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AKOR, A. E. PAULINE
PG/Ph.D/07/48424
EFFECT OF ACHIEVEMENT MOTIVATIONAL INSTRUCTIONAL
APPROACH ON PRIMARY SIX PUPILS’ NUMERICAL APTITUDE AND
RETENTION IN MATHEMATICS
DEPARTMENT OF SCIENCE EDUCATION
FACULTY OF EDUCATION
Fred Attah
Digitally signed by: Content manager’s
Name
DN : CN = Webmaster’s name
O= University of Nigeria, Nsukka
OU = Innovation Centre
EFFECT OF ACHIEVEMENT MOTIVATIONAL INSTRUCTIONAL APPROACH ON PRIMARY SIX PUPILS’ NUMERICAL APTITUDE AND
RETENTION IN MATHEMATICS
BY
AKOR, A. E. PAULINE
PG/Ph.D/07/48424
DEPARTMENT OF SCIENCE EDUCATION
FACULTY OF EDUCATION
UNIVERSITY OF NIGERIA NSUKKA
NOVEMBER, 2015
3
TITLE PAGE
EFFECT OF ACHIEVEMENT MOTIVATIONAL INSTRUCTIONAL APPROACH ON PRIMARY SIX PUPILS’ NUMERICAL APTITUDE
AND RETENTION IN MATHEMATICS
BY
AKOR, A.E. PAULINE
PG/Ph.D/07/48424
4
SUPERVISOR
PROF. K.O. USMAN
NOVEMBER, 2015
5
A THESIS SUBMITTED TO DEPARTMENT OF SCIENCE EDUCATI ON
UNIVERSITY OF NIGERIA NSUKKA IN FULFILMENT OF REQUIREMENTS FOR THE AWARD OF DOCTOR PHILOSOPHY
(Ph.D) DEGREE IN MATHEMATICS IN EDUCATION
6
CERTIFICATION
Akor, Awunghe-Ebuta Pauline a Postgraduate Student in the Department of
Science Education, with Registration Number PG/Ph.D/07/48424, has satisfactorily
completed the requirement for research work for the award of the degree of Doctor of
Philosophy (Ph.D) in Mathematics Education. The work embodied in this thesis is
original and has not been submitted in whole or part for any other degree of this or any
other university.
…………………………… ……………………… Akor, A.E Pauline Prof. K.O. Usman (Student) (Supervisor)
7
DEDICATION
This work is dedicated to Almighty God for his grace and to my beloved family.
8
ACKNOWLEDGEMENT
The researcher is thankful to Almighty God who made it possible for this study
to come to this stage. The researcher’s special thanks is to her Supervisor, Prof. K.O.
Usman for his interest and encouragement, God will pay you better Having spend all
her years of study in this University from Masters level till this moment, the researcher
appreciates mentors that have made her fit for the society. Mentors that easily come to
mind include; Prof. B.G. Nworgu, Prof. U.N.V. Agwagal, Prof. A. Ali, Late Prof. V.F.
Harbore Peters, Prof D.N. Ezeh and Prof. G. Offorma, may the Good Lord bless them
all.
The researcher cannot thank enough her readers at various stages of this work
especially Dr. (Mrs) Nworgu, L.N, Dr. Agah J., Dr. Nwabuku, and Dr. F.M. Onu who
painstakingly offered much of their time to see that the work was on correct course.
God bless you. To many others whose names are not mentioned, the researcher remain
thankful to you all.
9
TABLE CONTENTS
Title Page i Approval Page ii Certification iii Dedication iv Acknowledgment v Table of contents vi List of appendices ix List of tables x Abstract xii
CHAPTER ONE: INTRODUCTION
Background of Study 1
Statement of the Problem 13
Purpose of the Study 14
Significance of the Study 15
Scope of the Study 17
Research Questions 19
Hypothesis 20
CHAPTER TWO: REVIEW OF RELATED LITERATURE
Conceptual Framework 22
� Teaching and learning mathematics 23
� Concept and components of achievement motivation 27
� Achievement motivational instructional approach 28
� Traditional teaching method 36
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� Mathematics Achievement 37
� Numerical Aptitude 39
� Gender and mathematics Achievement 42
� Retention and Mathematics Achievement 44
� Diagrammatical Representation of the Conceptual Framework 46
Theoretical Framework 47
� David McClelland’s Motivational Needs Theory 47
� Need Achievement Motivation Theory 51
Review of Empirical Studies 52
� Studies on teaching approaches on primary six pupils gender 52
� Studies on teaching approaches on primary six pupils retention 57
� Studies on the Effect of Achievement Motivational Instructional
Approach on Primary Pupils Achievement 58
� Studies on the Effect of Achievement Motivational Instructional
Approach on Primary Pupils Retention 59
� Studies on the Effect of Achievement Motivational Instructional
Approach on Primary Pupils Numerical aptitude 61
Summary of Related Literature 61
CHAPTER THREE: RESEARCH METHOD
Design of the Study 63
Area of the Study 64
Population of the Study 65
Sample and Sampling Technique 65
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Instruments for Data Collection 65
Validation of the Instrument 67
Reliability 68
Experimental Procedure 69
Control of Extraneous Variable 70
Training of Teachers 71
Method of Data Collection 73
Method of Data Analysis 74
CHAPTER FOUR: RESULTS 75
Summary of Findings 88
CHAPTER FIVE: DISCUSSION, CONCLUSION AND SUMMARY
OF THE STUDY
Discussion 90
Conclusions 96
Educational Implications 97
Recommendations 98
Limitations 99
Suggestions for Further Studies 100
Summary 100
REFERENCES 102
APPENDICES 110
12
LIST OF APPENDICES
APPENDIX A: Mathematics Achievement Test (MAT) 110
APPENDIX B: Numerical Aptitude Test (NAT) 116
APPENDIX C: Lesson Plans (Experimental) 122
APPENDIX D: Lesson Plans (Control) 137
APPENDIX E: Table of Specification 153
APPENDIX F: Training Guide for Teachers 155
APPENDIX G: Primary Six Curriculum 158
APPENDIX H: Computation of the Reliability of MAT 179
APPENDIX I: Computation for reliability of NAT 181
13
LIST OF TABLES
Table page
1: Mean and Standard deviation of pretest posttest score of pupils taught mathematics with achievement motivational instructional approach and those taught with traditional approach 75
2: Mean and Standard deviation of numerical aptitude score of pupils
taught mathematics with achievement motivational instructional approach and those taught with traditional approach 76
3: Mean and Standard deviation of pretest posttest score of male and female pupils taught mathematics with achievement motivational instructional approach 77
4: Mean and Standard deviation of numerical aptitude score of male and female pupils taught mathematics with achievement motivational approach 78
5: Mean and Standard deviation of retention score of pupils taught mathematics with achievement motivational instructional approach and those taught with traditional approach 78
6: Mean and Standard deviation of retention numerical aptitude score
of pupils taught mathematics with achievement motivational instructional approach and those taught with traditional approach 79
7: Mean and Standard deviation of retention score of male and female pupils taught mathematics with achievement motivational instructional approach 80
8: Mean and Standard deviation of retention numerical aptitude score of male and female pupils taught mathematics with achievement motivational instructional approach 81
9: Analysis of Covariance (ANCOVA) of the mean achievement
score of pupils taught mathematics with achievement motivational instructional approach and those taught with traditional approach 82
10: Analysis of Covariance (ANCOVA) of the mean numerical aptitude
score of pupils taught mathematics with achievement motivational instructional approach and those taught with traditional approach. 83
11: Analysis of Covariance (ANCOVA) of the mean retention of
14
achievement score of male and female pupils taught mathematics with achievement motivational instructional approach. 85
12: Analysis of Covariance (ANCOVA) of the mean retention of numerical
aptitude score of male and female pupils taught mathematics with achievement motivational instructional approach. 86
15
ABSTRACT This study sought to investigate the effect of achievement motivational instructional approach on primary six pupils’ numerical aptitude and retention in mathematic. Eight research questions and ten research hypotheses guided the study. The design of the study was quasi experimental pretest posttest equivalent control group design. The study was carried out in Calabar municipality Local Government Area of Cross River State in the present south-south zone of Nigeria. The population of the study was 2400 primary six pupils’ from the 24 public primary schools in Calabar municipality education zone of Cross River State. Two out of the 24 schools were randomly selected for the study. The sample size for this study was 241. 125 pupils were assigned the experimental group and 116 pupils constituted the control group for the experimental group 70 of the pupils were males and 55 pupils were females. The instruments used for data collection were Mathematics Achievement Test (MAT) and Numerical Aptitude Test (NAT).The MAT was developed by the researcher and the NAT was a standardized test from the state ministry of education. The MAT was subjected to both face and content validation. MAT and NAT were trial tested on 30 pupils and the data generated was used to determine the reliability coefficient of MAT to be 0.86 and of NAT to be 0.83 using Richardson (20) K – R20 formula. MAT and NAT was administered on the groups before treatment started while post-MAT and NAT was administered at the end of the 3 weeks treatment period. After 2 weeks of administration of post-test, the items of both MAT and NAT were reshuffled and again administered on the group as a retention test. Scores from the pretest of MAT and NAT, posttest of MAT and NAT and the retention test were analysed using means, standard deviation and analysis of covariance (ANCOVA). Some of the major findings from the analysis were (i) Achievement motivational instructional approach was found to be capable of enhancing pupils’ achievement, numerical aptitude and retention in Mathematics than the traditional approach. (ii) Achievement motivational instructional approach does not result in differences in achievement, numerical aptitude scores between male and female pupils. (iii) The use of achievement motivational instructional approach improved retention of male and female pupils. Based on the findings, the implication were highlighted and recommendation were made towards better achievements, numerical aptitude and retention of primary six pupils’ in mathematics
16
CHAPTER ONE
INTRODUCTION
Background of Study
Mathematics has been described by many researchers and authors of different
times in different ways. While some tried to show its elegant precision, beauty and
brevity, others tried to show its structure and the training it provides. Ibrahim (2004)
said that among the training mathematics provides includes the ability to develop
powers of logical thinking, accuracy with figures and spatial awareness. The role of
mathematics in the field of science and technology is quite enormous and far-reaching
and the usefulness of mathematics in various fields of endeavors has been expatiated by
some writers including Usman (2002) and Agwagah (2004).
As a science subject, mathematics deals with counting, measuring and describing
shapes or objects. Mathematics can be regarded as a tool for basic science namely
physics, chemistry, biology, and even social sciences, for example geography,
economics, banking and finance. The role of mathematics is very important in everyday
life that its position is felt in all aspects of life. For instance, for the purpose of
economic survival, every citizen needs to be able to compare and estimate commodities
and cost of prices. The citizens requires some degree of competence in mathematical
computations for the purpose of carrying out routine daily businesses and for thinking
effectively. Akinsola and Popoola (2004), supported this fact when they said that
mathematics fosters intellectual skills that enable man analyze complex problems,
recognize logical relations between interdependent factors as well as formulate general
laws on their interrelationship in making precision statements. However it is necessary
for a person to have some knowledge of mathematics in order to become a useful and
17
effective member of the society. Which follows that no Nation can develop
scientifically and technologically without proper foundation in school mathematics
(Ejakpovi and Uveruveh, 2014). Therefore any attempt to treat mathematics with levity
in the country’s educational system may have serious consequences for Nigerians.
All nations of the world should take mathematics studies seriously because it is
the precursor of scientific as well as technological breakthrough and there is no end to
the usefulness of mathematics. A strong background in mathematics is therefore critical
for many jobs and carrier opportunities in today’s increasingly technological society in
Nigeria. Mathematics has been made compulsory at both primary and secondary school
levels of education (Federal Republic of Nigeria, 2004). The primary objectives of
mathematics are as it was spelt out at the Benin conference of 1977 on mathematics and
mathematics education in Nigeria as follows.
• To lay a solid foundation for the concept of numeracy and scientific thinking.
• To develop in the child the ability to adapt to his changing environment.
• To give the child opportunity for developing manipulative skills that will enable
him function effectively in the society within the limits of his capacity.
• To provide the basic tools for further advancement as well as prepare him for
trades and crafts of his locality.
• At the secondary school level to build on the foundation of the primary level so
that the child can make a useful living professionally, economically, politically
and socially (FRN, 2004).
The inculcation of mathematical culture should therefore begin early in life. The
training of children to be competent in this very important subject should start in the
18
primary school. The early years of primary experience with mathematics are very
crucial because they can affect the child’s attitude to mathematics for the rest of his or
her life. It is at this stage the child cultivates the understanding and application of
mathematics skills and concepts necessary to thrive in the ever changing technological
world (Ibrahim, 2004). The child at primary stage develops the essential element of
problem solving, communication, reasoning and connection within their study of
mathematics. If a child does not reach a satisfactory understanding of the basic
mathematical concept taught in primary school, he may find it difficult to assimilate
further concepts appropriately.
The teaching of primary mathematics therefore is necessary as it provide a solid
foundation for everyday living; develops the ability to recognize problems and to solve;
develop the ability of precision, logical and abstract thinking; and fosters the ability to
be accurate in solving both mathematical and real life problems among others
(Adedayo, 2001).
The primary mathematics curriculum is well designed to boost pupils’
achievements in cognitive and psychomotor capability. The content considered in the
revised curriculum for primary six are number and numeration, basic operation,
measurement, geometry and menstruation and everyday statistics (FME, 2007). The
curriculum provide maximal teaching aid for the teacher by prescribing topics,
objective or expected learning outcome stated in measurable terms, pupils and teachers
activities and adequate evaluation that will make the curriculum achieve its purpose.
The realization of good teaching and learning of primary mathematics lies in the hands
of teachers. The mathematics teacher should not merely impact information, but should
19
try to develop in the pupils the ability to use these information to further their
knowledge in mathematics.
The quality and ability of secondary school students according to Offorma,
(2000) are largely determined by the type of training and academic instruction received
at the primary school. Teachers need to apply different approaches at different times.
Different content requires different approaches and different levels of intellectual
engagement. These approaches according to Reeve (2006) will provide a deeper
understanding of the subject matter. Teachers therefore can select from modern
innovative approaches that will promote better teaching process thereby improving
mathematics performance.
Primary mathematics is beset with many problems that causes poor performance.
Some of these problems include inadequate training facilities that can bring out the best
in the Nigerian child (Adedayo, 2001). Many scholars and other users of mathematics
had one time or the other complained about the decline in teaching and learning of
mathematics at primary level. Such complains among others are poor teaching
techniques that keeps the class dull (Willie and Bondi 2011). Besides, poor foundation
in primary school mathematics might be as a result of incompetent mathematics
teachers in the school system and psychological fear of mathematics as a subject, lack
of and inadequate instructional materials to teach some important practically oriented
topics at the primary school level (Eriaikhueman, 2003).
Much of the recent researches by Adeniji (2014), Agwagah (2013) on
mathematics teaching and learning identified teacher’s method of teaching as one major
reason for this persistent pattern of under-achievements and poor performance. Many
20
teaching approaches that are not clearly specified are used in the teaching of
mathematics in primary schools. These approaches such as lecture methods, talk and
chalk method, individualistic method, sterile method, uninspiring and didactic
according to Adeniji (2014) are always combined and used in the teaching of
mathematics in the primary level. These methods according to Adeniji (2014) are
referred to as traditional method of teaching which the teachers primary roles is to
covey facts and procedures and the pupils role are to memorize the facts and practice
the procedure. This type of instruction according to Zakariyya (2014), emphasizes the
passive acquisition of knowledge and pupils become recipient of knowledge through
rote learning. In other words traditional teaching approach is an approach that lays no
emphasis on pupils constructing their own ideas. It is more of teacher centre and has
obvious and serious limitations (Agwagah, 2004).
Traditional methods does not give room for pupils’ activity and creative mind
that is required in the present day National development. Traditional mathematics
teaching is still the norm in our nation schools and has continued to dominate the
mathematics classrooms (Agwagah, 2004). Many scientific studies according to Adeniji
(2014) have shown that traditional methods of teaching mathematics not only are
inactive but also seriously stunt the growth of pupils’ mathematical reasoning and
problem solving skills. This implies that traditional teaching method has not been able
to sustain the development of children in mathematics, especially in the primary school
where a solid foundation is needed. The impact of low achievements in this all-
important subject is great, especially at the primary levels. Failure to learn mathematics
affects students’ performance at both secondary and tertiary level. According to
21
Akinsola and Popoola (2004) many pupils who left primary school on admission into
the secondary levels of education in Nigeria continue to perform poorly because of their
poor mathematics background in the primary school level.
In order to compliment the use of traditional methods, current studies on how
pupils learn science and science related subjects such as mathematics have started
revealing new ideas and approaches that will improve primary mathematics teaching
and learning. By contrast, in a contextual classroom, the teacher’s role is expanded to
include creating variety of learning experiences with a focus on understanding rather
than memorization. Research shows that, when teachers design task for novelty and
variety, pupils’ interest, motivation, engagement and mastery of mathematics increases
(Santrock, 2011). One of these approaches that is geared towards achieving this is the
achievement motivational instructional approach. Achievement according to Santrock
(2011) is the outcome of level of accomplishment in a specified programme of
instruction in a subject area or occupation which a pupil had undertaken in the recent
past. Furthermore, achievement also refers to how much an individual or learner has
mastered in a given subject or learning experience (Okwajiako, 2002). The perceived
value of achievement according to (Coskun, 2013) varies; it may be valued primarily
for promoting future success (Schooling, Job) or for bringing honour to ones family.
There are differences in perception of what it takes to achieve, for example, efforts
versus ability (Fuligni, 2001), listening versus participating Greenfield (2000) and
collaborating versus working individually, Martin (2009). According to Obieyem
(2011), achievement is pupils’ academic standing in relation to those of other people
tested with the same instrument. It therefore implies that achievement improves when
22
pupils set goals that are specific, proximal and challenging. These goals should be
optimally matched to the pupils’ skills. Okwajiako (2002) said achievement may be
influenced by motivation.
Motivation according to Rabideau (2013) can be defined as the driving force
behind all the actions of an individual. Motivation is based on ones emotions and
achievement related goals. In the view of Elliot, (1997) motivation is the dynamics of
our behaviour which involves our needs, desires and ambitions in life. In other words
motivation is the basic drive for all of our actions. Motivation in mathematics has two
aspects; that of creating or arousing interest and that of maintaining the interest after the
novelty of the work in hand have worn off. Pupils tend to remain interested in those
things they understand most completely (Ezeliora 2004).
A work group of the American Psychological Association Board of Education
Affairs (1997) considered learner centered principles as being very important in
enhancing pupils’ motivation and achievement. These principles according to
(Santrock, 2011) states that what and how much is learned is influenced by the learner’s
motivation to learn which is in turn influenced by the learner’s emotional states, beliefs,
interest, goals and habit. There are different forms of motivations which include
extrinsic, intrinsic, physiological and achievement motivation.
A renowned theorist McClelland (1961) in his theory of achievement motivation
said achievement motivation is seeking achievement and attainment of realistic but
challenging goals. This theory believe that there is a strong need for feedback as to
achievement and progress and a need for a sense of accomplishment. According to
Rabideau (2013), achievement motivation is the need for success or the attainment of
23
excellence. Individuals will satisfy their needs through different means and are driven
to succeed for varying reasons both internally and externally. That is having an innate
need to succeed or to reach high level of attainment. It follows that achievement
motivation is the foundation for all human motivation. That is people who experience
great levels of success are motivated to strive for more success.
Pupils who are high in achievement motivation (Coskun, 2010) have the
tendency to solve strenuous exercises, retain what they had learnt, recall what they had
learnt in the past and are able to review certain properties of mathematical shapes. This
is largely dependent on the way and manner pupils are taught as to acquire the
competence.
Based on the ongoing discussions, achievement motivational instructional
approach is the teaching behaviour that leads pupils to have tasked goal that are focused
on improvement and mastery. According to Coskun (2013), pupils’ taught with
achievement motivational instructional approach strive for success, show active
participation, always show the willingness to work. While Jegede and Jegede (1990)
stated that achievement motivational instructional approach is an approach if fully
utilized in the teaching of school subjects including mathematics will make
mathematics more meaningful and interesting. Hence this approach may be possible in
mathematics.
Achievement motivational instructional approach is an instructional approach
which holds the view that knowledge or experiences must not be forgotten. In other
words, the learner constructs knowledge in an attempt to integrate the past existing
knowledge with the new experience. When a learner is presented with new information,
24
the learner first tries to read, recall, review to understand the language before making
any precision statement. This is because in primary six classes, no information is
completely new. Every information is assumed to have been taught in the junior classes
and any new information should be connected to knowledge already in memory. The
pupils must actively construct knowledge from their existing mental framework for
meaningful learning to occur. At any point in time their ideas, knowledge and
experiences may be needed. Achievement motivational instructional approach offers
pupils an opportunity to activate their mental framework.
Achievement motivational instructional approach is organized into four categories,
namely
• Applying SQ3R meaning (scan questions, read, recall and review),
• Understanding the purpose of Mathematics Language instruction;
• Diagnosing and treating pupils difficulties and
• Using practical activities to aid studying.
Achievement motivational instructional approach is most appealing as it is an
actively learning approach engaged in thinking logically and quantitatively. The teacher
plays a critical role by guiding and providing the necessary directions to ensure that
mathematical ideas are recognized. Mcmillian, (2011) said if these processes are
adequately stimulated the pupils’ ability to think, retain, remember, read efficiently and
the speed of solving correct mathematical problems will be on the increase. While
Okwujioko (2002) had observed that pupils thought with achievement motivational
instructional approach tend to have higher numerical aptitude.
25
Numerical aptitude refers to a person’s potential ability as it relates to numbers
or quantities. According to Santrocks (2011), numerical aptitude is a potential ability of
an individual in a particular area of study and also a measure of one’s ability. It
estimates one’s capability to profit from further training of experience. Willie and
Bondi (2011) stated that pupils with high numerical aptitude always stand out distinct
in all they do, they are good in mental sums, recalling mathematical concepts that have
been taught in the past and a high retention of ideas. Numerical aptitude has always
taken the form of aptitude test which is designated to predict pupils or an individual
ability to learn a skill or accomplish something with further education and training
irrespective of area of coverage. Primary six pupils’ are expected to be in the same age
bracket, and having attended lessons together, write their examinations together.
This final examination which is either state or federal common entrance
examination or as it is popularly called in Cross River State placement examination is
what is referred to in this study as the numerical aptitude test. This examination is
monitored and under strict supervision by the state or federal ministry of Education and
passing this examination qualifies the pupils for admission into the secondary school.
Numerical aptitude test therefore is an attempt to differentiate effectively among pupils
the extent to which pupils have mastered important basic concepts and skills in their
capacity to reason quantitatively and logically and their ability to retain what had been
leant in the past. Time for numerical aptitude test is not always sufficient. It is not how
many questions a pupil can answer or do but how many correct questions a pupil can
answer correctly. For a pupil to perform high in this examination, there is need for
pupils to possess high retention of ideas or information.
26
Retention according to Okonkwo (2012) is the ability to store facts and remember what
you have learnt after a period of time and the ability to remember takes place more
effectively when experiences are passed across to pupils through an appropriate
instructional procedure which is capable of arousing pupils’ interest. (Ogbonna, 2007),
stated that retention is an important variable in learning mathematics and that
achievement last only when pupils are able to retain what they have learnt.
Many researchers such as Ogbonna (2007), Ezeh (2011), Okonkwo (2012) have
carried out studies in the past on retention in various fields, and all viewed retention as
important in sustenance of achievement. That is if a pupil performs well in a post test, it
is expected that the pupils perform very well in a retention test but if the reverse
happens, it is an indication that, the concepts and ideas did not register in the long term
memory. The teacher will then search for a better strategy that will make the pupil
retain what they have learnt in mathematics. Retention according to Teese, (2004) is a
vital factor in achievement motivational instructional approach on numerical aptitude
because without retention there will be no act of recalling, reviewing, understanding
mathematics language instruction, diagnosing and treating pupils difficulties and using
practical activities to aid studying. Both teachers and pupils must know the stuff stored
in the memory to be able to be active and function well. According to Nworgu, (2004),
Agwagah, (2013) boy’s increase interaction with teachers in class than girls and this
tend to influence better development of mathematics concepts among male pupils. Also
the pattern of interaction in class tends to make boys appear more confident in
mathematics than girls. It has been established that there is differential performance in
mathematical activities due to gender especially in favour of boys Agwagah (2004).
27
The gender issue in mathematics according to Harbor-Peters (2001), has been a source
of aversion. The believe that mathematics is a male stereotype especially as it is
regarded as abstract and difficult with attributes which boys are attracted to.
Incidentally, evidence from researchers show that there is no significant difference in
the performances of boys and girls in mathematics before the age of 11 (Harbor-Peters
2001).
A number of studies have verified the influence of gender on mathematics
achievement of pupils. This has led to different types of findings on the role of sex on
the mathematics achievement. In the finding of Umar and Momoh (2001) there was no
statistical difference in the performance of boys and girls on quantitative and other
aptitude test. Intrinsically motivation for both genders differ which consequently
influence the type of problems pupils may like to answer in mathematics test. This is
evident in the emphasis made by Urdan (2010) that motivational condition influence
both sexes to perform equally well in mathematics test and examination. It is influenced
to some extent by the interest level of the pupils and the ability to remember what was
taught in the past. This evidence tends to agree with Gregory (2011) who viewed that
primary six pupils are in the same age bracket of plus and minus eleven years (11 yrs)
and achievement in mathematics at this age is not noticeable as to whether boys or girls
do better. This study will investigate the differential effect of achievements
motivational instructional approach on males and females pupils’ numerical aptitude
and retention in mathematics.
Some researchers have evaluated the effectiveness of achievement motivational
instructional approach in different subject areas. For instance, Jegede & Jegede (1990)
28
carried out a study to ascertain if the use of achievement motivational instructional
approach could be found significantly effective in the teaching of English. A similar
study was conducted by Aydin and Coskun (2011), to ascertain if achievement
motivational instructional approach could better students’ performance in Geography.
Despite these significant results recorded in other subject areas, it becomes obvious that
much has not been done in the use of achievement motivational instructional approach
as a teaching approach in mathematics. This study therefore is aimed at finding if the
achievement motivational instructional approach will improve primary six numerical
aptitude and retention mathematics.
