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Primary Teachers' Perceptionsof Policy for CurriculumReform in MathematicsL. Kyriakides aa Pedagogical Institute , Nicosia, CyprusPublished online: 28 Jul 2006.
To cite this article: L. Kyriakides (1997) Primary Teachers' Perceptions ofPolicy for Curriculum Reform in Mathematics, Educational Research andEvaluation: An International Journal on Theory and Practice, 3:3, 214-242, DOI:10.1080/1380361970030302
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Educational Research and Evaluation 1380-3611/97/0303-0214$12.001997, Vol. 3, No. 3, pp. 214-242 © Swets & Zeitlinger
Primary Teachers' Perceptions of Policy for CurriculumReform in Mathematics*
L. KyriakidesPedagogical Institute, Nicosia, Cyprus
ABSTRACT
This paper reports and analyses findings from an investigation into Cypriot teachers'perceptions of national policy for curriculum reform in primary schools, with specialreference to Mathematics. Questionnaires were sent to three samples of teachers: a 10 percent sample of Cypriot teachers randomly selected from the total population; all Cypriotbeginning teachers; and all beginning teachers who graduated in 1992 from the Universityof Warwick in the United Kingdom. There were five main findings. First, pupils' abilityto solve investigations, and to gain mathematical knowledge were seen as of equal impor-tance while ability to talk about Mathematics the least important. Second, formativepurposes of assessment were accorded most, and summative purposes least, importance.Third, teachers approved of active pedagogy. Fourth, they conceptualised assessment as anatural part of teaching but paradoxically favoured formally structured techniques ofassessment. Fifth, statistically significant differences between perceptions of the Englishand Cypriot sample of beginning teachers were associated with the extent of centralcontrol on the curriculum. Implications for the implementation of curriculum policy arediscussed.
INTRODUCTION
The failure of much curriculum innovation has been attributed to theneglect by innovators of teachers' perceptions (Fullan, 1991). A longtrend in the literature (Nisbet, 1973; Steadman, Parson, & Salter, 1978)supports the view that teachers' perceptions are one of the most critical
*The research which is referred to in this article has been funded by the "A.G. LeventisFoundation" and by the O.R.S. Awards Scheme. Professor Jim Campbell was particularlyhelpful in discussing many of the issues raised in this article. An early version of thispaper has been presented at the ECER conference at the University of Bath in 1995.
Address correspondence to: L. Kyriakides, Pedagogical Institute, Nicosia, Cyprus. Tel.:010 357 24 97362. Fax: 010 357 24 80505. E-mail: [email protected].
Manuscript submitted: February 20, 1996Accepted for publication: January 21, 1997
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PRIMARY TEACHERS' PERCEPTIONS 215
factors for the effectiveness of the various models of curriculum change(Havelock, 1971). This has implications for policies of curriculum reformin most industrialised societies. In Cyprus in 1992, a reform programmewas introduced which was mainly concerned with content, pedagogy andassessment. A centre-periphery model of change (Schon, 1971) was used.The central government, through inter-departmental committees, drew upsyllabuses, curricula, planning guides and new textbooks which weredistributed to schools. In this context, the main purpose of this researchwas to investigate teachers' perceptions of the reform programme, and toexamine the extent to which the perceptions matched the objectives of thereforms.
The importance of teachers' perceptions is also supported by researchon teachers' thinking (Calderhead, 1987; Zeichner, Tabachnick, & Dens-more, 1987). Although such research does not provide us with a compre-hensive and theoretical framework for thinking about teaching, it doesprovide us with an insight into the process of curriculum change. Calder-head (1987) points out that research into teachers' thinking shows:
how unrealistic it is to conceive of innovation as a set of pre-formu-lated ideas or principles to be implemented by teachers. Innovativeideas are interpreted and reinterpreted by teachers over a period oftime and translated into practice in a process that involves teachersdrawing upon several different knowledge bases and interpretingand manipulating various interests (p. 17).
Teachers possess a body of specialised knowledge acquired through trainingand experience related to teaching methods, subject matter and child be-haviour together with other information resulting from their experienceof working with children in numerous contexts. Understanding the fac-tors influencing teachers is, therefore, necessary for any attempt to evalu-ate curriculum reform. This research is mainly concerned with the effectof the central control upon teachers' perceptions. It attempts to explorethe association between different forms of control over curriculum andassessment and teachers' perceptions. The importance of exploring theeffect of central control over the curriculum upon teachers' perceptionsof curriculum policy can be attributed to the fact that research into theseperceptions may contribute to teachers' meaningful involvement in theformation and evaluation of curriculum policy. Teachers' meaningful in-volvement in the process of change may have implications for the politi-cal ideology in the structure of the educational system. Skilbeck (1990)suggests that a sharp and uncompromising distinction between central-
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216 L. KYRIAKIDES
ised and decentralised systems is clearly inadequate in the situations mostof the countries are now addressing. He also supports the need for sharingroles and responsibilities. However, the extent and the nature of centralcontrol over the curriculum varies from one country to another.
In Cyprus, the centre controls curriculum practice through publishing aseries of textbooks in each subject and providing them free to all pupils.The textbooks are particularly influential on practice and Cypriot teachersrely heavily on them. Policy makers consider textbooks as equally impor-tant to the official curriculum. It is assumed that these textbooks will helpteachers to implement innovations designed by the centre, so that the im-plementation of curriculum policy is assured. Thus, textbooks are used toensure the implementation of curriculum reform. Moreover, the centre con-trols curriculum practice through school inspection, which is based upon apublished official ideology, and through appointments. Teachers who dem-onstrate an ability to implement the official ideology get promotion. Thenature and extent of central control is different in England, since pre-scribed textbooks are not permitted, inspection is conducted by a semi-independent agency, the office for Standards in Education (OFSTED), andappointments are made locally by individual school governing bodies.
Thus, it was decided to take one subject, Mathematics, as an illustra-tion of the reforms, and to investigate Cypriot teachers' perceptions indetail in this subject. Mathematics was chosen because it is a core subjectand relatively culturally free (Phillips, 1986). It was, therefore, possibleto compare perceptions of teaching Mathematics held by teachers in dif-ferent countries. Thus, in order to investigate the effect of state controlupon teachers' perceptions, comparison of the perceptions of Cypriotbeginning teachers and a sample of beginning teachers in England wasattempted. Educational systems in England and Cyprus differ not so muchin terms of curricular models underlying the reform of schooling, as in theextent and nature of central control over the curriculum. By comparingperceptions of these two groups, it is, therefore, possible to examinedifferences in perceptions arising from the extent of central control.
METHODS OF DATA COLLECTION AND SAMPLING
A questionnaire (see Appendix A) was sent to Cypriot teachers and agroup of English teachers. The content of the questionnaire was derivedfrom an analysis of curriculum policy in each country (Department ofEducation and Science, 1987, 1991; Ministry of Education, 1992). Therewere five broad areas of teachers' perceptions. First, a decision to ask
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PRIMARY TEACHERS'PERCEPTIONS 217
respondents to rank the purposes of teaching Mathematics was taken inthe light of a lack of an explicit policy about the relative importance ofpurposes of teaching Mathematics.
