MALAYSIAN PRE-SERVICE PRIMARY MATHEMATICS TEACHERS AND THEIR
LECTURERS: PRACTICE AND BELIEFS ABOUT MATHEMATICS, TEACHING
AND LEARNING
by
See Fong Ng
A Thesis submitted to the School of Education of the Uni‘ersit- of Birmingham
for the degree of
Doctor of Philosophy
1995
Supervised by Prof. Leone Burton
ABSTRACT
This thesis assesses the beliefs held by 32 Malaysian pre-service primary mathematics
teachers and their 4 mathematics lecturers about mathematics, mathematics teaching and
learning. The research aim was to explore how these beliefs, acquired from their school
experiences, interacted with their teacher training college programme. The college lecturers
used a didactic paradigm to inform the pre-service teachers about the non-didactic paradigm
of the New Primary School Curriculum, KBSR. The impact on the pre-service teachers of a
series of intervention activities, constructed according to the KBSR recommendations, was
investigated. The influence of pre-service teachers' beliefs on their micro-teaching in college
and practical teaching in schools was also examined.
Research methodology was interpretivist-ethnography coupled with action research. Data
was collected using participant-observation and continuous interviewing techniques,
verification of data was through triangulation. Analysis was qualitative, w, ith interpretation of
data accounted for in terms of the Malaysian context, perceptions of the participants of the
study and the researcher.
This research showed that though lecturers claimed to want to broaden the pre-service
teachers' perspectives of mathematics, they had to suspend that aim because they had to try
and help pre-service teachers improve their
NL
eak subject-matter knowledge. Both the
lecturers and the pre-service teachers continued to have a textbook and rules based view of

mathematics. The pre-service teachers espoused the belief that they wanted to teach
according to the KBSR, an expression borne out of the necessity to fulfil college assessment
needs. In their actual teaching, pre-service teachers were didacts. Lecturers' investment of
their self in their work was partly affected by the practices of positive discrimination. An
important theme to have emerged from the interviews with the participants of this study N
.
‘

as
the cultivation of fear, a result of punitive teachers as well as the nature of assessments. Fear
affected the pre-service teachers' learning and teaching behaviour and the lecturers' work.
The research is seen to have implications for teacher education and mathematics teaching
itself through the re-evaluation of the effects of the Malaysian government policy on positive
discrimination and continuous professional development of teachers.
DECLARATION
This thesis is a result of my own research and investigation. All the quotations are clearly
marked. It has never been accepted in substance for a degree and is not being concurrently
submitted in candidature for any other degree.
Swee Fong Ng
This thesis is dedicated to
my mother, Lim Yee Yoke
and
the memory of my father, Ng Lum.
ACKNOWLEDGEMENTS
The list of people I wish to thank is long. From the first days of my planning to the presentation
of the thesis, I have been supported by my family, friends, staff at the University of
Birmingham and colleagues.
My supervisor, Prof. Leone Burton of the University of Birmingham has been a continual
source of moral and intellectual support. Her patience has been limitless, reading drafts upon
drafts of my writing, providing me with thoughtful and critical comments.

Special mention must be accorded to Dicon Montford, Andrew Tee and Hilary Povey, for
graciously giving time to read my work so thoroughly. Their thoughtful and responsive
comments have helped to improve my work.
I extend my gratitude to John Shearwood and the staff of the University of Birmingham for
their support during my entire stay there.
The contribution of the members of BSERG has helped in my growth as a researcher. My
interaction with them has helped to broaden my perspective of research.
Particular note of thanks to my colleague in Malaysia, See Thean Seng, who helped to translate
the questionnaire into Bahasa Malaysia.
Two people that I particularly wish to thank for the part they have played in my life as a teacher
are the de La Salle Brothers, Brother Ultan Paul and Brother Vincent Corkery. Their influence
on my life as a teacher has been immense.
I want to thank my colleagues and students in Ipoh for their well-wishes and moral support. In
Birmingham, my gratitude goes to my research colleagues: Wilson Kofi Agbeke, Richard
Tabulawa, Noraini Che Hashim, Syed Nawawi, Tracy Lee, Alphonsus Yakubu, Alex Tang,
Derek Adams, Robina Mirembe, Jodhi Salleh, Changu Mannathoko, Claudia Marston and Raul
Pardinaz-Solis.
I also extend my thanks to the University of Birmingham who part sponsored my study.
I extend my gratitude to the men and women whom I interviewed. Their willingness to open
and share their views with a total stranger has helped to make this thesis possible. Special
thanks to the college where I did my ethnographic research, for their warm reception and giving
me access to their college activities.
I want to extend my gratitude to my friends in England, particularly Selma and Adrian
Montford and their family for making my stay in England richer in so many ways.
Finally my thanks to my family for not asking me to fulfil the expectations of a traditional
Chinese family, but letting me actualise my aspirations.
Table of Contents
I. Chapter One: Introdu
ction



