MATHEMATICS COACHING TO IMPROVE TEACHING PRACTICE: THE EXPERIENCES OF MATHEMATICS TEACHERS AND COACHES by Priscilla Bengo A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy Department of Curriculum, Teaching and Learning Ontario Institute for Studies in Education of the University of Toronto © Copyright by Priscilla Bengo 2013 MATHEMATICS COACHING TO IMPROVE TEACHING PRACTICE: THE EXPERIENCES OF MATHEMATICS TEACHERS AND COACHES Doctor of Philosophy Degree, 2013 Priscilla Bengo Department of Curriculum, Teaching and Learning University of Toronto Abstract The purpose of the study is to determine how coaching can be used effectively to improve instruction and student achievement while exploring teachers’ specific emotions during mathematics education reform initiatives that challenge the teacher’s beliefs about teaching and learning in mathematics. It also examines how teachers incorporate the reform changes into their practice in order for the new instructional practices to have the expected effect. I explored teacher learning which refers to the correct use of reform strategies by mathematics teachers so that they have the intended effects on student achievement with the support of a coach during reform initiatives. Through questionnaires, interviews, observations and archival material, the study determines the relationship between teachers’ specific emotions, teacher learning and teacher coaching in secondary school mathematics classrooms. As a result, the study highlights the issues associated with the implementation of mathematics education reform initiatives and implications. The findings show that mathematics education reforms produce emotional responses that can be described as both negative and positive. For example, some ii emotions include pride, joy, fear, feeling drained and ineffective. The four teachers in the study experienced these emotions because of factors such as a lack of knowledge of how to implement mathematics reform, beliefs about teaching and learning in mathematics that were inconsistent with the reform initiatives, the nature of coaching, and gains in student achievement and engagement. They also experienced negative emotions because of favorable in-school factors such as an administration that supported teacher efforts to implement mathematics reforms. The study shows that: a) coaching may not help teachers reconstruct their professional self-understanding when it fails to address their self-image issues; b) teacher learning may occur even when the teacher’s beliefs are inconsistent with reform initiatives; and c) even when teacher learning results from coaching, reforms do not present themselves as expected in the classroom. Coaches experienced positive and negative emotions as a result of how well the reforms were being implemented by teachers. The experiences of the two coaches during mathematics reforms indicate a need to support coaches as they help teachers use the reform strategies. The directions for future research are described. iii Acknowledgements Writing this thesis has not been as arduous as I had expected because of the support I obtained from individuals I mention below. I also learned a lot personally and professionally. I would like to thank the participants in my study. They were teachers and coaches who volunteered time from hectic schedules and welcomed me into their lives. I am very grateful for their perspectives as they are the basis of my learning. I would also like to thank my Thesis Committee, Dr. Doug McDougall, Dr. Gila Hanna, Dr. Jim Hewitt, and Dr. David Booth. I am very grateful for the support of Dr. Doug McDougall, my thesis supervisor, particularly during data collection and for his patience as he read versions of the thesis giving quick feedback. Dr. Gila Hanna continues to develop me professionally. I consider myself very lucky to be working with her. Dr Jim Hewitt and Dr. David Booth have supported me in many ways. Perhaps the most important was their kindness as I prepared to defend my thesis. I am also very appreciative of the constructive comments on the thesis that I obtained from my external examiner, Dr. Olive Chapman. To my family, for their unflinching support throughout my education. All that I have accomplished is, in many respects, due to them. And finally, to Hugh. I cannot thank you enough for your support in everything that I have done including this thesis journey. iv Table of Contents Abstract ii Acknowledgements iv Chapter 1: Introduction 1 1.1 Introduction 1 1.2 Research Context 2 1.2.1 The Role of the Coach in Facilitating Teacher Learning 3 1.2.2 Teacher Emotions during Mathematics Education Reform 6 1.2.3 Mathematics Education Reform 8 1.3 Purpose of the Study 9 1.4 Statement of the Problem 10 1.5 