Second, there was concern over the kind of Mathematics pedagogyconsidered important for the delivery of the curriculum. Although teach-ing methods are not directly subject to government policy, there is animplicit pedagogy in the curricular formulation in Cyprus. This may becharacterised as an activity-based approach to the teaching of Mathemat-ics. The fact that active learning is supported by the New Curriculum canbe attributed to the strong influence of Piaget and the Cockcroft Reportupon curriculum policy in Cyprus (Kyriakides, 1994). Thus, the newcurriculum of Cyprus directed teachers to give opportunities for pupils toparticipate in practical and investigative tasks. But despite the fact thatCypriot teachers concerned to obtain promotion must prove to their in-spector that they are able to implement the active pedagogy, this ideologyhas not widely influenced curriculum practice of primary Mathematics inCyprus (Baron, 1970). It is important to explore this gap between curric-ulum theory and curriculum practice. This study can be seen as an attemptto examine whether barriers to the implementation of policy lie in teach-ers' perceptions of teaching methods.
Third, until recently assessment was a neglected issue restricted to twoattempts to investigate the standards in Mathematics. A section of the newcurriculum is, however, focused on assessment. This section can be seen asthe first systematic attempt of the Ministry of Education to establish thebase upon which assessment in Cyprus can be developed. The new curric-ulum therefore reflects a new policy in assessment. Moreover, for the firsttime in the history of curriculum development in Cyprus, a debate amongthe officials of the Ministry of Education, the inspectors, the teachers andtheir trade union was under way in 1990. The dispute was mainly betweeninspectors and teachers and concerned primarily the extra work involved,and government's requirement to introduce a common form of record keep-ing. It is, therefore, important to identify teachers' perceptions of assess-ment policy. Moreover, an exploration of teachers' perceptions of the pur-poses for which assessment should be used and especially whether it shouldbe summative or formative is attempted. This is because Cypriot policydocuments do not refer explicitly to the purposes of assessment and be-cause there is a widespread doubt that the summative and formative pur-poses can be achieved in a single set of assessment arrangements. Summa-tive purposes concentrate on the overall levels of achievement of pupils.Information derived from summative assessment cannot easily be used tohelp teachers with their teaching, but can be used for selection (Broadfoot,
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218 L. KYRIAKIDES
1986, p. 59). This conflict is reflected in technical problems which need tobe faced (Brown, 1991, pp. 217-218; Murphy, 1988).
Fourth, the assumption that some techniques of assessment are moreappropriate than others is explored, emphasizing written tests of assess-ment policy in Cyprus. In addition, an examination of the relationshipbetween the appropriateness and ease of the various assessment tech-niques was needed, given the evidence about problems of manageabilityof national curriculum assessment (Campbell & Neil, 1994; ENCA,1992).Finally, teachers' perceptions of the relative importance of six ways ofimproving assessment was investigated in order to identify whether thecurrent curriculum reform will meet the needs of Cypriot teachers.
The population for the questionnaire can be classified into the follow-ing three groups. First, a randomly selected 10 per cent sample of thewhole group of Cypriot teachers was surveyed by a questionnaire in 1993,so as to establish a representative picture of the perceptions of primaryteachers in Cyprus. Second, questionnaires were sent to all the Cypriotteachers with one year of teaching experience when they were at the endof their training (May 1992) and when they were at the end of their firstyear of teaching (May 1993). Finally, a group of English teachers withone year's teaching experience was surveyed. Questionnaires were sentto them when they were at the end of their training (May 1992) and whenthey were at the end of their first year of teaching (May 1993). This groupwas mainly used to explore cultural factors, including the influence ofcentralised control, upon teachers' perceptions by comparing them withthe group of Cypriot teachers with one year of teaching experience.
Of the 380 Cypriot teachers approached 286 responded, a response rateof 73 per cent. All the English teachers who graduated from the Universi-ty of Warwick in 1992 were approached and a response rate of 65 per centwas obtained. The response rates imply that the findings do not lackvalidity for general application to their population. However, the sampleof English teachers is not a representative of the population of Englishteachers who were at the end of their first year of teaching practice. Semi-structured interviews with 20 teachers who responded to the question-naire were also conducted in order to test the validity of the questionnairefindings by matching the qualitative data derived from the interview witheach teacher against the quantitative data gathered by his/her individualquestionnaire. A measure of match was derived by comparing most of thequestionnaire with the interview data gathered by this study. Althoughthis measure does not necessarily imply that its validity is high, since it ispossible that they are both invalid, the use of both questionnaire andinterview methods provides a basis for triangulation of data.
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PRIMARY TEACHERS' PERCEPTIONS 219
FINDINGS FROM THE QUESTIONNAIRE
This section is divided into three parts. The first one deals with the find-ings arising from questionnaire responses of the randomly selected sam-ple of 10 per cent of Cypriot teachers, and the second with responses ofthe beginning teachers in Cyprus and England. A comparison betweenperceptions of the randomly selected sample of Cypriot teachers withperceptions of Cypriot beginning teachers is presented in the last section.
Findings from Questionnaire to Cypriot TeachersPurposes of Teaching MathematicsFigure 1 shows the mean rank of the perceived importance of each of fourpurposes of teaching Mathematics. Kendall Coefficient of Concordancewas calculated to show the degree of consensus about curriculum purpos-es in this ranking. A significant level of agreement amongst Cypriot teacherswas revealed (W1 = 0.31, Z = 2.19 V1 = 3.99, V2 = 7 1 4 , P <.005). Cypriotteachers gave high priority to purposes concerned with gaining Mathe-matical knowledge and solving investigative tasks. These two purposeswere considered of roughly equal importance since their mean ranks areclose to each other. The purpose which was ranked as the third mostimportant concerned the development of positive attitudes to Mathemat-ics whereas the one focused on pupils' ability to talk about Mathematicswas seen as the least important.
Purposes of AssessmentFigure 2 deals with perceptions of purposes of assessment. Kendall coef-ficient of concordance for Cypriot teachers' perceptions about purposesof assessment (W2 = .74, Z = 6.23, V.1 = 3.99, V2 = 714, p <.005) showsthat they agreed among themselves in their ranking of the relative impor-
1,5
MeanRank
2J5
3,5
Knowledge Attitudes Communication Problem-solving
Fig. 1. Teachers' perceptions about the purposes of Mathematics.
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220 L. KYRIAKIDES
tance of the purposes of assessment. The following observations arisefrom Figure 2. Formative assessment was considered as the most impor-tant by almost all the teachers. The next most important purpose of as-sessment is the teachers' self-evaluation which has a mean rank close to2.00, and is considered by 80 per cent of the teachers as the second mostimportant purpose. Since teachers' self-evaluation and formative assess-ment have direct feedback into the teachers' own teaching, it can beinferred that Cypriot teachers considered assessment as a means of pro-viding information to help them make decisions about their teaching. It isalso of interest to emphasise the low rating given to summative purposesof assessment and to the national monitoring. Their mean ranks are closeto 3.50, which means that they are clearly differentiated from the othertwo purposes. As far as the summative purpose is concerned, almost allthe teachers (95%) saw it as either the least or the second least importantpurpose. Similarly, 87 per cent saw national monitoring as the least or thesecond least important purpose. Thus, summative purposes and nationalmonitoring were considered as the least important purposes of assess-ment.