1
1.
1.

Background To The Study

1
1.2.

The Focus of this Study

3
1.3.

Outline Of The
Thesis

5
2.
Chapter Two: The Education System in Malaysia.

7
2.1.

Introduction

7
2.2.


Political Context

7
2.3.

Organisation and Structure of the Education System

9
2.3.1.

Pre-Independent Period (Pre
1957)

9
2.3.2.

Post Independent Period
(1957-1969)

10
2.3.3.

Post
1970
Period

11
2.4.

Structure of the Present Education System in Malaysia


12
2.4.1.

Primary Education.

12
2.4.2.

Lower secondary Education (Forms One to Three)

12
2.4.3.

Upper Secondary Education (Forms Four to Six).

13
2.4.4.

Pre-University Levels

13
2.5.

Fully Residential Schools (FRSs)

14
2.6.

Assessment


15
2.6.1.

Examination Dominance in Malaysia

16
2.6.3.

Mathematics Assessment in Malaysia

18
2.6.4.

The Role and Significance of Examinations In Malaysian Society

19
i
2.6.4.1. Exclusion from Examinations

21
2.6.4.2. Misuse of Information

23
2.6.5.

Teachers, Students and Parents' Responses

23
2.6.6.


Ego versus Task Involvement

25
2.7.

Tuition Culture in Malaysia

27
2.8.

Conclusion

28
3.
Chapter Three: KBSR: The New Primary School Curriculum

30
3.1.

Introduction

30
3.2.

The Origins of the Innovation

31
3.3.


Differences between the Traditional Curriculum and the ICBSR

32
3.3.1.

Key Characteristics of the ICBSR

33
3.3.1.1. Teaching Methods Under the KBSR

34
3.4.

The Specific Aims Of Mathematics Education Under the ICBSR

35
3.4.1.

The Stages in Primary Education

36
3.5.

Pedagogic Strategies

39
3.5.1.

Implications For Practice: Pupil Grouping


39
3.5.1.1. Hasty Implementatio
n
Resulting In The Lack Of Training And Professionalism
Among Many Education Personnel

42
3.5.1.2. Centralised Control And Hierarchical Organisational Structure Of Education

43
3.5.1.3. The Particular Socio-Political Context Of Malaysia

44
3.6.

Conclusion

47
4.
Chapter Four: Review of the Literature on Beliefs

49
11
4.1.

Introduction

49
4.2.


Beliefs: Problems of Definition

50
4.2.1.

The Construct 'Belief Used In This Thesis

51
4.2.2.

How Did Individuals Acquire Their Beliefs?

52
4.3.

Beliefs and Mathematics Teaching and Learning

53
4.4.

Mathematics Teachers' Beliefs

54
4.4.1.

Overview

54
4.4.1.1. The Need for Philosophical Discourse Around Mathematics


56
4.4.1.2. Teachers' Beliefs about Mathematics based on Empirical Evidence

58
4.4.1.3. Empirical Findings About Teachers' Beliefs about Mathematics Using Perry's
Scheme

59
4.4.1.4. Skemp's Perception of Mathematics Teachers' Views of Mathematics

61
4.5.

Curriculum Developers' Views of Mathematics

63
4.6.

The Relationship Between Teachers' Beliefs About Mathematics And Their
Practice

66
4.7.

Relationship Between Espoused Beliefs About Teaching And Learning And Actual
Instructional Practice

72
4.7.1.


The Role Of Reflection In Helping To Bridge The Gap Between Professed Beliefs
And Beliefs-In-Practice

79
4.8.

Changing Teachers' Beliefs

81
4.9.

Implications for Teacher Education

84
4.10.