Statement of the Problem
The use of inappropriate instructional approach has been identified as the major
causes of pupil’s poor achievement. The persistence use of traditional teaching
approaches in primary schools has stunt the growth of pupils mathematical reasoning
and problem solving skills thereby instilling fears in pupils such that, they run out of
school or graduate from primary school without understanding the major concept in
mathematics. Thus, effort are being made by educators and researchers to see if there
will be improvement especially through the use of appropriate teaching approaches and
skills that will enable the pupils strive to achieve when solving problems, increase the
participation level and develop the willingness to work. This will increase interest and
at the end attain a level of excellence and success. Although, many approaches such as
guided discovery, target task, expository and traditional methods have been in use,
mathematics performances especially at the primary level have not really improved.
Some researchers have equally tried to find out the effect of achievement motivational
29
instructional approach of subjects of other fields of endeavour and found the approach
useful and successful. This study therefore tries to investigate in the field of
mathematics.
Hence this study tries to investigate
• The effect of achievement motivational instructional approach on primary six
pupils’, numerical aptitude and retention in mathematics.
• If differences exist in the achievement of male and female primary six pupils
achievement, numerical aptitude and retention when achievement motivational
instructional approach is applied.
• The interaction effect of achievement motivational instructional approach and
gender on primary pupils’ achievement numerical aptitude, and retention in
mathematics.
Purpose of the Study
The main purpose of the study is to investigate the effect of achievement
motivational instructional approach on primary six pupils’ numerical aptitude
achievement and retention in mathematics in Cross River State.
Specifically the study is to
1. Determine the mean achievement score of pupils taught mathematics with
achievement motivational instructional approach and those taught with
traditional approach.
2. Ascertain the mean numerical aptitude score of pupils taught mathematics with
achievement motivational instructional approach and those taught with
traditional approach.
30
3. Determine the mean retention scores of male and female pupils taught
mathematics with achievement motivational instructional approach.
4. Ascertain the mean retention of numerical aptitude score of male and female
pupils taught mathematics with achievement motivational instructional approach
5. Determine the mean achievement scores of male and female pupils taught
mathematics with achievement motivational instructional approach.
6. Determine the mean numerical aptitude score of male and female pupils taught
mathematics with achievement motivational instructional approach
7. Determine the interaction effect of approaches and gender on mean achievement
scores of pupils in mathematics.
8. Determine the interaction effect of approaches and gender on mean numerical
aptitude scores of pupils in mathematics.
9. Determine the interaction effect of approaches and gender on mean retention of
achievement scores of pupils in mathematics.
10. Determine the interaction effect of approaches and gender on mean retention of
numerical aptitude scores of pupils in mathematics.
Significance of the Study
The findings of this study will be of greater benefits to pupils/students, parents,
ministry of education, curriculum planners professional bodies and the entire society.
On the theoretical significance, the study provides an insight on the theories of
McClelland (1961) and McClelland and Atkinson (1953) which have been acclaimed as
promoting teaching and learning. On the practical significance, the achievement
motivational instructional approach will help in developing the mental processes of
31
curiosity, and manipulation. Thus, this study has immense promise for improvement of
pupils’ performance in mathematics, since it is directed at finding the appropriate
teaching method, which could facilitate learning and retention of concepts, arousing of
curiosity and interest. The finding will also show the difference between achievement
motivational instructional approach and traditional teaching method. The finding will
provide in mathematics an alternative method of teaching mathematics, for easier
understanding and effective application by pupils. It will also help in overcoming
mathematics fear in pupils.
The study will help teachers to identify brilliant mathematics pupils and those
that need special attention on how they can improve. The study will provide useful
information to Teachers Training Institutions when publications on the work are made.
The institutions can then develop new programme of instructions based on achievement
motivational instructional approach. This study may help curriculum planners to plan
programmes that will encourage, develop and strengthen interest in pupils towards
solving mathematics.
All stake holders in education are required to contribute to the process of
achieving the objectives of mathematics teaching by studying the new approach and
implementing it. Other stake holders like the State Universal Basic Education Board
(SUBEB) and other school administrators should think more about the availability of
resource materials in the schools by devising ways of exposing the approach across the
schools. Since the state Universal Basic Education Board oversees every issue
pertaining to primary school, will bring about positive changes in schools by organizing
32
workshops, conferences and in-service training thereby encouraging the teachers. The
SUBEB take instructions and relate back to the state ministry of education.
Parents and guardians are committed to the success of the school. At state level
the Parents Teachers Association (P.T.A.) encourages hard work and innovation, when
a school is doing well academically, the P.T.A. will help in building classrooms and
provide resource materials and even pay for extra lessons to make the approach
successful. Since the Association is a major pressure group influencing government
policies for schools, will pressure rise the government. The government will take
necessary steps to make relevant books tailored towards the innovative methods and
approach like achievement motivational instructional approaches for teaching at
affordable prices. Professional bodies like (MAN) mathematics Association of Nigeria
and (STAN) Science Teachers Association of Nigeria will organize and write books on
these approaches and be as resource persons at workshops and seminars for teachers so
as to positively support the efforts of government.
Finally, the use of the appropriate teaching method in teaching primary
mathematics will enable pupils to build on their knowledge acquired by passing all final
mathematics examination with higher grades that will give them opportunity to do
mathematics related subjects and course in secondary and tertiary institution. Lastly this
study will serve as a source of literature to scholars and educational researchers.
Scope of the Study
The study will be limited to the effect of achievement motivational instructional
approach on primary pupils’ numerical aptitude, retention and achievement in
mathematics in Cross River State. Specifically the study will be conducted using
33
primary six pupils. The content is the entire primary six mathematics curriculum,
comprising of number & numeration, Basic operation, Geometry and menstruation,
statistics, and measurement. The content will be taught in accordance with achievement
motivational instructional approach. This takes the form of;
• Apply SQ3R (Scan Question, Read, Recall and Review) pupils must read
questions again and again to understand the area of mathematics the question is
taken from; Recall formulas, and Review properties of shapes and statistical
ideas.
• Understanding the mathematics language instruction for proper interpretation
e.g. write in figures, write in words, correct to decimal places, reduce to its
simplest term, work in standard form and many more.
• Diagnosing and treating pupils, difficulties teachers must diagnose the pupils to
know where and how to start, Definition of mathematical terms and concepts,
identification, solve logically or quantitatively.
• Using practical activities to aid studying example measurement, heights, angles,
and drawing.
The primary six curriculums has the details to make this approach effective
because it is subdivided into performance objectives, content, teacher activity, pupils’
activity, teaching and learning materials. The achievement motivational instructional
approach is chosen because it will expose all techniques involved in the solving of
primary mathematics and will give the pupils’ a sound ability to strive, participate
actively in mathematics classes and examinations and show the willingness to solve
mathematics problems at any time.
34
Research Questions
1. What is the mean achievement score of pupils taught mathematics with
achievement motivational instructional approach and those taught with
traditional approach?
2. What is the mean numerical aptitude score of pupils taught mathematics with
achievement motivational instructional approach and those taught with
traditional approach?
3. What is the mean achievement score of male and female pupils taught
mathematics with achievement motivational instructional approach?
4. What is the mean numerical aptitude score of male and female pupils taught
mathematics with achievement motivational instructional approach?
5. What is the mean retention of achievement score of pupils taught mathematics
with achievement motivational instructional approach and those taught with
traditional approach?
6. What is the mean retention numerical aptitude score of pupils taught
mathematics with achievement motivational instructional approach and those
taught with traditional approach?
7. What is the mean retention of achievement score of male and female pupils
taught mathematics with achievement motivational instructional approach?
8. What is the mean retention of numerical aptitude score of male and female
pupils taught mathematics with achievement motivational instructional
approach?
35
Hypothesis
H01: There is no significant difference between the mean achievement score of pupils
taught mathematics with achievement motivational approach and those taught with
traditional approach.
H02: There is no significant difference between the mean numerical aptitude score of
pupils taught mathematics with achievement motivational approach and those
taught with traditional approach.
H03: There is no significant difference between the mean achievement scores of male
and female pupils taught mathematics with achievement motivational approach.
H04: There is no significant difference between the mean numerical aptitude score of
male and female pupils taught mathematics with achievement motivational
approach
H05: There is no significant difference between the mean retention of achievement
scores of male and female pupils taught mathematics with achievement
motivational approach.
H06: There is no significant difference between the mean retention of numerical
aptitude score of male and female pupils taught mathematics with achievement
motivational approach
H07: There is no significant interaction effect of approaches and gender on mean
achievement scores of pupils in mathematics.
H08: There is no significant interaction effect of approaches and gender on mean
numerical aptitude scores of pupils in mathematics.
36
H09: There is no significant interaction effect of approaches and gender on mean
retention of achievement scores of pupils in mathematics.
H010: There is no significant interaction effect of approaches and gender on mean
retention of numerical aptitude scores of pupils in mathematics.
37
CHAPTER TWO
REVIEW OF RELATED LITERATURE
The literature review related to this study is organized under the following sub-
headings:
1. Conceptual Framework
• Teaching and learning of primary school mathematics
• Concept and components of achievement motivation.
• Achievement motivational instructional approach
• Traditional teaching method.
• Mathematics achievement
• Numerical aptitude.
• Gender and mathematics Achievement.
• Retention and mathematics achievement
2. Theoretical Framework
• David McClelland’s motivational need theory.
• Need Achievement Theory of motivation
3. Review of Related Empirical Studies.
• Studies on teaching approaches on primary six pupils gender
• Studies on teaching approaches on primary six pupils retention
• Studies on the effect of achievement motivational instructional approach on
achievement
• Studies on the effect of achievement motivational instructional approach on
retention.
• Studies on the effect of achievement motivational instructional approach on
numerical aptitude.
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Summary of Related Literature.
Teaching and Learning of Primary School Mathematics
Mathematics is all about finding solution to problems. All decisions taken are
based on such question as what and how this question is best answered by converting
every statement to mathematical statement before solution is sought (Eraikhuemen,
2003).
The depth of mathematical knowledge an individual has dictated is the level of
accuracy of his/her decision. This implies that before an individual can function in the
society, he/she must possess relatively good knowledge of mathematics. Obodo (1990),
noted that one contributory factor to teachers ineffectiveness in mathematics instruction
include lack of knowledge and interest in both teachers and pupils.
Another researcher Agyeman (1993) reported that a teacher who does not have
the academic and the professional teaching qualification would undoubtedly have a
negative influence on the teaching and learning of the subject and again, Coskun (2010)
added that a teacher who cannot demonstrate mastery of the concepts in a particular
subject matter area of mathematics is bond to having his/her pupils performing poorly
in mathematics. Teachers lack of knowledge of the mathematics concepts has remained
a very serious issue that needs attention. According to Betiku, (2002), Pupils
performance is a function of many variables including teacher characteristics, teacher
activities and pupils background which can either positively or negatively predict
pupils’ mathematics achievement.
But poor mathematics performance in Nigeria primary schools has generated an
over whelming need for a review of current teaching and learning approaches (Felix,
39
2009). The mathematical Association of Nigeria MAN (1977) once decleared a war
against poor achievement in mathematics (WAPAM). Unfortunately, WAPAM
achieve little in reversing the trend of poor mathematics achievement in Nigeria
schools. Poor achievement in mathematics in Nigeria primary schools has assumed an
alarming proportion and caused a lot of concern for many years. This study therefore is
to proffer a new approach towards reversing the trend. The effectiveness of a new
approach has to start from the foundation level which is the primary school level. The
primary level has its curriculum cutting across primary one to primary six.
Primary six mathematics curriculum comprises of mostly revision topics. At
primary six most topics have been taught at primary one to primary five. The primary
six mathematics curriculum emphasized on areas that need reading, recalling,
reviewing. The curriculum has been designed to take charge of topics, content
coverage, performance objectives, activities for teachers and pupils, materials to be
used where necessary and the evaluation. For a successful exposure of primary six
mathematics curriculum within the given time, the teachers should arrange the
curriculum to incorporate
i. The application of 3R (Read, Review, Recall)
ii. Understanding mathematics language instruction write in figures e.g. take to
decimal, significance etc reduce to simplest form with or without calculator,
calculate.
iii. Diagnose and treat pupils difficulties. E.g. define, state, mention, enumerate,
calculate etc.
40
iv. Using practical activities to ensure that learning takes place. E.g. measure, draw,
divide, locate etc. this will clearly expose the content of primary six mathematics
which when applied the achievement motivational instructional approach will
improve mathematics achievement and numerical aptitude which shows the
same mathematics content.
According to Yara (2009), attitudes of pupils can be influenced by the attitude of
the teacher and his method of teaching which agreed with Haigh (2008), who
emphasized on teaching learning process such that he gave what the teachers should do
to bring a lesson to a successful end as follows.
1. The teacher is to teach and the children learn –
• Remember that there are too levels of teaching ie shallow end teaching and Deep
end teaching.
• Use different approaches to teaching and learning.
• Apply different strategies at different times.
• Begin with the simple approach and progress from there
• Help children to make sense for themselves
• Don’t conflate content with process.
2. Guide children to discover for themselves
• Give children some ownership of their learning.
• Plan for children to discover what you want them to learn.
• Use questions to guide children to your teaching points.
• Decide whether you are questioning to assist or to assess.
• When you teach don’t test; when you test don’t teach
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• Don’t make children struggle.
• Teach off the children’s answers
3. Determine the pace of the lesson-
• Don’t talk too much
• Stick to the lesson objectives
• Don’t confuse speed with timing
• Refocus on the lesson objectives during the lesson.
4) Make the children independent
• -Teach children good learning behaviors
• First teach children to listen and then to speak
• Teach children to produce knowledge, not just to reproduce it.
• Create a classroom climate where children feel to question.
• Model the intelligent behaviours you are looking for.
5) Teach children to think
• Teach children to reason.
• Help children to behave more intelligently
6 Organize group work
• Train children to work in groups.
• Teach children to cooperate.
• Decide which your focus group for teaching is.
• Move around your group with purpose
• Help children to help each other with their learning.
42
According to Amoo and Efumbajo (2004), despite these efforts mathematics has
not secured its rightful position in the mind of pupils due to lack of interest as a result
of poor teaching. This study is aimed at providing an effective achievement
motivational instructional approach that will enhance achievement in mathematics.
Concept and Components of Achievement Motivation
The architect of self determination theory Richard Ryan and Edward Deci
(2009) refer to teachers who create circumstances for pupils to engage in self
determination as autonomy supportive teachers. These type of teachers according to
Santrock (2011) often have positive expectation for high ability pupils; they show the
pupils concession in all they do, give pupils enough time to answer questions, respond
to such pupils with more information and in a more elaborate way, criticize them less
often, praise them more often, seat them closer to the teachers desk, and even give them
close calls in grading. Aydin (2013) also said teacher monitors the pupils expectations
to ensure that they have a positive expectation by helping the pupils set their own goals,
plan how to reach the goals and monitor their progress towards the goals. Anderman
(2011) in his own view said goal setting is a key aspect of achievement motivation. He
maintain that pupils who set their goals, do challenging exercises, answer difficult
questions and uses their time and energy to achieve the standard objectives set.
According to Aydin (2013) achievement motivated pupils show curiosity and interest in
class by actively participating in class and active in mental problems, e.g. mental sums,
and show willingness to work thereby striving to attain excellence. Okwajiako (2002)
found out that achievement motivation improves when pupils set goals that are specific
“I want to get an A in the next mathematics test”.
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Santrock (2011) observed that teachers monitors the progress of pupils who have
high ability to retain what they had earlier learnt. That such are the pupils teachers use
to represent schools in debates and quizzes because the pupils can remember at short
notices and time. He maintained that such pupils always have extra lessons to boost
their intellectual abilities for to such pupils do the schools depend on in inside and
outside competition, who bring trophies of success and excellence to the schools.
Cavazos (2011), therefore said that how hard pupils will work can depend on
how much they expect to accomplish the set goals and how hard pupils work is
influenced by the value they place on the goals they have set. Researchers have found
that pupils achievement internal motivation and intrinsic interest in school tasks
increase when pupils have some choice and some opportunities to take personal
responsibilities for their learning (Bella, 2009). A teacher giving a group of pupils’
opportunity to measure the classroom and be able to present it in their own way that can
be mathematically meaningful. Such type of self determination can enhance
achievement motivation and Maclelland (1961) said that the motivation to achieve an
attainment of realistic but challenging goals is known as achievement motivation.
Achievement Motivational Instructional Approach
Achievement Motivational Instructional approach is a pupils’ dominated approach
which is aimed at enabling pupils to remember what had been stored in their long term
memory. The approach is categorized into four namely (i) SQ3R which is scan
question, read, recall and review (ii) understanding mathematics language instructions
(iii) diagnosing and treating pupils difficulties and (iv) using practical activities to aid
solving mathematics.
44
Coskun (2010) qualifies achievement motivational instructional approach as an
approach that cattered for every mathematical concept and the application of the
concepts as stipulated in the mathematics curriculum. Achievement motivational
instructional approach is aimed at building a child’s intellectual and potential ability. A
primary pupil need proper nurturing as the knowledge gained at this level can never
depart from them unless they were not properly nurtured. Most pupils leave primary
schools without knowing how to read, talkless of solving problems. Teachers there fore
need to keep the pupils under check and balance by making sure that previous
knowledge of the pupils is not forgotten. Other wise the teacher will see himself
marking time and will be considered not teaching. If a child leaves primary three to
primary 4, what the pupil is going to meet is not completely new. The teacher must
always make reference to past knowledge by involving the pupils to remember. By so
doing the pupils will be actively involved. That is when the achievement motivational
approach comes. This approach keeps a child active, curious, and always alert, it is
pupils’ dominated approach. The achievement motivational instructional approach is
organized into four categories namely
The First Step: Applying SQ3R (scan question, Read, Recall and Review)
According to Halonen (2009), various systems have been developed to help
pupils remember what they had learnt and what they are still learning. This system he
maintained benefits pupils by getting them to meaningful organize information, ask
question, reflect and review while Oshibodu, (1998), stressed that success in solving
primary mathematics relies on understanding the problems. He noted that SQ3R
enables pupils’ remember what have been taught in the past.
45
• SQ (Scan Question): The pupils go through the question over and over to get the
sense of the over all organization of ideas. The pupils should look at the topic and
subtopics that will be covered and then ask themselves questions about the materials
as they read. Most children cannot read and if you cannot read, you cannot
understand mathematics.
• Read: This is the ability to read very well and be able to interpret. Reading is a very
important aspect in the study of mathematics because without this ability, a child
will not be able to comprehend mathematical terms and will not be able to solve
mathematics. The child needs to learn how to read very well and with understanding
first before learning how to interprete the mathematical language into mathematical
statements. This will help the child to recognize mathematical symbols and signs.
Santox, (2011). agues that the three main goals of reading instruction should be to help
children
i. Automatically recognize words
ii. Comprehend text, and
iii. Become motivated to read and appreciated reading.
These goals are inter-related in that if children cannot recognize words, automatically
their comprehension suffers and if they can not comprehend the text, they are unlikely
to be motivated to read it. (Pressley & Harris, 2006) gave some strategies that teachers
can help pupils use to improve their reading as
• Overview text before reading
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• Look for important information while reading and pay more attention to it than
other information, ask yourself questions about the important ideas or relate them to
something you already know.
• Attempt to determine the meaning of words not recognized
• Monitor text comprehension
• Understand relationship between part of text.
• Recognize when you might need to go back and reread a passage (you didn’t
understand, to clarify an important idea, or to underline or summarized for study).
While Gunning (2010), observed that struggling readers can make tremendous progress
through programs that focus on learning letter-sound relationship which help in
decoding process that is so important to developing fluency; practices that facilitate
development of comprehension including summarizing and predicting; and teach
specific strategies to promote comprehension and retention of text material. Here
comprehension is extremely important because the focus in reading had shifted from
learning to read to reading to learn.
Reading more effectively therefore is by stressing reading for comprehension. The
teacher should help the pupils check for meaning that is whether it made sense or is
confusing, is understood and if the pupils know what was read, can summarize and
reflect. The teacher guides the pupils’ read the text and monitors the pupil to read with
understanding (checking their comprehension). This the teacher does by making sure
that they recognize important concepts and ideas. This will be done over and over to
enable the pupils determined the meaning of words. Example in writing and reading up
47
to one million teachers should guide the pupils’ to practice reading and writing up to
one million using Abacus and charts to aid them.
Teachers should encourage pupils to be active readers, the pupils should immerse
themselves in what they are reading and strive to understand what the author or the
problem is saying. The extent to which a solver understands the problem and the
nature of its solution depends largely on how rich and accurate his interpretation to
what he read is. According to Fuller (2003) success in solving mathematics
problems is due to the ability to read with understanding. That is the verbal
statement must be understood and the unknown must be detected by the pupils. For
example in open sentences, population, algebraic expression.
Recall: This according to Rabedeau (2013) is the ability to remember what was retained
in the long term memory. By occasionally reflecting and recalling on the materials and
questions, the pupils see its meaningfulness. The teacher now guides the pupils to
recall what they already know that is connected to the topic at hand. This can be done in
an interactive section or by writing simple problems for pupils to come out one after the
other to solve the problems on the board. This will enable the teachers know the ability
of the class and know how to plan the termly work. Example in counting in million
pupils should revise the previous work in counting to enable them remember how to
count up to even nine million with the aid of abacus and charts.
At this point, teachers should encourage the pupils to make up a series of questions
about what they had done and what they are still doing and try to answer them. e.g.
formulars, operations etc.
48
Review: The teacher guides the pupils to go over the work or problem and evaluate
what they know and what they do not know. Jegede and Jegede (1990) said at this
point pupils should re-read and study what they do not remember or understand well.
According to Sontrock (2011), SQ3R is a system that had worked well for elementary
high school pupils because it checks the pupils previous knowledge and their ability to
retain what they had learnt in the years past. Examples review properties, diagrams and
graphs.
The primary six mathematics curriculum emphasized on areas that need reading,
recall and review for proper teaching and learning. Rabedeau (2013) said that teachers
should always keep children on constant check by giving them surprise exercises such
as mental sums, dictation, classwork, assignments and from time to time check their
notebooks and even their test books. This he said will keep pupils alert in class and
after school. The pupils will always develop the ability to read and remember all they
had ever done that is their previous knowledge will always be updated.
The Second Step: Understanding the purpose of mathematics instruction.
According to Chukwu (2001), pupils fail mathematics examinations because of
their inability to recognize and follow the right instructions. Andermman (2010)
mentioned four mental operations important in solving mathematical problems as
• Recognize the problem and use definitions where necessary.
• Regroup as to transform the problem
• Remember known facts.
• Supplement by introducing auxiliary elements.
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He noted that instruction if followed correctly improve pupils achievement in
mathematics.
Examining some instructions such as
i) write in standard form
ii) Take to 2 significance figures
iii) Reduce to its lowest term
iv) Convert to decimals
v) Without the use of calculators, add, multiply and so on.
Pupils’ do not do what the instructions says but rather do the contrary and this leads
them in to a different method thereby arriving at different answers. Santrock (2011)
noted that mathematics is instructional in nature and succeeding in mathematics means
being able to interpret every mathematical statement to solvable problems before
solutions are sought. The teachers should explain this terms with specific example and
let the pupils examine the various mathematics instruction and solve accordingly.
The Third Step: Diagnosing and treating pupils difficulties.
According to Taiwo (1993), teachers should help pupils to actively construct
their understanding, set goals and plan, think deeply and creatively, monitor their
learning, solve real world problems. Alio in Akor (2005) noted that teachers should
closely guide the pupils as to discover answers to their instructional problems by using
investigating procedures. These procedures he maintained will enable pupils discover
or develop new rules and concepts. In an attempt to do this pupils should be asked to
define, evaluate, identify, solve, Recite and state. This according to Anderman (2010)
will enable the teachers know where pupils are lacking and the pupils will also know
50
what areas they have problems. Through the diagnoses the teachers will arrange for
extra lessons for pupils or device new ways to handle the problems. Thompson, (1995)
stressed that the teacher constantly monitors and verify flow of discussion and use
questions as informal assessment of pupils knowledge so that teachers can spot and
redirect errors and misleading immediately they occur.
The Fouth Step: Using practical activities to aid studying.
This is pupil centered activity oriented method of teaching which enables pupils
to work together. According to Adeniran,(2004), to learn mathematics and to use it
requires practice, repetition and drill. The teachers play a critical role in establishing a
rich environment to exploring and providing the necessary direction to ensure that
mathematical ideas are recognized. This procedure makes pupils use their minds to
think and reason together thereby building positive self concepts in them and promoting
interest. Harbor-Peters (2002) pointed out that practical method allows pupils to
discover for themselves and it is the most effective method of learning because it allow
learners to actively participate in the learning process. Also Karplus (1979) was of the
opinion that when doing practical exercises you are exposed to three types of methods
which are expository, Guided discovery and unguided discovery. Ahmed (2000) noted
that drilling and practices play an important roll in mastery of computational skills in
mathematics. This is achievement motivational instructional approach which gives the
pupils opportunity to brainstorm as they take active part in recalling and reviewing
concepts and facts they had learnt before in relation to what the teacher is teaching
presently. The achievement motivational instructional approach attempts to correct the
anomalies of the lecture and traditional teaching methods.
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Traditional Teaching Approach
Agwagah (2004) said traditional teaching approach is a “transmission” model in
which teachers try to convey knowledge to pupils directly. In a traditional classroom,
the teacher begins the lesson by giving the pupils a fact or rule. The teacher then works
a text book example and assigns pupils to work exercise from the textbook to help them
remember the fact or process, without really minding whether the pupils could even
read what was written, or link what was taught with any previous knowledge that could
help make the concept or idea clearer. Various teachers apply various approaches.
The teacher is after ending the scheme of work, and so gives out lessons to
pupils to copy on the board and read on their own. The teacher never goes back to find
out if the pupils copied correctly and if they understood the note and so lives the pupils
in a more confused state whereas in achievement motivational instructional approach,
the teacher will remain very much involved in the learning process, coordinating and
monitoring pupils build their own knowledge. This is explain by Rabedeau (2013)
when he said that the teacher learns to guide, not to tell, monitors the pupils towards
achieving their goals. Babara (1994) gave a distinction between achievement
motivational instructional approach and a traditional instructional approach as
Traditional Achievement motivational instructional
Teacher directs Pupils explore
Instruction is didactic Instructional is interactive
Instruction on single subject Pupils perform extended and disciplinary work
Pupils is knowledge dispenser Teacher is facilitator
Pupils work individually Pupils work collaboratively
Pupils assessed on fact knowledge
and discrete skills
Pupils assessed on performance.