Methods of Teaching and Assessment in MathematicsThe figures in Table 1 are based on the information derived from teach-ers' response to items of the questionnaire concerned with the implemen-tation of policy on Mathematics pedagogy and assessment. Percentagesof teachers agreeing and disagreeing with ways of teaching and assess-ment in Mathematics, medians and modes are shown in Table 1.
Mathematics PedagogyTwo observations concerned with perceptions of Mathematics pedagogyarise from Table 1. First, the great majority of Cypriot teachers (morethan 65%) agreed with the following aspects of Mathematics pedagogy:
MeanRank
Summative Teachers' self-assessment
Formative Evaluative
Fig. 2. Teachers' perceptions about the purposes of assessment.
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PRIMARY TEACHERS' PERCEPTIONS 221
Table 1. Percentages of Cypriot Teachers who Agree and those who Disagree with theFollowing Methods of Teaching and Assessment in Mathematics, and their Me-dians, and Modes.
Methods of teaching and assessment
(A) Mathematics Pedagogy(1) Fixed sequence of topics
(2) Practical activities as appropriate
Disagree1
14.8
for 9.7
Cypriot teachers who
Agree2
76.0
77.9
Median
4.003
4.00
Mode
4.00
5.00Key Stage 1 pupils ( 5 - 8 years old )as for Key stage 2 (9- 11)
(3) Practical activities as appropriate for 17.9 68.5 4.00 4.00high attaining pupils as for low
(4)
(5)
(6)
Needs for talk in each activity
Fixed time for teaching Mathematics
Mathematics should be taught mainlythrough investigations
(B) Issues of Assessment Policy(1) Assessment as natural part of teaching
(2)
(3)
(4)
Assessment on the basis of productsrather than process
Assessment of pupils' attitudes
Assessment of child's ability to applyMathematics in unfamiliar situations
4.4
55.8
17.5
0.5
52.7
23.2
10.9
86.9
20.5
65.0
98.4
25.7
54.7
78.3
4.00
2.00
4.00
5.00
2.00
4.00
4.00
4.00
2.00
4.00
5.00
2.00
4.00
4.00
1 = This group of teachers either disagrees or absolutely disagrees.2 = This group of teachers either agrees or absolutely agrees.3 = 1 :1 absolutely disagree; 2 :1 disagree; 3 :1 do not know/1 cannot say ; 4 :1 agree;
5:1 absolutely agree.
(1) Children should talk about Mathematics and present the results oftheir activities to their classmates
(2) Mathematics should be taught mainly through practical investigations(3) Practical activities are appropriate for children irrespective of their
age or ability(4) There is a fixed sequence of Mathematical topics for children to fol-
low
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222 L. KYRIAKIDES
Second, the item concerned with the need of having a fixed time forteaching Mathematics was rejected by more than half of the Cypriot teachersand both its median and mode is 2.00. However, the fact that the percent-age of teachers who neither agreed nor disagreed with this statement isalmost equal to 25 per cent and of those who agreed is equal to 20 per centshows that there was a variation among teachers' opinions. Thus, rejec-tion of a fixed time for teaching Mathematics cannot be seen as a repre-sentative opinion of the whole group of Cypriot teachers.
Assessment PolicyThe second part of Table 1 is concerned with issues of assessment policyin Mathematics. The great majority (more than 75%) of Cypriot teachersconsidered assessment as a natural part of teaching and supported assess-ment of pupils' ability to apply Mathematics in unfamiliar situations.However, items B.2 and B.3 displayed different patterns. Item B.3 wasaccepted by half of the Cypriot teachers but rejected by a quarter of them.On the other hand, item B.2 was rejected by half of the Cypriot teachersbut accepted by a quarter of them. Thus, it cannot be claimed that Cypriotteachers, as a group, rejected the idea that assessment should be based onpupils' outcomes rather than on process. Moreover, it cannot be claimedthat they agreed with assessment of pupils' attitudes to Mathematics.
We can finally observe that for most of the items of Table 1 (7 out of10) there was a very substantial agreement among Cypriot teachers. It canbe claimed that there was consensus among teachers' opinions aboutmethods of teaching and assessment in Mathematics.
Techniques of Assessment (Appropriateness and Ease)Teachers were asked to rank twice eight techniques of assessment inMathematics according to their appropriateness and their ease. The meanranks and the Kendall Coefficient of Concordance are presented in Table2. Moreover, columns 4 and 6 show the "absolute rank" of the mean rankswhich is constructed by ordering the mean ranks. (The "absolute ranks"are used only for display purposes, and their representation does notnecessarily imply an ordering of the perceived appropriateness and easeof these eight techniques.) It emerges clearly from the coefficients pre-sented in this table that Cypriot teachers agree among themselves in theirranking of the relative appropriateness of each technique and also agreeamong themselves in their ranking of the relative ease of each technique.However, the mean ranks tend to cluster close to each other, with smalldifferences between them. Nevertheless, the mean ranks suggest that tech-niques of assessment can be classified into the following groups accord-
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PRIMARY TEACHERS' PERCEPTIONS 223
ing to their perceived appropriateness. Structured observation and inter-view were considered as the most appropriate methods. The oral ques-tion-and-answer is the method considered as the next most appropriate.Methods in the middle range of appropriateness are the extended writtenquestions, multiple choice questions and direct written questions whichhave mean ranks very close to 4.5. Finally, unstructured observation wasseen as the least appropriate technique and sentence completion as thenext least appropriate.
We can now analyse further the features of the third column by explor-ing the figures at the bottom part of Table 2. This part has the eightmethods collapsed into two categories, namely oral and written tech-niques. The category of written techniques represents an average of themethods which have to do with a written test and the oral category repre-sents the rest of the techniques. The Kendall Coefficient of Concordanceshows a statistically significant agreement among teachers' ranking of
Table 2. Mean Ranks and 'Absolute' Ranks of Assessment Techniques according to Per-ceptions of Appropriateness and Ease.
No.
(1)
(2)(3)(4)(5)(6)(7)(8)
1)2)
Assessment Techniques
Multiple choice andmatching questionsUnstructured ObservationSentence CompletionOral question-and-answerExtended written questionStructured ObservationInterviewDirect written questionCoefficients:
CombinationsOral3
Written4
Coefficients:
Appropriateness
MeanRank
4.441
6.055.344.014.413.293.524.46
AbsoluteRank
5
8734126
W = 0.18-X2= 218.20df=7
1.351.65
W = 0.10^, = 0.99V2:
P<m
I2
- Z = 1.353= 174 p<.01
Ease
MeanRank
5.092
3.314.222.385.875.285.983.87
AbsoluteRank
5
2417683
W = 0.27-X2= 323.19df=7
1.421.59
W = 0.04 -V, = 0.99V2
P<m
12
-Z = 0.843= 167p<.05
1 1 = Most Appropriate -8 = Least Appropriate.2 1 = Most Easy - 8 = Least Easy.3 Oral techniques = Combination of techniques 2, 4, 6, and 7.4 Written techniques = Combination of techniques 1, 3, 5, and 8.