Significance of the Study 10 1.6 Background of the Researcher 11 1.7 Limitations of the Study 24 1.8 Plan of Thesis 25 Chapter 2: Literature Review 26 2.1 Introduction 26 2.2 Mathematics Education Reform 26 2.3 Educational Change 29 2.3.1 Challenges and Issues 30 2.4 Teachers’ Mathematics Beliefs 33 2.5 Teachers’ Emotions during Education Reform 41 2.5.1. Research on Teachers’ Emotions during Mathematics Education Reform 42 2.5.2. Research on Teachers’ Emotions during Reform Initiatives in other Subject Areas 47 2.6 Teacher Learning during Mathematics Education Reform 52 2.7 Teachers’ Mathematics Beliefs, their Emotions and Teacher Learning 56 2.8 The Role of Coaching 57 2.9 Summary 61 Chapter 3: Research Method 63 3.1 Research Design and Research Approach 63 3.2 Participants 65 3.3 Setting 68 3.4 Data Collection 69 3.4.1. Self-Assessment Surveys 71 3.4.2 Teacher Confidence Survey 72 3.4.3 Semi-Structured Interviews 73 3.4.4 Critical Incident Interviews 74 3.4.5 Archival Data 77 3.4.6 Classroom Observations 77 v 3.5 Data Analysis and Interpretation 81 3.5.1 First Level Coding 82 3.5.2 Pattern Coding 83 3.6 Validity and Reliability 83 3.7 Ethical Considerations 84 3.8 Conclusion 85 Chapter 4: Findings 86 4.1 Introduction 86 4.2 Criteria for Classification of Beliefs 87 4.3 The Case of Robert 87 4.3.1 Robert’s Beliefs about the Nature of Mathematics 88 4.3.2 Robert’s Beliefs about Mathematics Pedagogy 89 4.3.3 Robert’s Beliefs about Learning Mathematics 90 4.3.4 Robert’s Beliefs about Teaching Mathematics 89 4.3.5 Robert’s Teaching Practice 102 4.3.5.1 Mathematics Support 110 4.3.5.2 Robert’s Emotions during the Mathematics Reforms 111 4.4 The Case of Helen 114 4.4.1 Helen’s Beliefs about the Nature of Mathematics 114 4.4.2 Helen’s Beliefs about Learning Mathematics 116 4.4.3 Helen’s Beliefs about Teaching Mathematics 116 4.4.4 Helen’s Teaching Practice 125 4.4.5 Helen’s Emotions during the Mathematics Reforms 130 4.5 Teachers’ Beliefs and Practices 132 4.6 James’ Beliefs about the Nature of Mathematics 138 4.6.1 James’ Beliefs about Mathematics Pedagogy 138 4.6.2 James’ Beliefs about Learning Mathematics 139 4.6.3 James’ Emotions during Mathematics Reform 140 4.6.4 James’ Experiences with Coaching 142 4.7 Andrew’s Beliefs about the Nature of Mathematics 142 4.7.1 Andrew’s Beliefs about Mathematics Pedagogy 143 4.7.2 Andrew’s Beliefs about Learning Mathematics 143 4.7.3 Andrew’s Emotions during Mathematics Reform 145 4.7.4 Andrew’s Experiences with Coaching 146 4.8 Teacher Beliefs, Emotions and Coaching Experiences during Mathematics Reform 147 4.9 Christina’s Beliefs about the Nature of Mathematics 148 4.9.1 Christina’s Beliefs about Mathematics Pedagogy 149 4.9.2 Christina’s Beliefs about Learning Mathematics 149 4.9.3 Christina’s Beliefs about Teaching Mathematics 149 4.9.4 Christina’s Emotions during Mathematics Reform 153 4.10 Theresa’s Beliefs about the Nature of Mathematics 157 4.10.1 Theresa’s Beliefs about Mathematics Pedagogy 158 4.10.2 Theresa’s Beliefs about Learning Mathematics 158 4.10.3 Theresa’s Beliefs about Teaching Mathematics 159 vi 4.10.4 Theresa’s Emotions during Mathematics Reform 162 4.11 A Comparison of Christina’s and Theresa’s Beliefs and Emotions during Mathematics Reform 163 4.12 Summary 164 Chapter 5: Discussion and Conclusions 167 5.1 Introduction 167 5.2 Research question 1: What are Teachers’ Specific Emotions during Mathematics Education Reform Initiatives? 167 5.3 Research question 2: What Factors are Associated with Emotions that Teachers Experience? 168 5.4 Research question 3: What Factors Facilitate Teacher Learning during Mathematics Education Reform given these Emotions? 170 5.5 Research question 4: How does Instructional Coaching help Teachers Learn during Mathematics Education Reform? 174 5.6 Issues and Implications of Mathematics Reform 176 5.7 Suggestions for Future Research 179 References 181 List of Appendices A. Mathematics Beliefs and Attitudes Survey from Ten Dimensions of Mathematics Reform 197 B. Critical-Incident Interview Questions 200 C. Semi-Structured Interview for Teachers 201 D. Teacher Confidence Survey 202 E. Teachers’ Consent Letter 204 F. Administrative Consent Letter 206 G. Math Coaches’ Consent Letter 208 vii List of Tables Table 1: Instruments by Intention and Number of Participants 69 Table 2: Dimension 10, Teacher’s Attitude and Comfort with Mathematics 79 Table 3: Robert’s Beliefs about Learning Mathematics 90 Table 4: Robert’s Beliefs about Teaching Mathematics 91 Table 5: Robert’s Observed Performance in Example 1 93 Table 6: Robert’s Observed Performance in Example 2 97 Table 7: Robert’ s Observed Performance in Example 3 100 Table 8: Teacher Confidence Survey Results for Robert, Part 1 107 Table 9: Teacher Confidence Survey Results