Theory-enriched practical knowledge in mathematics teacher education
Oonk, W.
Citation
Oonk, W. (2009, June 23). Theory-enriched practical knowledge in
mathematics teacher education. ICLON PhD Dissertation Series. Retrieved from https://hdl.handle.net/1887/13866
Version: Corrected Publisher’s Version
License: Licence agreement concerning inclusion of doctoral thesis in the Institutional Repository of the University of Leiden
Downloaded from: https://hdl.handle.net/1887/13866
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Theory-enriched practical knowledge in
mathematics teacher education
Leiden University Graduate School of Teaching
Title: Theory-enriched practical knowledge in mathematics teacher education
Titel: Met theorie verrijkte praktijkkennis in de lerarenopleiding voor het vak rekenen-wiskunde & didactiek
ICLON, Leiden University Graduate School of Teaching
Print: Mostert & Van Onderen! Leiden Cover design: Reyndert Guiljam
Vertaling en Lay-out: Nathalie Kuijpers ISBN/EAN: 978-90-804722-9-7
© 2009, Wil Oonk
All rights reserved. No part of this thesis may be reproduced, stored in retrieval systems, or transmitted in any form of by any means, electronic, mechanical, photocopying, recording or otherwise without the prior written permission of the author.
Theory-enriched practical knowledge in
mathematics teacher education
Proefschrift
ter verkrijging van
de graad van Doctor aan de Universiteit Leiden,
op gezag van Rector Magnificus prof. mr. P.F. van der Heijden, volgens besluit van het College voor Promoties
te verdedigen op dinsdag 23 juni 2009 klokke 13.45 uur
door
Willy Oonk
geboren te Winterswijk
in 1940
Promotiecommissie
Promotores
Prof. Dr. N. Verloop
Prof. Dr. K.P.E. Gravemeijer Overige leden
Prof. Dr. J.H. van Driel
Prof. Dr. J.A. van Maanen
Dr. J.W.F. van Tartwijk
Prof. Dr. L. Verschaffel
Prof. Dr. T. Wubbels
5
Table of contents
1 General introduction 9
1.1 Background and context 9
1.2 Purpose and relevance 10
1.3 Research questions 11
1.4 Nature of the study 13
1.5 Outline of the thesis 13
2 Theory and practice in teacher education 15
2.1 Introduction 15
2.2 Orientations in teacher education programs 16 2.3 The concepts of theory and practice in teacher education 18
2.3.1 Theory in teacher education 18
2.3.2 Practice in teacher education 20
2.3.3 The knowledge base of the (prospective) teacher 21
2.3.4 Teacher practical knowledge 22
2.4 The relationship between theory and practice in teacher education 24 2.5 Theory and practice in primary mathematics teacher education
in the Netherlands 26
2.5.1 Introduction 26
2.5.2 History 26
2.5.3 New developments 29
2.5.4 Perspectives 30
2.6 Characteristics of a domain-specific instructional theory. Implications for the learning environment of mathematics teacher education 30
2.6.1 Introduction 30
2.6.2 The theory of learning and teaching to multiply 32 2.6.3 Characteristics of the theory of learning and teaching to multiply 40 2.6.4 Focal points for theory in mathematics teacher education 44
2.6.5 Conclusion 47
2.6.6 Perspective 49
2.7 The learning environment 50
2.7.1 Orientations for designing learning environments 50
2.7.2 Design research 52
3 The exploratory studies 55
3.1 Introduction 55
3.2 Prior development and research 58
3.2.1 Developing good practice 58
3.2.2 Good practice for teacher education 60
3.3 The making of MILE 62
3.3.1 Introduction 62
3.3.2 Preparing the recording of good practice 62
3.3.3 The scenario 64
3.3.4 The screen-test 65
3.3.5 Recording and editing 65
3.3.6 Making the records of real teaching practice accessible 66
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3.4 MILE, a digitalized teaching practice 67
3.5 The first exploratory research 69
3.5.1 Research question 69
3.5.2 Learning by investigating the recorded teaching practice 69
3.5.3 The process 70
3.5.4 Incentives in the learning environment 71
3.5.5 The main findings of pioneering 74
3.6 Larger scale field tests 75