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224 L. KYRIAKIDES
the relative appropriateness of these two categories. However, althoughthree of the oral methods were considered as the three most appropriatetechniques, unstructured observation was considered as the least appro-priate technique. This raises a question about whether the oral category isa coherent one in Cypriot teachers' perceptions. It can be argued that thethree oral techniques which were considered as the most appropriate arethose which are more formally structured.
The distribution of the mean ranks of ease of application of thesetechniques is also shown in Table 2. Oral question-and-answer was con-sidered as the most easy technique and unstructured observation as thenext most easy. Methods in the middle range of appropriateness are thedirect written question and the sentence completion. Finally, the meanranks of interview and extended written question are relatively large andcan be considered as the least easy techniques. The Kendall Coefficientof Concordance presented at the bottom part of Table 2 shows a statisti-cally significant agreement among Cypriot teachers' ranking of the rela-tive ease of oral and written techniques. The small value of Z can be,however, explored by looking at the "absolute ranks" of the "oral" tech-niques (1; 2, 6, and 8) which suggest that the second category consisted ofthe most easy and the least easy techniques. Although tentatively we canignore this significant difference, if we link this finding with that con-cerning the "absolute ranks" of the appropriateness of "oral" techniqueswe can claim that this category was not a coherent one in Cypriot teach-ers' perceptions.
The last, and probably the most important finding, has to do with thewell known dilemma that what is easily measured is of dubious educa-tional value. Interview and structured observation were considered as themost appropriate but the least easy techniques. Likewise, the direct writ-ten question and the unstructured observation were regarded as one of themost easy but least appropriate. However, oral question-and-answer wasseen as the third most appropriate and as the most easy method. It can beargued that, with one exception, there is a negative correlation betweenthe appropriateness and ease of techniques of assessment.
Perceptions about Ways of Improving AssessmentFigure 3 provides information about teachers' perceptions of methods ofimproving assessment. Kendall's Coefficient of Concordance shows thatCypriot teachers agreed among themselves in their ranking of the relativeimportance of the six ways of improving assessment (W = .40, Z = 2.37,V1 = 4.99, V2 = 888 and p <.005). It emerges from Figure 3 that the mostimportant ways of improving assessment were further training in tech-
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PRIMARY TEACHERS' PERCEPTIONS 225
MeanRank
3,5
5J5
B
Fig. 3. Teachers' perceptions of methods of improving assessment.A: Further training in assessment; B: Time free of class contact; C: Smaller classsize; D: Other adult in the class while assessment is occurring; E: More curriculumtime; F: Special guidelines.
niques of assessment and smaller class size, whereas the least importantwas the existence of another adult in the classroom. The other way ofimproving assessment which is differentiated from all the others is theone concerning time free of class contact which was seen as the secondleast important way.
Findings from Questionnaire to Beginning TeachersDifferences between Perceptions of Cypriot and English Beginning Teach-ersThis section illustrates a comparison between perceptions of Cypriot be-ginning teachers with those of English beginning teachers when theywere at the end of their training and when they were at the end of theirfirst year of teaching experience. It has been found that differences be-tween perceptions of these two groups of beginning teachers when theywere at the end of their training were primarily affected by the systemwithin which their training was operating. As student teachers live notonly in their university environment but also in their whole educationalenvironment, their perceptions were probably influenced by this as wellas their experiences as pupils in primary school and their teaching prac-tice (McIntyre & Morrison, 1967). Thus, Cypriot student teachers' per-ceptions about a sequence of teaching topics and a fixed teaching timewere explicable since they had never had different experiences. Likewise,their reaction to a school which is in a position to appoint other adults tohelp teachers and to decide about the amount of curriculum time spent inteaching Mathematics is explicable. This argument is supported further
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226 L. KYRIAKIDES
by the fact that there was neither difference between perceptions of sub-groups of English students nor between perceptions of sub-groups ofCypriot students who had different mathematical backgrounds, or attend-ed different programmes of initial teacher training.
Table 3 also illustrates statistically significant differences between teach-ers' perceptions at the end of their initial training and when they were atthe end of their first year of experience. The following observations arisefrom Table 3. First, statistically significant differences identified betweenperceptions of English and Cypriot beginning teachers when they were atthe end of their first year of experience are concerned with items forwhich these two groups of beginning teachers had different perceptionswhen they were at the end of their training. Second, one statisticallysignificant difference was identified between the perceptions of these twogroups when they were at the end of their first year of teaching experiencewhich was not identified when they were at the end of their training. Thisdifference had to do with how confident they felt about assessment inMathematics. Cypriot beginning teachers felt more confident in assess-ment of Mathematics than English beginning teachers. The fact that therewas no difference in how confident they felt about teaching Mathematicsimplies that the above difference has nothing to do with subject difficul-ties but may be due to difficulties from attempting to implement assess-ment policy in England (ENCA, 1992).
Table 3. Values of Kolmogorov Smirnov Two Sample Test Derived from the Compari-sons of Perceptions of English and Cypriot Beginning Teachers when They Wereat the End of their Training and when They Were at the End of First Year ofTeaching Experience.
No. Perceptions of teaching andassessment in Mathematics
(1) Fixed sequence of topics(2) Fixed time of teaching Maths(3) Assessment of product(4) Other adult in the class(5) More curriculum time in Mathematics(6) Appropriateness of written techniques
of assessment(7) Ease of written techniques(8) Appropriateness of oral techniques(9) Ease of oral techniques
(10) Confidence of assessment
End of IK-S Z
2.812.942.683.822.892.15
2.592.482.62
.T.T.P
.005.005.005.005.005.005
.005
.005
.005*
First year of ExperienceK-S Z
2.892.691.894.051.962.75
2.893.102.62
P
.005
.005
.005.005.005.005
.005
.005.005
* No statistically significant difference.
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PRIMARY TEACHERS' PERCEPTIONS 227
It should be, finally, acknowledged that the sample of English begin-ning teachers is of uncertain representativeness nationally. Thus, figuresabout the perceptions of the sample of English teachers, mentioned here,cannot be used to draw conclusions about perceptions of English begin-ning teachers as a whole since further research is needed to explore thenational picture. It can be, however, inferred that the statistically signifi-cant differences between Cypriot and English beginning teachers' per-ceptions when they were at the end of their training and when they were atthe end of their first year of experience were primarily affected by thesystem within which their training is operating.
Perceptions of Beginning Teachers at the End of Their Training and atthe End of Their First Year of ExperienceIt was also possible to compare perceptions of Cypriot beginning teacherswhen they were at the end of their training and when they were at the endof their first year of teaching experience. Although it was not possible toidentify those beginning teachers who answered the questionnaire twicesince the questionnaires were answered anonymously, the fact that therewas a very high response rate in both cases (76% and 82% respectively)and that the questionnaires were administered to the whole population,implies that figures derived from each sample can be used for generalisa-tion to its population. Thus, this comparison measures changes in percep-tions of Cypriot beginning teachers.
