use the four operations for calculations with whole numbers, decimal fractions and vulgar (and mixed) fractions, including correct ordering of operations and use of brackets.
10. Estimation
• make estimates of numbers, quantities and lengths, give approximations to specified numbers of significant figures and decimal places and round off answers to reasonable accuracy in the context of a given problem.
11. Limits of accuracy
• give appropriate upper and lower bounds for data given to aspecified accuracy (e.g. measured lengths);
• obtain appropriate upper and lower bounds to solutions of simple problems (e.g. the calculation of the perimeter or the area of a rectangle) given data to a specified accuracy.
12. Ratio, proportion, rate
• demonstrate an understanding of the elementary ideas and notation of ratio, direct and inverse proportion and common measures of rate;• divide a quantity in a given ratio;• use scales in practical situations, calculate average speed;
359
Appendix: VII
• express direct and inverse variation in algebraic terms and use this form of expression to find unknown quantities.
13. Percentages
• calculate a given percentage of a quantity;• express one quantity as a percentage of another, calculate percentage increase or decrease;• carry out calculations involving reverse percentages, e.g. finding the cost price given the selling price and the percentage profit.4. Syllabus content
14. Use of an electronic calculator• use an electronic calculator efficiently;• apply appropriate checks of accuracy.
15. Measures
• use current units of mass, length, area, volume and capacity in practical situations and express quantities in terms of larger or smaller units.
16. Time
• calculate times in terms of the 12-hour and 24-hour clock;• read clocks, dials and timetables.
17. Money
• solve problems involving money and convert from one currency toanother.
18. Personal and household finance
• use given data to solve problems on personal and household finance involving earnings, simple interest, discount, profit and loss;• extract data from tables and charts.
19. Graphs in practical situations
• demonstrate familiarity with Cartesian coordinates in two dimensions;• interpret and use graphs in practical situations including travel graphs and conversion graphs;• draw graphs from given data;• apply the idea of rate of change to easy kinematics involving distance-time and speed-time graphs, acceleration and retardation;• calculate distance travelled as area under a linear speed-time graph.
360
Appendix: VII20. Graphs of functions
• construct tables of values and draw graphs for functions of the form y = axn
where n = –2, –1, 0, 1, 2, 3, and simple sums of not more than three of these and for functions of the form y = kaxwhere a is a positive integer;• interpret graphs of linear, quadratic, reciprocal and exponential functions;• find the gradient of a straight line graph;• solve equations approximately by graphical methods;• estimate gradients of curves by drawing tangents.
21. Straight line graphs
• calculate the gradient of a straight line from the coordinates of two points on it;• interpret and obtain the equation of a straight line graph in the form y = mx + c;• calculate the length and the coordinates of the midpoint of a line segment from the coordinates of its end points.4. Syllabus content
22. Algebraic representation and formulae
• use letters to express generalized numbers and express basic arithmetic processes algebraically, substitute numbers for words and letters in formulae;• transform simple and more complicated formulae;• construct equations from given situations.
23. Algebraic manipulation
• manipulate directed numbers;• use brackets and extract common factors;• expand products of algebraic expressions;• factorise expressions of the form:
ax + ayax + bx + kay + kbya2x2– b2y2
a2+ 2ab + b2
ax2+ bx + c• manipulate simple algebraic fractions.
24. Indices
• use and interpret positive, negative, zero and fractional indices.
25. Solutions of equations and inequalities
• solve simple linear equations in one unknown;• solve fractional equations with numerical and linear algebraic denominators;
361
Appendix: VII
• solve simultaneous linear equations in two unknowns;• solve quadratic equations by factorization and either by use of the formula or by completing the square;• solve simple linear inequalities.
