Learning to Facilitate Productive Mathematical Discussion
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Learning to Facilitate Productive Mathematical Discussion: Teacher candidate participation in a practice-based elementary mathematics methods course Elizabeth Sugino David A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy University of Washington 2020 Reading Committee: Elham Kazemi, Chair Kenneth Zeichner Allison Hintz Program Authorized to Offer Degree: College of Education © Copyright 2020 Elizabeth Sugino David University of Washington Abstract Learning to Facilitate Productive Mathematical Discussion: Teacher candidate participation in a practice-based elementary mathematics methods course Elizabeth Sugino David Chair of the Supervisory Committee: Dr. Elham Kazemi College of Education A prevailing challenge in teacher education is the “problem of enactment,” a discrepancy in what teacher candidates (TCs) know or say about practice and what they can actually do or enact (Kennedy, 1999). Current practice-based teacher education research focuses on articulating pedagogies of practice and core practices to integrate theory and practice, attend to the sociocultural nature of TC learning, and support TCs to enact practices (Grossman, Compton, et al., 2009; Grossman et al., 2019; McDonald et al., 2013). While there is research on practice-based learning cycles, core practices, and pedagogies of practice, there is limited research documenting how TCs participate in these types of contexts and how they enact core practices. Purpose and Research Question. The purpose of this study was to understand TC participation: How does TC participation manifest and change in their practice-based mathematics methods course? I sought to characterize TCs’ participation around the practice of facilitating a productive mathematical discussion. Data and Methodology. Relevant data sources for this study included videotaped observations of TCs’ participation in the course, TC assessments and lesson plans, and field notes. Data was analyzed for broad themes and categories related to TC participation around facilitating discussion. Coding was guided by my conceptual framework, which focused on TC learning as participation in a community of practice. Iterative passes of the data looked for patterns and reoccurring themes related to development of a shared repertoire and joint enterprise. Findings. Findings documented changes in TCs’ talk about and enactment of facilitating productive mathematical discussion. TCs’ specificity in articulating the instructional goal, intentionality in facilitating discussions to reach these goals, and ownership over articulating and working on goals increased over the 10-week course. TCs were able to use tools (particularly lesson plans, board work, and talk moves) more intentionally in response to student thinking and in service of their instructional goal as they became familiar with these tools and routinized their use. As part of the shared repertoire, these tools reified practice as representations, decompositions, and approximations of practice and provided routines and opportunities for deliberate practice. Implications. Understanding what TCs learn in practice-based courses, particularly how they enact practice, contributes to understanding the efficacy of current practice-based approaches in teacher education. This study is one of a limited number of studies that examines TCs’ participation and what they learn and enact. My dissertation makes two contributions that address gaps in the literature: 1. Existence proof that there are shifts in TC beliefs and talk about teaching and enactment of the practice of facilitating a productive mathematical discussion in a 10-week practice- based methods course. 2. An image of TC participation to contribute to trajectories of TC learning and enactment of core practices in teacher education. My study considered the sociocultural approach common in teacher education and operationalized learning from that perspective, laying the groundwork for research on what particular pedagogies offer for TC learning. Understanding the changes in how TC participate and enact practice is useful to support teacher educators to continually refine and improve their practices and coursework. TABLE OF CONTENTS LIST OF FIGURES ...................................................................................................................... IV LIST OF TABLES ......................................................................................................................... V CHAPTER 1: INTRODUCTION ................................................................................................... 1 Background and Context of Practice-Based Teacher Education ............................................. 1 Problem Statement ................................................................................................................... 2 Research Purpose and Questions ............................................................................................. 3 Conceptual Framing: A Sociocultural Approach to Teacher Candidate Learning .................. 4 Learning as Changing Participation .................................................................................... 4 Using A Sociocultural Unit of Analysis ............................................................................. 5 Research Approach .................................................................................................................. 7 Researcher Positionality .......................................................................................................... 8 Assumptions ............................................................................................................................ 8 Rationale and Significance ...................................................................................................... 9 Definitions of Key Terminology Used in This Study ............................................................ 11 Organization of the Dissertation ............................................................................................ 14 CHAPTER 2: LITERATURE REVIEW ...................................................................................... 16 Defining High-Quality Mathematics Instruction ................................................................... 17 A Vision of High-Quality Mathematics Instruction ......................................................... 18 The Role of Discussion in High-Quality Mathematics Instruction .................................. 19 Dissertation Contribution to Research on High-Quality Mathematics Instruction ........... 27 Understanding Teacher Candidate Learning ......................................................................... 28 Learning as Changing Participation in a Community of Practice ..................................... 28 Efforts to Support TC Learning in Methods Courses ....................................................... 33 Dissertation Contribution to Research on TC Learning ................................................... 51 Practice-Based Teacher Education ........................................................................................ 53 Problematizing Teacher Education: The Theory – Practice Gap...................................... 53 Current Research on Practice-Based Structure, Pedagogy, and Curriculum .................... 54 Defining Practice-Based Teacher Education .................................................................... 60 Dissertation Contribution to Practice-Based Teacher Education Literature ..................... 77 Chapter Summary .................................................................................................................. 77 CHAPTER 3: CONTEXT – THE MATHEMATICS METHODS COURSE AND PARTICIPANTS .......................................................................................................................... 81 Organizing Learning Around Core Practices: Cycles of Enactment and Investigation ........ 81 Instructional Activities as “Structures” for Managing and Recomposing Practice .......... 83 Towards a Curriculum for Methods Courses: Ambitious Practices, Principles, and Knowledge ........................................................................................................................ 86 A Description of the Mathematics Methods Course .............................................................. 88 The Fall Quarter Course and Classroom Context ............................................................. 89 Study Participants .................................................................................................................. 93 CHAPTER 4: RESEARCH STRATEGY AND DESIGN ........................................................... 98 A Qualitative Approach to Understanding Teacher Candidate Learning .............................. 98 Sampling: Settings, Timeframes, Events, and Participants ................................................. 100 The Mathematics Methods Course ................................................................................. 100 i Selection of the Teacher Candidate Group ..................................................................... 100 Researcher Role .............................................................................................................. 101 Data Sources and Collection ................................................................................................ 101 Selected Course Sessions