The following three statistically significant differences derived fromthis comparison. First, the Kolmogorov Smirnov two sample test showsthat Cypriot beginning teachers considered interviews as a less easy tech-nique of assessment when they were at the end of their first year ofteaching experience than when they were at the end of their training (K-SZ = 1.432, p <.033). Since they did not feel more confident in assessingMathematics at the end of their first year of teaching experience thanwhen they were at the end of their training, it can be inferred that theyrealised from their teaching experience how difficult it is to use thistechnique of assessment. This finding is also in line with the fact thatbeginning teachers considered the category of oral techniques as less easywhen they were at the end of their first year of teaching experience thanwhen they were at the end of their training (K-S Z = 1.445, p <.031).However, there was no statistically significant difference according to theperceived appropriateness of these techniques. It can therefore be claimedthat there was no change in the educational ideology about techniques ofassessment which beginning teachers supported when they were at theend of their training and when they were at the end of their first year of
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228 L. KYRIAKIDES
teaching experience. Differences in the perceived ease of techniques ofassessment may be attributed to the fact that they have realised that oraltechniques are not as easy as they thought when they were student teach-ers.
In supporting my argument that their educational ideology had notdramatically changed, it is worth mentioning that there is only one statis-tically significant difference between their perceptions of teaching andassessment in Mathematics at these two stages of their professional life.When Cypriot beginning teachers were at the end of their first year ofexperience, they considered the purposes concerned with gaining knowl-edge and with solving practical problems as the most important purposeswhereas the purpose concerned with the development of positive atti-tudes to Mathematics was the next most important. When they were at theend of their training, they considered these three purposes as equallyimportant. Thus, there is a statistically significant difference betweentheir perceptions of the purpose concerned with the development of posi-tive attitudes to Mathematics (K-S Z = 1.35, p < .05). It can be claimedthat although they had not changed their perceptions about active pedago-gy, they considered the purpose concerned with the development of posi-tive attitudes to Mathematics as less important than when they were stu-dent teachers. This may imply that beginning teachers became less keenabout progressive ideology. This is a finding also in respect of changes ofEnglish beginning teachers' perceptions. The Kolmogorov Smirnov twosample test shows that English beginning teachers at the end of their firstyear of experience considered the purpose concerned with positive atti-tudes to Mathematics as less important (K-S Z = 2.285, p < .001) thanwhen they were at the end of their training. It can be, therefore, claimedthat similar changes in beginning teachers' perceptions of teaching andassessment in Mathematics have been identified among both Cypriot andEnglish beginning teachers. The only difference which has not been iden-tified among English beginning teachers concerned the difficulties ofassessment and has nothing to do with changes on the educational ideolo-gy they supported. This implies that changes in perceptions of Cypriotbeginning teachers were similar to those identified among a sample ofbeginning teachers in a less centralised system.
Differences between Perceptions of Cypriot Teachers and CypriotBeginning TeachersThis part is concerned with the differences in perceptions of curriculumreform in Mathematics between the randomly selected sample of 10 percent of Cypriot teachers and the group of Cypriot beginning teachers.
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2.271.621.831.62
1.422.15
.005
.010
.005
.010
.036
.005
PRIMARY TEACHERS' PERCEPTIONS 229
Table 4. Values of Kolmogorov Smirnov Two Sample Test Derived from the Compari-sons of Perceptions of Cypriot Beginning Teachers with the Randomly SelectedSample of Cypriot Teachers.
No. Perceptions of teaching and assessment in Mathematics K-S Z p
(1) Confidence in teaching Mathematics(2) Confidence in assessing pupils attainment in Mathematics(3) Importance of further training in techniques of assessment(4) Importance of purpose of teaching Maths concerned with
gaining knowledge(5) Fixed sequence of Mathematical topics(6) Assessment based on outcome rather than process
Both groups are representative of their population. Kolmogorov-Smirnovtwo sample tests revealed 6 statistically significant differences which arepresented in Table 4.
We can observe from this table that beginning teachers were less confi-dent in both teaching Mathematics and assessing their pupils' abilities inMathematics. As a consequence, they considered further training as amore important way of improving assessment than the general sample ofteachers. Moreover, the chi-square test revealed also a statistically signif-icant difference between the perceptions of these two groups about theitem concerned with pupils' self assessment (X2= 10.37, df= 2, p<. 006).More than half of the beginning teachers were not able to say whether ornot their pupils could assess themselves (54.1%) whereas one third of therandomly selected sample of Cypriot teachers (34.3%) were not able tosay whether their pupils could assess themselves. Although the percent-ages of teachers of both groups, who were not able to say if their pupilscould assess themselves, were high, a much higher percentage of begin-ning teachers did not know if their pupils could assess themselves. Thisdifference may be attributed to the fact that beginning teachers did notfeel as much confidence in assessing their pupils' attainment in Mathe-matics as the general sample of Cypriot teachers. Thus, their doubts onwhether their pupils know enough Mathematics to assess themselves mayreflect their own inexperience in assessing their pupils.
Statistically significant differences were also identified between theperceptions of these two groups about the following three items whichcan be seen as related to progressive ideology. Beginning teachers did notconsider the purpose concerned with how children could gain Mathemat-ical knowledge as important as did the general sample of Cypriot teach-
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ers. In addition, more beginning teachers disagreed that there should be afixed sequence of Mathematical topics to be taught and that assessmentshould be based on products rather than process. However, there was nostatistically significant difference related to any of the five items con-cerned with active pedagogy. This finding reaffirms the conclusion de-rived from Table 1 that there is a high consensus among Cypriot teachers'perceptions of active pedagogy.
The statistically significant differences identified above were exploredfurther by attempting to link them to the fact that perceptions variedaccording to teaching experience. Thus, perceptions of beginning teach-ers and perceptions of teachers who had 2-5 years of experience werecompared. These groups had the same initial teacher training qualifica-tion and more or less similar teaching experience as beginning teachers.Kolmogorov-Smirnov two sample tests and chi-square tests revealed thatthere was no statistically significant difference between the perceptionsof these two groups. At the second stage perceptions of beginning teach-ers were compared with those of Cypriot teachers who had 6-10 years ofexperience. Kolmogorov-Smirnov two sample tests and chi-square testsdid not reveal any statistically significant difference between the percep-tions of these two groups. There was, however, a statistically significantdifference on the extent to which they felt confident to teach Mathematics(K-S Z = 1.525 p < .019). Beginning teachers were less confident aboutteaching Mathematics than teachers who had 6-10 years of experience.At the third stage beginning teachers' perceptions were compared withthose of teachers who had more than 9 years of experience and less than20. The statistically significant differences which emerged were the sameas those emerged by comparing beginning teachers and the sample of thewhole group of teachers. Thus, the differences between beginning teach-ers and the general sample mainly arose from the perceptions of teacherswith more than 9 years of experience.
DISCUSSION
The evidence presented above is largely about Cypriot teachers' percep-tions. Thus, implications for the implementation of curriculum reform inCyprus can be drawn. However, it also raises more general issues regard-ing the development of curriculum and assessment policy in Mathemat-ics. Moreover, an exploration of the implications of the findings for cur-riculum theory is attempted in the last part of this section.