26. Graphical representation of inequalities
• represent linear inequalities in one or two variables graphically.(Linear Programming problems are not included.)4. Syllabus content
27. Geometrical terms and relationships
• use and interpret the geometrical terms: point, line, plane, parallel, perpendicular, right angle, acute, obtuse and reflex angles, interior and exterior angles, regular and irregularpolygons, pentagons, hexagons, octagons, decagons;• use and interpret vocabulary of triangles, circles, special quadrilaterals;• solve problems and give simple explanations involving similarity and congruence;• use and interpret vocabulary of simple solid figures: cube, cuboid, prism, cylinder, pyramid, cone, sphere;• use the relationships between areas of similar triangles, with corresponding results for similar figures, and extension to volumes of similar solids.
28. Geometrical constructions
• measure lines and angles;• construct simple geometrical figures from given data, angle bisectors and perpendicular bisectors using protractors or set squares as necessary;• read and make scale drawings.(Where it is necessary to construct a triangle given the three sides, ruler and compasses only must be used.)
29. Bearings
• interpret and use three-figure bearings measured clockwise from the north (i.e. 000°–360°).
30. Symmetry
• recognize line and rotational symmetry (including order of rotational symmetry) in two dimensions, and properties of triangles, quadrilaterals and circles directly related to theirsymmetries;• recognize symmetry properties of the prism (including cylinder) and the pyramid (including cone);• use the following symmetry properties of circles:
362
Appendix: VII
(a) equal chords are equidistant from the center;(b) the perpendicular bisector of a chord passes through the center;(c) tangents from an external point are equal in length.
31. Angle
• calculate unknown angles and give simple explanations using the following geometrical properties:(a) angles on a straight line;(b) angles at a point;(c) vertically opposite angles;(d) angles formed by parallel lines;(e) angle properties of triangles and quadrilaterals;(f) angle properties of polygons including angle sum;(g) angle in a semi-circle;(h) angle between tangent and radius of a circle;(i) angle at the center of a circle is twice the angle at the circumference;(j) angles in the same segment are equal;(k) angles in opposite segments are supplementary.
32. Locus
• use the following loci and the method of intersecting loci:(a) sets of points in two or three dimensions(i) which are at a given distance from a given point?(ii) which are at a given distance from a given straight line?(iii) which are equidistant from two given points?(b) sets of points in two dimensions which are equidistant fromtwo given intersecting straight lines.
33. Mensuration
• solve problems involving(i) the perimeter and area of a rectangle and triangle,(ii) the circumference and area of a circle,(iii) the area of a parallelogram and a trapezium,(iv) the surface area and volume of a cuboid, cylinder, prism, sphere, pyramid and cone (formulae will be given for the sphere, pyramid and cone),(v) arc length and sector area as fractions of the circumference and area of a circle.
34. Trigonometry
• apply Pythagoras Theorem and the sine, cosine and tangent ratios for acute angles to the calculation of a side or of an angle of a right-angled triangle (angles will be
363
Appendix: VII
quoted in, and answers required in, degrees and decimals of a degree to one decimal place);• solve trigonometrical problems in two dimensions including those involving angles of elevation and depression and bearings;• extend sine and cosine functions to angles between 90° and 180°; solve problems using the sine and cosine rules for any triangle and the formula
12ab sin C for the area of a triangle;
• solve simple trigonometrical problems in three dimensions.(Calculations of the angle between two planes or of the angle between a straight line and plane will not be required.)
35. Statistics
• collect, classify and tabulate statistical data; read, interpret and draw simple inferences from tables and statistical diagrams;• construct and use bar charts, pie charts, pictograms, simple frequency distributions and frequency polygons;• use frequency density to construct and read histograms with equal and unequal intervals;• calculate the mean, median and mode for individual data and distinguish between the purposes for which they are used;• construct and use cumulative frequency diagrams; estimate the median, percentiles, quartiles and interquartile range;• calculate the mean for grouped data; identify the modal class from a grouped frequency distribution.
36. Probability
• calculate the probability of a single event as either a fraction or a decimal (not a ratio);• calculate the probability of simple combined events using possibility diagrams and tree diagrams where appropriate. (In possibility diagrams outcomes will be represented by points on a grid and in tree diagrams outcomes will be written at the end of branches and probabilities by the side of the branches.)Syllabus content
37. Matrices
• display information in the form of a matrix of any order;• solve problems involving the calculation of the sum and product (where appropriate) of two matrices, and interpret the results;• calculate the product of a scalar quantity and a matrix;• use the algebra of 2 × 2 matrices including the zero and identity 2 × 2 matrices;
364
Appendix: VII
• calculate the determinant and inverse of a non-singular matrix.(A–1 denotes the inverse of A.)