What Do I Hope To Gain By Using This Theory To Underpin My Study?

87
4.11.

Summary

87
111
4.12.

Statement of the Problem

4.13.


Conclusion

5. Chapter Five: Methodology

5.1

Introduction

5.2.

The Choice of Ethnographic Research

5.2.1.

Confidentiality And The Potential Consequences Of Information

5.2.2.

Rapport with the Participants

5.2.3.

Self as Researcher

5.3.

Research Methods

5.3.1.


Interviews

5.3.1.1.

Permission To Tape The Interviews

5.3.2.

Participant Observation

5.3.2.1.

Some Of The Drawbacks Of Using Participant Observation

5.3.3.

I nterpretivist Assumptions

5.3.4.

Action Research

5.3.5.

Triangulation

5.3.6.

Keeping Field Notes


5.4.

Data Analysis

5.5.

Writing Up: Presenting the Findings

6. Chapter Six: The Research Design.

6.1.

Rationale for Design

6.2.

Pilot study in Birmingham

•
88
89
90
90
92
96
96
97
97
98

104
105
108
109
113
118
120
121
122
123
123
123
iv
6.3.

Gaining Leave for my Study

125
6.4.

Gaining Access For Fieldwork

126
6.5.

Choice of Research Sites

127
6.6.


Selecting the Participants of the Study

128
6.6.1.

Identification Of Different Groups

129
6.7.

Time Scale for the Study

129
6.8.

A Day In The Field

131
6.9.

Getting Down To The Fieldwork: Meeting The Participants Of The Study

131
6.9.1.

Interviews with Lecturers

132
6.9.2.


Questionnaires and Interviews With Pre-service teachers

132
6.10.

Intervention Activities

134
6.11.

Micro-Teaching

135
6.12.

Practicum

135
6.12.1. During the practicum

137
6.13.

Validity of Photographs

137
6.14.

Organisation and Analysis of Data


138
7. Chapter Seven: Background of The Lecturers and Pre-Service Teachers

139
7.1.

Introduction.

139
7.2.

Sex, Ethnicit
y
and Academic Qualifications of the Participants

139
7.2.1.

Sex and Ethnicity of the Lecturers

139
7.2.2.

Academic Qualifications And Past Experiences

139
7.2.3.

Sex, Ethnicity And Qualification
s

Of Pre-Service Teachers

140
v
7.3.

Were The Pre-service Teachers Happy With Their Career Choice?

144
7.3.1.

Parental And Familial Influence

145
7.3.2.

Mathematics Teaching As A Stepping Stone To Better Future Prospects

147
7.3.3.

Teacher Training As A Form Of Sponsored Higher Education

147
7.4.

Malaysian Mathematics Lecturers Views About The Pre-Service Teachers

148
7.5.


Summary of the findings

151
7.6.

Discussion of Findings

152
7.6.1.

Why Were There More Pre-Service Teachers With Lower Mathematics Grades In
The Study?

156
7.6.2. Why Were There More Women In The TIC?

160
7.6.3.

Why Were There More Malays With Low Mathematics Grades Chosen?

161
7.7.

Summary Of Discussion

164
8. Chapter Eight: Lecturers and Pre-service Teachers' Beliefs About Mathematics Based on
their Experiences in Schools and College


166
8.1.

Introduction

166
8.2.

Lecturers' Beliefs About Mathematics

166
8.2.1.

What Were The Lecturers' Epistemological Stand?

170
8.2.2.

In What Ways Did These Lecturers Try To Present A Broader View Of Mathematics
to The Pre-service teachers?

172
8.2.3.

Findings Based On The Lecturers' Accounts And The Input By The Head Of
Mathematics Department

174
8.3.


Pre-Service Teachers' Views Of Mathematics

179
8.3.1.

Findings Based On The Pre-service Teachers' Accounts

182
8.4.

Conclusion

184
vi
9. Chapter Nine: Lecturers' and Pre-service Teachers' Beliefs about Mathematics Teaching
and Learning

185
9.1.

Introduction

185
9.2.

Lecturers' Beliefs

185
9.2.1.


How did these lecturers describe their own teaching style?

185
9.2.2.

Facilitating and Group Work: A Question of Convenience and Topic Dependence. 188
9.2.3.