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PRIMARY TEACHERS' PERCEPTIONS 231
Purposes of Teaching MathematicsHowson (1989, p.18) believes that "clear objectives are needed but to beeffective they must be objectives accepted by teachers", a view that is thebasic focus of my research. It is clear from the questionnaire responsesthat Cypriot teachers' perceptions of the purposes of Mathematics gener-ally conform to the purposes emphasised in the current curriculum reformin Cyprus. They supported the purposes relating to investigative tasks andpromoting mathematical knowledge and thinking identified in both theprevious and the New Curriculum. However, the New Curriculum pro-posed that one purpose was the development of pupils' ability to talkabout Mathematics. Doubts about whether this should be seen as a pur-pose can be raised in so far as the role of language in teaching Mathemat-ics can be seen as a teaching method that may help pupils to see Mathe-matics as a language (Pimm, 1981) and as a part of our culture (Bishop,1989). Nevertheless, a low priority was given by Cypriot teachers to therole of pupils' language in teaching Mathematics which might be ex-plained by the fact that the New Curriculum did not make explicit theimplications of this purpose for teaching whereas implications of theother two purposes for teaching methods were provided. Moreover, theprevious curriculum had not promoted this as purpose at all and thereforeteacher training had not focused upon the role of language in teachingMathematics. To achieve this new purpose both ITT and INSET, in addi-tion to concentrating on the importance of the language in the teaching ofMathematics, should also provide teachers with more specific ways toapply language in classroom settings.
Mathematics PedagogyCypriot teachers had a coherent view about active pedagogy, emphasis-ing the value of practical activities, investigative tasks and discussion.But despite the fact that Cypriot teachers agree with active pedagogy andhave to prove to their inspector that they put it into practice, this ideologyhas not widely influenced curriculum practice of primary Mathematics inCyprus. Further research is needed to explore this gap between curricu-lum theory and curriculum practice. However, barriers to the implemen-tation of this pedagogy do not lie in teachers' perceptions of teachingMathematics. The interview data revealed that although Cypriot teachershold strong ideas favouring active pedagogy and invest much of theirself-identity in it, compromise with beliefs was commonly pragmatic.Cypriot teachers in recognising the discrepancy between active pedagogyand practical realities attributed it to the pressure of time arising from anoverloaded curriculum. They considered the content of the New Curricu-
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lum in Mathematics as difficult for their pupils to understand and therequirements of the curriculum policy as unmanageable. Thus, as with theoverloaded curriculum in England (Campbell & Neil, 1994), the over-loaded curriculum in Cyprus may be a significant barrier to the imple-mentation of active pedagogy.
It can be also claimed, paradoxically, that barriers to the implementa-tion of policy on curriculum reform in Mathematics may lie in the highdegree of central control at school level, through national textbooks, afixed sequence of topics and a defined length of curriculum time (Shuard,1984, p. 26) which cause a mismatch between the ideology promoted incurriculum policy and the administration of the system. And althoughteachers' perceptions about the purposes of Mathematics were similar tothe purposes outlined in curriculum policy, the fact that this control didnot promote flexible classroom strategies limited the policy's effective-ness.
Assessment PolicyAssessment policy in Cyprus is not clearly defined. It is therefore impor-tant to identify implications of teachers' perceptions for assessment poli-cy in Cyprus. Cypriot teachers perceived formative purposes of assess-ment as more important than the summative. This is in line with theargument of Torrance (1986) that "summative assessment is unlikely toprove helpful to teachers who are faced with the day-to-day reality offormative assessment". Broadfoot (1986) argues that the curriculum pol-icies of countries other than the UK promote a move from summative toformative assessment since they have realised the failure of the summa-tive assessment. Cypriot teachers would welcome the development of anassessment system which promoted the formative purposes of assess-ment, but would be less inclined to support one emphasising summativepurposes. Thus, the debate among the officials of the Ministry of Educa-tion, the inspectors and teachers may not be restricted to workload butraise fundamental issues of educational ideology. This is particularly truesince the Director of Primary Education announced the government'sintention to introduce a reporting system where teachers would be re-quired to assess pupils' overall achievement in each subject at the end ofeach academic year. This raises doubts about the policy commitment toformative assessment.
Although Cypriot policy documents argued that assessment should beseen as a natural part of teaching, the practical implications of such con-ception of assessment are not made explicit. This conception of assess-ment may simply reflect inspectors' acceptance of the objectives model
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(Kyriakides, 1994). However, Cypriot teachers considered assessment asa natural part of teaching. The interview data illustrate implications ofthis conception of assessment for teaching and specific links betweenmethods of teaching and assessment Mathematics. It can be claimed thatCypriot policy makers should attempt to explore links between purposes,teaching activities and assessment in order to develop an assessment pol-icy based on the consideration of assessment as a natural part of teaching.Thus, analysis of the evidence of teachers' perceptions about assessmentimplies that the debate about assessment policy in Cyprus should be fo-cused on how it can be linked to the policy on teaching Mathematics inorder to provide information to teachers about teaching Mathematics tak-ing into account their effort to implement the active pedagogy. A coher-ent assessment and curriculum policy should be developed for teacherdevelopment, irrespective of other purposes such as national monitoring.For example, in-service training might be used to focus on problem set-ting and applied Mathematics to illustrate the practical form that forma-tive assessment would take.
Two significant implications emerged from the data on Cypriot teach-ers' perceptions about the appropriateness and ease of the eight tech-niques of assessment. First, the ideological position in Cyprus is lessclear cut than in England. Cypriot teachers considered as more appropri-ate the techniques which operate under controlled conditions. This mightreflect the highly centralised educational system of Cyprus and especiallya perceived need to have "tangible proof to show to parents and inspec-tors. With the term tangible proof teachers meant information gatheredfrom assessment which can be easily understood by parents and inspec-tors since numbers can be used to represent pupils' attainment. However,the appropriateness of the techniques of assessment should be judged onthe kind of information they make available to teachers. Thus, inspectorsshould encourage teachers to use techniques which can help them diag-nose pupils' needs irrespective of whether they are under controlled con-ditions.
However, the Ministry of Education intends simply to publish a seriesof written tests, but not to provide anything related to interview or struc-tured observation which are considered as appropriate techniques by Cypriotteachers. Information derived from written tests does not clearly revealthe mathematical concept which is involved with a pupil's wrong re-sponse to a written test (Schwarzenberger, 1988). Thus, if assessmentpolicy emphasises only written tests, it would neither find ideologicalsupport among teachers nor improve assessment practice, but it wouldprovide the government with another way to control curriculum practice.
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Second, there was an inverse relationship between assessment techniquesseen as most appropriate and those seen as most easy. Teachers regardedinterview and structured observation as the most appropriate techniquesbut as the least easy. Thus, Cypriot teachers may face the same practicalproblems which Key Stage 1 teachers had to face with SATs in 1991.Logically this argues for in-service training on how teachers can use oraltechniques for their assessment in Mathematics, as much as it argues forusing only written tests. This would be welcomed by Cypriot teacherssince training on techniques of assessment was considered as the mostimportant way of improving assessment. It can also be claimed that in-service training should give high priority to structured observation andinterview which were seen as the most appropriate but least easy tech-niques. Thus, INSET focused on the use of interview and structured ob-servation may be a more effective way of improving assessment ratherthan the publication of more policy documents which are rarely consult-ed. This provides significant implications for educational policy in Cy-prus which has not systematically used INSET to bring about change andhas not been directed at the implementation of the current curriculumreform at the school level. The practice therefore goes against the evi-dence that innovations need both external and local support to succeed(Crandal, Eiseman, & Louis, 1986; Turnbull, 1985).