38. Transformations
• use the following transformations of the plane: reflection (M), rotation (R), translation (T), enlargement (E), shear (H), stretching (S) and their combinations (If M(a) = b and R(b) = c the notation RM(a) = c will be used; invariants under these transformations may be assumed.); • identify and give precise descriptions of transformations connecting given figures; describe transformations using coordinates and matrices. (Singular matrices are excluded.)
39. Vectors in two dimensions
• describe a translation using a vector represented by( xy ), A⃗Bor a;
• add vectors and multiply a vector by a scalar;
• calculate the magnitude of a vector ( xy ) as √ x2+ y2
• represent vectors by directed line segments; use the sum and difference of two vectors to express given vectors in terms of two coplanar vectors; use position vectors.
365
Appendix: VIII
OUTLINE OF MATHEMATICS PAPER
BOARD OF SECONDARY EDUCATION KARACHI
SECONDARY SCHOOL CERTIFICATE (SSC)
(CLASS X - SCIENCE GROUP)
Time: 3 Hours (Compulsory) Max. Marks: 100
Time: 30 Min. Section “A” Multiple Choice Questions (MCQ’S) (20 Marks)
Note: Choose the correction answers for each from the given options:
Q.1 MCQ’S (carrying 1 mark each) = 20
Time: 2 ½ Hours SECTION “B” & “C” Max. Marks: 80
Section “B” (Short-Answers Questions) (50 Marks)
Note: Answer any 10 questions from this Section
Q.2 - Q.16 (15 single item questions each carrying 5 marks)
366
Appendix: VIII
Section “C” (Detailed-Answers Questions) (30 Marks)
Note: Attempt any 3 questions from this Section including Q.No.19 which is compulsory
Q.17 Factorize the following:
Given four algebraic expressions each carrying 2.5 marks
(i) (iii)
(iii) (iv)
Q.18 Find the solution set of the following equations graphically. (10 marks)
(Find four ordered pairs of each equation).
Given a pair of linear equations in two variables
Q.19 Proof of a geometrical theorem carrying 10 marks
Q.20 (a) Question on information handling carrying 5 marks
(b) Question on factorization with the help of remainder theorem carrying 5 marks
Q.21 Question on practical geometry carrying 10 marks
367
Appendix: IX
OUTLINE OF MATHEMATICS PAPERUNIVERSITY OF CAMBRIGE INTERNATIONAL
EXAMINATIONSGENERAL CERTIFICATE OF EDUCATION ORDINARY LEVEL (O-
LEVEL)
SYLLABUS D (4024/12)
MATHEMATICS (SYLLABUS D) 4024/12Paper 1 May/June (YEAR)
2 hoursCandidates answer on the Question Paper.
Additional Materials: Geometrical instruments
READ THESE INSTRUCTIONS FIRST
Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen.You may use a pencil for any diagrams or graphs.Do not use staples, paper clips, highlighters, glue or correction fluid. DO NOT WRITE IN ANY BARCODES.
Answer all questions.
If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks.
ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER.
The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 80.
ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER.
This paper contains on average 25 questions (every question is discrete in carrying marks)
368
Appendix: IX
MATHEMATICS (SYLLABUS D) 4024/22Paper 2 May/June (YEAR)
2 hours 30 minutesCandidates answer on the Question Paper.
Additional Materials: Geometrical instrumentsElectronic calculator
READ THESE INSTRUCTIONS FIRST
Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen.You may use a pencil for any diagrams or graphs.Do not use staples, paper clips, highlighters, glue or correction fluid. DO NOT WRITE IN ANY BARCODES.
Section AAnswer all questions.
Section BAnswer any four questions.