Lecturers' Epistemology and the KBSR

191
9.2.4.

Lecturers' Reasons for the Difficulties Faced by the Pre-service Teachers in
Implementing the Instructional Practices of the KBSR

194
9.3.

Summary

199
9.4.

Pre-service Teachers' Beliefs about Mathematics Teaching and Learning

200
9.4.1.


Characteristics Of Good Mathematics Teachers

201
9.4.2.

Pre-Service Teachers' Views of How They Were Taught And How They Learned
Mathematics

203
9.4.3.

Pre-Service Teachers' View Of Good And Weak Mathematics Students

204
9.5.

Beliefs Acquired As A Result Of Their College Experiences

209
9.6.

Summary

219
9.7.

Conclusion

220
10. Chapter Ten: Micro-Teaching


223
10.1.

Introduction

223
10.2.

The Missed Opportunity of Micro-teaching

223
10.2.1. Observable Characteristics of Micro-teaching Sessions

232
10.2.2. Peer-Teachers' Difficulty With the KBSR Methods

232
VII
10.2.3. Pre-service Teachers' Perceptions of Micro-teaching

234
10.3.

Conclusion

240
11.
Chapter Eleven: Intervention Activities


241
11.1.

Introduction

241
11.2.

Evaluation
Of
Activities By Pre-Service Teachers

245
11.3.

Activity One

245
11.4.

Activities Two and Three

252
11.5.

Activity Four: Odd and Even Number Activity

256
11.6.


Activity Five

262
11.6.1. Evaluation Process

263
11.7.

The Issues that Emerged from the Intervention Activities

267
11.7.1. Issue One: Behaviour Of Pre-service Teachers That Was Contradictory To That
Encouraged by the KBSR

267
11.7.2. Issue Two: Pre-service Teachers' Receptivity to Alternative Forms Of Teaching

268
11.7.3. Issue Three: Pre-service Teachers' Resistance To Change And Their Ability To
Subvert Change

269
11.8.

Pre-service Teachers' Evaluation Of The Activities

270
11.9.

Lessons Learned From The Intervention Phase Of The Fieldwork


271
12.
Chapter Twelve: Practical Teaching

274
12.1.

Introduction

274
12.2.

Teacher-Driven Practice

274
12.2.1. Algorithmic, Drill and Rote Learning: An Exercise in Futility?

276
12.2.2. Another Example of Drill and Rote Learning: A Matter of Conversion

290
12.3.

Teacher versus Pupil-Centred Teaching

293
12.4.

Collaborative Group Work And Activity Based Teaching And Learning


298
12.4.1. Appropriate Models

309
12.4.2. Mathematics Knowledge

311
12.4.3. Sound Pedagogical Skills

312
12.4.4. Pre-service Teachers' Beliefs About Children's Mathematical Knowledge

312
12.5.

Resource-based Teaching

314
12.6.

Mathematics Knowledge of Pre-service Teachers

321
12.7.

The Role Of Reflection In The Lives Of The Pre-Service Teachers

329
12.8.


Punitive Teachers: A Full Cycle

329
12.9.

Summary

332
12.10.

Conclusion

334
13. Chapter Thirteen: Fear And Mathematics Anxiety

335
13.1.

Introduction

335
13.2.

Emotions and Mathematics Learning

336
13.3.

Examples of Punitive Teaching


338
13.4.

Coping Behaviours Adopted By The Pre-Service Teachers To Deal With
Authoritarian And Punitive Teachers

343
13.5.

The Adverse Effects Of Punitive Teaching On The Teaching And Learning Of
Mathematics

344
13.6.

Teaching and Learning Mathematics To Pass Examinations: Another Source of
Mathematics anxiety

347
ix
13.7.

Managing of Students During Class And Group Activities: Who Knows What
to Do?

348
13.8.

Summary


353
13.9.

Conclusion

354
14. Chapter Fourteen: Conclusions and Recommendations

355
14.1.

Introduction

355
14.2.

Summary Of The Findings

356
14.3.

Emerging Issues

361
14.3.1. Social Justice And The Education System

362
14.3.2. The Need For Continuous Professional Development In Mathematics Teacher
Education


366
14.4.

Contributio
n
From Policy Makers And Practitioners

368
14.5.

Areas For Further Research

371
14.6.

