TABLE OF CONTENTS
DECLARATION ……………………………………………………………………………………………..ii
SUMMARY ………………………………………………………………………………………………….. iii
ACKNOWLEDGEMENTS ………………………………………………………………………………iv
FUNDING ACNOWLEDGEMENTS…………………………………………………………………. v
TABLE OF CONTENT……………………………………………………………………………………vi
LIST OF ADDENDA ……………………………………………………………………………………… x
LIST OF FIGURES ………………………………………………………………………………………..xi
LIST OF TABLES ……………………………………………………………………………………….. xiii
CHAPTER 1 Background and overview ……………..
1.1 Background ………………………………………………………………………………………… 1
1.2 Framework of the study ………………………………………………………………………… 5
1.3 Research problem ……………………………………………………………………………….. 7
1.3.1 Aims and objectives of the study ………………………………………………………. 8
1.4 Terminology ………………………………………………………………………………………… 8
1.5 Research design ………………………………………………………………………………….. 9
1.6 Research ethics clearance ……………………………………………………………………. 9
1.7 The structure of the dissertation …………………………………………………………….. 9
1.8 Conclusion ………………………………………………………………………………………… 10
CHAPTER 2 Teacher knowledge and children’s early numeracy ………………….. 12
2.1 Introduction ……………………………………………………………………………………….. 12
2.2 Number concept development ……………………………………………………………… 15
2.2.1 Perspectives on counting ………………………………………………………………. 21
2.2.2 Innate number knowledge ……………………………………………………………… 25
2.2.3 Explicit instruction of number concepts ……………………………………………. 26
2.2.4 Language as a tool in numeracy learning ………………………………………… 27
2.2.5 Learning difficulties and learner support ………………………………………….. 30
2.3 Teachers’ trajectory towards adaptive expertise ……………………………………… 32
2.4 Professional development after initial teacher education ………………………….. 35
2.5 Learning communities …………………………………………………………………………. 37
2.6 Teacher’s subject knowledge of number concept development ………………… 39
2.7 The teacher as stable, adaptive expert practitioner …………………………………. 40
2.8 Conclusion: Teachers’ ‘toolkit’ and number concept development …………….. 42
CHAPTER 3 Research Design…………………………………………………………………. 43
3.1 Introduction: A case of grade R teachers’ knowledge ………………………………. 43
3.2 Sampling: An intact group of teachers …………………………………………………… 46
3.3.1 Observations ……………………………………………………………………………….. 48
3.3.2 Interviews ……………………………………………………………………………………. 48
3.3.3 Advantages and disadvantage of interviews …………………………………….. 50
3.3.4 Application of interviews in this research …………………………………………. 50
3.4 Interview questions …………………………………………………………………………….. 52
3.6 Validity and reliability ………………………………………………………………………….. 54
3.7 Ethical considerations …………………………………………………………………………. 55
3.8 Conclusion ………………………………………………………………………………………… 56
CHAPTER 4 The data of the study …………………………………………………………… 57
4.1 Introduction ……………………………………………………………………………………….. 57
4.2 Narrative of the research process: From collection of data to analysis of data61
4.3 The outcome of the analysis ………………………………………………………………… 67
4.3.1 A stimulating mathematics environment is important for the teacher ……. 67
4.3.2 Grade R teacher qualification not yet recognized ………………………………. 68
4.3.3 Teachers value concrete manipulatives for teaching learners number
concepts ……………………………………………………………………………………………… 71
4.3.4 Teachers recognize that grade R is play orientated …………………………… 73
4.3.5 Grade R maths curriculum is not inclusive ……………………………………….. 74
4.3.6 Too many worksheets for learners ………………………………………………….. 73
4.3.7 Teachers value professional development ……………………………………….. 74
4.3.8 Professional performance reviews diminish teachers’ inclusive pedagogy
………………………………………………………………………………………………………….. 74
4.3.9 Teachers know that learners struggle with number concepts ……………… 75
4.3.10 Teachers do not yet fully understand levels of numerical development . 75
4.3.11 Teachers need to know about number concept development ……………. 75
4.4 Conclusion ………………………………………………………………………………………… 79
CHAPTER 5 Discussion and conclusion ……………………………………………………. 80
5.1 Introduction: “Abafundisi bawazini ngezibalo zabantwana”? …………………….. 80
5.2 Research findings: The main categories ………………………………………………… 80
5.2.1 A stimulating maths environment is important to the teacher ………………. 81
5.2.2 Grade R teacher qualification is not yet recognized …………………………… 85
5.2.3 Teachers value concrete manipulatives for teaching learners number
concepts ……………………………………………………………………………………………… 91
5.2.4 Teachers recognize that grade R is play orientated …………………………… 95
5.2.5 Grade R maths curriculum is not inclusive ……………………………………….. 98
5.2.6 Too many worksheets for learners ………………………………………………… 102
5.2.7 Teachers value professional development ……………………………………… 104
5.2.8 Professional performance reviews diminish teachers’ inclusive pedagogy
………………………………………………………………………………………………………… 106
5.2.9 Teachers know that learners struggle with number concepts ……………. 107
5.2.10 Teachers don’t understand levels of numerical development …………… 107
5.2.11 Teachers need to know about number concept development ………….. 107
5.5 Conclusion ………………………………………………………………………………………. 110
Reference list …………………………………………………………………………………………… 111
ADDENDUM A …………………………………………………………………………………………. 125
ADDENDUM B …………………………………………………………………………………………. 126