If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks.You are expected to use an electronic calculator to evaluate explicit numerical expressions.If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place.For π, use either your calculator value or 3.142, unless the question requires the answer in terms of π.
The number of marks is given in brackets [ ] at the end of each question or part question.The total of the marks for this paper is 100.
369
Appendix: IX
Section A [52 marks]
Answer all questions in this section.
Q.1 – Q. 7 (each question contains multiple parts and every part is distinct in carrying marks)
Section B [48 marks]
Answer four questions in this section.
Each question in this section carries 12 marks.
Q8 – Q.12 (each question contains multiple parts and every part is distinct in carrying marks)
370
Appendix: X
LIST OF SCHOOLS SSC
DISTRICT (SOUTH)Sr. No.
Names of Schools
1 Aisha Bawani Academy, Shahrah-e-Faisal2 Al Habib Grammar School, PECHS, Block 23 Al Hamd Kids Heaven Secondary School,
Mehmoodabad4 Al-Farooq Secondary School, Manzoor Colony5 Al-Murtaza School, P.E.C.H.S6 Al-Sehar Secondary School, Manzoor Colony7 Ameer Bahadur Children Academy, Upper Gizri8 Brooks Grammar School, Chanesar Halt9 Central Model High School, P.E.C.H.S
10 Customs Public School, P.E.C.H.S11 Defence Foundation School, P.E.C.H.S12 Defence Institute and Computer Centre, Defence View13 Ebrahim Ali Bhai Govt. Boys High School K.A.E.C.H.S14 Excellence Model School, Kharadar15 Faran Public School, Azam town16 Fatimiyah Boys School, Britto Road Karachi17 Fatimiyah Girls School, Britto Road Karachi18 Govt Girls Higher Secondary School, Green Belt,
Mehmoodabad19 Govt. Girls Higher Secondary School, Chanesar Goth
(Urdu Medium)20 Govt. Girls Secondary School, Akhtar Colony21 Govt. Noor-e-Islam High School, Green Belt
Mehmoodabad22 Govt. Norwegian High School Azam Basti23 Green Flag Boys Secondary, K.A.E.C.H.S24 Green Flag Girls Secondary School, K.A.E.C.H.S25 Greenwich Public School, .P.E.C.H.S26 Gulistan (SAL) Boys Secondary School, S.M.C.H.S27 Gulistan (SAL) Girls Secondary School, S.M.C.H.S28 Habib Girls School, Garden29 Habib Public School, Sultanabad30 Happy Home School, Clifton31 Haq Foundation School, Muslimabad32 Heaven Foundation Secondary School, Manzoor Colony33 High Rise Academy School, Akthar Colony34 Hyderi Public School, Sarwar Shaheed Road, Saddar
371
Appendix: X
35 Imran Public School, Mehmoodabad Gate36 Iqra Huffaz Boys Secondary School, Razi Road,
P.E.C.H.S37 Karachi Cambridge School, Shahrah-e-Quaideen38 Karachi Cambridge School, Tariq Road39 Karachi Public School, K.A.E.C.H.S40 M.E Foundation Secondary School, Mehmoodabad No.641 Mama Baby Care School, Saddar42 Meezan School System, Mehmoodabad No.543 Meritorious Schools Network, P.E.C.H.S44 Muslim Public School, Manzoor Colony45 Nasra Secondary School, Soldier Bazar, Saddar46 New Generation's School, P.E.C.H.S47 New St. Andrews School, Defence Phase I48 Oxford English High School, Sultanabad49 Pak Grammar School, Garden East50 PECHS Girls School ,51 Progressive Public School Dhoraji Colony52 Radiant English School, Mehmoodabad No.553 Rainbow Public School, Azam town54 Rose Petal Primary & Secondary School, Soldier Bazaar
155 Saifiyah Boys High School, Saddar56 St Paul's English High School, Saddar57 St. Anthony's School, Karachi Cantt.58 St. Joseph’s Convent School, Saddar59 St. Matthew's Model High School, PECHS, Block 660 The Islamic Public School, P.E.C.H.S
DISTRICT (EAST)Sr. No.
