TEACHING TOWARD EQUITY IN MATHEMATICS By Beverly Caswell A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy Graduate Department of Curriculum, Teaching and Learning Ontario Institute for Studies in Education University of Toronto © Copyright by Beverly Caswell (2011) TEACHING TOWARD EQUITY IN MATHEMATICS Doctor of Philosophy (2011) Beverly Caswell Department of Curriculum, Teaching and Learning UNIVERSITY OF TORONTO ABSTRACT This research is a qualitative case study examining changes in urban Canadian elementary teachers’ conceptualizations of equity and approaches to pedagogy in their mathematics teaching in relation to their involvement in multiple professional learning contexts. The study focuses on four major professional development (PD) efforts in which five focal teachers participated over a school year. Data sources include researcher observations, field notes, video-recordings of PD sessions and classroom mathematics teaching, as well as a series of one-on-one interviews. Data analysis revealed three main ideas related to equity that were adopted by focal teachers: 1) the importance of developing awareness of students and their communities; 2) teaching strategies to scaffold students’ development of mathematical proficiency; and 3) strategies for structuring student-driven, inquiry- based learning for mathematics. The multiple contexts of professional learning presented contradictory messages. Thus, teachers took up some ideas and left others behind and sometimes took up ideas that served conflicting goals of education. Future studies of teacher PD should focus on the teacher’s perspective and the role of any individual PD within the multiple contexts of professional learning in which teachers participate. ii ACKNOWLEDGEMENTS I would like to thank my committee members Indigo Esmonde, Kathy Bickmore, and Joan Moss, who provided a wealth of expertise and guidance throughout the dissertation process. A very special thank you goes to my supervisor Indigo Esmonde. Her innovative, equity-minded, intellectually stimulating, and academically rigorous courses inspired my research in equity in mathematics. I am grateful for the many hours Indigo has dedicated in the support and guidance of the design, methodology, and analysis of my PhD dissertation. Her ability to see the bigger picture while ensuring that the smaller details are in place has been invaluable. I feel very fortunate to have Kathy Bickmore and Joan Moss on my PhD Dissertation committee. Kathy‟s wisdom, deep commitment to exploring issues of equity, and her timely comments challenged me to think beyond the boundaries of my current knowledge. Joan‟s wealth of knowledge about current research in mathematics education, innovative teaching practices, and her deep curiosity of how children think and learn have provided many insights. Thank you as well to Jim Hewitt, the internal external examiner who contributed many helpful suggestions regarding the methodology, literature review, and clarifications of the theoretical framework. Thank you also to David Wagner for agreeing to be my external examiner - your work in mathematics and social justice is inspiring. I am very grateful to Indigo‟s Radical Math research team: Miwa Takeuchi, Lesley Dookie, Cal Armstrong, James Eslinger, who offered thoughtful advice and encouragement along the way. A special thanks to Miwa who shared many insights and readings during the data collection and analysis process. iii Thank you to Tara Goldstein and Joan Moss for suggesting that I work with Indigo Esmonde. As well, I‟d like to thank my colleagues at the Centre for Urban Schooling - Jeff Kugler, Nicole West-Burns, and Dominique Riviere - for hosting equity focused events at OISE. A special thanks to Jeff Kugler for paving the way to the research site. I also thank my colleagues at the Dr. Eric Jackman Institute of Child Study for providing models of exemplary teaching in mathematics. Many thanks to Alice Klein and Lois Fine for providing space for a writer‟s retreat in the beginning and final stages of the writing process. Thank you also to Thelma Akyea and Christine Davidson for their support in formatting the document. Finally, I acknowledge the Council of Ontario Directors of Education (CODE) and OISE Initial Teacher Education as sponsors of the research. Some sections of the dissertation draw on previous publication of these findings (see Caswell in References). iv Table of Contents Abstract ............................................................................................................................. II Acknowledgements ......................................................................................................... III Dedication ..................................................................................................................... VIII CHAPTER 1: TEACHING TOWARD EQUITY IN MATHEMATICS .................... 1 CHAPTER 2: LITERATURE REVIEW ....................................................................... 5 Teaching for Equity in Mathematics: Four Themes ............................................... 5 Theme 1: Examining the achievement gap. ............................................................ 6 Theme 2: Providing access to high levels of mathematics. .................................... 8 Theme 3: Exploring issues of social justice through mathematics. ........................ 9 Theme 4: Culturally relevant pedagogy and student identity ............................... 10 Theoretical Framework ............................................................................................ 14 Professional Development (PD) ............................................................................... 18 PD in mathematics education................................................................................ 18 PD with an equity focus. ....................................................................................... 19 CHAPTER 3: RESEARCH METHODOLOGY ......................................................... 22 Rationale .................................................................................................................... 22 Developing a reflexive stance ................................................................................... 24 The School.................................................................................................................. 26 Participants ................................................................................................................ 26 Tracey, Grade 1 Teacher. ...................................................................................... 27 Stan, Grade 2/3 Teacher. ....................................................................................... 28 Leah, Grade 2/3 Teacher. ...................................................................................... 28 Sally, Grade 4 Teacher. ......................................................................................... 28 Stewart, Grade 5 Teacher. ..................................................................................... 29 Data Collection .......................................................................................................... 29 Interviews. ............................................................................................................. 31 Classroom Observations ........................................................................................... 42 Professional development (PD) sessions.................................................................. 43 Teaching-Learning Critical Pathways (T-LCP). ................................................... 45 Culturally Relevant and Responsive Pedagogy (CRRP) Seminar Series and Participatory Action Research (PAR) Projects. .............................................. 50 v Junior Undiscovered Math Prodigies (JUMP). ..................................................... 56 Institute of Child Study (ICS ). ............................................................................. 58 Data Analysis ............................................................................................................. 59 A. Analyzing the interviews. ................................................................................ 60 B. Analyzing the PD. ............................................................................................ 65 Overview of Findings and Discussion ..................................................................... 67 CHAPTER 4: FINDINGS FROM PD IDEAS TAKEN UP AND/OR REJECTED FROM THE MULTIPLE CONTEXTS OF PROFESSIONAL DEVELOPMENT ..................................................................................................... 69 Teaching-Learning Critical Pathways (T-LCP) .................................................... 70 Junior Undiscovered Math Prodigies (JUMP) ....................................................... 75 Culturally Relevant and Responsive Pedagogy (CRRP) Seminar Series and Participatory Action Research (PAR) ............................................................... 80 PAR enacted in classrooms: Using PAR to explore Recess Issues. ..................... 82 Institute of Child Study – Inquiry PD ..................................................................... 87 CHAPTER 5: FINDINGS - TEACHERS’ CONCEPTUALIZATIONS OF EQUITY IN MATHEMATICS ACROSS INTERVIEWS .................................................... 90 Overview of teachers’ conceptions of equity