Professional and Cultural Influences on Teachers' Perceptions and Cur-riculum TheoryLittle information is available relating to the effects of professional train-ing and teaching experience upon teachers' perceptions (Borko, Lalik, &Tomchin, 1987; Butcher, 1965; Callis, 1950). The comparison betweenperceptions of Cypriot beginning teachers when they were at the end oftheir training and when they were at the end of their first year of experi-ence revealed that their educational ideologies had not dramatically changed.Similar conclusions were derived from comparison of perceptions of Englishteachers when they were at the end of their training and when they were atthe end of their first year of teaching experience. Moreover, comparisonsbetween perceptions of beginning teachers and the general sample ofCypriot teachers revealed statistically significant differences. Further ex-ploration of these differences has shown that there is no statistically sig-nificant difference between perceptions of beginning teachers and per-ceptions of teachers with less than 10 years of experience. The differenc-es between beginning teachers and the general sample mainly arose fromthe perceptions of teachers with more than 9 years of experience. Thisfinding implies that although the length of teaching experience was asso-
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PRIMARY TEACHERS' PERCEPTIONS 235
ciated with the development of teachers' perceptions, it did not have animmediate effect upon teachers' perceptions.
Furthermore, having in mind all the statistically significant differencesbetween perceptions of beginning teachers and those of the general sam-ple of Cypriot teachers it can be claimed that young teachers tended toagree with more "progressive" opinions than older teachers. These differ-ences can be linked to findings of earlier research which has shown thatyounger people are more "progressive" and humanitarian in general thanolder people (Ashton, Knee, & Davies, 1975; Butcher, 1965; Callis, 1950).Delamont (1987, p. 11) argues that research shows that "the younger, lessexperienced teachers were more favourable to progressive ideals than theolder more experienced teachers". However, the findings of this studyseem to be also in line with the findings of research into teachers' think-ing which challenged the view that teachers' personal values and beliefsabout teaching were changed and modified through professional educa-tion and experience in the classroom (Tabachnick & Zeichner, 1985;Zeichner et al., 1987).
On the other hand, it has been shown that the extent of central controlon the curriculum is a significant influence upon teachers' perceptions.Statistically and educationally significant differences between Cypriotand English beginning teachers were associated with the extent of centralcontrol on the curriculum. A similar finding was identified by a compari-son of perceptions of these two groups when they were at the end of theirtraining. And since teachers' perceptions are elaborated rather than radi-cally changed by professional training, it might be argued that Cypriotand English teachers' perceptions of teaching and assessment in Mathe-matics reflect different experiences of educational systems based on dif-ferent ideologies. The statistically significant differences between per-ceptions of Cypriot and English teachers can be explained if they are seenas reflecting a comparison between perceptions of a group of teacherswho have experienced a centralised system, and a group of teachers withexperience of a less centralised system.
The differences between teachers' perceptions in England and Cyprusmay also be linked with a theory of curriculum change. Since culturalfactors influence teachers' perceptions which in turn are crucial for theeffectiveness of any curriculum change, change cannot be created simplyby the production of curriculum and assessment policy documents. It is,therefore, important to establish a culture in primary education whichwelcomes the idea of change. This is in line with Fullan's (1991) sugges-tion that neither a centralised nor a decentralised system in themselvespromote curriculum change. What is needed is to identify and build upon
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teachers' perceptions and encourage them to promote curriculum devel-opment at the school level and at the same time to welcome support fromthe centre. Thus, a new model of curriculum change should be developedfocused on teachers' perceptions since the transformation of curriculumreform into practice depends partly on their perceptions. Research deal-ing with teachers' perceptions and the factors which are able to influencethem will contribute to the development of such a model and to a furtherevaluation of the recent curriculum reform in Cyprus.
REFERENCES
Ashton, P., Knee, P., & Davies, F. (1975). Aims into practice in the primary schools: Aguide for teachers. London: University of London Press.
Baron, M. (1970). A report on the teaching of Mathematics in the Greek elementary andsecondary schools in Cyprus. Nicosia: Ministry of Education.
Bishop, A.J. (1989). Mathematics education in its cultural context. In P. Murphy & B.Moon (Eds.), Development in learning and assessment (pp.85-97). London: Hodderand Stoughton.
Borko, H., Lalik, R., & Tomchin, E. (1987). Student teachers' understanding of success-ful and unsuccessful teaching. Teaching and Teacher Education, 3, 77-90.
Broadfoot, P. (1986). Alternatives to public examinations. In D.L. Nuttall (Ed.), Assess-ing educational achievement (pp. 54-77). London: The Falmer Press.
Brown, M. (1991). Problematic issues in national assessment. Cambridge Journal ofEducation, 21, 215-229.
Butcher, H.J. (1965). The attitudes of student teachers to education: A comparison withthe attitudes of experienced teachers and a study of changes during the trainingcourse. British Journal of Social and Clinical Psychology, 4, 17-24.
Calderhead, J. (1987). Exploring teachers' thinking. London: Cassell.Callis, R. (1950). Change in teacher-pupil attitudes related to training and experience.
Educational Psychological Measurement, 10, 718-727.Campbell, R.J., & Neill, S. (1994). Primary teachers at work. London: Routledge.Crandal, D.P., Eiseman, J.W., & Louis, K.S. (1986). Strategic planning issues that bear on
the success of school improvement efforts. Educational Administration Quarterly,22, 21-53.
Delamont, S. (1987). The primary school teacher. London: The Falmer Press.Department of Education and Science (1987). National curriculum: Task group on as-
sessment and testing - A report. London: HMSO.Department of Education and Science (1991). Mathematics in the national curriculum.
London: HMSO.ENCA (1992). Evaluation of national curriculum assessment at key stage 1. University of
Leeds: School of Education.Fullan, M.G. (1991). The new meaning of educational change. London: Cassell.Havelock (1971). Planning by innovation through dissemination and utilisation of knowl-
edge. University of Michigan: Centre for Research and Utilisation of ScientificKnowledge - Institute of Social Research.
Howson, G. (1989). Maths problem: Can more pupils reach higher standards? London:Centre for Policy Studies.
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Kyriakides, L. (1994). Primary teachers' perceptions of policy for curriculum reform inCyprus with special reference to Mathematics. Unpublished doctoral dissertation,University of Warwick, Coventry.
McIntyre, D., & Morrison, A. (1967). The educational opinions of teachers in training.British Journal of Social Clinical Psychology, 6, 32-37.
Ministry of Education (1992). The new curriculum. Nicosia: Ministry of Education.Murphy, P. (1988). TGAT: A conflict of purpose. Curriculum, 9, 152-158.Nisbet, J. (1973), The school council. Case studies of educational innovations: 1. At the
central level. Paris: CERI/OECD.Phillips, R.W. (1986). Cross national research in Mathematics education. In T.N.
Postlethwaite (Ed.), International educational research. Oxford: Pergamon Press.Pimm, D. (1981). Mathematics? I speak it fluently. In A. Floyd (Ed.), Developing math-
ematical thinking (pp. 139-149). London: Addison Wesley with Open UniversityPress.