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Koran (2001) observed that in a traditional lesson, the teacher is the master
source of knowledge and exercise control over the pupils. He does most of the talking.
Research studies has shown that average teacher does 70% talking in the classroom,
and the pupils get the impression that they can learn only when their teacher is present
and teaching. But Gbamanja (1991) observed that the traditional method makes pupils
to easily get bored, frustrated and easily loose interest in mathematics. Also it does not
take care of the individual differences of the pupils in terms of learning abilities.
Despite the ineffectiveness of the traditional method, most teachers are
sometimes force to use it. This is due to large class size, lack of instructional materials
or mathematics teachers and the urgent need to cover the syllabus so that pupils may
face their examination. In view of this, Azuka (2000) observed that pupils poor
performance in mathematics examination might be due to the teaching method adopted.
Hence the need to explore an effective teaching approach as achievement motivational
instructional approach.
Mathematics Achievement
Mathematics achievement is a measure of what the pupils had learned or what
skills the pupils had mastered (Gregory, 2011). Achievement that assess skills in
mathematics is known as mathematics achievement. Mathematics achievement serve a
wide variety of purpose from the informal quiz on a single facet of a topic to a formal
final examination which systematically samples the curriculum of the entire school year
and helps to rank pupils for the purpose of assigning grades and making
recommendations. According to Akinsola and Popoola (2004), mathematics
53
achievement carefully developed or selected to represent faithfully the major objectives
of instructions, provide pupils with information about these instructional objectives and
their best feed back on how well they have mastered what is expected of them. In the
same vain Koran (2001) said preparing pupils for mathematics achievement test and
reviewing with them the results of the test, will reinforce instruction and provide the
teacher with valuable information on where instruction has succeeded and where
additional efforts is needed.
Mathematics achievement tests according to Edestein (1985) are designed to
measure the knowledge and skills that individuals learn in a relatively well-defined area
through formal or informal educational experiences. Thus, mathematics achievement
tests include tests designed by teachers for use in the classroom and standardized tests
developed by school districts, states, national and international organizations, and
commercial test publishers. Harbor-Peter (2002), said mathematics achievement tests
have been used for: (a) summative purposes such as measuring pupils’ achievement,
assigning grades, grade promotion and evaluation of competency, comparing pupils
achievement, within the school system across states and nations, and also evaluating the
effectiveness of teachers programmes, and states in accountability programmes; (b)
formative purposes such as identifying pupils strengths and weaknesses, motivating
pupils, teachers, and administrators to seek higher levels of performance, and informing
educational policy; and (c) placement and diagnostic purposes such as selecting and
placing pupils, and diagnosing learning disabilities, giftedness, and other special needs.
Koran (2001) conducted a research on teachers and pupils motivation effects on
pupils’ mathematics achievement at junior secondary school level. The result of post-
54
test scores of the research showed that there is a significant difference in the
achievement levels of the two groups in favour of the pupils’ in motivated group which
is the experimental group.
Numerical Aptitude
According to Sontrock (2011) numerical aptitude are used by individuals to
measure ability to perform tasks involving the manipulation of numbers. The questions
on numerical aptitude range from simple arithmetic, for example, addition and
subtraction, to more intricate questions where you need to interpret numerical
information presented as graphs, tables and diagrams. As Edelstein (1985) put it that
there is no widely accepted definition of the difference between numerical ability and
numerical aptitude and as far as psychometric tests are concerned the two terms are
interchangeable. According to Gregory (2011) if one applying for a job which involves
working with figures on a day-to-day basis, the employer will regard ones numerical
aptitude as a valuable predictor of performance on the job. However, since most jobs
require someone to work with numbers at least some, numerical aptitude tests are
among the most widely used of psychometric tests. Okwajiako (2002) said there are
several hundred numerical aptitude tests from different suppliers in the market and they
all vary in both the number and difficulty of the questions that they contain. The
duration of the particular test will depend on the job/ purpose someone is applying for
and how many other tests he has taken on the day. Even though there are so many
ability tests available to teachers/employers, the types of questions used in these test
can be classified into:
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Numerical Aptitude - Computation
These questions involve basic mathematics including: subtraction, addition,
division, multiplication, ratios, fractions, percentages and decimals. You will need to
practice making quick and accurate calculations if you want to score well on these
questions.
Numerical Aptitude - Estimation
These questions involves basically to make quick estimates. You do not have
time to actually calculate these answers.
Numerical Aptitude - Reasoning
These questions test your reasoning ability rather than your ability to do
calculations. They invariably include some number series questions where you need to
work out which number or numbers are missing from the series and may also include
questions where a mathematical problem is posed in words and your task is to apply the
necessary logic to find the solution. To also do well, one must have a high retentive
ability. This can be called quantitative aptitude.
Numerical Aptitude - Data Interpretation
These tests commonly use: line graphs, scatter-plots, pie charts and tables which
you need to understand and manipulate to answer the questions. Data is sometimes
shown in more than one format and you may need to understand how the data relate to
each other before you can begin to answer the question. Scores in the computation and
estimation tests will depend on someone ability to add, subtract, multiply and divide
quickly and accurately. Someone can practice the type of questions that will be given in
rival estimation practice tests. Data Interpretation and numerical reasoning tests require
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to do fewer calculations than computation and estimation and someone may be allowed
to use a calculator. The achievement motivational instructional approach enables a child
face any numerical aptitude examination because a child that is trained with the
approach will certainly strive for excellence.
Numerical aptitude test
According to Edestein (1985), numerical aptitude test is designed to differentiate
among pupils with respect to their developed learning ability, and they are useful for
predictons, selection, guidance and grouping or for assessing the general academic
ability of a class or school population and tracing growth over a period of time.
Edestein maintained that aptitude test is not tied to a specific content, rather they are
required for a given age group only e.g. (primary six). From this base, aptitude test is
an attempt to differentiate effectively among pupils the extent to which they have
mastered important basic concepts and skills in their capacity to reason quantitatively
and logically and their ability to retain what they have learnt in the past. He maintained
that numerical aptitude tests are administered under exam conditions and strictly timed,
a typical test might allow 30-40 minutes for 30-40 questions. Okwajiako (2002)
observed that the questions are almost always presented in multiple-choice format and
may become more difficult as you progress through the test. These tests usually have
more questions than someone can comfortably complete in the time allowed, and so
advised pupils not to be worried if they do not finish the test - it is the number of
correct answers which counts.
To ascertain this the primary six placement examination to secondary schools is
used as numerical aptitude test. This examination comes at the end of their primary
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school year and it is an examination that will incorporate the entire curriculum running
from number and numeration to daily statistic the questions are asked in a way that
exhibits achievement motivational instructional approach on numerical aptitude and
retention. The aptitude test is said to cover areas of Computation, Estimation,
Reasoning which is the Quantitative Aptitude, Data Interpretation. It is a test that is set
by specialist outside the class. For instance Common Entrance or the placement
examination is not controlled by teachers teaching the pupils but by people unknown to
schools. It is controlled by the State Ministry of Education.
Gender and Mathematics Achievement
Pupils differ in their explanation of the cause of poor achievement especially in
mathematics. According to Ebeh (2000), individuals sometimes find themselves in
situation of feelings where they appear helpless about perceived events of threats or
problems and such a situation might affect normal function. This situation normally
comes during the process of test and evaluation especially in mathematics. Amoo and
Efumbajo (2004) said that most of the time, the teachers aids in the problems facing
pupils. Ezeudu (1998) observed that some of the problems centered on frequency and
type of teacher/pupils interactions, bias and views of staff, intimidation of girls by boys
within lessons, nature of mathematics, and assessment techniques used. In contrary to
the views of Ezeudu, Martin (2009) said, to learn mathematics and to use it requires
mastery, and to master to a skill requires practice, repetition and drill concentration.
Lack of concentration on the parts of pupils especially the female pupils. Female pupils
after school engage themselves in domestics work like cooking, plating of hairs, sowing
of cloths when they are through they get tired and will not be able to read. When they --
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are in class with their male counterparts, the male do far better than the girls because
the female never read the previous work.
In a study carried out by Nworgu, L.N. (2004) on gender gab in science
achievement reveled that gender gab between male and female students was reduced
and enhanced the overall achievement of boys and girls in science when gender
sensitization package was used. This implies that with enough sensitization and
motivation both boys and girls will perform equally. Boys and girls according to
Eraikhuemen (2003) if given equal opportunities will perform equally in mathematics.
Oftentimes usually feel withdrawn in mathematics and teachers do not care to motivate
and upgrade their willingness to work. This may contribute to gender inequality in
mathematics achievement but given the necessary encouragement the female are
capable of striving in mathematics as their male counterparts.
Al-Emadi, (2003) observed that boys exert better mathematics achievement than
the girls because the boys from the beginning are encouraged to be more independent
than the girls, therefore differential treatment of sex has given the boys more
confidence than girls and this enhances better performance in favour of boys, in
mathematics. There is always a belief that mathematics is difficult, abstract and a male
subject. Again Al-Emadi, asserted that teachers interact with male pupils more than
with the females. Franden (2003) advised teachers on how to avoid gender bias and
provide girls friendly mathematics and science education. In agreement with this
(Aydin 2013), in a primary class of 40 pupils, girls numbered 28 and males 12 showing
that girl children are outnumbering their male counterparts in school. Furthermore their
ability to strive and their level of participation in a mathematics lesson has not shown
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any significant difference. As a result, the views of the pupils about the scale of the
achievement in mathematics lesson has not shown any meaningful difference according
to the variable of gender. He concluded that female pupils these days are equally good
in mathematics as their male counterparts. The effect of achievement motivational
instructional approach will investigate the gap between males and females as it will
expose both sexes to things learnt in the past and in the present.
Retention and Mathematics Achievement
Aydin (2013) said retention is a necessary ability to primary six pupils and also
observed that primary pupils’ with well laid foundation are bound to do well in all
primary subjects because they always keep themselves busy, they strive to attain
success, and have the willingness to work. Also that such pupils do well because they
can afford to remember or reflect on their previous knowledge. Ali (2000) also viewed
that teaching mathematics using vernacular could improve retention thereby improving
mathematics achievement. Before a pupil gets to primary six, they have been taught
mathematics from primary one to five. So Ali added that the teachers of primary school
have a critical roll to play by establishing a rich environment to explore and provide the
necessary direction to ensure that mathematical ideas are recognized and retained such
that at primary six recalling, reviewing mathematics concepts and ideas becomes easy.
In the study of Eze, (2011)the students who were taught mathematics using
computer as tutor and tool performed better in mathematics achievement because they
could exhibit higher retention than those who were not taught with computer.
Retention in mathematics is engineered by the method used in teaching and
achievement in mathematics is enhanced when retention is highly exhibited. Similarly,
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Santrock (2011) said that pupils who are taught with achievement motivational
instructional approach exhibit high achievement and this high achievement is as a result
of their ability to retain mathematical ideas. This study therefore is geared towards
finding the effect of achievement motivational instructional approach on primary six
pupils numerical aptitude and retention in mathematics.
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Diagrammatical Representation of the Conceptual Framework
The diagram above shows the process of teaching and learning of primary school
mathematics using achievement motivational instructional approach as necessary
approach to pupils numerical aptitude, retention and achievement in mathematics.
Traditional teaching method
Achievement Motivational instructional method
Teaching method
Attributes/components of achievement motivation
Components of TM used (lecture, talk and chalk & didactic, etc)
Learning by male/female/Gender
Assessment instrument MAT x NAT
Achievement
Retention
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Theoretical Framework
Theory of Achievement Motivation
David McClelland's Motivational Needs Theory
Motivational needs theory was developed by American David Clarence
McClelland in 1961. McClelland is most noted for describing three types of
motivational needs:- achievement motivation denoted as (n-ach), authority/power
motivation denoted as (n-pow) and affiliation motivation denoted as (n-affil). These
motivational needs are found to varying degrees in all individuals, and this mix of
motivational needs characterizes a person's or manager's style and behaviour, both in
terms of being motivated and in the management and motivating others. The n-ach
person is 'achievement motivated' and therefore seeks achievement, attainment of
realistic but challenging goals, and advancement in the job. The theory believes that
there is a strong need for feedback as to achievement and progress, and a need for a
sense of accomplishment. The need for authority and power (n-pow) person is
‘authority motivated’. Such a person need to be influential, effective and to make an
impact. There is a strong need to lead and for their ideas to prevail. There is also
motivation and need towards increasing personal status and prestige. The n-affil person
is affiliation. To be liked and held in popular regard. These people are team players.
McClelland said that most people possess and exhibit a combination of these
characteristics. Some people exhibit a strong bias to a particular motivational need, and
this motivational or needs 'mix' consequently affects their behaviour and
working/managing style. McClelland suggested that a strong n-affil 'affiliation-
motivation' undermines a manager'? objectivity, because of their need to be liked, and
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that this affects a manager's decision-making capability. A strong n-pow 'authority-
motivation' will produce a determined work ethic and commitment to the organisation,
and while n-pow people are attracted to the leadership role, they may not possess the
required flexibility and people-centred skills. McClelland argues that n-ach people with
strong 'achievement motivation' make the best leaders, although there can be a tendency
to demand too much of their staff in the belief that they are all similarly and highly
achievement-focused and results driven, which of course most people are not.
McClelland particular fascination was for achievement motivation (n-arch)
McClelland identified the need for a 'balanced challenge' in the approach of
achievement-motivated people. McClelland contrasted achievement-motivated people
with gamblers, and dispelled a common pre-conception that n-ach 'achievement-
motivated' people are big risk takers. On the contrary - typically, achievement-
motivated individuals set goals which they can influence with their effort and ability,
and as such the goal is considered to be achievable. This determined results-driven
approach is almost invariably present in the character make-up of all successful
business people and entrepreneurs. McClelland suggested other characteristics and
attitudes of achievement-motivated people:
• Achievement is more important than material or financial reward.
• Achieving the aim or task gives greater personal satisfaction than receiving praise or
recognition.
• Financial reward is regarded as a measurement of success, not an end in itself.
• Security is not prime motivator, nor is status.
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• Feedback is essential, because it enables measurement of success, not for reasons of
praise or recognition (the implication here is that feedback must be reliable,
quantifiable and factual).
• Achievement-motivated people constantly seek improvements and ways of doing
things better.
• achievement-motivated people will logically favour jobs and responsibilities that
naturally satisfy their needs, ie offer flexibility and opportunity to set and achieve
goals, eg., sales and business management, and entrepreneurial roles.
McClelland firmly believed that achievement-motivated people are generally the
ones who make things happen and get results, and that this extends to getting results
through the organization of other people and resources, although as stated earlier, they
often demand too much of their staff because they prioritize achieving the goal above
the many varied interests and needs of their people.
McClelland (1953) postulated that participants high in achievement motivation
have a tendency to set realistic learning goals and consequently prefer tasks having
moderate difficulty than either easy or very difficult tasks while participants low in
achievement motivation have a tendency to avoid situation of uncertainty. They prefer,
consequently, easy and very difficult tasks that minimize uncertainty of failure and
success. This study in line with the theory of achievement motivation by McClelland
tries to find out the effect of achievement motivational instructional approach on
primary school/pupils’ numerical aptitude and retention in mathematics. According to
Aydin and Coskun (2011), achievement motivational instructional approach is capable
of increasing the achievement motivation of pupils that will reflect to their behaviour
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what they hard learned and achieved. They maintained that the achievement
motivational instructional approach gives pupils the disposition to participate actively
in the learning process thereby offering them opportunity to strive for success and
continue to show the willingness to work. Haigh (2008), in his view advice teachers to
teach meaningfully by helping pupils set goals that are challenging but realistic. This
he said will help the children attain high level of success and excellence. This theory is
based on the belief that pupils learn best when they gain knowledge through exploration
and active learning which are attributes of achievement motivational instructional
approach. In addition, one of the features of the theory that is relevant to this study is
the motion of teachers guiding pupils to set goals which they can influence with their
effort and ability which is in the character make up of all successful people. A
significant part of the theory is that it adopted the approach of reading, recalling,
reviewing, understanding mathematics language instruction, diagnosing and treating
pupils’ difficulties and using practical activities that keeps pupils busy and actively
solving mathematics problems, which a traditional classroom does not offer. The theory
seems to offer a means of investigating the growth of pupils understanding of the
concepts in mathematics in a very detailed way.
In conclusion McClelland’s motivational need theory in connection to
achievement motivational instructional approach presents clues and approaches to how
pupils activities in mathematics can be improved by applying reading, recalling,
reviewing and practical activities. Also uniquely draws the theories of achievement
motivation into classroom practices for meaningful learning. And finally beliefs that
there is a strong feedback as to achievement and progress.
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Need Achievement Motivation Theory
The need achievement motivation theory rests on the belief that most persons
want to achieve and experience levels of aspiration in a given environment.
Contributors of need achievement motivation theory are J. W, Atkinson and David
McClelland, (1953). According to Atkinson, (1953), when an individual is actively
involved on a task, he sets himself a standard to conquer. This standard is called the
level of aspiration. Caraway, (1985) pointed out that level of aspiration is a longing for
what is above one, with advancement as its goal. Aspiration has to do with the desire to
improve or to rise above one's present status. There are two set of factors which
interacts to determine the level of aspiration. They are the personal factors and the
cultural factor/environmental factors. Bella (2009) explained that personal factor relate
to such personality traits as intelligence, interest, gender, self concept, activity level,
socio-economic status and previous training experience. Cultural and environmental
factors include parental ambition, social values and social reinforcement. Need
achievement is more influenced by environmental factors. Some environmental factors
encourage the development of immediate aspiration.
According to Gregory (2011) the implication of need achievement theory is that
the teacher should create learning environment conditions that will help learners
adequately assess their abilities and opportunities available so that they can set realistic
and attainable goals. In this way learners will experience success in school activities
and thereby build positive self-concept which enhances need achievement motive.
Owing to the dominance of the teacher in the traditional teaching approaches, pupils are
not engaged in the classroom activities because such environment is not provided. This
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results into rote learning and memorization of facts with little transfer of knowledge.
Opara (2002) observed that the method hardly increased pupils enthusiasm and interest.
Meaningful learning activities built on prior knowledge motivate pupils and foster their
interest in their effort to executively control their own cognitive process. The fourth
stage of achievement motivational instructional approach which is using practical
activities to aid studying falls in line with the need achievement motivation theory since
it gives the pupils the opportunity to interact with themselves and the environment. The
achievement motivational instructional approach is an approach that McClelland called
‘balanced challenge’. It is on approach that exposes pupils to various ways of solving
problems.
Review of Empirical Studies
Teaching Approaches on Primary Pupils Gender
Amoo and Efunbanjo (2004) carried out a survey study on the attitudes of
primary school teachers to the teaching of mathematics. Two hundred and fifty primary
school teachers in Noforija-Ekpe, Lagos State irrespective of class taught participated
in the study. A self developed questionnaire that consisted of 20 items was used and
the method of analysis were t-test and multiple regression analysis were employed. The
results revealed that teaching of mathematics is beset with problem of non male and
female teachers to the teaching of mathematics. The characteristics of teachers that is
gender, qualification and area of specialization jointly contributes 76.5% to teachers
attitudes towards mathematics at primary school level. It suggests that there is strong
influence of the characteristics on attitude towards mathematics which was on how to
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teach mathematics in the primary schools as to enhance sustainable technological
development.
Ali (2000), investigated the effects of the use of Edo and Igbo for Teaching and
learning mathematics in Nigeria primary schools. Three groups of subjects participated
in the study. The groups were further broken down to primary 5 and primary 6. The
study made use of primary 5 and primary 6 pupils drawn from various states of Igbo
speaking and Edo speaking. The mode of instruction was that some were taught using
Edo and Igbo alone, some Edo and English and Igbo and English while the third
category which was the control group consisted of primary 5 and primary 6 selected
from various places of Igbo and Edo speaking areas who were taught mathematics in
English alone. All the primary 5 pupils were taught the same mathematics namely
practical and descriptive geometry drawn from the National primary mathematics
syllabus, the primary Education mathematics curriculum (PEMC).
Teachers who were involve for experimental group 1 and 2 were provided with
daily lesson plans prepared in Igbo and Edo languages. Those of the control group
taught mathematics with English alone had the lesson plan in English. Two respective
twenty item post-test, the Primary Mathematics Test (PMT) for primary five and
another for primary six drawn from the two respective mathematics topics. The validity
index was 0.79 and the reliability was 0.86. At the end of the five weeks of teaching,
the subjects were post-tested on the PMT and the PMT was scored and analyzed. The
results revealed that the use of vernacular in teaching primary 5 and 6 yielded feasible
results and both boys and girls had the same opportunities and no significance different
in their ability.
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Ife Centre for psychological studies (2010) examined whether there was a
significant gender gap in Mathematics achievement, and the nature of the gender gap.
It also investigated factors associated with the differential performance of girls and
boys and their retentive ability in mathematics class. The site for this study was a rural
primary school in Kwazulu Natal. Quantitative data was drawn from primary 6
mathematics achievement test results conducted in 2008 and 2009. In addition,
individual semi structured interviews and focus group interviews were conducted with
8 pupils (Male = 4, females = 4) from the 2009 cohort of primary six pupils. The
findings of the study revealed a gender gap in mathematics achievement in favour of
girls and that girls tend to remember what they have been taught more than the boys.
Sam, Joshua and Asim (2010) conducted a study to empirically verify the
existence or otherwise of gender inequality and retention in mathematics achievement
of rural male and female primary school pupils in Cross River State, Nigeria; and
whether parental socio-economic status and school proprietorship taken independently
are significant factors in the achievement of the pupils. By stratified and simple random
sampling, 2000 pupils 50% males, 50% females) were selected and a 30 items, four
options multiple choice mathematics achievement test (MAT) was constructed which
was pre-tested and post-tested. The independent t-test analysis of significance revealed
gender inequality and the girls having high retention over the boys. Researchers such as
Agwagah (2013), Korau (2008) have reported that boys out perform girls because boys
increase interaction with teachers and this influence better development of mathematics
concepts among male pupils. Also the pattern of interaction in class tends to make boys
appear more confident in mathematics than girls. The type of pattern of interaction
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mathematics teachers use in classroom matters because this will show the effectiveness
of teachers in teaching mathematics. Achievement motivational instructional approach
enables the teacher to exercise optimum interaction in a mathematics class. Pupils are
made to read, recall, review, use practical approach in solving problems. Teachers can
only achieve this when they have knowledge of content and can plan instructions for
pupils with different abilities and learning styles. By so doing pupils retention will be
upgraded and the issue of whether boys or girls do better will be taken care of.
Nnamani, (2010), investigated the effect of information and communications
Technology (ICT) Instructional package on, achievement of pupils with different
learning styles in primary science. The ICT instructional package used in this study
consists of prepared lessons on the two primary science topics taught in the study. The
study focused on two of the Felder Silverman’s dimensions of learning styles
(active/respective and visual/verbal) which have link with the learning process in a
classroom. The study also examined the influence of gender on achievements of pupils
with different learning styles in primary science. A quasi-experimental pretest posttest
non-equivalent control design was employed for the study. The study employed the
multi-stage sampling technique. A total of 177 primary five pupils who were clearly
demarcated on the two dimension of learning styles were investigated and sampled
from two schools in Nsukka Urban within Nsukka Educational Zone participated in the
study. Two instruments served the purpose which were learning style instrument and
achievement test tagged pupils achievement test in Primary Science (PATIPS). The
results of the study indicated that pupils made use of different learning styles during
learning and that gender influencing the learning styles of the pupils. The use of ICT in
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the delivery of primary science instruction enhance the achievement scores of pupils in
primary science and gender did not significantly influence the achievement scores of
pupils with different learning styles.
In the reference to the study conducted by Nworgu, L.N. (2004). The study was
designed to investigate the effect of gender sensitization of science teachers on gender
gap in science achievement and interest among students. The study was guided by four
research question and six hypothesis and adopted a non equivalent control group
design. The population comprise of all JS II students from six secondary schools
sampled from of seventeen co-educational schools in Nsukka Local Government Area.
The experimental Schools (3) were exposed to gender sensitization package while the
remaining three used conventional instructional approach (control). The reliability of
the instruments were established using Kudder Richardson formula 20 (K-R20) for
ISAT and Crombach’s alpha for ISIS. The reliability indices were found to be 0.84 for
ISAT and 0.76 for ISIS. Means and standard deviations were used to provide answers
to research questions while analysis of covariance (ANCOVA) was used to test the
research hypothesis at 0.05 level of significance. The result of the study showed that
gender sensitization package reduced gender gap that existed between male and female
students in science achievement and interest. Furthermore gender sensitization package
enhanced the overall achievement of boys and girls in science. Again the interactive
effect of sensitization and gender was statistically significant for achievement but not
for interest.
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Teaching Approaches on Primary Pupils Retention
Eraikhuemen (2003) also carried out a study on mathematics as an essential tool
for Universal Basic Education (UBE); implications for primary school mathematics that
can boost pupils ability to recall facts but cumulative evidence point to the fact that the
generality of pupils and teachers find mathematics uninteresting and pupils
unacceptable dimension. He pointed out that the needed involvement of the
mathematical association of Nigeria for effective teaching and learning of primary
school mathematics are Awareness campaign; for better methods. Problematic topics
identification, teachers retraining; and sourcing for fund. In conclusion Government
expects that the entire Nigeria populace will patriotically assume ownership of the
program by.
• Initiating and participating in continuing policy dialogues on the programme,
• Sensitizing all citizens to the need for all Nigerian children of school going age
to take full advantage of the free, compulsory UBE progrmame.
• Encouraging the out of school population to take advantage of the schooling
literacy and non-formal education programmes which will be an integral
ingredient of UBE.
• Mobilizing all and sundry to contribute (ideas-where possible, logistics, moral
support, etc). This was due to high retention of ideas. He also examine the
gender effect which he pointed out females tend to do better than boys this days
in mathematics.
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Furthermore, according to Ali (2000), because of the understanding of the
subject due to the use of vernacular, the level of retention increased thereby elevating
the interest and achievement in mathematics.
Ogbonna (2007) carried out a study on the effect of two constructivist
instructional models on students achievement and retention in Number and Numeration.
The study was carried in Abia State and a quasi experimental design was used. The
study used 290 JS III students. The findings revealed that the students who were taught
with the two constructivist instructional models (IEPT and TLC) achieved and retained
higher than those taught with the conventional method. Also female students
performed better than their male counterparts. The results from the studies conducted
by Aydin and Coskun (2011), and Perez, (2013) show significance difference in
mathematics achievement and retention between male and female students.