Names of Schools
1 Al-Abbas Secondary School, Qayyumabad2 Alpha Secondary School, Shah Faisal Colony3 Army Public School (COD), Rashid Minhas Road,
Gulshan-e-Iqbal 4 Ataturk School, Gulistan-e-Johar, Block 135 Banglore Town School, Banglore town6 Bright Career Public Secondary Schools, Gulistan-e-Johar7 C.F. English Grammar Secondary School, Korangi8 C.P Berar High School for Girls, Dhoraji9 Chiniot Islamia School and College, Opp. Safari Park
Gulshan-e-Iqbal10 Dehli Mercantile School, D.M.C.H.S11 Fareedi Memorial Girls Secondary School, Gulistan-e-
Johar12 Ghaus-ul-Azam High School, Gulshan-e-Iqbal
372
Appendix: X
13 Golden Model School, Goldentown, Shah Faisal Colony14 Government Boys Secondary School, Airport15 Government Boys Secondary School, Jail Road16 Green Channel Grammar School, Nasir Colony, Korangi17 Happy Home School, Modern Housing Society18 Hayat-ul-Islam Public School, Gulshan-e-Iqbal19 Ideal English Secondary School, Korangi No. 220 Jinnah Academy, Gulzar-e-Hijri21 Kingston English Grammar School, Korangi No.222 Little Folk’s Secondary School, Kashmir Road23 Morning Glory Grammar School Shah Faisal Colony24 Muhammadi Public School, Gulistan-e-Johar, Block 1325 Mukkaram Ali Memorial School Shah Faisal Colony26 Nasir English Secondary School, SKC Landhi No. 227 National High School, Gulshan-e-Iqbal28 National Public School, Lukhnow Society, Korangi29 New Model High School, Dar-us-Salam Society, Korangi30 New Roomi Boys & Girls Secondary School, Korangi No 231 Noor Academy Primary and Secondary School, Korangi 2
½32 Orchard Grammar School, Gulistan-e-Johar, Block 1333 Practical Schooling System, Gulshan-e-Iqbal34 Primrose Public School, Shah Faisal Colony35 Programmer Girls School, Gulshan Iqbal36 Radient Grammar School, Gulshan Iqbal Block 1337 S.M Public Academy, Gulistan-e-Johar, Block 1338 Sadequain Academy , NIPA, Gulshan-e-Iqbal39 Scosit Secondary School, Korangi40 Shaheen Public School, Gulshan-e-Iqbal41 Sohail Academy Secondary School, Landhi No.142 St. Peter’s School, near Kashmir Road43 Stratford School Gulshan-e-Iqbal44 The American Foundation Cambridge School, Gulistan-e-
Johar45 The Crescent Academy, Gulshan-e-Iqbal, Block 346 The NR School, Korangi, No.647 The RAS School, Korangi, No.448 Usman Grammar School, Shah Faisal Colony49 Warraich Public Secondary School, Qayyumabad50 White House Grammar School, Gulshan-e-Iqbal
DISTRICT (CENTRAL)Sr. No.
