experiences of grade 2 teachers with addition and subtract

348 Pages·2012·6.17 MB·English

USING MENTAL CALCULATION TO PERFORM THE FOUR MATHEMATICAL
OPERATIONS: EXPERIENCES OF GRADE 2 TEACHERS WITH ADDITION AND
SUBTRACTION IN SELECTED SCHOOLS IN LUSAKA, ZAMBIA

By

Muhau Tabakamulamu

A thesis submitted to the University of Zambia in fulfillment of the requirements for the
degree of Doctor of Philosophy in Mathematics Education

THE UNIVERSITY OF ZAMBIA
LUSAKA
2010
i
COPYRIGHT
Copyright © 2010 by Muhau Tabakamulamu. All rights reserved. No part of this Thesis may be
reproduced or stored in any form without the written permission of the author or the University
of Zambia

ii
DECLARATION
I, MUHAU TABAKAMULAMU, declare that this Thesis
(a) Represents my own work;
(b) Has not previously been submitted for a degree of either this or another university; and
(c) Does not incorporate any published work or material from another thesis.

Signed:…………………………………………………………………………………….
Date:……………………………………………………………………………………….

iii
APPROVAL
This Thesis of MUHAU TABAKAMULAMU has been approved as fulfilling the requirements
for the award of the Degree of Doctor of Philosophy in Mathematics Education by the University
of Zambia

Signature Date
…………………………………. ……………………………………………
…………………………………. ……………………………………………
…………………………………. ……………………………………………
…………………………………. ……………………………………………

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ABSTRACT
Since the 1980s, mathematics educators around the world have accepted the view that to develop
numeracy effectively, young children need initially to use strategies for mental calculation rather
than to memorise textbook procedures. The term mental calculation refers to informal, often
untaught calculation methods used by children to solve a variety of arithmetic problems. This
primarily qualitative study used a quasi-experimental design to assess the extent to which
teachers in early primary mathematics in Zambia could adopt the use of strategies for mental
calculation for double-digit addition and subtraction. The study also sought to determine the
impact of teachers’ use of such strategies on pupils’ performance in mathematics.
Participants were 10 Grade 2 teachers (5 from control schools and 5 from experimental schools)
and 311 Grade 2 pupils. The Grade 2 pupils, 167 of whom were from experimental schools and
144 from control schools, were evenly distributed with regard to sex, age, intellectual ability and
socioeconomic background. In experimental schools the study had two phases: Grade 2 teachers
attended a staff development workshop to prepare them to implement the study; followed by the
main study when the teachers implemented in the classroom the ideas discussed during the
workshop. In control schools the same set of mathematics topics were covered, but Grade 2
teachers there used the usual textbook procedures. Data were collected through lesson
observations, interviews with teachers, teachers’ journal entries, and document analysis; while
pupils’ performance was assessed by means of two numeracy tests. One numeracy test was
administered at the beginning of the main study, and the other at the end of the study.
Results of the study suggested that over the ten-week implementation period teachers in
experimental schools changed their existing beliefs about mathematics teaching and learning and
to some extent their classroom practices as well, to support the use of strategies for mental
calculation for double-digit addition and subtraction. Their pupils performed significantly better
in the post-test compared to pupils in control schools, and developed more positive attitudes
towards learning mathematics. Based on these findings, it was recommended among other
things that, to show pupils that their informal solution strategies were valued, teaching in early
primary mathematics should build on them. At the same time teachers should demonstrate that
standard textbook procedures resulted from pupils’ informal strategies and were more efficient.
v
DEDICATION
This Thesis is dedicated to my parents, my late father Pastor Moses Tabakamulamu Singulwani
and my mother Namatama Muyunda Tabakamulamu, who together struggled with little
resources to ensure that I had a good education, although my father did not live long enough to
see the final results of his efforts; and to my wife Kubecte and my children Namatama and Sepo,
who now understand why I had to work so hard to complete this task.
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ACKNOWLEDGEMENTS
A monumental work of this kind cannot be accomplished alone. In view of this, I would like to
express my sincere thanks and gratitude to the following:
• In Zambia my supervisor, Professor Vasyl S. Kostyuk, who never gave up on me even
though my research project seemed to go on forever; colleagues in the Department of
Mathematics and Science Education who kept asking, “When are you completing your
doctoral programme?”; Professor Michael J. Kelly who though retired agreed to read a
draft of the work; and the University of Zambia which funded my study programme;
• In the UK Professor Mike Askew and Professor Margaret Brown of King’s College,
University of London, who supervised my work while I was there and allowed me to
modify and use in Zambia research materials used in the Leverhulme Project (UK); and
their colleagues Tamara Bibby and Jeremy Hodgens who, not long from completing their
own doctoral programmes, showed me that it could be done; and
• Others too numerous to mention, whether in Zambia or in the UK, who made my work
lighter by what they said or what they did.

