Measuring Teachers’ Beliefs Quantitatively (eBook)

Foreword 6
Foreword and Acknowledgment 7
Table of Contents 8
List of Tables 12
List of Figures 14
Abstract 15
Kurzzusammenfassung 17
1. General Introduction 20
1.1 The relationship between teachers’ beliefs and their practices 21
1.2 Measuring teachers’ beliefs and some problems in the measurements 21
1.3 Methodological arguments of the approach offered to solve problems in measuring beliefs 24
1.4 The theoretical framework and the structure of the TBTP 26
1.4.1 The theoretical framework of the TBTP 26
1.4.2 The structure of the TBTP 27
1.5 Studies conducted for constructing and validating the TBTP 29
1.5.1 The first preliminary study 29
1.5.2 The second preliminary study 30
1.5.3 The first validation study 30
1.5.4 The second validation study 30
1.5.5 The third validation study 30
2. The First Article [The different mathematics performances in PISA 2012 and a curricula comparison: Enriching the comparison by an analysis of the role of problem solving in intended learning processes] 33
2.1 Introduction and background 34
2.1.1 The comparison of performances from Indonesia and Singapore in international comparison studies 36
2.1.2 Overview of Secondary Education System and the Curricula 38
2.1.2.1 Indonesia 38
2.1.2.2 Singapore 39
2.2 Theories of the interpretation of problem solving 40
2.3 Research questions 42
2.4 Method 42
2.5 Results 46
2.5.1 The comparison of mathematics contents 46
2.5.1.1 The comparison of the statistics topic 46
2.5.1.2 The comparison of the geometry and measurement on two-dimension (2D) shape topic 48
2.5.2 The comparison of the examination of the role of problem solving 49
2.6 Discussions and concluding remarks 51
2.7 Limitations and further studies 53
References 54
3. The Second Article [Teachers’ beliefs and how they correlate with teachers’ practices of problem solving] 57
3.1 Introduction 58
3.2 Theoretical background: Beliefs 58
3.3 Method 59
3.4 Results 60
3.4.1 Teacher A 60
3.4.1.1 Observation 60
3.4.1.2 Interview 61
3.4.2 Teacher B 61
3.4.2.1 Observation 61
3.4.2.2 Interview 63
3.4.3 Teacher C 63
3.4.3.1 Observation 63
3.4.3.2 Interview 64
3.5 Discussion 64
3.6 Concluding remarks 65
References 66
4. The Third Article [Measuring teachers’ beliefs: A comparison of three different approaches] 67
4.1 Introduction 68
4.2 Theoretical background 70
4.2.1 Beliefs about the nature of mathematics and beliefs about teaching and learning of mathematics and problem solving 70
4.2.2 Problems in measuring beliefs: the weaknesses of Likert scale items 71
4.3 Method 73
4.3.1 Participants 73
4.3.2 Data collection and analysis 73
4.3.2.1 Interviews along with observations 73
4.3.2.2 The Likert Scale (LS) instrument 75
4.3.2.3 The Rank-Then-Rate questionnaire (TBTP) 75
4.3.2.4 The RD-16 instrument 77
4.4 Results 78
4.4.1 Andre’s interview along with an observation 78
4.4.1.1 The observed lesson 78
4.4.1.2 Andre’s beliefs interpreted from his interview 79
4.4.2 Candra’s interview along with an observation 80
4.4.2.1 The observed lesson 80
4.4.2.2 Candra’s beliefs interpreted from his interview 81
4.4.3 The correspondences between the surveys and interviews 82
4.4.3.1 Teachers’ responses to the Likert Scale instrument 82
4.4.3.2 Teachers’ responses to the TBTP 83
4.4.3.3 Teachers’ responses to the RD-16 84
4.5 Discussion 85
4.6 Conclusion and limitations 87
References 88
Appendix 90
5. The Fourth Article [Investigating the influence of the social contexts focusing on students’ abilities on the relationship between teachers’ beliefs and practices] 93
5.1 Introduction 94
5.2 Theoretical framework 96
5.2.1 Beliefs about the nature of mathematics 96
5.2.2 The concepts of the relationship between beliefs about the nature of mathematics and teaching and learning mathematics as well as problem solving 97
5.2.3 Students’ abilities as one of social contexts at school 98
5.3.4 Methodological arguments and structures of the newly developed instrument 99
5.3 Method 101
5.3.1 Research questions 101
5.3.2 Participants 102
5.3.3 Data collection and analysis 102
5.3.3.1 Survey 102
5.3.3.2 Interview 103
5.3.3.3 Observed and videotaped lessons 104
5.4 Results 105
5.4.1 Survey: Teachers’ responses to the TBTP questionnaire 105
5.4.2 Interviews and videotaped lessons: Fitria 107
5.4.2.1 Interview 107
5.4.2.2 Videotaped lesson 108
5.4.3 Interviews and videotaped lessons: Doni 109
5.4.3.1 Interview 109
5.4.3.2 Videotaped lesson 110
5.5 Discussion 111
5.6 Conclusion and limitations 113
References 114
Appendix 117
6. The Fifth Article [Offering an approach to measure beliefs quantitatively: Capturing the influence of students’ abilities on teachers’ beliefs] 119
6.1 Introduction 120
6.2 The theoretical framework for constructing the TBTP 122
6.2.1 Beliefs about the nature of mathematics 122
6.2.2 The relationship between beliefs about the nature of mathematics and beliefs about teaching and learning of mathematics 123
6.2.3 The relationship between beliefs about the nature of mathematics and beliefs about teaching and learning of problem solving 124
6.2.4 Challenges in measuring beliefs quantitatively: The influence of students’ abilities 125
6.3 The study 126
6.3.1 Research questions 126
6.3.2 Instrument: The TBTP 127
6.3.3 Data Analysis 129
6.3.4 Participants 130
6.4 Results 131
6.4.1 Teachers’ beliefs about teaching and learning 132
6.4.1.1 The comparison between HA and LA classes 132
6.4.1.2 The comparison within HA and LA classes 133
6.4.2 Students’ abilities on the relationship between the beliefs about mathematics and beliefs about teaching and learning of mathematics and problem solving 135
6.4.3 The interplay of students’ abilities, teachers’ backgrounds and teachers’ beliefs 136
6.5 Discussion and Conclusion 136
6.5.1 Limitations 139
References 140
Appendix 144
7. The Sixth Article [Capturing how students’ abilities and teaching experiences affect teachers’ beliefs about mathematics teaching and learning] 145
7.1 Introduction 146
7.2 Theoretical framework 147
7.2.1 Beliefs about mathematics and about mathematics teaching and learning 147
7.2.2 The effect of students’ abilities on teachers’ beliefs and practices 148
7.2.3 Experiences in teaching mathematics 148
7.2.4 Problems in measuring beliefs for large samples of teachers 149
7.3 Method 150
7.3.1 Participants 150
7.3.2 Data collection and analysis 150
7.3.2.1 Instrument 150
7.3.2.2 Interview 152
7.4 Results and discussion 152
7.4.1 Teachers’ responses to the TBTP 152
7.4.2 A further investigation 154
7.4.2.1 Elisa 154
7.4.2.2 Candra 155
7.5 Conclusion, limitations and a further study 157
References 157
Appendix 160
8. General Discussion 161
8.1 Discussion 161
8.2 Limitations and outlook 167
References 168
Appendix: The TBTP Questionnaire 172
GENERAL INSTRUCTION 172
BACKGROUND INFORMATION 173
GENERAL NOTE 173
MATHEMATICS LESSON 173
PROBLEM SOLVING 176
MATHEMATICS 179