Names of Schools
1 Albatross Grammar School, Hyderi2 Albatross Grammar School, North Nazimabad3 Al-Eman Education System, Block 10, F.B.Area
373
Appendix: X
4 Asra Public School, U.P More North Karachi5 Bahria Foundation School, Liaqatabad 6 Bright Career Public Secondary School - F.B Area 7 Crescent Grammar School, Surjani Town, Sector 18 Dawn Public School, North Karachi9 Education World, North Nazimabad
10 Falcon House Grammar School, North Nazimabad11 Gallant Public Secondary School, Nazimabad No.512 Glamour Children Secondary School, Liaquatbad No. 413 Happy Palace Grammar School, F.B. Area14 Harvard Public Grammar School, North Nazimabad15 Iqra Roza-tul-Atfal, School Nazimabad No. 216 Karachi Generation School, 11-B, near Saleem Centre,
North Karachi17 Karachi Honors School, Block 17, F.B.Area18 Kazmi Grammar Primary School, Allama Iqbal Town,North
Nazimabad19 Lycos Grammar School, 11/C/1, North Karachi20 MA Tutor Academy, Shadman Town, North Karachi21 Manhattan Grammar School, near Nagan Chowrangi22 Metropolitan Academy, Incholi23 Mount View Secondary School, North Nazimabad, Block I24 National Grammar Higher Secondary School, North
Nazimabad 25 New Preston Grammar School, Nazimabad No.226 Oxford Cambridge School, Rizvia Society27 Pak Horizon Grammar School, Sector 11-F North Karachi28 Preston Grammar School, Rizvia Society29 Progressive Children's Academy, Nazimabad No. 430 Rangers Public School and College, North Nazimabad31 R.G Public School, North Nazimabad32 Royal Grammar Secondary School, Nazimabad No.233 Rasheeda Memorial Secondary School, Sector 11, North
karachi34 Saeeda Academy, 11/C/1, North Karachi35 Sesame Cambridge School, North Nazimabad36 Shaheen Cambridge School Nazimabad, No.137 Shaheen Mama Montessori Nazimabad No.138 Shahwilayat Public School, F.B. Area39 Shining Star English Secondary School, North Nazimabad 40 Sir Syed Children's Academy, Nazimabad41 SK Grammar School, Muslim Town, North Karachi42 S.M.B. Academy School Boys & Girls, North Karachi43 St. George's School, North Nazimabad 44 St. Jude's High School, North Nazimabad45 St. John's High School, North Nazimabad46 Sultan Muhammad Shah School, Karimabad 47 Trueman Education System, North Nazimabad
374
Appendix: X
48 Western Grammar Secondary School, Nazimabad No. 349 Wonderland Grammar School, 11/C/1, North Karachi50 Yasir Academy, North Nazimabad
DISTRICT (WEST)Sr. No.
Names of Schools
1 Al Hera Secondary School, Sector 11 ½, Orangi Town2 Danish Children School, Tauheed Colony, Sector 11,
Orangi Town3 Government Boys Secondary School, Lasipara, Baldia
Town4 Islamia Public School, Zia Colony No. 2, Orangi Town5 Premier Grammar School, Rasheedabad, Baldia Town6 Shoeby Grammar Secondary School, Sector 5, Orangi7 S.M. Hafiz-ur-Rahman High School, Sector 11 ½, Orangi
Town8 Sir Gee Schooling System, Sector10, Orangi Town9 Syed Sulaiman Nadvi Secondary School, Sector 11 ½,
Orangi Town10 Unique Grammar Secondary School, Tauheed Colony,
Sector 11, Orangi
DISTRICT (MALIR)Sr. No.
Names of Schools
1 City Public School, Model Colony, Primary, Secondary, Malir
2 Government Boys Secondary School, Malir Colony (for boys)
375
Appendix: X
3 Info-Line English Grammar School, Murad Memon Goth, Malir
4 Model Day Care Secondary School, Model Colony, Malir5 Sana English Grammar School, Malir6 Sun Rise Progressive School, 23/13 Model Colony, Malir7 Superior Grammar School, R-66 Pak Kausar Town, Malir
Town8 Sweet Home School, Model Colony, Malir9 The Harvards House Of Education, B-97, Kehkashan
Society, Malir Halt10 White House Grammar School, Airport Branch, Model
Colony
LIST OF SCHOOLSGCE
DISTRICT (SOUTH)Sr. No.