3.7 Making MILE educative 77
3.8 The second exploratory research 80
3.8.1 Research question and method 80
3.8.2 Identifying theory in action 80
3.8.3 Theory in action. An example 81
3.8.4 Some results 82
3.9 Practice based professionalization and enriched practical knowledge 82 3.9.1 The necessity of enriching practical knowledge theoretically 82 3.9.2 The learning environment for the next research 83
4 The small scale study 85
4.1 Introduction 85
4.2 Method 86
4.2.1 Context and participants 86
4.2.2 The learning environment 87
4.2.3 The instruments 90
4.2.4 Procedure 93
4.2.5 Data collection and triangulation 93
4.3 Anne’s use of theory: a case study 94
4.3.1 Anne’s work plan 94
4.3.2 The initial assessment 97
4.3.3 Anne’s use of theory in class 99
4.3.4 Video stimulated interview 102
4.3.5 Anne’s concept map 107
4.3.6 The final assessment 108
4.3.7 The final interview 111
4.3.8 The numeracy test 113
4.3.9 Data analysis and results of Anne’s use of theory 113 4.4 Results and conclusion of the small scale study 116
4.4.1 Results 116
4.4.2 Conclusion and discussion 119
4.5 Implications of the small scale study for the large scale study 120 5 The large scale study 123
5.1 Introduction 123
5.2 Research questions 123
5.3 Method 127
5.3.1 The context and the participants 127 5.3.2 Design of the learning environment 128
5.3.3 Training the teacher educators 131
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5.3.4 The instruments 133
5.3.5 Procedure and data collection 134
5.3.6 Data analysis 135
5.4 Analysis and results 145
5.4.1 Introduction 145
5.4.2 Analysis and results of the first research question 146 5.4.3 Analysis and results of the second research question 153 5.4.4 Analysis and results of the third research question 159 5.4.5 The role of the teacher educator 164
5.5 Conclusion of the large scale study 165
6 General conclusion and discussion 169
6.1 Introduction 169
6.2 Conclusions 170
6.2.1 The exploratory studies 170
6.2.2 The small scale study 170
6.2.3 The large scale research 171
6.3 Towards a local theory of integrating theory and practice 177
6.4 Limitations 182
6.5 Suggestions for future research 183
6.6 Implications for teacher education 184
7 Summary 189
8 Samenvatting 203
9 References 217
Appendices part I 239
Appendix 1 Fifteen signals of use of theory by student teachers 239 Appendix 2A The development and try-out of the ‘Concept list’
(short version) 241
Appendix 3A Try-out of ‘The Theorem’ (short version) 244 Appendix 4 Cognitive network of student, constructed by Anne 245 Appendix 5 Two of Anne’s teaching narratives for theoretical concepts 246 Appendix 6 Anne’s reflective note for ‘the suitcase full of balls’ 248
Appendix 7 Characteristics concept map 250
Appendix 8 Key questions for the final interview 251 Appendix 14 Descriptive statistics of questionnaire
large scale study (n = 256) 252
Notes 253
Curriculum vitae 259
Dankwoord 261
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Appendices part II (on added CD-rom; mainly in Dutch)
Appendix 2B The development and try-out of the ‘Concept list’
(extended version)
Appendix 3B Try-out of ‘The Theorem’ (extended version)
Appendix 9 The ‘individual learning question’ and ‘What has been learned’
Appendix 10 The development of the reflection-analysis tool Appendix 11 The initial assessment in the large scale study
Appendix 12 The final assessment in the small scale and large scale studies Appendix 13 Descriptive statistics of questionnaire small scale study (n = 13) Appendix 15 Sample meaningful units
Appendix 16 Guidelines for rating nature and level of use of theory Appendix 17 Sample nature and level of theory use (n = 15) Appendix 18 Numeracy test small scale study
Appendix 19 Numeracy test large scale study Appendix 20 Rating form numeracy test Appendix 21 Sample numeracy test Appendix 22 Teacher educators’ manual
Appendix 23 Examples of video material used for the initial and the final assessment