Studies on the Effect of Achievement Motivational Instructional Approach on
Primary Pupils Achievement
The relationship between achievement motivation and performance was
established in a study by Jegede (1990) whose work sought to determine the effect of
achievement motivational instructional approach and study habits on Nigeria primary
school pupils’ academic performance in English language learning. The experimental
variable (study habit and achievement motivation) were manipulated and their effects
on the dependent variable (English language performance) were observed. There were
four experimental groups for the study. All the groups were pre-and post-tested on the
measure of achievement motivation, study habits and English language performance.
The target population for the study was primary six pupils in mixed primary schools in
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Ilorin Nigeria. Four schools in that area were randomly selected and assigned to
treatment groups (three experimental and one control group) 40 pupils were selected in
each school (N = 160) for the study.
Bakare’s (1970) Academic Need Achievement motivation scale was used to tap
pupils achievement motivation. There were 36 standardized statements, to which the
pupils responded on a 5-point scale according to how true each statement is of him or
her. The validity and reliability were verified. Analysis of covariance (ANCOVA) was
used to test for the significance of the data. Thus there were significant differences
among the experimental groups performance in English. The findings lend further
support to the research hypothesis that pupils who were administered the combination
of improved study habit and higher achievement motivation would perform better in
English than any of the other groups as (study habit, achievement motivation and
control). The result also showed a significant different among the male and female
pupils where the boys performed better than the girls.
Studies on the Effect of Achievement Motivational Instructional Approach on
Primary Pupils Retention
Aydin and Coskun (2011) investigated the relationships between the
achievement motive of primary school pupils and the relationship between the
achievement motivational instructional approach. Class level”, parent, educational
level”, family income level. A total of 151 pupils took part in the study. A survey
model was used and the achievement motive scale develop by Fox, (2004) was used as
data collecting tool. t –test and one way analysis of variance (ANOVA) were used in
the analysis of data. At the end of the study the arithmetic mean of the views of pupils
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on the scale of achievement motivation has been determined to be 3.74. The views of
pupils about the scale of primary mathematic lesson achievement motivation has shown
significance difference according to class level but did not show any significant
difference according to ‘gender’ mother’s education level; father’s education level and
family income status”. Based on the findings of the study, suggestion for increasing the
achievement motivation of the pupils towards primary mathematics curriculum have
been developed to show that such pupils have the ability to strive for success,
participate actively in mathematics lessons, show the willingness to work, maintain
working and the ability to retain and be able to remember what they had learnt in the
past.
Pe rez, (2013) worked on a framework for understanding what might influence
children’s retention. She employed the framework of individualism and collectivism in
the bridging of cultures project and saw it as a source of understanding why the star
chart may have bombed as a motivational tool. She started learning about the success of
groups collectively and to use the power of the group to help everybody succeed.
Equipped with a new understanding of culture and in particular the collectivism of her
pupils, Pe’rez reconceptualized the chart from the means of encouraging pupils to earn
more stars for themselves to a visual aid that stimulated and encouraged the children to
think about achievement motivation as a group issue. The pupils all looked at the chart
together and talked about it and asked questions. From the children’s collectivistic
perspective, the chart seem to be a potential motivator for group achievement rather
than individual achievement. The study also revealed that both boys and girls can work
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effectively well given the same opportunity and the system made them to understand
better thereby giving them high retention.
Studies on the Effect of Achievement Motivational Instructional Approach on
Primary Pupils Numerical aptitude
Okwajiako (2002) took up a research to investigate the relationship between
achievement motivational instructional approach and numerical aptitude among
primary six pupils in Abia State. In this study, a total of 1024 pupils were randomly
selected across the primary schools in the state. The design used was ex-post facto and
three measurement instruments were used in collecting data; the achievement
motivation questionnaire, numerical aptitude test which was designed as quantitative
aptitude and mathematics achievement test. At the end, the result of the study showed
no significant difference in achievement motivational instructional approach and
numerical aptitude of the primary school pupils. Also no significant difference in the
achievement motivational instructional approach and mathematics achievement. The
study again viewed that there was a significance difference in gender where the males
performed better than the female.
Summary of Related Literature
The poor achievement in primary mathematics was attributed to poor
foundation, poor teaching methods, lack of interest in both teachers and pupils, lack of
knowledge of the subject. These have continued to pose a great concern to mathematics
educators, researchers, parents and even Government. It is in the basis to find a solution
to poor achievement of primary pupils in mathematics that made researchers to search
for methods that will improve pupils’ achievement in the subject. Hence, the
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introduction of achievement motivational instructional approach in teaching
mathematics. Many methods of solving primary mathematics had been in use.
However, research finding indicated that pupils’ are lacking in ability of solving
numerical aptitude problems and retention. The achievement motivational instructional
approach exposes the gymics in solving primary mathematics. It gives the pupils the
opportunity to work closely with the previous knowledge, affording the pupils the
ability to remember or recall all that was taught in the past thereby making their
reasoning, and retentive abilities very active also exposing the pupils aptitude
potentials. It is an approach that systematically unfold how to approach any
mathematical problem.
The review also revealed that gender disparity has long been a problem in our
researches and up till date it has not been clear on issues of gender because there is no
clear distinction as to which sex perform better than the other in mathematics
achievement. Under the framework for the study, McClelland’s motivational need
theory and need achievement theory of motivation were considered relevant and
suitable for this study. A lot of related empirical studies were reviewed in order to guide
the researcher in selecting appropriate design for the study, statistical tools and other
procedures for achieving the purpose of the study. Hence the effect of achievement
motivational instructional approach on primary six pupils numerical aptitude, on
gender, retention and achievement as mathematics.
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CHAPTER THREE
RESEARCH METHOD
In this chapter, the method to be used are presented under the following
headings, Research design, area of study, sample and sampling techniques, instrument
for data collection, validation of the instrument, trial testing, reliability of the
instrument, experimental procedure, control of extraneous variable, scoring of the
instrument, and method of data analysis.
Design of the Study
Quasi-experimental design was adopted in this study. Specifically, the pretest-
post test non-equivalent control group design. According to Gall, Gall and Borg (2007)
quasi-experimental design can be used when it is not possible for the researcher to
randomly sample the subjects and assign them to treatment groups without disrupting
the academic program of the schools involved in the study. Therefore, this design is
considered suitable for this study because intact classes (non-randomized groups) were
assigned to the two different groups in order to determine the effect of achievement
motivational instructional approach on primary school pupils numerical aptitude,
achievement and retention in mathematics. The design is symbolically represented
thus:
E O1 X1 O2 O3
C O1 X2 O2 O3
Where E - experimental group
C = control group
O1 = pretest
X1 = treatment experimental
X2 = treatment control
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O2 = Post test
O3 = Retention test
Area of the Study
This study was conducted in Calabar municipality Education Zone of Cross
River State Nigeria. The State is bounded by the North by Benue State, East by Akwa
Ibom and Abia States, North East by Ebonyi State, West and Southwest by Cameroun
and in the South by Atlantic ocean. The State is divided into 3 senatorial districts;
North, central and southern senatorial districts. The State comprises of 18 local
government areas of which Calabar municipality local government area is one of them.
Each local government area of the state has education authority zonal offices that
overseas the management of both public and private schools in the local government
areas.
The major languages spoken there are Efik, Ejachem and English. The local
government area is bounded by Odukpani local government area in the north south by
Calabar South local government area, in the west by Akpabuyo local government area
and in the east by the ocean and Odukpani.
Calabar municipality is one of the last local governments in the southern
senatorial districts of Cross River State and the education authority controls more
schools than any other local government because of its position as the centre of
business and as head quarters of the State. This area was chosen due to its position as
the centre and head of all educational activities where large number of pupils and
teachers reside and frequent supervision is carried out by education authority zone. This
will enable the researcher to supervise the workability of achievement motivational
instructional approach on primary school pupils in this zone.
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Population of the Study
The population of the study consist of all primary six (6) pupils in Calabar
municipality Education zone. The zone is made up of twenty four (24) public primary
schools (from the education authority zone of Calabar municipality local government
area of Cross River State as of March 2014) all of which are mixed. The schools joined
together has a population of about 2400 primary six pupils with boys numbering about
1,180 and girls about 1,220 (from the examination unit of State Ministry of Education
of Cross River State as of March 2014) where all primary six pupils are registered.
Sample and Sampling Technique
The sample for the study consisted of 241 public primary six pupils drawn from
24 public primary schools of Calabar Municipality education zone of Calabar
Municipality Local Government Area of Cross River State. Purposive sampling
technique was used to select Calabar Municipality education zone out of 18 education
zones in Cross River State. The Calabar Municipality education zone comprises of 24
public primary schools with 2,400 primary six pupils. Two schools of sample size
241primary six were selected using simple random sampling technique from 24 public
primary schools. All the schools are mixed each having 3 classes of A, B, C. One of the
schools was assigned experimental with 125 pupils and the other assigned control with
116 pupils and are used as intact classes.
Instruments for Data Collection
Two instruments were used for this study. The Mathematics Achievement Test
(MAT) (Appendix A, pg 110) and Numerical Aptitude Test (NAT) (Appendix B pg
116). The Mathematics Achievement Test (MAT) consist of 50 multiple choice test
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items and was developed by the researcher. The Mathematics Achievement Test (MAT)
consists of two sections. Section A shows the demographic variables which are name
of school, gender: Male [ ] Female [ ] and candidate register number. Section B
contain the main items which are made up of four (4) clusters.
Cluster A comprising of application of SQ3R question meant to guide a pupils reading,
recalling and reviewing. Total items in this cluster are 10 items.
Cluster B Comprising understanding mathematics language instruction with the total of
15 items meant to guide the pupils in understanding and interpretation of mathematical
statements.
Cluster C Diagnosing and treating pupils difficulties comprising of 15 items meant to
investigate areas of difficulties as to intensify strategy for solving mathematics.
Cluster D using practical activities to aid studying comprising of 10 items meant to
guide pupil working in teams practically.
The 50 multiple choice items using options A to E and are divided according to
the steps involve in achievement motivational instructional approach. The objective of
each topic (or section) guided the researcher on the depth the MAT items should cover.
The test blue print used in constructing the instrument was developed by the researcher
based on the relative emphasis in each of the sub-topic in primary six mathematics
curriculum appendix G pp. 158.
The question in each of the sections were classified into the three (3) cognitive
levels namely knowledge (K), comprehension (C), and Application, (A) which is the
lower cognitive process (LCP) for primary level of Education. The MAT items were
used to assess pupils’ cognitive achievement in primary mathematics topics.
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The Numerical Aptitude Test (NAT) was made up of two section A and B.
section A comprising of candidates name, number and gender: Male [ ] Female [ ]
while section B comprises of the main items from 1 to 50 which are in multiple choice
The NAT was a placement examination into Junior Secondary one developed by the
state ministry of education Cross River State. NAT is also a 50 multiple choice items
which is used to test the numerical aptitude of the pupils. The NAT was also used to
assess pupils’ cognitive achievement in primary six mathematics after being taught with
achievement motivational instructional approach. It is expected that the knowledge
gained from the approach will be applied to answer questions in numerical aptitude,
both in pre-testing and post-testing.
The researcher developed unit lesson plans appendix (C pp. 122) in all the
primary six mathematics topics to be used based on the test blue print using
achievement motivational instructional approach which will be used to teach
experimental group. The traditional lesson plan was also developed in all the primary
six mathematics topic to be used without involving achievement motivational
instructional approach. appendix (D pp. 137)
Validation of the Instrument
The MAT was face validated by two experts in curriculum and instructions and three
experts in mathematics education. Two of these experts from university of calabar and
three from University of Nigeria Nsukka. The validators were requested to
(a) check the suitability and clarity of the test items.
(b) Add any other items(s) which is/are relevant but had not been included in the
instrument.
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(c) Remove ambiguous or irrelevant statements in order to improve the structure of
the items. Based on the comments and suggestion of these experts, some of the
items were modified.
(d) To check the lesson plans if necessary informations were included
To ensure content validity of MAT, a test blue print or table of specification was
constructed based on the emphasis placed on each objective and content area of
Primary Six curriculum. The table of specification was based on the lower cognitive
processes; knowledge, comprehension and application. A total of fifty (50) multiple
choice items were drawn for MAT based on the lower cognitive processes. In addition
to the validation of the instrument, the lesson plans for the effective teaching of primary
six mathematics curriculum were face validated by experienced mathematics teachers.
The NAT was not validated because NAT was a standardized test from the state
ministry of education.
The MAT and NAT were trial tested to determine their stability using test-retest
method of administration on an intact class of 30 pupils at Government Primary School
Akpabuyo, Akpabuyo Local Government Area of Cross River State. This school is not
part of the sampled area for the study but have some similarities like the composition of
the pupils (mixed), the structural facilities and the same curriculum. The test retest was
carried out within an interval of two weeks.
Reliability
The data obtained from the trial testing of MAT and NAT was used to determine
the reliability coefficient of MAT and NAT. Kuder-Richardson formula (K-R20) was
found most appropriate. The reliability for MAT was 0.86 and NAT was 0.83. The
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reason for the choice of K-R20 was because the items are multiple and dichotomously
scored. K – R 20 was also to check the internal consistency of the instrument. (see
appendixes, H and I, pp. 175 and 181 respectively).
Experimental Procedure
The Numerical Aptitude Test (NAT) which is an intelligence test though not
structured by the researcher was adopted from the State Ministry of Education and also
tested alongside the Mathematics Achievement Test (MAT). The pretest of both
instruments were first conducted before the commencement of the treatment. The
pretest exercise provided the base line data that was used to compare pupils in both
groups (experimental and control). The pupils from both experimental and control
groups were taught primary six work using primary six curriculum. The experimental
group were specifically taught using achievement motivational instructional approach.
The approach was used for the purpose of mathematics achievement test and for the
purpose of any numerical aptitude test. The NAT was mostly to test the level of their
intelligence.
Furthermore, the experimental group were taught 5 lessons of 80 minutes each
(2 days at 40 minutes each) using the lesson plans based on achievement motivational
instructional approach likewise the control group were taught 5 lessons of 80 minutes
each (2 days at 40 minutes each) using the traditional teaching method. The training
lasted for 2 weeks at the end of the treatment; posttest was administered on the two
groups. Experimental group was administered with posttest of MAT and NAT and the
control group with MAT and NAT too. After the posttest, two weeks later the same
MAT and NAT were reshuffled and renumbered and re-administered to the same pupils
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(experimental and control groups) to test their level of retention. The scores obtained
from the two groups recorded and compared to determine the achievements of the
groups.
Control of Extraneous Variable
1. Experimental Bias: To avoid experimental bias, the regular class teachers in the
participating schools taught their own pupils in their group. The researcher was
therefore not directly involved in administering the instrument. To control invalidity
that could be caused by teacher variability and to ensure uniform standard in the
conduct of the research, the researcher personally prepared the teaching lesson plans
(Achievement motivational instructional approach and a traditional lesson plan
appendix C and D pp. 122 and 137 respectively). The researcher trained the
participating teachers and they were not allowed access to the test instruments until the
time it was to be administered. A three day intensive training programme was organized
for the participating teachers in the experimental school. The experimental group
teachers were trained giving detailed explanation.
2. Maturation: While the experimental treatment is in progress, changes in the research
participants (pupils) are likely to occur. Pupils might become more proficient, more
self-confident or more independent in solving mathematics problem. We might attribute
this gainful development to exposure of achievement motivational instructional
approach. It may not be clear whether the improvement was due to the approach or to
maturation. To tease out the effect of maturation, the control group of pupils who
received no exposure on achievement motivational instructional approach is equally
observed. If the group that received exposure perform better than control group that did
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not receive exposure, it will be reasonable to say that the achievement motivational
instructional approach not maturation led to the growth in the ability to think and solve
mathematical problems. To control this, the effective use of achievement motivational
instructional approach should be encouraged in schools by organizing workshops and
seminars that can make the approach clearer to teachers. These will irrespective of the
child’s age (maturity) will make a child grow in ability to think and solve problems in
mathematics.
3. Testing: In this research the two test (MAT and NAT) used the same format. Pupils
might show improvements simply as an effect of their experience with the pretest. In
other words, they have become “test-wise”. But to control this, the items in the test
should be alternated.
4. Experimental mortality or Attrition: This is a phenomenon of losing research
participants during the course of the experiment. Some pupils either from the
experimental or control groups may drop out of the study, miss pretesting or posttesting
or are absent during some sections, attrition might result from factors such as illness,
the study is too demanding or threatening. This threatens an experiment’s internal
validity. In order to control those who missed either pretest or posttest should not be
considered. That is there will be no results for them and should be removed from the
study.
Training of Teachers
The training on achievement motivational instructional approach was conducted
in the experimental school. The teachers of the experimental classes were used for the
training. There are three (3) classes with one teacher a class therefore three teachers
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were trained for the programme. The programme of the activities for the three days was
as follows.
Day One
1. Introduction of participants on the purpose of the training exercise
2. Discussion focusing on teachers’ experiences on pupils’ inability to solve
mathematics problems correctly.
3. The researcher request to know the various approaches teachers have been
applying in the teaching and learning of mathematics.
4. The researcher tries to find out from the teachers why primary pupils exhibit
incompetencies in solving mathematics.
Day Two
The researcher went straight to the application of the achievement motivational
instructional approach to solving mathematics
5. The teachers should guide the pupils to read every mathematical statement
correctly and be able to recall and review what the child had done in the past i.e.
Application of (3R) e.g. properties of shapes, Differentiate currencies,
multiplication…,
6. Every verbal statement in mathematics must be understood and converted to a
mathematical statement that is understanding mathematics language instruction.
For instance pupils should be able to translate. Write in figures; write in words;
take to 3 decimal place; convert to percentage and so on.
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7. Diagnosing and treating pupils difficulties by giving them first simple problems
to solve as to find out areas they have problems. Give mental sums everyday to
check their ability to reason and calculate problems at a short possible time.
8. Teachers should divide their classes into groups to allow for practical exercises
and competition among themselves. The pupils should be allowed opportunity
of using appropriate instructional materials.
Day Three
9. Discussion of the unit lesson plans according to the topics.
10. Class interaction through groups performance and by coming out to the board to
teach themselves and solve problems while the researcher guides.
11. Teacher evaluate group by group and individually.
12. Closing
At the end of the training, the researcher organized a micro teaching session for the
experimental teachers to ensure that they have mastered the application of the different
stages of the instructional approach, expected of them. The teacher training guide are
reflected in (Appendix F pp. 155).
Method of Data Collection
There are 50 multiple choice items in both MAT and NAT. Each item was
scored one (1) mark. The pretest and posttest scores of both MAT and NAT were
collected for all the pupils who sat for the test except those whose results were
incomplete for final analysis.
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Method of Data Analysis
The pretest and posttest scores that were obtained from the administration of the
MAT and NAT instrument (Appendix A & B pp. 110 and 116) were analysed using
mean, standard deviation for the research questions and Analysis of Covariance
(ANCOVA) for testing of the hypotheses at 0.05 level of significance.
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CHAPTER FOUR
RESULTS
This chapter is concerned with the presentation of result from data analysis. The results
are presented in tables according to the research questions and hypotheses that guided
the study.
Research Question 1:
What is the mean achievement score of pupils taught mathematics with achievement motivational approach and those taught with traditional approach?
Table 1: Mean and Standard deviation of pretest posttest score of pupils taught mathematics with achievement motivational approach and those taught with traditional approach
Variable Pre test Posttest Mean gain
N SD SD
Achievement motivational approach
125 15.44 5.22 33.65 5.56 18.21
Traditional approach 115 14.94 3.58 15.42 4.80 0.48
The result presented in Table 1 show that the achievement motivational approach
(experimental group) had a pretest mean 15.44 with a standard deviation of 5.22 and a
posttest mean 33.65 with a standard deviation of 5.56. The difference between the
pretest and posttest mean for achievement motivational approach (experimental group)
was 18.21. The Traditional approach (control group) had a pretest means 14.94 with a
standard deviation of 3.58 and a posttest mean 15.42 with a standard deviation of 4.80.
The difference between the pretest and posttest mean for Traditional approach (control
group) is 0.48. For both achievement motivational approach (experimental group) and
Traditional approach (control group), the posttest means were greater than the pretest
mean with achievement motivational approach having higher mean gain. This is
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indicative that achievement motivational approach improved pupils’ achievement in
mathematics.
Research Question 2:
What is the mean numerical aptitude score of pupils taught mathematics with achievement motivational approach and those taught with traditional approach?
Table 2: Mean and Standard deviation of numerical aptitude score of pupils taught mathematics with achievement motivational approach and those taught with traditional approach
Variable Pre test Posttest Mean gain
N SD SD
Achievement motivational approach
125 14.98 5.44 39.08 7.09 24.10
Traditional approach 115 10.47 3.91 16.56 5.98 6.09
The result presented in Table 2 show that the achievement motivational approach
(experimental group) had a pretest mean 14.98 with a standard deviation of 5.44 and a
posttest mean 39.08 with a standard deviation of 7.09. The difference between the
pretest and posttest mean for achievement motivational approach (experimental group)
was 24.10. The Traditional approach (control group) had a pretest means 10.47 with a
standard deviation of 5.91 and a posttest mean 16.56 with a standard deviation of 5.98.
The difference between the pretest and posttest mean for Traditional approach (control
group) is 6.09. For both achievement motivational approach (experimental group) and
the Traditional approach (control group), the posttest means was greater than the pretest
mean. This is indicative that achievement motivational approach improved pupils’
mean numerical aptitude score.
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Research Question 3:
What is the mean achievement score of male and female pupils taught mathematics with achievement motivational approach?
Table 3: Mean and Standard deviation of pretest posttest score of male and female pupils taught mathematics with achievement motivational approach
Variable Pre test Posttest Mean gain
Gender N SD SD
Male 70 15.28 5.72 34.89 5.22 19.61
Female 55 15.65 4.55 33.09 5.97 17.44
The result presented in Table 3 show that the male group had a pretest mean 15.28 with
a standard deviation of 5.72 and a posttest mean 34.22 with a standard deviation of
5.22. The difference between the pretest and posttest mean for male group is 19.61. The
female group a pretest means 15.65 with a standard deviation of 4.55 and a posttest
mean 33.09 with a standard deviation of 5.97. The difference between the pretest and
posttest mean for female group is 17.44. For each of the two groups, the posttest means
are greater than the pretest means with male group having slightly higher mean gain.
This is indicative that achievement motivational approach appears to have improved
male pupils’ achievement in mathematics more than that of female.
Research Question 4:
What is the mean numerical aptitude score of male and female pupils taught mathematics with achievement motivational approach?
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Table 4: Mean and Standard deviation of numerical aptitude score of male and female pupils taught mathematics with achievement motivational approach
Variable Pre test Posttest Mean gain
Gender N SD SD
Male 70 14.66 4.85 39.40 7.82 24.74
Female 55 15.38 6.13 38.67 6.09 23.29
The result presented in Table 4 show that the male group had a pretest mean 14.66 with
a standard deviation of 4.85 and a posttest mean 39.40 with a standard deviation of
7.82. The difference between the pretest and posttest mean for male group is 24.74. The
female group a pretest means 15.38 with a standard deviation of 6.13 and a posttest
mean 38.67 with a standard deviation of 6.09. The difference between the pretest and
posttest mean for female group is 23.29. For each of the two groups, the posttest means
are greater than the pretest means with male group having slightly higher mean gain.
This is indicative that achievement motivational approach appears to have improved the
numerical aptitude score of both male and female pupils.
Research Question 5:
What is the mean retention of achievement score of pupils taught mathematics with achievement motivational approach and those taught with traditional approach?
Table 5: Mean and Standard deviation of retention score of pupils taught mathematics with achievement motivational approach and those taught with traditional approach
Variable Post test Retention score Mean gain
N SD SD
Achievement motivational approach
125 33.65 5.56 37.43 4.75 3.78
Traditional approach 115 14.42 4.80 16.21 4.00 1.79
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The result presented in Table 5 show that the achievement motivational approach
(experimental group) had a posttest mean 33.65 with a standard deviation of 5.56 and a
retention mean score of 37.43 with a standard deviation of 4.75. The difference between
the posttest and retention mean score for achievement motivational approach
(experimental group) was 3.78. The Traditional approach (control group) had a posttest
means score of 14.42 with a standard deviation of 4.80 and a retention mean score of
16.21 with a standard deviation of 4.00. The difference between the posttest and
retention mean score for Traditional approach (control group) is 1.79. For achievement
motivational instructional approach (experimental group) and the Traditional approach
(control group), the retention means score were greater than the posttest mean score
with achievement motivational approach having higher mean retention gain. This is
indicative that achievement motivational approach enhanced higher retention than the
Traditional approach.
Research Question 6:
What is the mean retention numerical aptitude score of pupils taught mathematics with achievement motivational approach and those taught with traditional approach?
Table 6: Mean and Standard deviation of retention numerical aptitude score of pupils taught mathematics with achievement motivational approach and those taught with traditional approach
Variable Post test Retention score Mean gain
N SD SD
Achievement motivational approach
125 39.08 7.09 41.48 4.65 2.40
Traditional approach 115 16.56 5.98 17.05 6.10 0.49
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The result presented in Table 6 show that the achievement motivational approach
(experimental group) had a posttest numerical aptitude mean 39.08 with a standard
deviation of 5.56 and a retention mean score of 41.48 with a standard deviation of 4.65.
The difference between the posttest and retention mean score in numerical aptitude for
achievement motivational approach (experimental group) was 2.40. The Traditional
approach (control group) had a posttest numerical aptitude means score of 16.56 with a
standard deviation of 5.98 and a retention mean score of 17.05 with a standard
deviation of 6.10. The difference between the posttest and retention mean score in
numerical aptitude for Traditional approach (control group) is 0.49. For both
achievement motivational approach (experimental group) and Traditional approach
(control group), the retention means score were higher than the posttest mean score
with achievement motivational approach having higher mean retention gain. This is
indicative that achievement motivational approach enhanced retention more than the
Traditional approach.
Research Question 7:
What is the mean retention of achievement score of male and female pupils taught
mathematics with achievement motivational approach?