Names of Schools
1 Aisha Bawany Academy, O-Level, 185, Shahrah-e-Faisal2 Al-Aira Group Of Schools, 13-E, Muhammad Ali Society,
Dhoraji3 Army Public School, O-Level, 158, Iqbal Shaheed Road,
Saddar4 Bay View Academy, SL - 3, 12th Street, Phase 8, D.H.A5 Bay View High School, College Campus, 8-Flench Street, Civil
376
Appendix: X
Lines6 Beaconhouse School System , P. E. C. H. S, Opp. Greet Belt
Mehmoodabad7 Beaconhouse School System Defence Campus, Saba
Avenue, Phase 8, DHA8 Convent of Jesus and Mary,101-Clifton9 Foundation Public School, O-Level, Defence Campus
10 Foundation Public Scool, College Campus, P. N. Shifa , Phase 2, DHA
11 Habib Public School, M.T. Khan Road12 Haque Academy, 208 - A, 32nd Street ,Phase 8, DHA13 Head Start School System, 41-C, P.E.C.H.S, Block 614 Inspire School of Advanced Studies, C-S-C, 2nd Floor, Phase
7, Ext. D.H.A15 Jaffar Public School, 245 / 1 / H, P.E.C.H.S, Block 616 Karachi Cadet School, 241 / B / 4, P.E.C.H.S, Block 217 Karachi Grammar School, 19 ,Street , Block 5, Khayaban-e-
Saadi, Clifton18 Kingsley American School, 28 - B / 1, P.E.C.H.S, Block 6 19 River Oaks Academy, 43 / 15 / F, Block 6, P.E.C.H.S20 Springfield School, ST - 5, K.D.A. Scheme No. 121 St. Joseph’s Convent School, Shahrah-e-Iraq, Saddar22 St. Michael's Convent School, St - 5, Kehkashan, Block 7,
Clifton23 St. Patrick's High School, Saddar24 St. Paul's English High School, Opp. P.N.S Dilawar, Saddar25 St. Peter's High School, 81-Muslimabad 26 Suffah Saviors School, 13 - C, P.E.C.H.S, Block 627 The Anchorage School,145 C, Hali Road, P.E.C.H.S, Block 228 The Aureole School, C - 54, Block 2, Kehkashan Clifton29 The C.A.S. School, Saba Avenue, Phase 8, D.H.A30 The City School, Darakshan Campus, Phase 6, D.H.A31 The City School, PAF Chapter, O-Levels, Shaheed-e-Millat
Road 32 The City School, Senior Boys Branch, 42 - Q, Block 6,
P.E.C.H.S33 The City School, Senior Girls Branch, 42 - T, Block 6,
P.E.C.H.S34 The Indus Academy, 62-Old Clifton35 The OASYS School, C 53, Block 2, Clifton36 Toronto School of Academic Excellence, 10 / D, Muhammad
Ali Society37 Usman Public School, D - 196, Block 2, P.E.C.H.S38 Washington International School, 32nd Street, Phase 8,
D.H.A39 Westminster School & College, D - 120, Block 4, Clifton 40 World Academy, 14 CF, Old Clifton, Near Mohatta Palace
377
Appendix: X DISTRICT (EAST)
Sr. No.
Names of Schools
1 Bahria Foundation College, Block 7,Abul Hasan Isphani Road, Gulshan-e-Iqbal
2 Beaconhouse, Jubilee Campus, Darulsalam Housing Society, Korangi
3 Beaconhouse School System, Cambridge Branch, E-23, Block 7, Gulshan-e-Iqbal
4 Chiniot Islamia School & College, Block 7, Gulshan-e-Iqbal, Opp. Safari Park
5 Dawood Public School, Bahadurabad, Dawood Co-Operative Housing Society
6 Delsol, The School, Muhammad Ali Housing Society, Tipu Sultan Road
7 Montessori Complex Cambridge School, C - 83, Block 14, Gulistan-e-Jauhar
8 National High School, Block 13-A, Hasan Square, Gulshan-e-Iqbal9 Practical Schooling System,C-2, Block 13-D, Gulshan-e-Iqbal
10 Progressive Public School, 130-Faran Society, Dhoraji Colony11 Shaheen Public School, 14th Street, Block 2, Gulistan-e-Jauhar12 ST. Gregory's High School,C - 5, Block 3, Moti Mahal,
Gulshan-e-Iqbal13 Summit Educational System, B - 61, Block 3, Gulshan-e-Iqbal14 The American Foundation Cambridge School, C-65,Block 13,
Gulistan-e-Jauhar15 The City School Gulshan Boys Campus, PB - 6, N.C.E.C.H.S,
Gulshan-e-Iqbal16 The Educational Centre, 214 C, Block 6, Gulshan-e-Iqbal17 The Fahims School System, B - 13, Block 13 D / 2, Gulshan-
e-Iqbal18 The Froebel's School, E - 26, Block 7, Gulshan-e-Iqbal19 The Metropolitan Academy,18 Street, Block 15, Gulistan-e-
Jauhar20 White House Grammar School, 9th Street, Block 4, Gulshan-e-
Iqbal
DISTRICT (CENTRAL)Sr. No.