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TABLE OF CONTENTS
Page
Copyright declaration ii
Declaration iii
Certificate of Approval iv
Abstract v
Dedication vi
Acknowledgements vii
List of Tables xvi
List of Figures xvii
List of Appendices xviii
List of Abbreviations and Acronyms xix

CHAPTER 1: INTRODUCTION 1

1.0 Introduction 1
1.1Background to the Study 1
1.1.1 Zambia: Brief Facts and Figures 1
1.1.2 The Education System in Zambia 6
1.1.3 Medium of Instruction in Education 8
1.1.4 Learner Performance in Primary Mathematics 13
1.2 Statement of the Problem 17
1.3 Purpose of the Study 17
1.4 Objectives of the Study 17
1.5 Research Questions 18
1.6 Significance of the Study 19
1.7 Definition of Terms 19
1.8 Limitations and Delimitations of the Study 20
1.9 Layout of the Thesis 21

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CHAPTER 2: REVIEW OF RELATED LITERATURE 23

2.0 Introduction 23
2.1 Influences for Change in Numeracy Teaching Practices 23
2.1.1 Realistic Mathematics Education in the Netherlands 24
2.1.2 The National Numeracy Strategy in the United Kingdom 27
2.1.3 Standards-Based Mathematics Curricula in the United States 28
2.2 Mental Calculation Strategies Used by Children 30
2.2.1 Children’s Strategies for Single-digit Addition and Subtraction 30
2.2.2 Children’s Strategies for Double-digit Addition and Subtraction 31
2.3 Teaching Mental Calculation Strategies 34
2.4 Theories of Learning Reflected in Current Developments in Early Primary
Mathematics Teaching and Learning 35

2.4.1 Radical Constructivism 36
2.4.2 Sociocultural Theories of Learning 41
2.4.3 Social constructivism 48
2.4.4 Implications of Social Constructivism for the Mathematics Classroom 51
2.5 Teacher Change and Developments in Early Primary Numeracy Teaching Practices 53

2.5.1 Characteristics of Change 55
2.5.2 Local Characteristics 58
2.5.2.1 Changing Teacher Beliefs 59
2.5.2.2 Teacher Knowledge and Educational Change 61
2.5.2.3 Changing Teaching Practices 67
2.5.3 External Factors 71
2.6 Evaluating Mathematics Innovations 71
2.7 Summary of the Literature Review 72

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CHAPTER 3: RESEARCH DESIGN AND METHODOLOGY 75

3.0 Introduction 75
3.1 Broad Methodological Approach 75
3.2 Research Design 79
3.2.1 The Mixed Method Strategy Used in this Study 79
3.2.2 Quasi-experimental Design 80
3.2.3 Case Studies 82
3.2.4 Staff Development Workshop 82
3.3 Sample 83
3.3.1 Sample and Sample Selection 83
3.3.2 Description of Research Sites 85
3.3.2.1 Control Schools 86
5.3.2.2 Experimental Schools 89
3.4 Methods 92
3.4.1 Lesson Observation 92
3.4.2 Interviews with Teachers 94
3.4.2.1 Group Interviews 95
3.4.2.2 Post-observation Interviews 95
3.4.2.3 Post-treatment Interviews 96
3.4.3 Teachers’ Journal Entries 96
3.4.4 Numeracy Assessment Tests 96
3.4.5 Document Analysis 98
3.4.6 Procedures for Data Collection 99
3.4.6.1 Negotiating Access to Research Sites 99
3.4.6.2 Data Collection 100
3.4.7 Data Analysis 102
3.4.7.1 Analysis of Quantitative Data 102
3.4.7.2 Analysis of Qualitative Data 104
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