Conclusion

372
Appendix A: The Education System of Malaysia

1
Appendix B: The Philosophy of Primary Education in Malaysia

2
Appendix C: Questionnaire for Mathematics Lecturers

4
Appendix D: Interview Questions for the Pre-service Teachers


6
Appendix
E:

Approval Letters 19
Appendix F: Introduction to the Pre-service Teachers (Bahasa Malaysia Version)

29
Appendix G: Self-Evaluation Form for Practical Teaching

30
Appendix H: Map: Political Boundary of Malaysia

31
Appendix I: Characteristics of 'Good' Teachers

32
x
Appendix J: Questionnaire on Micro-Teaching

34
Appendix K: Handout for Odd and Even Numbers

35
Appendix L: Shapes with Straight and Curved Edges

38
Appendix M: Pupils' Conceptions of 1 cm
2



39
Appendix N: School Based Experience

42
References

(i) - (xxvii)
xi
List of Photographic Plates
Photo 10.1 Wooden solids available in the college and those made by Zul and Zamna

226
Photo 10.2: Chart 10.1 which was used for set induction

227
Photo 10.3: Finished work of 'pupils'

229
Photo 10.4: Aziziah and Nolia step-by-step lesson

232
Photo 10.5 Showing pre-service teachers pre-occupied with their own work.

233
Photo 10.6 Showing pre-service teachers sleeping during micro-teaching

234
Photo 12.1: The ubiquitous long division teaching aid.


283
Photo 12.2: Another pre-service teacher using a similar long division teaching aid: Notice (i)
pupils left out of activity and (ii) the multiplication tables pinned on the soft-
board

289
Photo 12.3: Spectator mathematics and pupil working individually in front of the class.

297
Photo 12.4: Spectator mathematics and pupil inserting number into pocket.

297
Photo 12.5: Nissan's pupils playing with the tiles

303
Photo 12.6: Letchumi's pupils entertaining themselves.

305
Photo 12.7: A core group of pupils engaged in the activity, others looking on.

309
Photo 12.8: Pupils looking very bored during a mathematics activity.

310
Photo 12.9: Pupil left out of activity.

311
Photo 12.10: Pupils answering quiz questions on cardboard.

316

Photo 12.11: Liza wrote questions on manila cardboard.

318
i
Photo 12.12: 'Attractive' teaching aids.

320
ii
List of Tables
Table 6.1: Table showing the different levels where approval had to be gained

127
Table 6.2: Table listing the fieldwork schedule

130
List of Charts and Attachments
Chart 7.1: Distribution of Pre-service Teachers According to Ethnicity and Sex

141
Chart 7.2: Distribution of Pre-service Teachers Across States

141
Chart 7.3: Distribution of Modern Maths Grades Across Races

142
Chart 7.4: Distribution of Modern Maths Grades Across Pre-service Teachers

143
Chart 7.5: Pre-service Teachers' Responses to their Career Choice


144
Chart 12.1: Long division teaching aid

282
List of Diagrams
Diagram 10.1: Classroom arrangement during micro-teaching

225
List of Attachments
Attachment: Attractive envelope to hold the quiz questions

308
List of Cartoons
Cartoonist's impression of the didactic paradigm

2
Cartoonist's impression of a Malaysian mathematics classroom

342
Chapter One
Introduction
1.1. Background To The Study
Lat:

I just can't get this into my head.
Frankie: Then there's something wrong with you. This is Form
Three work. You are two years behind time!!! (Lat, 1981)
I want to unpick the above conversation and the message illustrated by the cartoon strip on the
following page to convey to the reader the situation of mathematics teaching and learning in
Malaysia in the 1960s and the evolution of mathematics education since then. The conversation