Table 7: Mean and Standard deviation of retention score of male and female pupils taught mathematics with achievement motivational approach
Variable Post test Retention test Mean gain
Gender N SD SD
Male 70 34.09 5.22 45.83 4.57 11.74
Female 55 33.09 5.97 44.47 4.91 11.38
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The result presented in Table 7 show that the male group had a post test mean 34.09
with a standard deviation of 5.22 and a retention test mean 45.83 with a standard
deviation of 4.91. The difference between the post test and retention test mean for male
group is 11.74. The female group a post test means 33.09 with a standard deviation of
5.97 and a retention test mean 44.47 with a standard deviation of 4.91. The difference
between the post test and retention test mean for female group is 11.38. For each of the
two groups, the retention mean scores were greater than the post test means. This is
indicative that achievement motivational approach appears to have improved both male
and female pupils’ retention in Mathematics.
Research Question 8:
What is the mean retention of numerical aptitude score of male and female pupils
taught mathematics with achievement motivational approach?
Table 8: Mean and Standard deviation of retention numerical aptitude score of male and female pupils taught mathematics with achievement motivational approach
Variable Post test Retention test Mean gain
Gender N SD SD
Male 70 39.40 7.82 46.79 4.78 7.39
Female 55 38.67 6.09 44.09 4.50 5.42
The result presented in Table 8 show that the male group had a post test mean 39.40
with a standard deviation of 7.82 and a retention test mean 46.79 with a standard
deviation of 4.78. The difference between the post test and retention test in numerical
aptitude for male group is 7.39. The female group had a post test means 38.87 with a
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standard deviation of 6.09 and a retention test mean 44.09 with a standard deviation of
4.50. The difference between the post test and retention test mean for female group is
5.42. For each of the two groups, the retention mean scores were higher than the post
test means. This is indicative that achievement motivational approach appears to have
improved the retention of numerical aptitude score of both male and female pupils.
Hypotheses 1
H01: There is no significant difference between the mean achievement score of pupils
taught mathematics with achievement motivational approach and those taught with
traditional approach.
Table 9: Analysis of Covariance (ANCOVA) of the mean achievement score of pupils taught mathematics with achievement motivational approach and those taught with traditional approach
Source Type III Sum
of Squares
df Mean Square F Sig.
Corrected Model 22183. 263a 4 5545.816 202.633 .000
Intercept 11307.820 1 11307.820 413.164 .000
Preachievement 0.071 1 0.071 0.003 .959
Group 21755.839 1 21755.839 794.914 .000
Sex 24.108 1 24.108 .881 .349
Group * Sex 7.543 1 7.543 .276 .600
Error 6431.671 235 27.369
Total 171892.000 240
Corrected Total 28614.930 239
a. R Squared = .775 (Adjusted R Squared = .771)
The result in Table 9 shows that an F-ratio of 794.914 with associated probability value
of 0.000 was obtained with regards to the mean achievement score of pupils taught
mathematics with achievement motivational approach and those taught with traditional
approach. Since the associated probability (0.000) was less than 0.05, the null
hypothesis (H01) was rejected. Thus, there was a significant difference between the
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mean achievement score of pupils taught mathematics with achievement motivational
approach and those taught with traditional approach. This implies that the use of
achievement motivational approach improves achievement of pupils in mathematics.
Hypotheses 2
H02: There is no significant difference between the mean numerical aptitude score of
pupils taught mathematics with achievement motivational approach and those
taught with traditional approach.
Table 10: Analysis of Covariance (ANCOVA) of the mean numerical aptitude score of pupils taught mathematics with achievement motivational approach and those taught with traditional approach
Source Type III Sum
of Squares
df Mean Square F Sig.
Corrected Model 30437. 464a 4 7609.366 174.430 .000
Intercept 23257.323 1 23257.323 533.128 .000
Preaptitude 11.321 1 11.321 0.260 .611
Group 24893.149 1 24893.149 750.626 .000
Sex 41.366 1 41.366 .948 .331
Group * Sex 1.164 1 1.164 .027 .870
Error 10251.699 235 43.624
Total 232733.000 240
Corrected Total 40689.163 239
a. R Squared = .748 (Adjusted R Squared = .744)
The result in Table 10 shows that an F-ratio of 174.430 with associated probability
value of 0.000 was obtained with regards to the mean numerical aptitude score of pupils
taught mathematics with achievement motivational approach and those taught with
traditional approach. Since the associated probability (0.000) was less than 0.05, the
null hypothesis (H02) was rejected. Thus, there was a significant difference between the
mean numerical aptitude score of pupils taught mathematics with achievement
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motivational approach and those taught with traditional approach. This implies that the
use of achievement motivational approach improves the mean numerical aptitude score
of pupils in mathematics.
Hypotheses 3
H03: There is no significant difference between the mean achievement scores of male
and female pupils taught mathematics with achievement motivational approach.
. The result for this hypothesis is presented in Table 9
The result in Table 9 shows that an F-ratio of 0.88 with associated probability value of
0.349 was obtained with regards to the mean achievement score of male and female
pupils taught mathematics with achievement motivational approach. Since the
associated probability (0.349) was greater than 0.05, the null hypothesis (H03) was not
rejected. Thus, there was no significant difference between the mean achievement score
of male and female pupils taught mathematics with achievement motivational approach.
This implies that the use of achievement motivational approach does not result in
difference in achievement between male and female pupils in mathematics.
Hypotheses 4
H04: There is no significant difference between the mean numerical aptitude score of
male and female pupils taught mathematics with achievement motivational
approach
The result for this hypothesis is presented in Table 10
The result in Table 10 shows that an F-ratio of 0.95 with associated probability value of
0.331 was obtained with regards to the mean numerical aptitude score of male and
female pupils taught mathematics with achievement motivational approach. Since the
associated probability (0.331) was greater than 0.05, the null hypothesis (H04) was not
100
rejected. Thus, there was no significant difference between the mean numerical aptitude
score of male and female pupils taught mathematics with achievement motivational
approach. This implies that the use of achievement motivational approach does not
result in difference in the numerical aptitude score between male and female pupils in
mathematics.
Hypotheses 5
H05: There is no significant difference between the mean retention of achievement
scores of male and female pupils taught mathematics with achievement
motivational approach.
Table 11: Analysis of Covariance (ANCOVA) of the mean retention of achievement score of male and female pupils taught mathematics with achievement motivational approach.
Source Type III Sum
of Squares
df Mean Square F Sig.
Corrected Model 21752. 811a 4 5440.703 281.875 .000
Intercept 7132.551 1 7132.551 369.528 .000
Postachievement 0.438 1 0.436 0.023 .880
Group 4945.824 1 4945.824 256.236 .000
Sex 1.702 1 1.702 .088 .767
Group * Sex 84.685 1 84.685 4.387 .037
Error 4535.923 235 19.302
Total 189998.000 240
Corrected Total 26298.733 239
a. R Squared = .828 (Adjusted R Squared = .825)
The result in Table 11 shows that an F-ratio of 0.09 with associated probability value of
0.767 was obtained with regards to the mean retention of achievement score of male
and female pupils taught mathematics with achievement motivational approach. Since
the associated probability (0.767) was greater than 0.05, the null hypothesis (H05) was
not rejected. Thus, there was no significant difference between the mean retention of
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achievement score of male and female pupils taught mathematics with achievement
motivational approach. This implies that the use of achievement motivational approach
does not result in difference in retention of achievement between male and female
pupils in mathematics.
Hypotheses 6
H06: There is no significant difference between the mean retention of numerical
aptitude score of male and female pupils taught mathematics with achievement
motivational approach
Table 12: Analysis of Covariance (ANCOVA) of the mean retention of numerical aptitude score of male and female pupils taught mathematics with achievement motivational approach.
Source Type III Sum
of Squares
df Mean Square F Sig.
Corrected Model 22972.555a 4 5743.139 205.567 .000
Intercept 5904.934 1 5904.937 211.358 .000
Postaptitude 340.330 1 340.330 12.193 .001
Group 3551.091 1 3551.091 127.106 .000
Sex 0.552 1 0.552 0.020 .888
Group * Sex 25.794 1 25.794 0.923 .338
Error 6565.441 235 27.938
Total 206719.000 240
Corrected Total 29537.996 239
a. R Squared = .778 (Adjusted R Squared = .774)
The result in Table 12 shows that an F-ratio of 0.02 with associated probability value of
0.888 was obtained with regards to the mean retention of numerical aptitude score of
male and female pupils taught mathematics with achievement motivational approach.
Since the associated probability (0.888) was greater than 0.05, the null hypothesis (H06)
was not rejected. Thus, there was no significant difference between the mean retention
of numerical aptitude score of male and female pupils taught mathematics with
achievement motivational approach. This implies that the use of achievement
102
motivational approach does not result in difference in the retention of numerical
aptitude score between male and female pupils in mathematics.
Hypotheses 7
H07: There is no significant interaction effect of approaches and gender on mean
achievement scores of pupils in mathematics.
The result for this hypothesis is presented in Table 9
The result in Table 9 shows that an F-ratio of 0.278 with associated probability value of
0.600 was obtained with regards to the interaction effect of approaches and gender on
the mean retention of achievement scores of pupils in mathematics. Since the associated
probability (0.600) was greater than 0.05, the null hypothesis (H07) was not rejected.
Thus, there was no significant interaction effect of approaches and gender on mean
achievement scores of pupils in mathematics.
Hypotheses 8
H08: There is no significant interaction effect of approaches and gender on mean
numerical aptitude scores of pupils in mathematics.
The result for this hypothesis is presented in Table 10
The result in Table 10 shows that an F-ratio of 0.027 with associated probability value
of 0.870 was obtained with regards to the interaction effect of approaches and gender
on the mean numerical aptitude scores of pupils in mathematics. Since the associated
probability (0.870) was greater than 0.05, the null hypothesis (H08) was not rejected.
Thus, there was no significant interaction effect of approaches and gender on mean
numerical aptitude scores of pupils in mathematics.
Hypotheses 9
H09: There is no significant interaction effect of approaches and gender on mean
retention of achievement scores of pupils in mathematics.
103
The result for this hypothesis is presented in Table 11
The result in Table 11 shows that an F-ratio of 4.387 with associated probability value
of 0.037 was obtained with regards to the interaction effect of approaches and gender
on the mean retention of achievement scores of pupils in mathematics. Since the
associated probability (0.037) was less than 0.05, the null hypothesis (H09) was rejected.
Thus, there was significant interaction effect of approaches and gender on mean
retention of achievement scores of pupils in mathematics.
Hypotheses 10
H010: There is no significant interaction effect of approaches and gender on mean
retention of numerical aptitude scores of pupils in mathematics.
The result for this hypothesis is presented in Table 12
The result in Table 12 shows that an F-ratio of 0.027 with associated probability value
of 0.338 was obtained with regards to the interaction effect of approaches and gender
on the mean retention of numerical aptitude scores of pupils in mathematics. Since the
associated probability (0.338) was greater than 0.05, the null hypothesis (H010) was not
rejected. Thus, there was no significant interaction effect of approaches and gender on
mean retention of numerical aptitude scores of pupils in mathematics.
Summary of Findings
The summary of the findings is presented below:
• There was a significant difference between the mean achievement score of
pupils taught mathematics with achievement motivational approach and those
taught with traditional approach.
• There was a significant difference between the mean numerical aptitude score of
pupils taught mathematics with achievement motivational approach and those
taught with traditional approach.
104
• There was no significant difference between the mean achievement score of
male and female pupils taught mathematics with achievement motivational
approach.
• There was no significant difference between the mean numerical aptitude score
of male and female pupils taught mathematics with achievement motivational
approach.
• There was no significant difference between the mean retention of achievement
score of male and female pupils taught mathematics with achievement
motivational approach.
• There was no significant difference between the mean retention of numerical
aptitude score of male and female pupils taught mathematics with achievement
motivational approach.
• There was no significant interaction effect of approaches and gender on mean
achievement scores of pupils in mathematics.
• There was no significant interaction effect of approaches and gender on mean
numerical aptitude scores of pupils in mathematics.
• There was significant interaction effect of approaches and gender on mean
retention of achievement scores of pupils in mathematics.
• There was no significant interaction effect of approaches and gender on mean
retention of numerical aptitude scores of pupils in mathematics.
105
CHAPTER FIVE
DISCUSSION, CONCLUSION AND SUMMARY OF THE STUDY
This chapter presents the discussions, conclusions, educational implications,
recommendations, limitations and suggestions for further researchers and summary of
the study. The discussions were done according to the following re-stated findings:
DISCUSSION
This study sought to investigate the effect of achievement motivational
instructional approach on primary six pupils’ numerical aptitude and retention in
mathematics. The results revealed that there was a significant difference between the
mean achievement score of pupils taught mathematics with achievement motivational
approach and those taught with traditional approach. This implies that the use of
achievement motivational instructional approach improves achievement of pupils in
mathematics. Evidence from the results revealed that the mean gain for the achievement
motivational instructional approach group was 18.21 in table 1 and the traditional
approach group was 0.48 same table 1. The findings of this study is similar to those of
Jegede & Jegede (1990) who found out that, there was significant difference in the
performance of pupils in English taught with achievement motivational instructional
approach.
It is interesting to note that the traditional approach group which was the control
for the experiment lost some mean value based on the difference between the posttest
and pretest means. It is evident that other factors other than methods of instruction can
lead to some changes in the achievement of pupils (Rothman, 2004).
106
The second finding of the study was that, there was a significant difference
between the mean numerical aptitude score of pupils taught mathematics with
achievement motivational approach and those taught with traditional approach. This
implies that the use of achievement motivational instructional approach improves the
mean numerical aptitude score of pupils in mathematics. The findings showed that the
mean gain of pupils taught mathematics with achievement motivational instructional
approach group was 24.10 and is higher than that of the traditional approach group
(6.09) in table 2. This result indicated that the achievement motivational instructional
approach group improved their numerical aptitude score better than the traditional
approach group.
The result on methods of instruction and numerical aptitude score negates that of
Okwuajioko (2002) who found out that there was no significant difference in
achievement motivational instructional approach and numerical aptitude of the primary
school pupils. The use of achievement motivational instructional approach enhances in-
depth and proper connection, organization and integration of concepts into pupils’
knowledge structure through Scan Question, Read, Recall and Review practice. This in
turn may have aided improved numerical aptitude score of pupils
The third finding of the study revealed that there was no significant difference
between the mean achievement score of male and female pupils taught mathematics
with achievement motivational instructional approach. This implies that the use of
achievement motivational approach does not result in difference in achievement
between male and female pupils in mathematics. This finding differs from that of
Agwagah, (2000) who established that there is differential performance in mathematical
107
activities due to gender especially in favour of boys. It also varies from the opinion of
Harbor-Peters (2001) who observed that mathematics is a male stereotype especially as
it is regarded as abstract and difficult with attributes which boys are attracted to. Also
Al-Emadi, (2003) observed that boys exert better mathematics achievement than the
girls because the boys from the beginning are encouraged to be more independent than
the girls, therefore differential treatment of sex has given the boys more confidence
than girls and this enhances better performance in favour of boys, in mathematics.
However, the findings is in line with that of Aydin (2013) who concluded that
female pupils these days are equally good in mathematics as their male counterparts.
Also, Urdan (2010) stated that motivational condition influence both male and female
to perform equally well at all levels in mathematics test and examination. The use of
achievement motivational instructional approach will help to bridge the gap between
males and females observed by other researchers in the past and in the present.
The fourth findings from table 4 was that there was no significant difference
between the mean numerical aptitude score of male and female pupils taught
mathematics with achievement motivational instructional approach. This implies that
the use of achievement motivational instructional approach does not result in difference
in the numerical aptitude score between male and female pupils in mathematics. This
finding is in line with that of Umar and Momoh (2001) who stated that there was no
statistical difference in the performance of boys and girls on quantitative and other
aptitude test. The achievement motivational instructional approach used in this study
was taught to both male and female equally and also the equality in the achievement of
male and female pupils in table 3 and 4 agrees with Gregory (2011) who viewed that
108
primary six pupils are in the same age bracket of plus and minus eleven (11) years and
achievement in mathematics at this age is not noticeable as to whether boys or girls do
better. This was probably responsible for equality in the observed achievement of male
and female pupils used in this study. This implies that when male and female pupils are
given similar condition to operate they perform equally.
The fifth finding was that there was no significant difference between the mean
retention of achievement score of male and female pupils taught mathematics with
achievement motivational instructional approach. This implies that the use of
achievement motivational instructional approach does not result in difference in
retention of achievement between male and female pupils in mathematics. The result
presented in Table 5 indicates that both achievement motivational instructional
approach and traditional approach appears to have similar retention influence. The
achievement motivation instructional approach in table five had a higher retention
influence. This appears to be consistent with the studies conducted by Aydin and
Coskun (2011), and Pe’rez, (2013) that showed no significance difference in
mathematics achievement and retention between male and female students. The
similarity in the retention of male and female pupils was in agreement with that of
Aydin and Coskun (2011), and Perez, (2013) whose respective works did not show any
significant difference according to gender. This could be attributed to the fact that the
pupils were given enabling environment to work together effectively. They were
equally given the same opportunity and conditions that made them to understand better
thereby obtaining similar retention.
109
The sixth findings in table 7 and 8 were that there was no significant difference
between the mean retention of numerical aptitude score of male and female pupils
taught mathematics with achievement motivational instructional approach. This implies
that the use of achievement motivational instructional approach does not result in
difference in the retention of numerical aptitude score between male and female pupils
in mathematics. This finding appears to be inconsistent with the study conducted by
Okwuajioko (2002) whose findings shows that there is a significance difference in the
numerical aptitude of the primary school pupils due to gender with males performing
better than the female. The work of Sam, Joshua and Asim (2010) on the other hand
revealed significant gender inequality and the girls having high retention over the boys.
The contradicting findings may not be far from the different conditions under which the
studies were conducted. The no significant difference between male and female pupils
in the mean retention of numerical aptitude score might have been caused by the fact
that the treatment was equally appealing to both males and females.
Other findings revealed that there was no significant interaction effect of
instructional approaches and gender on mean achievement scores of pupils in
mathematics. The result therefore implies that the combined effect of instructional
approaches and gender on mean achievement scores of pupils did not influence their
achievement in mathematics. In other words, the effectiveness of the interaction was the
same for males and females groups with respect to their achievement. The no
interaction effect between instructional approaches and gender on mean achievement
scores of pupils in mathematics could be attributed to the fact that instructional
approaches are school factors while gender is a biological and socio-cultural factors.
110
This finding tends to agree with Gregory, (2011) who found out that there was no
significant interaction effect between instructional approaches and gender on mean
achievement scores of pupils in mathematics.
Again, no significant interaction effect of instructional approaches and gender on
mean numerical aptitude scores of pupils was detected. The no significant interaction
effect between instructional approaches and gender on mean numerical aptitude scores
of pupils could be attributed to the impact of extra-cognitive numerical aptitude tasks
due to the treatment on male and female pupils. Both male and female pupils
experienced and enjoyed the treatment atmosphere in different ways. This might have
resulted in the combined effect of the treatment and gender not influencing any change
in the numerical aptitude scores of pupils. This result is inline with Okwujiako (2002)
who also acknowledged that there was no significance interaction effect of instructional
approach and gender on mean retention of numerical aptitude.
Significant interaction effect of instructional approaches and gender on mean
retention of achievement scores of pupils in mathematics was evidential. The result
therefore implies that the combined effect of instructional approaches and gender on
mean retention of achievement scores of pupils influence their achievement in
mathematics. In other words, the effectiveness of the interaction was not the same for
males and females groups with respect to their achievement. This implies that when
instructional approaches interaction with gender, male and female pupil appears to
retain what they have been taught in mathematics differently. This result agreed with
Eze (2011) who found out that there was a significance interaction effect of
111
instructional approaches and gender on mean retention of achievement scores of
students in mathematics.
Finally no significant interaction effect of instructional approaches and gender
on mean retention of numerical aptitude of pupils was detected. The result therefore
implies that the combined effect of instructional approaches and gender on mean
retention of numerical aptitude scores of pupils did not influence their retention in
numerical aptitude. In other words, the effectiveness of the interaction was the same for
males and females groups with respect to their numerical aptitude. This implies that
when instructional approaches interaction with gender, male and female pupil appears
to retain what they have been taught in numerical aptitude equally.
CONCLUSIONS
The study set out to investigate the effect of achievement motivational
instructional approach on primary six pupils’ numerical aptitude and retention in
mathematics. Based on the findings of this study, the following conclusions have been
made; the achievement motivational instructional approach was found to be capable of
enhancing pupils’ achievement and retention in mathematics and numerical aptitude.
Consequently, achievement motivational instructional approach could revamp teaching
and learning of mathematics and numerical aptitude with reasonable functionality.
Another conclusion drawn from the results of this study is that achievement
motivational instructional approach narrowed the gap that existed between the
achievement of male and female pupils as reported by Aydin and Coskun (2011). The
instructional approach provided male and female pupils with the opportunities to solve
mathematical and numerical aptitude tasks well. The use of achievement motivational
112
approach does not result in difference in the numerical aptitude score between male and
female pupils in mathematics.
The results of this study also lead to the conclusion that the use of achievement
motivational instructional approach improved the retention of numerical aptitude score
between male and female pupils in mathematics.
It can also be concluded that no significant interaction effect of instructional
approaches and gender on mean achievement scores of pupils in mathematics. The
combined effect of instructional approaches and gender on mean achievement scores of
pupils did not influence their achievement in mathematics.
Lastly the results of this study lead to the conclusion that when instructional
approaches interaction with gender, male and female pupil appears to retain what they
have been taught in mathematics differently.
EDUCATIONAL IMPLICATIONS
The results of this study have some implications to mathematics education,
especially in the area of teaching and learning. For instance, achievement motivational
instructional approach provided a framework for integration of how to Scan Question,
Read, Recall and use Review practice into pupils’ knowledge structure. A deficiency on
Scan Question, Read, Recall and use Review practice on the part of the pupil may have
accounted for persistent failure in mathematics and students hating mathematics.
Therefore, proper use of achievement motivational instructional approach may help
pupils to effectively solve mathematics problems
113
With the achievement motivational instructional approach, pupils’ retention in
mathematics can be improved. This in turn will make the teaching and learning of
mathematics as well as problem solving better than it has been. If this is done, it will
not only increase achievement of pupils but will help them understand mathematics
concepts better.
For curriculum designers, these results will guide them in the development and
designing of the primary school curriculum for mathematics and numerical aptitude. It
might in turn influence them to plan curriculum documents in relation to the strategies
for solving problems associated with the content
The results will help pupils have a better understanding of how to handle several
tasks in mathematics and numerical aptitude. This will consequently improve their
achievement in mathematics and numerical aptitude. In this respect, pupils will be
motivated to put in extra efforts on their own part to improve their achievement without
waiting on what the other stakeholders will do.
RECOMMENDATIONS
Based on these findings, it was recommended that achievement motivational
instructional approach should be part of mathematics education curriculum
implementation programme. This will enhance achievement and retention in
mathematics and numerical aptitude.
Teachers of mathematics need to be periodically given orientation course on the
use of achievement motivational instructional approach to help them get used to this
instructional approach.
114
Achievement motivational instructional approach activities need much time. The
preparation of official school time-table should take into cognizance of that and make
provisions for extra time to accommodate the use of this method.
Mathematics teachers should also be motivated so as to persist when they encounter
obstacles and difficulties in applying this approach as it is very demanding and time
consuming.
Teachers should make efforts to direct the presentation of mathematics lessons from the
traditional approach to a more learner centered approach which is achievement
motivational instructional approach.
LIMITATIONS
The generalizations drawn from this study are subject to the following limitations;
The teachers were all trained for the teaching of the research lessons, and the
researcher ensured that the same teaching materials, teaching methods and pupil
activities were used, but other intervening variables like mastery of content, teaching
experience, communication skills, and classroom environment skills of the teachers
might have affected the results of the study.
The achievement motivational instructional approach if well applied is time consuming
and normally required more time than the normal school time-table could tolerate.
The achievement motivational instructional approach is relatively strange to the
mathematics teachers and there are no available textbooks on the approach for teachers
to refer to and even for pupils to use.
115
Suggestions for Further Studies
• This study is limited to the mathematics and numerical aptitude achievement, a
similar study could be carried out in different subject area and the results
compared to this results.
• A study on the effect of Achievement motivational instructional approach with
other innovative approaches on the mathematics and numerical aptitude
achievement could be carried out.
• Another investigation could be carried out with variables like, interest, school
location, larger sample size etc.
SUMMARY
This study sought to investigate the effect of achievement motivational
instructional approach on primary six pupils’ numerical aptitude and retention in
mathematics. Eight research questions and ten hypotheses guided the study.
Discussions of findings were done according to the hypotheses that guided the study.
conclusions were drawn from the results of the investigation. It was concluded that the
achievement motivational instructional approach was found to be capable of enhancing
pupils’ achievement and retention in mathematics and numerical aptitude. It was also
concluded that achievement motivational instructional approach does not result in
difference in the numerical aptitude score between male and female pupils in
mathematics, it was equally concluded that when instructional approaches interaction
with gender, male and female pupil appears to retain what they have been taught in
mathematics differently among others.
116
Some recommendations were made to the Government, education authorities
and teachers, the educational implications that stem from this study were also outlined
by the researcher, and lastly the limitations and suggestions for further studies based on
the results of the study were proposed.
117
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APPENDIX A
Mathematics Achievement Test (MAT)
Section A
Name of School ----------------------------
Class – Primary Six (6) Gender: Male [ ] Female [ ]
Time allowed 1 ½ hrs Candidate No: -------------------------------------
Section B
Cluster A: (Application of SQ3R)
(1) An equilateral triangle has the following properties except.
(a) All the 3 sides of an equilateral triangle are equal in length
(b) All the 3 angles are equal
(c) All the 3 lines of symmetry meet at a point.
(d) Each line of symmetry bisects the base at right angles, and also bisects the
angle at the vertex
(e) All of the above.
2. Write in figures Eight billion, seven hundred and sixty-five million, four
hundred and thirty-two thousand, five hundred and forty three.