Names of Schools
1 Bahria Foundation College, IV E - 11 / 8, Nazimabad, No. 42 Beaconhouse School System, (Cambridge), F-118 / 119,Block
7,North Nazimabad3 Falconhouse Grammar School, F - 71, Block B, North Nazimabad4 Generation's School, F - 100, Block B, North Nazimabad5 Happy Home School, 12 / A, Hussainabad, F.B Area, Block 2
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Appendix: X
6 Karachi Public High School, D-32, Block-L, North Nazimabad7 Ladybird Grammar School, F - 124, Block F, North
Nazimabad8 Little Folks Paradise Cambridge School, Block F, North Nazimabad9 Raunaq-e-Islam Sara Bai School, L - 6, Block M, North Nazimabad
10 The City School Senior Boys, 102, F, Block F, North Nazimabad
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Appendix: XI
LIST OF SUBJECT EXPERTSSSC
Mr. Ameenullah Farooqi (Senior Examiner BSEK and AKU-EB),Head of Mathematics Department, Nasra Public School
Mr. Amjad Roshan (Head of Mathematics DepartmentArmy Public School and College, Malir Cantt.
Mr. Habib Ur Rehman, (Gold Medalist), Head Examiner, Paper Setter (BSEK) and Master Trainer of Science Teachers,Principal, Orchard Grammar School
Mr. Husnain Javaid, Vice Principal and Coordinator of Mathematics,Fatimiyah Education Network (Boys Section)
Mrs. Kausar Tahir, Senior Mathematics Teacher,Happy Home Secondary School
Mr. Muhammad Shahid ,Head of Mathematics Department, Sheikh Khalifa Bin Zaid (SKBZ) College, DHA
Mr. Nadeem Ahmad Kirmani,Professional Development Facilitator, Senior Mathematics Teacher, Al-Murtaza School (Professional Development Center)
Mrs. Naeema Akhter, Senior Subject Specialist (Mathematics),Government Girls Higher Secondary School, Chanesar Goth (U.M)
Mr. Rais Uddin Siddiqui, Principal,Customs Public School
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Appendix: XI
Mr. Zahid Ahmed Latif, Teacher Educator (Mathematics)Administrator and Principal, Alpha Public School Shah Faisal Colony
LIST OF SUBJECT EXPERTS GCE
Mr. Abdul Wasiq, Senior Mathematics Teacher Habib Public School
Mrs. Aileen Soares, HOD and Senior Mathematics Teacher,St. Joseph’s Convent School
Mr. Iftikhar Ahmad Khan, Senior Mathematics Teacher,Beaconhouse School System
Mr. Muhammad Adnan Jamil, HOD and Senior Mathematics Teacher,Washington International School and Jaffar Public School
Mr. Muhammad Asim, HOD and Senior Mathematics Teacher,Toronto School of Academic Excellence,Senior Mathematics Teacher, The City School
Mr. Muhammad Faizan Hashmani, Senior Mathematics Teacher,Foundation Public School
Mr. Muneer Ahmad Naveed, Senior Mathematics Teacher,Beacon Askari Secondary and Cambridge School
Mr. Nadeem Ahmad, Senior Mathematics Teacher,
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Appendix: XI
Bay View High School
Mr. Syed Muhammad Hussain, Head of Mathematics Department,Karachi Grammar School
Mrs. Zareen Jawaid, Senior Mathematics Teacher,Aisha Bawany Academy (Cambridge Section)
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