MAKING SENSE OF MATHEMATICS THROUGH NUMBER TALKS: A CASE STUDY OF THREE TEACHERS IN THE ELEMENTARY CLASSROOM by MIRANDA GAYLE WESTBROOK A Dissertation Submitted to the Faculty in the Curriculum and Instruction Program of Tift College of Education at Mercer University in Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY Atlanta, GA 2019 MAKING SENSE OF MATHEMATICS THROUGH NUMBER TALKS: A CASE STUDY OF THREE TEACHERS IN THE ELEMENTARY CLASSROOM by MIRANDA GAYLE WESTBROOK Approved: ________________________________________________________________________ William O. Lacefield, III, Ed.D. Date Dissertation Committee Chair ________________________________________________________________________ Justus J. Randolph, Ph.D. Date Dissertation Committee Member ________________________________________________________________________ Jeffrey S. Hall, Ed.D. Date Dissertation Committee Member ________________________________________________________________________ Jane West, Ed.D. Date Director of Doctoral Studies, Tift College of Education ________________________________________________________________________ Thomas R. Koballa, Jr., Ph.D. Date Dean, Tift College of Education DEDICATION To my loving husband, Chad, I am forever indebted to the unconditional love, support, and patience you bestowed as I engaged in this endeavor. You always encouraged me to persevere, and together, we transformed this dream into a reality. I am truly blessed to have you in my life. To my mom and dad, you inspired me to follow my dreams and taught me the value of hard work. The morning phone calls were always uplifting, and I love you both with all my heart. To Brenda, thank you for understanding and supporting me on this journey. To Linda, you were always confident that I would achieve this goal. Your enthusiasm and interest in my work gave me the strength I needed to keep writing. To Lucas and Miranda, thanks for checking on my progress each day. Although it seemed impossible at times, you never doubted that I would succeed. To Brian, thanks for listening and answering my questions along the way. To Michelle and Ashley, thanks for all the laughs. Every day is truly an adventure. To all my family, friends, and colleagues, thank you for always being there and offering your support. iii ACKNOWLEDGMENTS To my committee, Dr. Lacefield, Dr. Randolph, and Dr. Hall, thank you for your patience, kindness, and encouragement throughout this entire process. Your feedback and support were invaluable, and I couldn’t have accomplished this task without you. Thank you for believing in me. To my editor, Elizabeth, I cannot thank you enough for all of your help along the way. Your prompt responses allowed me to move forward with my work without hesitation. I couldn’t have done it without you! To my research participants, thank you so much for inviting me into your classrooms. Without you, this study would not have been possible. Your love for teaching inspired me, and I enjoyed learning from each of you. iv TABLE OF CONTENTS Page DEDICATION ................................................................................................................... iii ACKNOWLEDGMENTS ................................................................................................. iv LIST OF TABLES ...............................................................................................................x LIST OF FIGURES ........................................................................................................... xi ABSTRACT ..................................................................................................................... xiii CHAPTER 1. INTRODUCTION TO THE STUDY ............................................................... 1 Common Core State Standards Initiative ...........................................................5 Conceptual Framework ......................................................................................9 Theoretical Framework ....................................................................................11 Statement of the Problem .................................................................................13 Purpose of the Study ........................................................................................14 Research Questions ..........................................................................................15 Limitations .......................................................................................................16 Assumptions .....................................................................................................17 Definitions of Key Terms ................................................................................18 Summary ..........................................................................................................20 2. REVIEW OF THE LITERATURE ................................................................ 22 Theoretical Framework: Constructivism ........................................................ 23 Historical and Philosophical Underpinnings of Constructivism ..........28 Three Types of Knowledge ..................................................................31 Social Constructivism ..........................................................................34 Number Sense ..................................................................................................35 Developing Number Sense Understanding ..........................................38 Mental Computation ............................................................................42 Computational Fluency ........................................................................43 Mental and Flexible Strategies .............................................................44 v TABLE OF CONTENTS (Continued) CHAPTER Page Mathematical Discourse...................................................................................48 Classroom Culture and Social Relationships .......................................50 The Teacher’s Role ..............................................................................54 Mathematical Language ...........................................................55 Questioning ..............................................................................56 Autonomous Learners ..............................................................57 Tasks, Knowledge, and Management ......................................58 Meta-Analysis of Mathematical Discourse ..........................................60 Empirical Literature Search Strategy ...............................................................61 Classroom Number Talks: Empirical Research ...............................................62 Overview of Empirical Research .....................................................................78 Summary ..........................................................................................................79 3. RESEARCH DESIGN AND METHODOLOGY .......................................... 80 Problem and Purpose Statement ......................................................................80 Research Questions Reiterated ........................................................................81 Research Design and Rationale .......................................................................82 Participants, Setting, and Sample Strategy ......................................................83 Data Collection and Instrumentation ...............................................................86 Semistructured Interviews and Classroom Observations ....................87 Artifacts................................................................................................88 Data Analysis ...................................................................................................88 Role of the Researcher .....................................................................................90 Dependability and Credibility ..........................................................................91 Ethical Safeguards ...........................................................................................94 Summary ..........................................................................................................95 4. FINDINGS .......................................................................................................96 Purpose Statement and Research Questions Reviewed ...................................96 Participant Overview .......................................................................................97 Mrs. Miller ...........................................................................................98 Mrs. Addison........................................................................................99 Mrs. Knight ..........................................................................................99 Interview and Observation Protocol ................................................................99 Participant Experiences and Perspectives in Mathematics ............................100 Organization of Data Analysis .......................................................................102 Trustworthiness of Results .............................................................................103 Within-Case Analysis ....................................................................................104 Role of Number Talks in Developing Number Sense ......................105 vi TABLE OF