View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Carolina Digital Repository A STUDY OF TEACHER TRANSITIONS TO A REFORM-BASED MATHEMATICS CURRICULUM IN AN URBAN SCHOOL: THE INTERACTION OF BELIEFS, KNOWLEDGE, AND CLASSROOM PRACTICES Wendy S. Bray A dissertation submitted to the faculty of the University of North Carolina at Chapel Hill in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the School of Education (Culture, Curriculum, and Change). Chapel Hill 2007 Approved by Advisor: Mary Ruth Coleman Reader: Juli Dixon Reader: Susan Friel Reader: Judith Meece Reader: Dwight Rogers @2007 Wendy S. Bray ALL RIGHTS RESERVED ii ABSTRACT Wendy S. Bray: A Study of Teacher Transitions to a Reform-Based Mathematics Curriculum in an Urban School: The Interaction of Beliefs, Knowledge, and Classroom Practices (Under the direction of Mary Ruth Coleman) This collective case study examines how four third-grade teachers’ beliefs and knowledge influenced their ways of supporting and limiting student thinking in their first year using a reform-based mathematics curriculum at an urban school. Of focus is the role teachers’ beliefs and knowledge play in supporting and limiting student thinking when student difficulties arise during instruction on multiplication and division. Situated in the growing body of research associated with current reforms in mathematics education, this study is also informed by general education research on urban schools, teacher beliefs, teacher knowledge, and teacher change. Data sources for case studies on individual teachers include classroom observations, pre-/post-observation interviews, beginning/end-of-year measures of teacher beliefs and knowledge, records of an on-going mathematics professional development project, and student achievement data. Each case study describes teacher’s beliefs and knowledge at the beginning and end of the year, presents a case story illuminating the teacher’s patterns of response to student difficulties and their relationship to the teacher’s beliefs and knowledge, and summarizes data from global measures of teaching. In addition to development of multiple case studies, a simultaneous cross-case analysis was undertaken to illuminate patterns across cases and increase the potential for generalizing beyond the particular cases. iii Findings from this study suggest that some aspects of reform-oriented mathematics instruction are more readily adopted than others. While beliefs and knowledge both appear to influence teacher response to student difficulties, certain aspects of instruction seem more greatly influenced by teacher beliefs while others appear more greatly influenced by teacher knowledge. In addition, evidence suggests that teachers’ differential classroom experiences during initial use of reform-based mathematics curriculum were related to the degree to which teachers’ evolving beliefs and knowledge moved closer to alignment with reform- based mathematics practices. Finally, the urban context of this study was found to influence teachers’ transitions to reform-based mathematics teaching practices in a variety of ways. Study findings have several implications for efforts to support teachers’ transitions to reform-based mathematics programs and practices within and outside of urban school settings. These are discussed along with directions for future research. iv To my parents, for always believing in me v ACKNOWLEDGEMENTS I am indebted to all of the individuals who participated in this study. I especially want to acknowledge the generosity and courage of the teachers who welcomed me into their classrooms to study their initial efforts at reform-based mathematics teaching. I wish to thank my dissertation committee – Drs. Mary Ruth Coleman, Juli Dixon, Susan Friel, Judith Meece, and Dwight Rogers – for their thoughtful advice and encouragement during this research project and throughout my doctorial studies. I am especially grateful to my dissertation chair, Dr. Mary Ruth Coleman, for all of her support, both personal and professional. I sincerely appreciate the Off-Campus Dissertation Research Fellowship I received from the UNC-CH Graduate School. I am also grateful to Dr. Juli Dixon for helping me to find a school site for this research. Both were instrumental in making this study possible. Thank you to my friends and family who have provided support and encouragement through completion of this work. I especially want to thank my friend Erin for editorial support. Also, I am grateful to my parents, in-laws, and babysitters for taking care of Trevor while I spent hours at the computer, and to Trevor for being the kind of baby that makes it okay for mommy go away for hours at a time. Last, but certainly not least, I want to thank my husband Kevin for supporting me in every possible way. vi TABLE OF CONTENTS LIST OF TABLES................................................................................................................... xi LIST OF FIGURES ...............................................................................................................xiii Chapter I. INTRODUCTION ........................................................................................................ 1 Overview of Study ........................................................................................................ 1 Purpose of Study and Research Questions...............................................................3 Focus on Teacher Response to Student Difficulties during Problem Solving.........4 Review of the Literature ............................................................................................... 5 Mathematics Reform and Student Thinking............................................................5 The Challenge of Reforming Mathematics Teaching............................................12 The Challenge of Urbanicity..................................................................................15 Knowledge for Teaching Mathematics..................................................................17 Knowledge for Teaching Multiplication and Division ..........................................25 Beliefs and Mathematics Teaching........................................................................33 Beliefs Beyond Mathematics .................................................................................40 The Process of Reforming Mathematics Teaching................................................43 A Synthesis of the Research Literature – My Analytical Framework ........................ 48 II. RESEARCH METHOD.............................................................................................. 52 Research Design.......................................................................................................... 53 Overview and Justification of Research Design ....................................................53 Establishing Trustworthiness.................................................................................56 vii Establishing Transparency of Researcher Position................................................56 Sample Selection Procedures...................................................................................... 58 Selection of the Research Site................................................................................59 Selection of Case Study Participants .....................................................................60 Selection of School Leader Participants ................................................................61 Data Collection Procedures......................................................................................... 62 Core Classroom Observations................................................................................62 Pre- and Post-Observation Interviews ...................................................................68 Beliefs Survey........................................................................................................71 Teacher Knowledge Interview...............................................................................73 Records of the Teacher Development Project .......................................................75 Interviews with School Leaders.............................................................................76 Student Data...........................................................................................................78 Data Management Procedures .................................................................................... 78 Data Analysis Procedures ........................................................................................... 80 Analysis during Data Collection............................................................................80 Analysis after Data Collection...............................................................................81 Development of Case Stories.................................................................................89 Cross-case Analysis ...............................................................................................90 III. FINDINGS.................................................................................................................. 93 The School Context: Lincoln Heights Elementary ..................................................... 94 School Culture, History, and Demographics .........................................................94 Mathematics-Related