(a) 8765432543 (b) 8756432543 (c) 876532443
(d) 8755431588 (e) 856, 432 54321
3. In a class the ratio of the number of boys to the number of girls is 3: 4. There
are 18 boys in the class. How many girls are in the class
(a) 24 (b) 25 (c) 23 (d) 28 (e) 26
4. Correct 2.992 to 2 decimal places
(a) 2.99 (b) 29.9 (c) 2.10 (d) 299 (e) 3.0
5. Express 45 as a product of prime factors
(a) 3 × 3 × 5 (b) 2 × 3 × 5 (c) 4 × 3 × 3 (d) 9 × 5 (e) 3 × 3 × 6
6. Convert 100
15 to percentage
(a) 25% (b) 15% (c) 75% (d) 30%
7. What does the letter d represent in the expression 81-d = 32
(a) 49 (b) 42 (c) 38 (d) 113 (e) 1.25
126
8. There are 40 pupils in the class. If 25% are absent, how many pupils are present
(a) 30 (b) 10 (c) 40 (d) 20 (e) 15
9. By how much is (3/4 + 1/12 + 2/3) greater than 1.
(a) ½ (b) ¾ (c) 1/5 (d) 2/5 (e) 4/20
10. Arrange 0.306, 0.7, 0.089 in ascending order.
(a) 0.306 , 0.7, 0.089 (b) 0.7, 0.306, 0.089 (c) 0.089, 0.7, 0.306
(d) 0.306, 0.089, 0.7 (e) 0.089, 0.306, 0.7
Cluster B: (Understanding the mathematics language instruction)
11. Write 5 ×5×5×5×5×5 in index form
(a) 510 (b) 56 (c) 55 (d) 57 (e) 5×52
1.2 what fraction is shaded
(a) 6
5 (b)
6
2 (c)
6
1 (d)
8
3 (e)
8
2
13. The number of people in a group is known as
(a) census (b) figure (c) population (d) demograph (e) frequency
14. What is the correct formular for finding simple interest
(a) S.I = R
100 T P ×× (b) S.I =
100
T R× (c) S.I =
100
R T P ××
(d) S.I = RP
T R 100
×××
(e) S.I P100
T R
××
15. If the current rate of £1 = N225.00, by calculation convert £12.00 to Naira
(a) N4800 (b) N2700 (c) N6800 (d) N3300 (e) N4500 16. How many odd numbers are between 1 and 20
(a) 2, 4, 6, 8, 10 (b) 10 (c) 5 and 10 (d) 8 (e) 12
17. How many degrees does the hour hand of a clock make as it moves from 1 to 2
O’clock.
(a) 450 (b) 600 (c) 150 (d) 300 (e) 900
18. Write down your finishing direction starting at North, turn clockwise 900
(a) South West (b) South South (c) North South (d) East (e) West
19.
(a) 5.5km/h (b) 3.6km/h (c) 4.5km/h (d) 2.5km/h (e) 6.6km/h
110km/h 20km/h ?
127
20. Reduce 75
15 to its simplest fraction
(a) 5
1 (b)
5
3 (c)
15
5 (d)
15
1 (e)
4
3
21. If the number of people infected with HIV in Nigeria is 2900 000 and Ghana is
320,000. By how much is Nigeria greater than Ghana.
(a) 2, 580, 000 (b) 2, 560,000 (c) 1,250,000 (d) 320,000
(e) 2900, 000
22. If a = 5, b = 6 and C = 1 without calculator find a
c b a ××
(a) 10 (b) 6 (c) 8 (d) 5, (e) 4
23. Find the square root of 81
16
(a) 81
16 (b)
9
4 (c)
9
2 (d)
8
4 (e)
9
3
24. Find the sum of 2 ½ and the product of 1 ¼ and 1/3 and leave the answer in its
simplest form
(a) 32
1 (b) 2
12
11 (c) 3
12
11 (d) 4
12
11 (e) 3
5
5
25. Find the missing number in the box 9
4
3 =
(a) 16 (b) 12 (c) 15 (d) 21 (e) 18
Cluster C: (Diagnosing and treating pupils difficulties.)
26. Write 209 in Roman numerals
(a) CCIX (b) CMX (c) XXIV (d) CIXC (e) XCIV
27. What is the median of an even distribution
(a) Average of the number (b) the middle number
(c) the average of the two middle numbers (d) the last number
(e) the first number.
Use the figure below to answer question 28 and 29
C
D E
B
P
F
G
Q
A
H
I R I
128
28. What type of triangle is ABC
(a) Equilateral (b) Isosseles (c) Right-angled (d) obtuse (e) acute.
29. In the triangle side BC is called
(a) Adjacent (b) Hypotenuse (c) opposite (d) Parallel
(e) Longitudinal.
30. Reduce the figure below to a smaller size using a scale of 1: 5
(a) (b)
(c) (d) (e)
31. If the scale is 1cm = 10m, what will be the measurement of 10m on the ground
(a) 100m (b) 120m (c) 150m (d) 125m (e) 90m
32. By folding a rectangle along its lines of symmetry. How many lines of
symmetry does a rectangle have
(a) 3 (b) 2 (c) 4 (d) 5 (e) 1
33. Use your protractor and measure the angle X and y and their sum will be equal
to
(a) 900 (b) 1800 (c) 3600 (d) 450 (e) 800
34. What was the highest number thrown
(a) 3 and 4 (b) 3 and 5 (c) 2 and 5 (d) 4 and 2 (e) 4 and 5
35. If find
(a) 3
2 (b) 0.25 (c) 0.5 (d)
5
3 (e) 0.75
2
0.25
8 3
?
6
20cm
15cm 15cm
20cm
5cm
3cm
4cm
3cm 3cm
5cm
4cm
2cm
5cm
2cm
6cm
4cm
y
x
129
36. If Find
(a) 18 (b) 16 (c) 12 (d) 24 (e) 48
37. 14 × [ ] = 504 find [ ]
(a) 40 (b) 50 (c) 36 (d) 46 (e) 35
38. What is the value of 49 - 9 16 +
(a) 6 (b) 7 (c) 0 (d) 3 (e) 21
39. A boy got 50 marks out of 75 in a test. What percentage is this
(a) 66% (b) 65% (c) 68% (d) 66.67% (e) 55%
40. A factory uses 35 tonnes of coal every 5 days, how many tones are used in 15
days
(a) 15 tonnes (b) 65 tonnes (c) 12 tonnes (d) 105 tonnes (e) 48 tonnes
Cluster D: (Using practical activities to aid studying)
Use the data given to answer questions 41 and 42 i.e. 10, 9, 8, 13, 17, 16, 13, 13, 9
41. What is the mode
(a) 10 (b) 9 (c) 13 (d) 16 (e) 17
42. What is the median score
(a) 9 (b) 16 (c) 13 (d) 10 (e) 8
43. What is the sum of the interior angle of a hexagon
(a) 6000 (b) 4200 (c) 1350 (d) 7200 (e) 1500
44. A polygon whose sides and angles are equal is called
(a) A regular polygon (b) square (c) equilateral triangle
(d) convex polygon (e) concave polygon
45. All are example of cuboid except
(a) box of sugar (b) match box (c) building block
(d) All of the above (e) maggi
46. By measurement, what do you discover about the length of the diameter of a
circle.
(a) All diameter of a circle are equal in length
35
21
3:5
36
?
3:1
130
(b) All diameters of a circle are different in length
(c) All diameter of a circle are shorter
(d) All diameters of a circle are round
(d) None of the above.
47. If find
(a) (b) (c)
(d) (e)
48. The sum of two numbers is 24. one of the numbers is twice the other, find the
two numbers
(a) 4 and 5 (b) 6 and 8 (c) 12 and 15 (d) 16 and 8 (e) 15 and 12
If
49. What is the correct name of the angle
(a) < AOB (b) < OBA (c) <OAB (d) <BOA
(e) < BAO
Use this information to answer questions 50.
Thirty pupils in a class throw dice. The number each pupil got is
4 6 4 1 5 5 4 3 2 5
6 3 5 2 4 3 6 2 1 3
4 1 3 6 5 2 3 1 5 2
50. What was the median number
(a) 5.5 (b) 6.5 (c) 4.5 (d) 3.5 (e) 6.2.
15 2
30 45
16 ?
48 ?
16 2
48 32
16 3
48 35
16 3
48 30
16 4
48 40
16 5
48 35
180km/h 45km/h 4 km/h
B
A
O
131
APPENDIX B
Numerical Aptitude Test (NAT)
132
SECTION NUMERICAL APTITUDE TEST NAT
OBJECTIVES
INSTRUCTION: Each question carries one mark. Choose the correct answers from
OPTIONS A-E for each question and work write down the letter on your answer
booklet
1. Express 400102 in words
(a) Four thousand one hundred and two
(b) Four million one hundred and two
(c) Four hundred thousand one hundred and two
(d) Four thousand and two
(e) Forty thousand one hundred and two
2. Write in figure Eighty-Six thousand, Seven Hundred and Sixty-Four
(a) 68784 (b) 87764 (c) 80064 (d) 86764 (e) 860764
3. What is the place value of 5 in 47.015? (a) 5 tens (b) 5 units
(c) 5 thousandths (d) 5tens (e) 5 hundredths
4. Express 940 in Roman Numerals
(a) XLXC (b) CMXL (c) MCLX (d) CDML (e) MCLX
5. Find the sum of the following numbers 348, 25,1425 and 113
(a) 1921 (b) 1911 (c) 1081 (d) 1231 (e) 1913
6. Which of the following is a prime number?
(a) 1(b) 4 (c) 10 (d) 15 (e) 2
7. The difference between 0.0754 and 1 is
(a) 0.9246 (b) 0.2946 (c) 1.0754 (d) 0.4296 (e) 1.0292
8. Which of the following numbers cannot be divided by 3 without any reminder?
(a) 30 (b) 42 (c) 54 (d) 69 (e) 74
9. Calculate 2013-2015+2002-2000
(a) 0 (b) 4 (c) 2 (d) 2013 (e) 2006
10. Find the sum of 1/3 of 18 and ¼ of 4
(a) 6 (b) 12 (c) ½ (d) 4 (e) 7
11. What is the cost of 5kg of carrots if two kg of carrots cost 80?
(a) 120 (b) 150 (c) 200 (d) 400 (e) 800
133
12. Express 40 Kobo as a fraction of 3 naira.
(a) 40 (b) 15 (c) 1/15 (d) 3/40 (e) 2/15
13. Reduce 21/28 to its lowest terms
(a) 7/14 (b) 7/14 (c) 3/7 (d) ¾ (e) 2/15
14. Find the value of y it 4/7y=22/3
(a) 42/3 (b) 22/3 (c) 52/3 (d) 11/3 (e) 4/7
15. Three-Quarters of a certain number is 12. What is the number?
(a) 24 (b) 20 ( c) 16 (d) 8 (e) 36
16. What fraction of 2m is 25cm?
(a) 1/5 (b) 1/8 (c) 2/25 (d) ¼ (e) 2/5
17. Change 151/100 to a decimal number
(a) 0.151 (b) 1.51 (c) 15. 1 (d) 15.2 (e) 01.51
18. Obi and Doreas shared 120 stamps in the ratio 2:3 how many stamps was Obi’s
share?
(a) 60 (b) 40 (c) 72 (d) 48 (e) 20
19. What must be added to 1/8 to make5/6?
(a) 17/24 (b) 7/8 (c) 20/24 (d) 12/28 (e) 21/8
20. Find the product of 81/2 and 6
(a) 17 (b) 51 (c) 84 (d) 33 (e) 34
21. Change 2.75 to an improper fraction
(a) 55/2 (b) 11/4 (c) 275/10 (d) 9/2 (e) 3/35
22. How many 200ml glasses can you fill from a l5litres container of fruit juice?
(a) 10 (b) 20 (c) 25 (d) 30 (e) 50
23 What is 2/3 of N=45.00
(a) =N=30.00 (b)=N=20.00 (c) =N=60.00 (d) =N=50.00 (e) =N=25.00
24. Divine’s father is 36 years old. If divines’ age is one third of the father’s age,
what is Divine’s age?
(a) 24yers (b) 18years (c) 12years (d) 9 years (e) 30 years
25. 4men take 5days to dig a trench. How many men will dig the same trench in 2
days?
(a) 4 men (b) 10 men (c) 8 men (d) 6 men (e) 12 men
134
26. Find the area of a square with length 9cm long.
(a) 18cm2 (b) 36cm2 (c) 45cm2 (d) 36cm2 (e) 81cm2
27. Simplify 3 1/3 +4 12+7/18
(a) 73/2 (b) 123/4 (c) 82/9 (d) 45/36 (e) 754/36
28. What is the average seed of a motorist who covered 50 km in 30 minutes?
(a) 50 km/h (b) 100km/h (c) 300km/h (d) 45km/h (e) 150km/h
29. Find the area of the shape below
(a) 31cm2 (b) 40 cm2 (c) 48cm2 (d) 36cm2 (e) 60cm2
30 Find the simple interest on=N=600.00at 3% after 3years
(a) =N=54.00 (b)=N=60.00 (c) =N=36.00 (d)=N=72.00 (e)=N=18.00
31. How many cubes of side 1 1/3 cm can be contained in a box whose internal
Measurement is a cube of sides 8 cm?
(a) 512 (b) 216 (c) 1.33 (d) 826 (e) 270
32. The volume of a rectangular box is 101/2cm3. if it is 31/2 cm long ande 11/3 cm
wide How high is the box?
(a) 21/4 cm (b) 41/2 cm (c) 202/3 cm (d) 11/3 cm (e) 51/3cm
33. Find the volume of a cylinder whose radius is 7 cm and height 4cm. (take π
=22/7).
(a) 154cm3 (b) 88cm3 (c) 308cm3 (d) 972cm3 (e) 616cm3
34. Express 4 cubic meters in cubic centimeters.
(a) 0.004cm3 (b) 4000cm3 (c) 160000cm3 (d) 40000000cm3 (e) 4cm3
35. There are 6 packet of sweets. Each packet contains 36 sweets. How m any
sweets will each of 18 pupils receive?
(a) 140 sweets (b) 120 sweets (c) 180 sweets (d) 12 sweets (e) 24 sweets.
36. Reduce 12:48:60 to its simplest form.
2cm
5cm 7cm
3cm
135
(a) 4: 3:6 (b) 1:4:5 (c) 2:3:4 (d) 1:3:4 (e)2:6:10
37. Decrease 35 by 25%
(a) 61.25 (b) 26.25 (c) 21.10 (d) 75.24 (e) 8.15
38. Add together 4044+44+4+440
(a) 4532 (b) 5432 (c) 2453 (d) 4453 (e) 4523
39. What is the least common multiple of 18,24and 84?
(a) 1512 (b) 2152 (c) 5121 (d) 1521 (e) 84
40. What is the square root of 225?
(a) 25 (b) 15 (c) 35 (d) 51 (e) 52
41. How many days are there in 96 hours?
(a) 3days (b) 5days (c) 6 days (d) 8 days (e) 4 days
42. Given that Q =6, P=5,M=4,N—2. Evaluate Q × P
(a) 10 (b) 3 (c) 5 (d) 15 (e) 4 M+N
43. Correct 0.0074 to two-significant figures.
(a) 0.0 (b) 0.00 (c) 74 (d) 0.0074 (e) 0.74
44 Simplify3.2691x104
(a) 32961 (b) 32691 (c 326910000 (d) 32.691 (e) 32.96
45 What is the mode in 0,1.2 4,0,3,7and 10?
(a) 7 (b) 17 (c) 1 (d) 0 (e) 3and2
46. What fraction of the rectangle below is shaded?
(a) 1/5 (b) 2/5 (c) ¼ (d) 1/3 (e) 1/2
47. Given that the perimeter of a square is 40cm. find the area.
(a) 16cm2 (b) 100cm2 (c) 20cm2 (d) 400cm2 (e) 1600cm2
48. What is the index form of 2x2x2x2x3x3? (a) 8x6x3 (b) 24x32 (c) 26x33 (d) 23x34 (e) 25x32
136
49 Find angle P in the figure below
(a) 1800 (b) 540 (c) 630 (d) 900 (e) 600
50. Simplify the ratio 20g: 11/4kg
(a) 1.16 (b) 152:2 (c) 2:125 (d) 10:25 (e) 20:250
P Q
R 126
0
S
137
APPENDIX C
UNIT LESSON PLAN (1) FOR EXPERIMENTAL GROUP.
Name of School:
Subject: Mathematics
Title: Number and Numeration
Class: Primary Six (6)
Average Age: 11 years
Sex: Male ( ) Female ( )
Duration: 40 mins (2 periods in 2 days)
Specific objectives:
At the end of the lesson, the pupils should be able to:
1. Read and write numbers up to one billion
2. Add, subtract in place value
3. Give the place value of digits with decimal and identification of fractions
4. Read and compare population of cities HIV infected persons
5. Express in ratio, percentages and proportion
6. Solve problems on quantitative aptitude on numbers, direct and indirect
proportion and open sentence.
Previous knowledge:
It is expected that the pupils familiar with areas taught in primary 3,4 and 5 and as such
can
1. Count in English up to one million and also in Roman numerals
2. Writes in figures and in words
3. Do some addition and subtraction
4. Identify population charts
Instructional materials:
1. Abacus and charts for numbers
2. Charts of factors and multiples of numbers, population charts and HIV/AIDS
charts.
138
Instructional procedures:
CONTENT TEACHER ACTIVITY PUPILS ACTIVITY APPROACH E valuation
Whole
numbers
The teacher involves the pupils
to do some previous exercises on
board on numbers by making the
pupils read and write numbers up
to one million
He guides the pupils to recall
counting in place value. To be
sure whether the pupils
understand mathematics
language, instruction, the teacher
engage the pupils to write in
words and figure one after the
other on the board.
The teacher guides the pupils to
recall writing numbers in
standard form 100 10 x 101
The teacher ensure the effective
use of 3R.
The pupils recall counting
up to 1 billion. The pupils
count and write in various
place values and filling the
missing numbers.
The pupils writes in words,
figure and standard.
NUMERALS WORD
FORM
1,000,000 One million
10,000,000 Ten million
50,000,000 Fifty million
100,000,000 One hundred
millions
500,000,000 Five hundred
million
1000,000,000 One billion
The approach
involves
reading,
recalling,
receiving,
understanding
of mathematics
language and
instruction.
Mental
sums, class
work and
home work
Fraction
The teacher guides the pupils to
divide and oranges to identify
fractions and reduce fractions to
its simplest form and to add and
subtract fraction
The pupils recalls and
review fractions by relating
it to sharing
The pupils do many
exercises.
1/4
1/4
1/4
1/4
1 /41 /4
The approach
used were
practical
activity
reading,
recalling,
reviewing and
understanding
mathematics
language and
instruction
Group
presentatio
n and home
work
Multiplication
The teacher guides the pupils to
identify multiples e.g
1. List the multiples of 10
and 12
2. Find the LCM of 10 and
The pupils try to provide
answers multiple of
10=,10,20,30,4050,60
Multiples of 12 = 12, 24,
36,48,60,72.
Diagnosing and
treating pupils
difficulties
139
12
3. Write numbers in index
form
4. Solve some quantitative
aptitude problems.
Factor of 10 =2x5
LCM= 2x2x3x5 = 60 and 27
= 33
64 = 20
1000 = 103
Population
The teacher gives suitable
information that will keep pupils
in the construction of population
data. He guides pupils to define
population and leads the pupils to
give the population of their
houses, churches, towns.
The teacher guides the pupils to
read and compare the population
of families in a village. Read and
compare the population of HIV
infected people by looking at
different charts presented in the
class..
The pupils goes home to
carry out the experiment by
counting the number of
people in their houses,
church and by getting
information from records
and data.
Reading and
using practical
activity to aid
studying
Percentage
ratio
proportion
The teacher guides the pupil to
express ratio in its simplest form.
Find the percentage. Identify
direct and indirect proportion e.g
1. Reduce to its simplest
form 20:28:32
2. Find the cost of a articles
at N125.25 each.
The pupils solves many
exercises. Direct proportion
as xxy
x=ky
and indirect as x x 1/y
x=k/y
The pupils solves the
problems 5:7:8
1 article cost N125.25
9 xN125.25
=N1127.25 Use 4 to
divide all
Recall
Review
And
Understanding
Mathematics
Language
Instruction
Open sentences
The teacher guides the pupils to
solve problems on open
sentences by making use of 3R
read recall review and solve
problems the teacher guides the
The pupils recall solving
problems in open sentences.
1) add the same number
both side
2) subtract the same number
Recall
Review
And
Understanding
Mathematics
Mental
sums,
group by
group
presentatio
140
pupils understand the
mathematics language before one
can solve problems in open
sentences.
both side
3)multiply both side by the
same number
4) divide both sides by the
same non-zero number.
e.g., 5 + [ ] = 25
∴ 25 - = 20
∴ 5 + 20 = 25
3
y = 9 y = ∴ 9 × 3
y = 27
language
instruction
Diagnosing
And treating
Pupils
Difficulties.
n in class
and class
work.
UNIT LESSON PLAN 2 EXPERIMENTAL GROUP
Subject: Mathematics
Class: Primary 6
Topic: Geometry and Mensuration
Duration: 40 minutes
Sex: Male [ ] - Female [ ]
Behavioural objectives:
At the end of the lesson the pupils should be able to:
1. Identify Heights, Distance, time and speed.
2. Name features of given shapes and polygons.
3. Identify lines of symmetry, edges, phases and vertices of various plane shapes.
4. Identify basic properties of shapes
5. Solve quantitative aptitude problems.
Previous knowledge:
1. The pupils are familiar with travelling from one place to another.
2. The pupils can identify planeshapes.
Instructional Materials:
1. Metre rule, wall metre rule.
2. Measuring tapes or rope
141
3. Different types of shapes ranging from three dimensional shapes to polygon
CONTENT TEACHER ACTIVITY PUPILS
ACTIVITY APPROACH
EVALUATION
Measuring of
height and
distance
1. The teacher uses practical
activity to aid studying.
2. The teacher divides the
pupils into groups and
leads them to obtain
readings of their heights.
3. The teacher guides the
pupils to read
measurement of things in
the class and home.
The pupils in
group by group
actively participate
in the various
measurement of
their height,
materials in the
classroom and at
home.
Using
Practical
activities to
aid studying
CONTENT TEACHER ACTIVITY PUPILS
ACTIVITY APPROACH
EVALUATION
Polygons and
shapes angles
The teacher divides the class
into groups. The teacher guides
the pupils to identify and recall
the names and features of
different shapes given:
i. Rectangle
ii. Square
iii. Circles
iv. Shapes and
v. Polygons
The teacher guides the pupils to
review properties of plane
shapes.
The teacher also uses practical
activity to aid studying by using
paper cut outs and by folding to
determine the lines of
symmetry.
The pupils:
1. Identify, recall
the different
shapes using 3R.
2. Reviewed the
properties of
shapes. Do a
practical exercise
by folding paper
cutouts to
determine the lines
of symmetry of
various shapes.
The pupils fold
many papers
cuttings to
different shapes
and polygons.
Reading to
understand,
Recall area of
simple shapes
and review
shapes and
their
properties
By folding of
paper and
cutting to
determined
lines of
symmetry
Pupils’ cut
paper to
various shapes
guided by the
teacher also
fold paper to
show various
lines of
symmetry.
142
Engage the pupils to give the
number of vertices, edges and
phases of shapes.
The teacher engage the pupils to
measure angles with the use of
a protractor e.g. angle in a
triangle = 180
He teacher guides the pupils in
the application of 3R
The pupils
measure angles
from triangles
drawn by them.
Measure the
angles of some
triangles.
A Square
By folding a square to
get four lines of symmetry .
The pupils fold
paper cutting a
square to get its
line of symmetry.
Boys and girls
mixed together
and divided
into groups.
Mental sums,
group by group
presentation in
class and class
work.
Collaborative
learning to
folding and
cutting paper to
get lines of
symmetry.
Hexagon
The sum of the interior angles
of a triangle = 180 :- 180 x 4 =
720
The pupils
divides the
hexagon into 4
triangles.
Collaborative
143
UNIT LESSON PLAN (3) FOR EXPERIMENTAL GROUP
Subject: Mathematics
Title: Measurement
Class: Primary 6
Duration: 40 minutes (2 periods)
Sex: Male ( ) Female ( )
Behavioural objectives: At the end of the lesson, the pupils should be able to:
1. Identify a right angled triangle
2. State Pythagoras rule
3. Define area, volume and perimeter
4. Read and tell time in seconds, minutes and hours.
5. Define distance, speed and time solve some quantitative aptitude problems.
Previous knowledge:
1. The pupils can find area of rectangles, squares and circles
2. The pupils tell time and days in a week or months up to one year
3. The pupils are familiar with entering a car and travelling a distance.
Instructional materials:
1. Cardboards showing rectangles of equal areas but different perimeters.
2. Nail boards, rubber band, balls,cylindrical tins, charts containing word problem
watch, second pendulum stop watch
.
Instructional procedure
CONTENT TEACHER ACTIVITY PUPILS ACTIVITY APPROACH E valuation
Right angle
triangle
The teacher guides the
pupils to identify right angle
triangle
The teacher guides the
pupils on the application of
3R. Then to draw a right
angle triangle of sides 3cm,
The pupils identifies a right
angle triangle
3cm
4cm
5cm
The pupils calculate many
more right angle triangle
problems.
The approach
used by the
teacher will
involve
reading,
recalling,
reviewing
Pupils
come out
one after
the other
to draw
and solve
on the
144
4cm, 5cm
The teacher guides the
pupils to identify the sides as
hypotenuse, opposite and
adjacent and he then guide
the pupils to state
Pythagoras rule
a2 +b2 = c2 where a and b are
the adjacent and opposite
and c the hypotenuse.
The teacher guides the
pupils to construct squares
on each of the 3 sides, then
divide the squares into unit
squares to get the square of
each.
The teacher guides the pupil
in guides of 3R.
The pupils count the unit
squares to get the actual
squares.
54
3
This is showing 9 + 16 = 25
The pupils applied the use
of 3R.
Understanding
the language
instruction
and using
practical
activities to
aid studying
board
Areas
perimeter
andvolume
The teacher guides the
pupils to calculate area,
perimeter and volume by
applying the appropriate
formula
Area of rectangle = Lxb
Perimeter = 2(lxb)
The pupils activity
participate in the
calculations of what the
teacher wrote by correctly
reviewing the formula and
recalling some facts.
Area of triangle = ½ base x
height e.g
Area of parallelogram
b x h
Recalling and
reviewing
The approach
used here is
diagnosing
and treating
pupils
instructions
Recalling and
reviewing
Time, speed
and
distance
The teacher leads the pupils
to define time, speed and
distance as speed = Distance
The pupils recall telling
time. The pupils calculate
problems with time, speed
Recall,
review,
understand the
7cm
10cm
Base of parallelogram = 10cmHeight = 7cmArea = 10cmx7cm = 70cm2
145
Time
Distance = Speed x Time
Time = Distance
Speed
The teacher guide the pupils
to solve problems. An
aeroplane travelled to Lagos
at 839km/hr for 4 hours what
distance was covered by the
aeroplane.
and distance. The pupils try
more examples
The pupils copy down.