between two Malaysian boys was illustrated by Lat, a Malaysian cartoonist famous for his
perceptive depiction of Malaysian life in the late 1960s. In the strip, Lat, a Malay, was
explaining to Frankie, a Chinese, his difficulties with his form three (15 +) mathematics.
Frankie subsequently helped Lat, adopting the transmission teaching style which I experienced
in school, later practised as a teacher, and observed primary teachers using in their primary
classrooms. The transmission pedagogy continues to flourish.
Over a period of about thirty years, various attempts have been made to improve the teaching
and learning of mathematics, the latest of which is the New Primary School Curriculum better
known by its Malaysian acronym KBSR, introduced in 1983. Despite all the various reforms, it
appears from ministerial and academicians' reports that the situation is little changed.
Chapter One: Introduction
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Cartoonist's impression of the didactic paradigm
•
Mathematics is perceived by Malaysians as a difficult subject. As a teacher of mathematics
with thirteen years experience, I found that difficulty with mathematics cuts across all groups:
ethnic, social class and gender. However, it is a common stereotype that Malays, compared to
the non-Malays, are weaker in mathematics. In the early nineties, Malay politicians chose to
highlight these differences, principally because of the "deteriorating performance of students
especially those in the rural areas"
(New Sunday Times,
1/12/1991). The performance of these
students was judged based on their examination results. After the politicians voiced their views
a few academicians and teachers were interviewed to present their perspectives on this issue
(e.g.
New Straits Times,
25/07/12992, 7/10/1992). Because the issue of learners' epistemology
was not addressed, suggestions to try and improve the situation went round in circles, finally
ending in calls to adopt the Malaysian Chinese schools' style of teaching and learning
Chapter One: Introduction

2
mathematics, namely drill and rote learning, methods already in place in existing schools. Drill
and rote learning is seen as effective for some students, especially when the system of
education emphasises paper and pencil assessments to test the amount that students can
remember. However, my experience suggests that such students lack the confidence to apply

the mathematics they have learnt to problem-solving situations. They have difficulty voicing
their views and doubts and engaging in mathematical discourse. Another more insidious but
related problem is the dependency of learners on the authority of the teachers and the textbook.
With the KBSR, the education authorities hoped to introduce a more humanitarian and
egalitarian concept of learning to primary children than the one offered by the old curriculum.
However my observation, and information gleaned from press reports, primary teachers,
primary children and their parents all suggests that these aims of the KBSR have yet to be
realised. It is the intention of this thesis to try and answer why the reforms of the KBSR have
not taken root in schools.
While the KBSR calls for a non-didactic approach to teaching and learning which is not
consistent with the teaching-learning experiences of the teachers, ministerial statements
advocate the already widespread practice of rote learning (see
New Straits Times,
25/10/91). In
the UK, Burton (1992a) wrote about a similar confusion. "The United Kingdom National
Curriculum is experienced by teachers in a confusing manner because different messages are
carried by different parts of the documentation and by ministerial statements." (Burton, 1992a,
p. 381)
1.2. The Focus of this Study
For the past thirty years Malaysian students have been offered mathematics as a body of

.
knowledge through a teacher-centred, transmission paradigm. With the introduction of the
KBSR in 1983, it was expected that students would be exposed to a more experiential learning,
what 'progressives' termed 'pupil-centred' learning. The introduction of experiential learning to
Chapter One: Introduction
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3
a society familiar with only the didactic teaching-learning paradigm posed the following
questions for me:

•
Teachers and learners, exposed to school mathematics via the didactic paradigm would
have constructed for themselves certain beliefs about mathematics, teaching and
learning, that are consistent with their past experiences. What are these beliefs?
•
With the introduction of the KBSR, there is the expectation that teachers will adopt the
KBSR pedagogy. it seems to me that it would be problematic for both practising and pre-
service teachers to fulfil this expectation as they are only familiar with the didactic
paradigm. In Malaysia, it is a common practice to recruit practising teachers to be
lecturers in teacher training colleges. What efforts are made to prepare practising
teachers, college lecturers and pre-service teachers, to fulfil the expectations of the
KBSR?
•
What are the mathematics lecturers' and pre-service teachers' understanding of the KBSR
epistemology?
•
Would an intervention programme, which employed activities based on the KBSR
recommendations, have any impact on the pre-service teachers beliefs?
•
How far do lecturers' and pre-service teachers' espoused beliefs matched their enacted
beliefs?
I thus chose to study the beliefs acquired by lecturers and pre-service teachers about
mathematics, mathematics teaching and learning, as a framework by which to investigate how
their past experiences interacted with their ability to take on board the reforms of the KBSR. I
chose to study the practices of lecturers because I concur with Servais who wrote that
Teacher trainees should be instructed by highly competent teachers
who display in their own teaching the qualities required of the future
teacher. (1971, p.244)
Chapter One: Introduction
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4