Schon, D.A. (1971). Beyond the stable state. Harmondsworth: Penguin.Schwarzenberger, R. (1988). Targets for mathematics in primary education. Stoke-on-
Trent: Trentham books.Shuard, H. (1984). Contemporary trends in primary school mathematics: Implications for
teacher education. In R. Mooris (Ed.), Studies in mathematics education: Vol. 3.The mathematical education of primary school teachers. Paris: UNESCO.
Skilbeck, M. (1990). Curriculum reform: An overview of trends. Paris: OECD.Steadman, S. D., Parson, C , & Salter, B. G. (1978). An inquiry into the impact and take-
up of schools council funded activities: A first interim report. London: SchoolsCouncil.
Tabachnick, B.R., & Zeichner, K. (1985). The development of teacher perspectives: Finalreport. Madison, WI: Wisconsin Centre for Educational Research.
Torrance, H. (1986). Expanding school-based assessment: Issues, problems, and futurepossibilities. Research Papers in Education, 1, 48-59.
Turnbull, B.J. (1985). Using governance and support systems to advance school improve-ment. The Elementary School Journal, 85, 337-351.
Zeichner, M.K., Tabachnick, B.R., & Densmore, K. (1987). Individual, institutional, andcultural influences on the development of teachers' craft knowledge. In J. Calderhead(Ed.), Exploring teachers' thinking (pp. 21-59). London: Cassell.
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APPENDIX A. THE QUESTIONNAIRE
I am conducting research into teachers' perceptions of the national curric-ulum and assessment in Mathematics. I would be grateful if you couldtake twenty minutes or so to complete this questionnaire, anonymously.
PART A: In this part put a tick in the appropriate box
1. SEX: MaleD Female •
2. Length of teaching experience (including this year as 1 full year)1 year •2-5 years •6-10 years D11-20 years DMore than 20 years •
3. Which of the following initial teacher training qualifications do youhold? (Tick as many as apply)Teacher's Certificate • B.Ed./B.A.(Q.T.S.) DB.A. • B.Sc.D PGCED Other •
4. Did you take Mathematics as a main or subsidiary subject during yourinitial training?Yes • No D
5. Which of the following post-experience qualifications do you hold?(Tick as many as apply)B.Ed. • B.A. • B.Sc. • M.A. •M.Ed.D Advanced Diploma • Other •
6 Did any of your post-experience qualification had to do with Mathe-matics or Education?Yes • No D
7. Do you hold any formal post of responsibility for Mathematics inyour school?Yes • No D
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PRIMARY TEACHERS' PERCEPTIONS 239
8. Size of your class:Under 20 • 21-23 • 2 4 - 2 6 • 27-29 D 30-32 D33-35 D More than 36 •
9. Which of the following year groups are in your class? (Tick as manyboxes as apply)Reception • Year 1 • Year 2 • Year 3 •Year 4 • Year 5 • Year 6 D Other D
10. How confident would you say you are about teaching Mathematics inprimary school?Not at all confident • Confident in a limited way •Quite confident • Very confident • Don't know/can't say D
11. How confident would you say you are about assessing children'sattainment in Mathematics in primary school?Not at all confident • Confident in a limited way •Quite confident • Very confident • Don't know/can't say •
PARTBThe following two questions (12 and 13) indicate four purposes of teach-ing and assessing Mathematics respectively. Please rank the importanceyou attach to the four purposes using the numbers 1 to 4 for each ques-tion. Give 1 to the purpose you regard as the most important, 2 to the nextmost important and so on, with 4 meaning the least important.12. Children should learn Mathematics in order to:
a) be able to talk about Mathematics and to discuss •their performance
b) gain knowledge of basic concepts and facts in Maths •c) develop positive attitudes to Mathematics •d) engage in practical investigations and problem-solving •
13. The main purpose.of assessment in Mathematics should be to:a) provide information to enable teachers or parents •
to make comparisons across classes and pupilsb) contribute to teachers' self-evaluation •c) help identify and diagnose pupils' learning needs •d) provide information to the government on how well •
the educational system is operating
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PART CPlease rate each of the following items (Nos. 16-27) by circling the appro-priate number. The numbers represent the following values: 1 = Abso-lutely disagree; 2 = Disagree; 3 = Don't know/can't say; 4 = Agree;5 = Absolutely agree.
14. There is a fixed sequence of Mathematical topics 1 2 3 4 5which it is necessary for children to follow.
15. Assessment should form a natural part of teaching 1 2 3 4 5activities.
16. The methods of teaching as well as the methods of 1 2 3 4 5assessment should be subject to whole schooldecision-making
17. Practical activities in Mathematics are as appropriate 1 2 3 4 5for Key Stage 2 pupils as for Key Stage 1 pupils
18. Practical activities in Mathematics are as appropriate 1 2 3 4 5for high attaining pupils as for low attainers
19. Much of the value of an activity or an investigation 1 2 3 4 5can be lost unless pupils can talk about their results
20. It is necessary for children to do Mathematics at a 1 2 3 4 5fixed time every day
21. Children must have direct experience of using 1 2 3 4 5Mathematics in a wide range of contexts across thecurriculum
22. Teachers should assess on the basis of pupils' 1 2 3 4 5learning products rather than the learning process
23. Assessment should include the assessment of pupils' 1 2 3 4 5attitudes to Mathematics
24. Mathematics should be taught mainly through 1 2 3 4 5practical investigations.
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PRIMARY TEACHERS' PERCEPTIONS 241
25. Teachers should assess the child's ability to apply 1 2 3 4 5Mathematics in unfamiliar situations
26. INSET in Mathematics should mainly deal with 1 2 3 4 5problems which I have to face in my classroom.
27. What I have been expected to teach in Mathematics in 1 2 3 4 5my class in this year is manageable
28. Below are 8 techniques of assessment. Rank these techniques twice(column A and column B). In column A give 1 to the most appropri-ate, 2 to the next most appropriate and so on with 8 meaning the leastappropriate. In column B give 1 to the technique which you considerthe easiest to use, 2 to the next easiest and so on with 8 meaning theleast easy.
Column A Column BAppropriateness Ease
a) Multiple choice and matching questions • •b) Unstructured observation of pupils'work O Dc) Sentence completion • •d) Oral question-and-answer D •e) Extended written questions D •f) Structured observation of children's work D •g) Interviewing individual children • •h) Setting direct written questions • D
29. Below are 6 ways of improving assessment in Mathematics. Pleaserank these to reflect your opinion. Give 1 to the most important, 2 tothe next most important and so on with 6 meaning the least impor-tant.
a) In-service training related to practical problems •of teaching and assessment
b) Time free of class contact •c) Smaller class size than now •d) Other adult in the classroom while assessment •
is occurringe) More curriculum time in Mathematics •f) Special guidelines from a staff meeting or •
mathematics co-ordinator
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242 L. KYRIAKIDES
30. Do you think that pupils in your own classroom have understoodenough Mathematics to assess most of their own work in Mathemat-ics? (Tick one box)Yes CH No D Don't know/can't say •
31. Please feel free to write below any other comment about teaching andassessment of Mathematics.
Thank you very much for your help.Leonidas Kyriakides
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