Time taken to cover the
Distance = Speed x Time
= 839 x 4
= 3356km
language
instruction
and
diagnosing
and treating
their
difficulties
Using
practical
activity
Quantitative
aptitude
The teacher guides the
pupils in the use of 3R to
solve quantitative aptitude
problems.
The pupils apply 3R to
understand the instructional
225km 50km/h ?4.5h
Time = = = 9/2 = 4.5hr SP 50
D 225
Understanding
mathematics
language
instruction
before
solving.
Mental
sums, group
by group
presentation
in class and
class work.
146
UNIT LESSON PLAN 4 FOR EXPERIMENTAL GROUP
Subject: Mathematics
Topic: Statistics
Class: Primary 6
Sex: Male ( ) Female ( )
Age: 11 years
Duration: 40 minutes
Objectives:- At the end of the lesson the pupils should be able to
1. Define mean, median and mode of a set of data.
2. Form set of data from given numbers of items
3. Read and interpret pictograms and bar charts
4. Represent information on bar charts
Previous Knowledge
1. The pupils are familiar with numbers.
2. The pupils can name in the class, at home, in school
3. The pupils can do addition, multiplication and division.
Instructional Materials:
Pencils, graph paper, coin/dice, pack of cards and charts.
Instructional Procedures:
CONTENT TEACHER ACTIVITY PUPILS ACTIVITY APPROACH Evaluation
Mean,
median,
mode
The teacher guides the
pupils in the use of 3R as to
define mean, median and
mode of a set of data.
Mean of a set of data means
average median means the
middle number depending
if the set of data is add or
even and mode means the
number that occurs most.
The pupils recall various
definitions and write them
down with examples.
The pupils collects the data
into number and frequency.
NO 8 9 10 11
FREQ 4 4 8 4
Total = 20
Mean=8x4+9x4+10x8+11x4 4+4+8+4
Read
Recall
Review
Diagnosing
and treating
pupils
difficulties
147
The teacher presents a set of
data representing the ages
of 20 primary 6 pupils as 8,
10, 9, 11, 10, 9, 8, 8, 8, 10,
10, 11, 9, 10, 11, 10, 10, 10,
9, 11.
The teacher guides the
pupils to calculate mean,
median and mode ages. As
the pupils recalls and
review their formulars.
= 32+36+80+44 20
= 192 = 48 = 93/5
20 5 = 9.6
Median
88889999101010101010101
011111111
Since there are 20 numbers
½ of 20 = 10 each
Median = middle number
= 10th+11th numbers
10+10 = 20 = 10
2 2
Median = 10
Modal No. = 10 (occur
most) has the highest
frequency.
Using
practical
activities to
aid studying
Pupil’s give
their different
ages and use
to find mean,
median and
mode. A
teacher
guides the
pupils to read
and write the
numbers in an
ungrouped
data in
ascending or
descending
order
Data
collection
and
presentation
Bar graph
Pictogram
The teacher in the effective
application of 3R to collect
guides the pupils to collect
data by performing some
experiment like tossing a
coin once or twice and
collect the information.
The teacher divides the
pupils into groups and
encourage them to work in
group.
The teacher encourage the
pupils to collect data by
The pupils with the use of
graph books represents the
resulting experiment on data
which is translated to charts
e.g bar chart.
The pupils participate
actively in the experiment
by throwing a dice and
tossing coins to get their
readings and practice many
more examples with tossing
a coin many times
Throwing a dice once to six
Using
practical
activity to aid
studying
The pupils
work in
groups to
achieve better
results
Recalling,
Read
Revising
understanding
148
using tallies after which a
frequency table is gotten
and then represent the
information on a bar chart.
The teacher solves a
problem of tossing of coin
10 times e.g TH TH, HH,
TH, HT, HT HTTT,TT, HT
Outcomes Tallies Freq
HT IIII 4
TH III 3
HH I 1
TT II 2
10
No. of outcomes
0
1
2
3
5
HH HT TH TT
times and also use pack of
cards. The pupils do this
exercises to generate data
which they use to draw the
bar graph.
mathematics
language
instruction.
Diagnosing
and treating
pupils
difficulties
and using
practical
activities to
aid studying
149
UNIT LESSON PLAN (5) FOR EXPERIMENT GROUP
Subject: Mathematics (1)
Topic: Basic Operation
Class: Primary Six (6)
Sex: Male ( ) Female ( )
Duration: 40 mins (2 days)
Behavioural objectives: At the end of the lesson the pupils will be able to:
(1) Identify the different operational signs
(2) Write and interoperate BODMAS
(3) Write numbers in index form
(4) Write in significance figure
(5) Identify squares and square root of numbers
(6) interpret words in open sentence
(7) solve problem on qualitative aptitude involving three or more operations.
Previous Knowledge
(1) The pupil can add subtract, multiply and divide
(2) They can interpret words in open sentences
(3) Identify square roots of numbers
Instructional Materials
Sum cards, Multiplication facts and charts, Flash cards
Procedure:
150
CONTENT Teacher Activity Pupils Activity Approach E valuation
Squares,
Square notes
numbers
The teacher guides the
pupils in the proper use
of 3R to identify square
of numbers and square
roots of numbers. The
teacher also guides the
pupils to solve some
exercises.
The pupils identify
squares of numbers
and square roots and
solve some exercises
e.g.
52 = 25
82 = 64
102 = 100
152 = 225
Applying
3R
Read,
Recall and
Review
CONTENT TEACHER ACTIVITY PUPILS
ACTIVITY APPROACH Evaluation
Multiplication
The teacher drills pupils
on multiplication. The
teacher guides the pupils
in the effective use of 3R
recall the multiplication
time table by making them
recite and write down 2
times table to 12 x
timetable
To diagnose their
difficulties, the teacher
tests the pupils mentally
by giving mental sums
and finds out the
important of
multiplication and its
application.
The teacher multiplies 3
digit numbers decimal by
decimal
The pupils recall
the
multiplication
time table
starting from 2
times table to 12
times table.
Pupils solve
problems on
multiplication
using three digit
numbers and
decimal to
decimal. The
pupils solve
mental sum
while they
quickly provide
the answers at a
limited time.
Read, Recall,
Review
Active
participation
in solving
diagnosing
pupils
difficulties.
Recall and
reviewing
Application
of 3R and
understanding
mathematics
language
instruction
The teacher
guides pupils
in the use of
Abacus to
write numbers
in millions,
billions,
trillions and do
the necessary
multiplications.
151
= 5, = 4
= 8, = 10
The pupils identify
the numbers in square
root.
Addition and
Subtraction
The teacher guides the
pupils in the use of 3R
to identify place value
in addition of whole
numbers and decimal.
The teacher guides
pupils to solve problems
on addition and
subtraction
The pupils recall
whole numbers,
fractions and decimal.
Solve problems in
addition and
subtraction
Read
Recall
Review
Order of
operations
The teacher guides the
pupils in the use of 3R
to understand the
meaning of BODMAS
as
B = Bracket 1st
O = of 2nd
D = Division 3rd
M = Multiplication
A = Addition
S = Subtraction
Guides pupils to apply
the order in solving
basic operational
problems.
The pupils apply the
order in solving
exercises on order of
operations
5 of (3 + 8) – 2
5 of 11 – 2
5 x 11 – 2
55 – 2
= 53
Read
Recall,
Review,
Diagnosing
and
treating
pupil’s
difficulties.
Mental sums,
group by
group
presentation
in class and
class work.
152
APPENDIX D
UNITY LESSON PLAN (1) FOR CONTROL GROUP
Subject: Mathematics
Title: Number and Numeration
Class: Primary 6
Duration: 40 minutes (2 days)
Sex: Male [ ], Female [ ]
Specific objection:
At the end of the lesson, the pupils should be able to:
1. Read and write numbers up to one billion
2. Add, subtract in place value
3. Give the place value of digits with decimal and identification of fractions
4. Read and compare population of cities HIV infected persons
5. Express in ratio, percentages and proportion
6. Solve problems on quantitative aptitude on numbers, direct and indirect
proportion.
Previous knowledge:
It is expected that the pupils had been taught works on primary 3,4 and 5 and as such
can
1. Count in English up to one million and also in Roman numerals
2. Writes in figures and in words
3. Do some addition and subtraction
4. Identify population charts
Instructional materials:
1. Abacus and charts for numbers
2. Charts of factors and multiples of numbers, population charts and HIV/AIDS
charts.
153
Instructional procedures:
CONTENT TEACHER ACTIVITY PUPILS
ACTIVITY APPROACH
Evaluation
Whole
numbers
The teacher leads the pupils
to count up to one million. He
also leads the pupils to write
in words e.g
NUMERALS WORD FORM
1,000,000 One million
10,000,000 Ten million
50,000,000 Fifty million
100,000,000 One hundred millions
500,000,000 Five hundred million
1000,000,000 One billion
The pupils count
up to one million.
They write in
words and
figures up to one
billion
The pupils copy
what the teacher
writes into their
notebooks.
What is the
difference
between one
million and
one billion.
How can you
write
25million in
words.
Fractions
The teacher leads the pupils
to identify fractions, reduce
fractions to its simplest form
and to add and subtract
fractions.
The pupils
identify fractions
such as ½ , 1/3
¾ , ¼
As the teacher
does
1/4
1/4
1/4
1/4
1 /41 /4
Divide the
circle into
five and write
the fraction
Multiples
The teacher leads the pupils
to
i. List the multiples of
10 and 12
The pupils
copy’s what the
teacher had
written on the
154
ii. Find the LCM of 10
and 12
The teacher solves for the
pupils to copy.
Multiple of 10=10,20,30,40
Multiple of 12=12,24,36,48
Factors of 10=2 x5
Factors of 12= 2 x 2 x 3
LCM = 2 x 2 x 3 x 5= 60
Write in index
27 = 33
64 = 26
100 = 103
board into their
notebooks
Practice
solving on
their own
Population
The teacher leads and guides
the pupils in the construction
of population data. The
teacher leads the pupils to
define population and to give
the population of their
classes, houses, towns and
churches.
Population is the number of
persons in a locality.
The pupils do
what the teachers
had done in class
by writing down
population and
goes home to
find the answers
to others on their
own
Pupils ask
questions on
how they can
read and
write
population
Ratio
Proportion
The teacher leads the pupils
to express ratio in its simplest
form, find percentage and
identify direct and indirect
proportion.
The teacher solves the
following:
(1) Reduce to its simplest
form 28:32 5 7 8
The pupils copy
what the teacher
has written on
the board
Pupils ask
questions on
how to solve
direct and
indirect
proportion.
155
(2) Find the cost of a
articles at N125.25
each.
1 article cost N125.25
9 articles cost 9 x N125.25 =
N1127.25
Open
sentences
The teacher leads the pupils
to revise open sentences by
reading recalling reviewing
and solving problems the
teacher makes the pupils
understand the mathematics
language before one can solve
problems in open sentences.
Pupils copy from
the board what
the teacher has
written
The pupils
ask questions
Teacher
ask pupils
questions.
156
UNIT LESSON PLAN 2 FOR CONTROL GROUP
Subject: Mathematics
Class: Primary 6
Topic: Geometry and Mensuration
Duration: 40 minutes each (2 days)
Sex: Male [ ] - Female [ ]
Behavioural objectives:
At the end of the lesson the pupils should be able to:
1. Identify Heights, Distance, time and speed.
2. Name features of given shapes and polygons.
3. Identify lines of symmetry, edges, phases and vertices of various plane shapes.
4. Identify basic properties of shapes
5. Solve quantitative aptitude problems.
Previous knowledge:
1. The pupils are familiar with travelling from one place to another.
2. The pupils can identify plane shapes.
Instructional Materials:
1. Metre rule, wall metre rule.
2. Measuring tapes or rope
3. Different types of shapes ranging from three dimensional shapes to polygon
CONTENT TEACHER ACTIVITY PUPILS
ACTIVITY APPROACH
Evalu-
ation
Measuring of
height and
distances
The teacher leads the
pupils to obtain reading
of their heights .
The teacher leads the
pupils to read
measurement of things
in their class or home
The pupils will
copy what the
teacher does in
the class.
The pupils
ask questions
157
Polygons
plane shapes
and angles
The teacher leads the
pupils to identify:
i. Rectangles
ii. Squares
iii. Circles, other
shapes and
polygons
The teacher leads the
pupils to name the
properties of
planeshapes.
The teacher leads the
pupils to identify lines
of symmetry, vertices,
edges and phases of
shape
The teacher leads the
pupils to measure
angles with the use of
protractor as to find out
that the sum of angles
in a triangle is equals
1800
A square 4 lines
of symmetry
Hexagon
The sum of the interior
angles of hexagon = 4 x
180 = 7200
The pupils
writes the
properties of the
various shapes
and polygons
The pupils listen
to the teacher
and copy’s what
the teacher
writes on the
board.
The pupils copy
into their books.
Without
knowing how
lines of
symmetry of a
square are
gotten.
Questions
The pupil ask
questions
such as why
is the answer
720.
Teacher ask pupils questions.
158
UNIT LESSON PLAN (3) FOR CONTROL GROUP
Subject: Mathematics
Topic: Statistics
Class: Primary 6
Sex: Male ( ) Female ( )
Age: 11 years
Duration: 40 minutes each (2 days)
Objectives:- At the end of the lesson the pupils should be able to
1. Define mean, median and mode of a set of data.
2. Form set of data from given numbers of items
3. Read and interpret pictograms and bar charts
4. Represent information on bar charts
Previous Knowledge
1. The pupils are familiar with numbers.
2. The pupils can name in the class, at home, in school
3. The pupils can do addition, multiplication and division.
Instructional Materials:
Pencils, graph paper, coin/dice, pack of cards and charts.
Instructional Procedures:
CONTENT TEACHER ACTIVITY PUPILS
ACTIVITY APPROACH
Evalu-
ation
Right angle
triangle
The teacher leads the pupils
to draw a right angled
triangle with sides 3cm, 4cm
and 5cm
3cm
4cm
5cm
The pupils
draw the
diagram as
drawn by the
teacher.
Questioning
159
The teacher leads the pupils
to identify hypotenuse,
opposite and adjacent. He
guides the pupils to state the
Pythagoras rule as a2 + b2 =
c2. The lead pupils to use the
formula to solve problems.
The pupils
copy all that
the teacher
writes on the
board into
their
notebooks.
Area
perimeter
and volume
The teacher guides the pupils
to calculate Area perimeter
and volume by applying
approximate formula Area of
rectangle = L xb
Perimeter = 2 (L+b)2
Area of parallelogram b x h
Area of triangle ½ base x
heighte.g
7cm
10cm
Base of parallelogram = 10cmHeight = 7cmArea = 10cmx7cm = 70cm2
The pupils
write down
the different
formulas into
their
notebooks
and copy the
problem.
Questioning
Time
Distance
and Speed
The teacher leads the pupils
to define time, distance and
speed as Speed = Distance
Time
Distance = Speed x Time
Time = Distance
Speed
The teacher leads and guides
the pupils to solve a problem
e.g iAn aeroplanetravelled to
Lagos at 839km/hr for 4
hours what distance was
The pupils
follow what
the teacher
did and copy
into their
notebooks
The pupils
copy what the
teacher had
done
Questioning
Teacher
ask pupils
questions.
160
covered by the aeroplane.
Time taken to cover the
distance = 4 hrs
Distance = speed x time
= 839km/hr x 4 hrs
= 3356km
161
UNIT LESSON PLAN (4) FOR CONTROL GROUP
Subject: Mathematics
Topic: Statistics
Class: Primary 6
Sex: Male ( ) Female ( )
Age: 11 years
Duration: 40 minutes each (2 days)
Objectives:- At the end of the lesson the pupils should be able to
1. Define mean, median and mode of a set of data.
2. Form set of data from given numbers of items
3. Read and interpret pictograms and bar charts
4. Represent information on bar charts
Previous Knowledge
1. The pupils are familiar with numbers.
2. The pupils can name in the class, at home, in school
3. The pupils can do addition, multiplication and division.
Instructional Materials:
Pencils, graph paper, coin/dice, pack of cards and charts.
Instructional Procedures:
CONTENT TEACHER ACTIVITY PUPILS
ACTIVITY APPROACH
Evalu-ation
Mean median
and mode
The teacher leads pupils to define mean,
median and mode of a set of a data as
mean is average of a set of numbers,
median is the middle number depending
on the set of data, whether it is odd or
even while mode is the number that
occurs most e.g the teacher presents a
set of data representing the ages of 20
The pupils
defines
mean,
median and
mode and
write it
down as
defined by
The pupils
ask questions
to enable
them
understand.
Teacher
ask pupils
questions.
162
Data
representation
Bar graph
pictogram
primary 6 pupils as
8, 10, 9, 11, 10, 9,8, 8, 8, 10, 10, 11, 9,
10, 11, 10, 10, 10, 9, 11.
The teacher leads and guides them to
solve as follows
8+10+9+11+10+9+8+8+8+10+10+11+9
+10+11+10+10+10+9+11.__________
20
192 = 48= 93/5 = 9.6
20 5
The teacher leads the pupils to toss 2
coins 100 times.
Leads the pupils to prepare bar graphs
to represent the resulting scores.
Guides the pupils to represent the result
on bar graph
The teacher solves a problem of tossing
2 coins 10 times as
TH TH, HH, TH, HT, HT HTTT,TT,
HT
Outcomes Tallies Freq
HT IIII 4
TH III 3
HH I 1
TT II 2
10
the teacher
The pupils
copy into
their note
books as the
teacher
writes.
10+10 = 20 2 2
= 10
Mode = 10
The pupils
do as
instructed
by the
teacher.
Represent
the
information
on a bar
graph.
The pupils
copy the
problem
and the
solution
into their
note books
Questioning
Questioning
163
No. of outcomes
0
1
2
3
5
HH HT TH TT
164
UNIT LESSON PLAN (5) FOR CONTROL GROUP
Subject: Mathematics (1)
Topic: Basic Operation
Class: Primary Six (6)
Sex: Male ( ) Female ( )
Duration: 40 mins each (2 days)
Behavioural objectives: At the end of the lesson the pupils will be able to:
(8) Identify the different operational signs
(9) Write and interoperate BODMAS
(10) Write numbers in index form
(11) Write in significance figure
(12) Identify squares and square root of numbers
(13) interpret words in open sentence
(14) solve problem on qualitative aptitude involving three or more operations.
Previous Knowledge
(1) The pupil can add subtract, multiply and divide
(2) They can interpret words in open sentences
(3) Identify square roots of numbers
Instructional Materials
Sum cards, Multiplication facts and charts, Flash cards
CONTENT TEACHER ACTIVITY PUPILS
ACTIVITY APPROACH
Evalu-
ation
Multiplication
The teacher leads the pupils
to multiply 3 digit numbers
by solving some examples on
the board e.g.
(1) 0738 x 50
x 7.38 36900
(2) The teacher again takes
The pupils
identifies the
numbers in squares
and copy what has
been given on the
board into their
notebook
165
an example on
multiplication by decimal
2.8 or 28 X 3.1 31 28 84 868 = 8.68 (3) Multiplication by fraction
3/8 x 8/9
= 3 x 8 = 1/3 8 x 9
Or
½ x 4/5 = 1 x 4 = 4/10 2 x 5 = 2/5
Indices
The teacher drills the pupils
on numbers in index form
9 = 3 x 3 = 32
27 = 3 x 3 x 3 = 33
125 = 5 x 5 x 5 = 53
The teacher uses mental sums
to make the pupils read,
recall and review all about
powers of numbers
The pupils respond
to the teachers
instruction by
copying what the
teacher writes on
the board.
Questioning
Order of
Operation
The teacher makes the
meaning of BODMAS
understood by the pupils by
explaining the order as B
(Bracket) is done first O (of)
done next D (Division) next
M (Multiplication) next A
(Addition) next S
(Subtraction) last the teacher
The pupils copy
what the teacher
writes on the board.
questionings
166
leads the pupils to solve 5 of
(3 + 8) – 2
Fractions by fractions
multiplications of 3 digits
(1) (738 x 10) x 5
=7380 x 5
=36900
(2) 4597
* 8000
367,7600
(3) Multiplication of decimal
by decimal by decimal
2.8 x 3.1 = 28
* 31 (considering 2p.d)
28
+ 84 868 = 8.68
(4) Multiplication by
Fractions by Fraction
3/8 x 8/8 =3 x 8 = 1/3 Or ½ x 4/5 = 1 x 4 = 2/5 2 x 5
Leads pupils to add and
subtract
The pupils copy
what the teacher
writes on the board.
Questioning
Addition and
subtraction
squares and
square roots
of numbers
The teacher explains the
meaning of squares of
numbers as multiplying the
number to itself.
He leads the pupils to
produce numbers with perfect
square and guides the pupils
The pupils copy
what the teacher
writes on the board
Questioning
167
to solve problems and square
roots
52 = 5 x 5 = 25
82 = 8 x 8 = 64
102 = 10 x 10 = 100
152 = 15 X 15 75 15 225
Division
The teacher led pupils to
recall, review division by
doing some mental drills in
division e.g. 10 : 2, 100 : 5
25.5 : 5
The pupils copy
what the teacher
writes on the board
Questioning
Teacher
ask pupils
questions.
168
APPENDIX E
Table of Specification
CONTENT DIMENSION ABILITY PROCESS DIMENSION
Class Lower cognitive processes
S/
N
Topics % 30%
K
30%
Com.
40%
APL
100%
1 APPLY SQ3R (SCAN Question)
i) Read, recall and review open
sentence, interprete mathematical
sentences
ii) Recall Basic operation
(BODMAS), Basic statistics,
percentages
iii) Review: properties of shapes,
counting in place value and
quantitative reasoning.
20%
3
3
4
10
2 Understanding the purpose of
mathematics language instruction
i) write in words
ii) Express decimal to fractions and
vise versa
iii) Reduce to its lowest term.
iv) Give answer to 3 significance
figures
v) Without calculator add, multiply,
divide
vi) Express in percentage.
30%
4
5
6
15
3 Diagnosing and treating pupils
difficulties:
i) Definition of concepts
30%
169
ii) Identification of concepts
iii) Solve mathematical problems.
iv) Time, Distance and speed
4 5 6 15
4 Using practical activities to aid
studying:
i) measurement; length Distance,
angles
ii) Converting given lengths, distance
iii) Drawing of circle, graphs and
review their properties.
iv) Data collection mean, media,
mode range, Bar chart
v) Solve quantitative problems
20%
3
3
4
10
Total 100% 14 16 20 50
Topics considered in the construction of the table of specification are: number and
numeration, basic operation, measurement, geometry and menstruation and statistics.
170
APPENDIX F
Training guide for Mathematics Teachers on Achievement Motivational
Instructional Approach.
Introduction
This training is to familiarize you with the achievement motivational
instructional approach. We know as teachers we are conversant with many teaching
methods such as demonstration, discussion, laboratory, lecture, target task, discovery,
expository traditional and enquiry. Although these methods have been in use for years,
pupils performance in internal and external examination continues to be poor. This is a
fact that every mathematics teacher can bear witness. Research studies have identified
teaching methods used by teachers as the main contributing factor to pupils poor
performance. Therefore, there is the need for primary school teachers to look for better
and rewarding methods of teaching mathematics in the primary schools that will give
the pupils a better foundation in mathematics.
In this training exercise, the possibility of using achievement motivational
instructional approach in teaching mathematics to primary six pupils will be considered.
This is to investigate whether achievement motivational instructional approach could
facilitate learning, enhance retention, and the ability to manipulate numbers and
achievement in mathematics in the primary schools. Operationally, achievement
motivational instructional approach is a method where pupils are trained to be mentally
coordinated by making sure that previous knowledge is updated, it is a method that
ensure that pupils can read questions very well to their proper understanding;
1. Recall and review facts and knowledge previously done that is related to what is
treated at hand.
2. Understand Mathematics Language instruction.
3. Diagnosing and treating pupil’s difficulties.
4. Using practical activities to aid studying.
The method is time consuming and demands patience from both the pupils and the
researchers. This method gives the pupil’s satisfying intellectual reward. This in-turn,
helps in better memory, facilitate retention arouse interest and transfer of knowledge.
171
The success of this method highly depends on the teachers. As such your cooperation is
highly solicited throughout the period of this investigation.
Teachers and Pupils role in Achievement Motivational Instructional Approach
In achievement motivational instructional approach, the teacher acts as a
facilitator of learning. He over-sees all the activities of the pupils. He directs and
constantly monitors pupils to understand every verbal statement made in mathematics
by reading the statement over and over as to device a workable plan. The teacher
should use simple and related procedures that could give clue and understanding to
getting the correct procedure that will lead to the correct answer. The teacher does not
respond negatively to pupil’s wrong attempts to question, as not to frustrate their effort.
Instead, the teacher encourage them through the use of rewarding work such as
try again, you can do it, etc. this will make the pupils constantly think of the problem at
hand and try to find solution to it.
In a situation where the class size is large, the teacher starts off the lesson with
mental sums. This will spur everybody in class thereby making the pupils show active
concentration and participation because they must finish within a limited time. Again if
the class is large and there is inadequate supply of instructional materials, effective
supervision becomes very difficult. As such, the teacher should divide the pupils into
small working groups, each with enough instructional materials, for easier and effective
supervision. That will enable each pupil participate and be involved throughout the
lesson”
At the beginning (at entry behaviour), of each lesson approach, the teacher
should diagnose the productivities of the pupils by giving simple tasks that majority can
attempt. This will enable the teacher find out their problems and stimulate their
curiosity to learn. The objectives of the activities in the lesson should be explained to
the pupils as well as the guide lines on the use of the instructional approach especially
where it involves instructional materials. At the end of every activity, an interactive
session, should follow to find out if the activity has helped in providing the required
method or formular to the instructional problem and getting the correct solution. The
way and manner, and formular used in solving problem should be such that anywhere
such a problem is seen, the approach goes. The pupils should be encouraged to express
172
their views to their teachers and amongst themselves, so as to exchange ideas. This will
improve interaction between themselves, the teacher and the learning materials. Hence
the pupils communication skills, computational and intellectual ability, retentive ability
are improved. Pupils should feel free to learn, ask questions on ideas they did not
understand especially in understanding mathematics language instruction. The teacher
on the other hand, should attend to all their problems and difficulties they encounter in
carrying out their activities. Thus the teacher should guide, reinforce, motivate and
stimulate the pupils effort to work harder towards achieving the objectives of the
lesson. The teacher does this by providing feedback on their performance.
Traditional Method
The teachers of the control group will be presented with unit lesson plan of all
the areas offered in primary six. The teachers will use the plans with the textbook. They
first use solved examples from the textbook, write on the board for pupils to copy. After
which the teacher takes one or two simple problems from the exercises in the textbook
and then give classwork in the textbook. The teachers do not mind whether the pupils
understand what he did or not and most teachers do not even mark the classwork or
homework.
Pupils ask questions to get clarification but teachers use lecture methods to give
the answer which in most cases is not understood by pupils. Teachers out of laziness
give their notebook to pupils to copy for others on the board and most of these pupils
can neither read well nor spell as to copy rightly. In a control class pupils are always
writing, no interaction of any kind. The class is always dull and uninteresting. Pupils
hardly know each other’s ability. They are lazy and weak in solving problems. The
teachers do not really try to arouse pupils by giving them mental sums that will act as a
stimulant to thinking.
For the experimental and control groups, the teaching will be done in 10 teaching
periods of 40 minutes each. That will last for three (3) weeks at 5 periods per week. On
the last day of the two weeks the posttest will be administered. Lastly, the pupils will
not be informed of the purpose of this investigation. This may influence their
performance in the posttest at the end of the exercise.
Thank you.
173
APPENDIX G
PRIMARY SIX CURRICULUM
THEME EVERYDAY STATISTICS
TOPIC PERFORMANCE OBJECTIVES
CONTENT ACTIVITIES TEACHING AND
LEARNING MATERIALS
EVALUATION GUIDE
TEACHER PUPILS
1.
Population
Pupils should be
able to:
1. interpret,
pictograms and
bar graphs.
2. state the
meaning of
population
3. appreciate the
use of
pictograms and
bar graphs in
representing
population of
people or data.
Pictograms
and bar
graphs
1. Brings teaching materials to
the class.
2. Introduces the topic and
guides the pupils to define
population.
3. Presents a bar graph chart of
population of a town showing
men, women, boys and girls and
leads the pupils to examine the
graphs and deduce the
population of men, women, boy
and girls.
4. Displays the population chart
of a village as:
men - 20,000
women – 30,000
boys - 40,000
1. Brings pencil,
ruler, exercise
book, eraser to
the class.
2. Define
population.
3. Give the
population of
men, women,
boys and girls in
the bar graph.
4. Represent the
information on a
pictogram and
bar graph.
5. Work in
group.
Population
data chart
pictogram
chart bar
graph
Pupils to:
1. prepare
pictogram
and bar
graph of
given data.
2. prepare
pictogram
and bar
graph using
data gotten
from the
need of the
population of
boys, men,
women and
girls in his
174
girls - 36,000
and guides the pupils to prepare
a pictogram and bar graph of
cows needed by the population
where 2000 men need 1 cow
women need 1 cow 4000 boys
need 1 cow 4000 girls need 1
cow.
5. Encourage the pupils to work
in groups.
6. Leads the pupils to appreciate
the use of pictograms and bar
graphs in representing
population of people or any
data.
6. Appreciate
the use of
pictograms and
bar graphs in
representing
population of
people or any
given data.
environment.
2.
Measurem
ent of
Central
Tendency
Pupils should be
able to:
1. find the mode
of data.
2. appreciate the
use of mode in
analyzing
population of
i. mode 1. Brings teaching materials to
the class.
2. Gives colours of 2,000 cars
as follows
green - 448
red - 452
white - 562
blue - 538 and leads pupils to
1. Observe and
study the
teaching
materials
brought by the
teacher.
2. Represent the
given
175
people or data
and in daily
activities
find the modal colour and to
represent the information on a
bar graph
3. Leads the pupils to appreciate
the use of mode in analyzing the
population of people or data
information in
bar graph and
finds the mode.
176
PRIMARY SIX CURRICULUM
THEME: NUMBER AND NUMERATION
TOPIC PERFORMANCE OBJECTIVES
CONTENT ACTIVITIES TEACHING AND
LEARNING MATERIALS
EVALUATION GUIDE
TEACHER PUPILS
1. Whole
Numbers
Pupils should to
able to:
1. count in
millions and
billions
i. Counting
in millions
and billions
1. Revise the previous work in
counting up to counting in
million
2. Guides pupils to count in
millions up to nine hundred
millions
1. Revise
counting up to
one million
2. Count in
millions up to
nine hundred
million.
Abacus and
Charts of
numbers
Pupils to:
1. count in
millions up
to a specified
number.
2. write and read
up to one
million
ii. Writing
and reading
up to one
million
3. Guides pupils to read up to
one billion as shown below
Numeral Word form
1,000,000 one million
10,000,000 ten million
50,000,000 fifty million
100,000,000 one hundred
million
500,000,000 five hundred
million
1000,000,000 1 billion
1. Practice
reading and
writing of
numbers up to
one million
2. Devise other
practices or
methods to write
and read up to
one billion
Abacus and
Charts of
numbers
2. write and
read up to
one million
177
2. Devises other practices or
methods to write and read up to
one billion.
3. solve
problems
involving
quantitative
reasoning
iii.
Quantitativ
e reasoning
Guides pupils to answer
question in quantitative
reasoning
3. do given
exercise on
quantitative
reasoning.
178
PRIMARY SIX CURRICULUM
THEME: NUMBER AND NUMERATION
TOPIC PERFORMANCE OBJECTIVES
CONTENT ACTIVITIES TEACHING AND
LEARNING MATERIALS
EVALUATION GUIDE
TEACHER PUPILS
4. solve problem
on quantitative
reasoning
iv.
Quantitativ
e reasoning
Leads pupils to solve problems
on quantitative aptitude e.g.
Find the missing number such
that the resulting fraction is
expressed as 0.25
Solve problems
on quantitative
aptitude
4. solve
problems on
quantitative
aptitude.
3.
Demograp
hy
Pupils should be
able to:
1. read, write
and compare
population of
big cties
i.
population:
• Families
• Classes
• Towns and
cities etc.
1. Guides pupils to define
population.
2. Leads pupils to give the
population of:
• Their houses
• Classes
• Town etc.
3. Guides pupils to read and
1. Define
population.
2. Give
population of
their houses,
classes, towns
etc.
3. Read and
write
Demography
map of
Nigeria
video of
populations
Pupils to:
1. define
population.
2. read and
write the
population of
big cities in
Nigeria.
3. read and
2
0.25
?
179
write populations of some cities
e.g. Lagos, Kano, Aba in the
country using map of Nigeria.
populations of
some cities e.g.
Lagos, Kano,
Aba in the
country using
the map of
Nigeria.
compare
population.
2. read and
compare
population of
HIV positives in
different
countries.
ii. Reading
and
comparing
of
populations
Guides pupils to read and
compare population of HIV
positive from different countries
of the world
Participate in
reading and
comparing
populations of
HIV positives in
different
countries in the
world
World Atlas
and some
published
information
from WHO
on
HIV/AIDS
etc.
4. read and
compare
population of
HIV
positives in
some given
countries in
the world.
3. appreciate the use of counting in thousands and millions and population in demography, epidemiology, etc.
Guides pupils to appreciate the
importance of population
studies in demography,
epidemiology, etc.
Appreciate the
study of
population in
demography and
epidemiology.
180
PRIMARY SIX CURRICULUM
THEME EVERYDAY STATISTICS
TOPIC PERFORMANCE OBJECTIVES
CONTENT ACTIVITIES TEACHING AND
LEARNING MATERIALS
EVALUATION GUIDE
TEACHER PUPILS
4. Ratio
and
proportion
Pupils should be
able to:
1. solve
problems on
ratio
2. appreciate the
application of
ratio in everyday
life.
3. solve
quantitative
reasoning
problem
involving ratio
i. Ratios 1. Leads pupils to revise
previous work done on ratios
2. Guides pupils to solve
problems on population e.g.
In a city of 10,000 people 100
of them are HIV positive. Find
the ratio of those infected to the
total population.
Total population 100,000
Infected population – 100
The ratio of infected to total
population is 100: 10,000 or
1:100 or 1/100.
3. Leads pupils to appreciate the
application of ratio in everyday
life.
4. Leads pupils to solve
quantitative problems related to
1. Revise the
previous work
on ratios
2. Solve
problems on
ratios
3. Appreciate
the application
of ratios in
every day life.
4. Solve
quantitative
reasoning
problems related
to ratios.
Charts of
solved
problems on
ratios
Pupils to:
1. solve
given
problems on
ratios
2. solve
some
quantitative
reasoning
problems on
ratios.
181
ratios.
4. solve
problems in
direct
proportion.
5. appreciate
applications of
direct
proportions in
daily life
activities.
ii. Direct
proportion
1. Guides pupils to solve direct
proportion problems e.g.
A man saves money everyday.
If he saves N30 each day, how
much can be saved in 4 days?
Saving (N) day
30 1
80 2
90 3
120 4
He saves N120 in 4 days.
2. Leads pupils to notice that his
saving is in direct proportion to
the number of days.
3. Leads pupils to appreciate the
application of direct proportion
in everyday life.
1. Solve
examples on
direct
proportion.
2. Notice that
the saving is in
direct proportion
to the number of
days.
3. Appreciate
the application
of direct
proportion in
everyday life
Charts of
solved
examples on
Direct
proportions.
3. solve
given
problems on
direct
proportions.
6. solve
problems on
quantitative
reasoning
involving direct
proportion
iii.
Quantitative
reasoning
Leads pupils to solve problems
on quantitative reasoning
involving direct proportion.
Solve
quantitative
aptitude
problems
involving direct
proportion
4. solve
problem on
quantitative
aptitude
involving
direct
proportion.
182
PRIMARY SIX CURRICULUM
THEME: MEASUREMENT
TOPIC PERFORMANCE OBJECTIVES
CONTENT ACTIVITIES TEACHING AND
LEARNING MATERIALS
EVALUATION GUIDE
TEACHER PUPILS
7. Weight Pupils should be
able to:
1. work word
problems on
weights.
2. express the
same weight in
different unit
gram, kilogram
tonne
3. appreciate the
relationship of
different unit of
measurement.
World
problems
on weights
1. Guides pupils obtaining
measurements of their
weight, rock sample etc
using weighing scales.
2. Explains that weight of
small objects expressed in
kilograms while heavy
objects are expressed in
tones.
1 tonne = 1000kg
1000g = 1kg
3. Leads pupils to appreciate
the relationship between
different units of
measurement.
1. Practice
converting weights
in tones to kilogram
and vice versa.
2. Identify objects
whose weights
could be expressed
in tones, in
kilograms and in
grams.
3. Practice solving
word problems on
weights.
4. Pupils appreciate
the relationship
between different
units of
Samples of
minerals
different
types of
weighting
scales and
spring
balance.
Pupils to;
1. convert
weights
expressed in
tones to
kilograms
and vice
versa.
2. solve
word
problems on
weights.
183
measurement e.g.
grams, kilograms,
tones.
8. Time Pupils should be
able to:
1. tell time in
seconds and
minute.
2. solve
quantitative
aptitude
problem on
time.
i. Timing
in minutes
and
second.
1. Guides pupils to find the
time it will take the class
captain or class monitor to
trek the width of the class in
seconds or minutes, using
the seconds-pendulum and
also stop watch and compare
the result.
2. Leads pupils to solve
quantitative aptitude
problems on time.
3. Gives further assignments
on timing.
1. Work in groups
to time in seconds
and minutes.
2. Time them selves
on how long it will
take them to
complete various
activities. Solve
quantitative
aptitude problem on
time.
3. solve assigned
exercises
Second
pendulum,
stop-watch
Pupils to:
1. time
certain
events in
seconds and
minutes.
184
PRIMARY SIX CURRICULUM
THEME: MEASUREMENT
TOPIC PERFORMANCE OBJECTIVES
CONTENT ACTIVITIES TEACHING AND
LEARNING MATERIALS
EVALUATION GUIDE
TEACHER PUPILS
3. read timetable
of journeys
especially by
trains and
aeroplanes.
4. value the need
for time in real
life.
ii. Reading
time-table
of journeys
1. Brings time table of
journey by train or by
aeroplane.
2. Guides the pupils to
use these time tale to
estimate the time-
interval it will take a
train or aeroplane to get
to a specific
destination.
3. Leads the pupils to
value time in real life.
1. Use time table of
train to estimate the
time it will take a train
to get to a designated
destination.
2. Use time-table to
estimate the time it
takes an aeroplane to
get to a specific
destination.
3. Value the need for
time in real life.
Time-table
of train,
aeroplane
from
different
airlines
Pupils to:
1. obtain time
table or schedule
of flights from
any airlines to
estimate the
time it takes an
aeroplane to get
to specific
destination.
2. obtain time
table of train
and estimate the
time it will take
the train to get
to specific
destination.
185
8. Time
athletics
Pupils should be
able to estimate
time to complete
races.
Pupils value the
use of
mathematic in
every day living.
Standard
time for
races
1. Given record times
for 100m, 400m, 800m
by men and women
from different
competitions for
different years.
2. Lead pupils to value
the use of maths in
every day life.
1. Make the table for
races and time value
the use of maths in
every day life.
2. Value the use of
mathematics in every
day life
Charts
showing
races and
time for
100m,
440m and
800m
Pupils to:
1. estimate time
a boy will take
to run 100m.
2. Estimate time
a girl will take
to run 100m
9. Speed Pupils should be
able to work
more problems
on speed
Solve more
quantitative
aptitude
problem on time
and speed.
Average
speed.
1. Guides the pupils
using the idea of steady
speed to explain
average speed.
2. Further explains that
the ratio of distance
covered and time taken
is called speed. Speed
is expressed in km/hr,
etc.
3. Lead pupils to solve
more quantitative
aptitude exercises
1. Mention the distance
of their homes from the
school and the time it
takes them to cover it.
2. Give the distance
covered by the train,
bus or aeroplane to
travel from one town to
another and the time
taken.
3. Compute the speed
for the train, bus or air
journeys from one
Clock face
stop watch
railway
time-table,
bus time-
table, air
time-table
Pupils to:
1. determine
how long it
takes to travel
by bus, train
aeroplane from
one town to the
other.
2. solve more
problems on the
topic to obtain
time taken for a
journey distance
186
related time and speed town to the other.
4. Solve more
quantitative aptitude
exercises relate to time
and speed.
covered and
average speed.
187
PRIMARY SIX CURRICULUM
THEME: ALGEBRAIC PROCESSES
TOPIC PERFORMANCE OBJECTIVES
CONTENT ACTIVITIES TEACHING AND
LEARNING MATERIALS
Evaluation Guide
TEACHER PUPILS
Open
sentences
People should
be able to
1. solve
problems
expressed as
open sentence.
2. interpreter
words into open
sentences and
solve them.
3. solve related
problems on
quantitative
aptitude.
Open
sentences
1. Prepares teaching materials
and brings them to class.
2. Leads the pupils on revision
of open sentence.
3. Gives open sentence words to
be interpreted and solved e.g.
equal number is 60 oranges are
in three baskets, if the total
number of oranges is 60, how
many are in one basket?
4. Leads the student to solve as
follows. Let the number of
oranges in each basket be M so
that M + M + M = 60
3m = 60
M = 60/3 = 20.
5. Leads the pupils to solve
quantitative aptitude related
1. prepare their
own flash cards
are bring to
class.
2. Carry out
revision on open
sentences as
guided by the
teacher.
3. Interpret word
problems into
open sentence
and solve them.
4. solve the
problems on
pupils flash
cards.
1. Charts of
worked
examples,
flash cards
on open
sentences.
2. Charts and
flash cards
on worked
example of
quantitative
aptitude test.
Pupils to:
1. solve
problems on
open
sentence.
2. to
interpret
words into
open
sentence and
solve them.
3. solve
quantitative
aptitudes
involving at
least three
arithmetic
OPERATIO
188
problems involving three or
more arithmetic operations in a
sample
5. solve
quantitative
aptitude
problems
involving three
or more
arithmetic
operations in a
sample.
NS in a
sample.
189
PRIMARY SIX CURRICULUM
THEME EVERYDAY STATISTICS
TOPIC PERFORMANCE OBJECTIVES
CONTENT ACTIVITIES TEACHING AND
LEARNING MATERIALS
Evaluation Guide
TEACHER PUPILS
Angles Pupils should be
able to:
1. Measure
angles in
degrees
1.
Measureme
nt of angles
1. Brings teaching
materials to the class.
2. Uses board and
protractor, to guide the
pupils in the correct
placement of the
protractor and leading of
the value of a given
angle by using various
angles drawn on the
chalkboard.
3. Emphasizes that
angles are measured in
degree and indicate the
symbol) e.g. 600
1. Bring protractor
ruler and writing
materials to the class.
2. Draw and measure
angles in the
chalkboard and in their
workbooks.
3. Verify the teaching
of angle measurement
by their colleagues
Mathematica
l set an
chalkboard
protractor
Pupils to:
1. measure
identified
angles from
diagram in
their text
books, work
books etc.
2. draw
various plane
shapes and
measure
resulting
angles to the
nearest
degree.
2. Measure
angles in a plane
1. Asks pupils to indicate
the edges, vertices and
1. Identify the number
of edges vertices and
Protractors,
net of
Pupils to:
1. identify
190
surfaces of given three
dimensional shapes.
2. Leads pupils to
measure the size of
angle, indicate lines that
are parallel and
perpendicular in each of
the given shape.
3. Leads the pupils to
appreciate the relevance
of angle to daily life.
surfaces for different
shapes.
2. Use protractors to
determine the sizes of
angles in a given shape
and confirm the result
of these measurements.
3. Identify lines that are
parallel and
perpendicular in three
dimensional shapes.
4. Use graph sheets to
produce models of
given shapes.
5. Appreciate the
relevance of angles to
daily life.
polygons,
adhesive
tapes, graph
sheets and
clinometers.
the edges,
vertices and
faces of
given three
dimensional
shapes.
2. measure
the sizes of
angle in a
two
dimensional
shapes
3. prepare
nets and
models of
identified
three
dimensional
shapes.
191
PRIMARY SIX CURRICULUM
THEME: GEOMETRY AND MENSTRUATION
TOPIC PERFORMANCE OBJECTIVES
CONTENT ACTIVITIES TEACHING AND
LEARNING MATERIALS
Evaluation Guide
TEACHER PUPILS
3. review basic
properties of
a. Isosceles
b. Equilateral
c. Right angle
d. Scalene
triangles.
ii. Review
of basic
properties
of
a. Isosceles
b.
Equilateral
c. Right
angle
d. Scalene
triangles
1. Brings teaching materials to
the class.
2. Leads pupils to identify
isosceles, equilateral, right
angle and scalene triangular
shapes
3. Guides pupils to draw the
different triangular shapes.
4. Guides pupils to review the
properties of triangular shapes
such as equal sides, equal base
angles right angle, unequal
sides of triangles.
1. Observe the
materials
brought by the
teacher.
2. Identify
isosceles,
equilateral, right
angle and
scalene
triangular
shapes.
3. Draw the
different
triangular
shapes.
4. Review the
properties of
triangular
shapes such as
Isosceles,
equilateral,
right angle
and scalene
triangular
shapes,
metre rule
tape,
protractor
3. draw the
different
triangular
shapes.
4. state the
properties of
different
types of
triangular
shapes.
192
equal sides,
equal base
angles, right
angle, unequal
sides of
triangles.
4. review the
basic properties
of a circle
iii.
Properties
of a circle
(review)
iv.
Quantitativ
e reasoning
1. Brings teaching materials to
the class
2. Leads pupils to identify the
circle
3. Guides pupils to draw a circle
4. Leads pupils to review the
properties of a circle.
5. Leads the pupils to solve
quantitative aptitude problems
such as
Where the pupils is expected to
match the shapes to its
properties.
1. Observe the
materials
brought by the
teacher.
2. Identify the
circle
3. Draw the
circle
4. Review the
properties of a
circle.
5. Solve
quantitative
aptitude
problems as
directed by the
teacher
Circular
shapes pi-
demonstratio
n board,
pencil
5. draw
given
circular
shapes
6. state the
properties of
a circle.
7. solve
some
quantitative
aptitude
problems.
Isosceles
triangle
square
rectangle
Four sides
Equal three
sides equal
Base angles
equal
193
Department of Science Education,
University of Nigeria,
Nsukka.
2/02/2014
Sir/Madam,
Request to Validate a Research Instrument
I am a post graduate student of the University of Nigeria Nsukka, currently
undertaking a research project aimed at finding out the effect of achievement
motivational instructional approach on primary six pupils’ numerical aptitude,
achievement and retention in mathematics.
I therefore wish to use your school(s) for the exercise which wish involve
action participation of pupils and teachers of primary six (6). This exercise will last
for about three (3) weeks.
Thanks for your cooperation
Mrs. Pauline Akor
PG/Ph.D/07/48424.
194
APPENDIX H
Computation of the Reliability of MAT S/N R W p q pq
1 15 15 0.50 0.50 0.25 2 12 18 0.40 0.60 0.24 3 17 13 0.57 0.43 0.25 4 13 17 0.43 0.57 0.25 5 11 19 0.37 0.63 0.23 6 12 18 0.40 0.60 0.24 7 17 13 0.57 0.43 0.25 8 17 13 0.57 0.43 0.25 9 14 16 0.47 0.53 0.25
10 14 16 0.47 0.53 0.25 11 12 18 0.40 0.60 0.24 12 8 22 0.27 0.73 0.20 13 13 17 0.43 0.57 0.25 14 13 17 0.43 0.57 0.25 15 17 13 0.57 0.43 0.25 16 16 14 0.53 0.47 0.25 17 19 11 0.63 0.37 0.23 18 12 18 0.40 0.60 0.24 19 14 16 0.47 0.53 0.25 20 15 15 0.50 0.50 0.25 21 15 15 0.50 0.50 0.25 22 19 11 0.63 0.37 0.23 23 16 14 0.53 0.47 0.25 24 15 15 0.50 0.50 0.25 25 14 16 0.47 0.53 0.25 26 13 17 0.43 0.57 0.25 27 16 14 0.53 0.47 0.25 28 15 15 0.50 0.50 0.25 29 12 18 0.40 0.60 0.24 30 17 13 0.57 0.43 0.25 31 13 17 0.43 0.57 0.25 32 11 19 0.37 0.63 0.23 33 12 18 0.40 0.60 0.24 34 17 13 0.57 0.43 0.25 35 17 13 0.57 0.43 0.25 36 14 16 0.47 0.53 0.25 37 14 16 0.47 0.53 0.25 38 12 18 0.40 0.60 0.24 39 8 22 0.27 0.73 0.20 40 8 22 0.27 0.73 0.20 41 24 6 0.80 0.20 0.16 42 23 7 0.77 0.23 0.18 43 21 9 0.70 0.30 0.21 44 17 13 0.57 0.43 0.25
195
45 21 9 0.70 0.30 0.21 46 17 13 0.57 0.43 0.25 47 13 17 0.43 0.57 0.25 48 19 11 0.63 0.37 0.23 49 24 6 0.80 0.20 0.16 50 15 15 0.50 0.50 0.25
Total 11.85 R = Number of Examinees that choose correct option W = Number of examinees that choose wrong options p = Proportion of examinees that choose correct option q = Proportion of examinees that choose wrong options pq = Product of proportion of those that choose correct option and those that choose wrong options S2 = Variance of the total score on the test n = Number of items in the test K-R(20) = Kuder-Richardson formula 20
Σ−−
=−21
11
)20(b
S
pq
n
nRK
=
−
− 16.74
85.111
150
50
= )16.01(49
50 −
= 1.02(0.84) = 0.86
196
APPENDIX I
Computation of the Reliability of NAT using K-R(20) S/N R W p q pq
1 17 13 0.57 0.43 0.25 2 16 14 0.53 0.47 0.25 3 19 11 0.63 0.37 0.23 4 12 18 0.40 0.60 0.24 5 14 16 0.47 0.53 0.25 6 15 15 0.50 0.50 0.25 7 15 15 0.50 0.50 0.25 8 19 11 0.63 0.37 0.23 9 16 14 0.53 0.47 0.25
10 15 15 0.50 0.50 0.25 11 24 6 0.80 0.20 0.16 12 15 15 0.50 0.50 0.25 13 16 14 0.53 0.47 0.25 14 13 17 0.43 0.57 0.25 15 13 17 0.43 0.57 0.25 16 17 13 0.57 0.43 0.25 17 16 14 0.53 0.47 0.25 18 19 11 0.63 0.37 0.23 19 12 18 0.40 0.60 0.24 20 14 16 0.47 0.53 0.25 21 15 15 0.50 0.50 0.25 22 15 15 0.50 0.50 0.25 23 19 11 0.63 0.37 0.23 24 16 14 0.53 0.47 0.25 25 15 15 0.50 0.50 0.25 26 14 16 0.47 0.53 0.25 27 13 17 0.43 0.57 0.25 28 16 14 0.53 0.47 0.25 29 15 15 0.50 0.50 0.25 30 12 18 0.40 0.60 0.24 31 17 13 0.57 0.43 0.25 32 13 17 0.43 0.57 0.25 33 11 19 0.37 0.63 0.23 34 12 18 0.40 0.60 0.24 35 17 13 0.57 0.43 0.25 36 17 13 0.57 0.43 0.25 37 14 16 0.47 0.53 0.25 38 14 16 0.47 0.53 0.25 39 12 18 0.40 0.60 0.24 40 8 22 0.27 0.73 0.20 41 8 22 0.27 0.73 0.20 42 14 16 0.47 0.53 0.25 43 23 7 0.77 0.23 0.18 44 21 9 0.70 0.30 0.21
197
45 17 13 0.57 0.43 0.25 46 21 9 0.70 0.30 0.21 47 17 13 0.57 0.43 0.25 48 17 13 0.57 0.43 0.25 49 19 11 0.63 0.37 0.23 50 24 6 0.80 0.20 0.16
Total 11.95 R = Number of Examinees that choose correct option W = Number of examinees that choose wrong options p = Proportion of examinees that choose correct option q = Proportion of examinees that choose wrong options pq = Product of proportion of those that choose correct option and those that choose wrong options S2 = Variance of the total score on the test n = Number of items in the test K-R(20) = Kuder-Richardson formula 20
Σ−−
=−21
11
)20(b
S
pq
n
nRK
=
−
− 84.63
90.111
140
40
= )19.01(39
40 −
= 1.02(0.81) = 0.83