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Replacing the "Raise Your Hand to Speak" Rule with New Social and Sociomathematical Norms in an Elementary Mathematics Classroom

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Replacing the University of Central Florida STARS Electronic Theses and Dissertations, 2004-2019 2014 Replacing the "Raise Your Hand to Speak" Rule with New Social and Sociomathematical Norms in an Elementary Mathematics Classroom Lisa Brooks University of Central Florida Part of the Education Commons Find similar works at: https://stars.library.ucf.edu/etd University of Central Florida Libraries http://library.ucf.edu This Doctoral Dissertation (Open Access) is brought to you for free and open access by STARS. It has been accepted for inclusion in Electronic Theses and Dissertations, 2004-2019 by an authorized administrator of STARS. For more information, please contact [email protected]. STARS Citation Brooks, Lisa, "Replacing the "Raise Your Hand to Speak" Rule with New Social and Sociomathematical Norms in an Elementary Mathematics Classroom" (2014). Electronic Theses and Dissertations, 2004-2019. 4720. https://stars.library.ucf.edu/etd/4720 REPLACING THE “RAISE YOUR HAND TO SPEAK” RULE WITH NEW SOCIAL AND SOCIOMATHEMATICAL NORMS IN AN ELEMENTARY MATHEMATICS CLASSROOM by LISA A. BROOKS B.S. University of Central Florida, 1992 M.Ed. University of Central Florida, 2006 A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Education in the School of Teaching, Learning, and Leadership in the College of Education and Human Performance at the University of Central Florida Orlando, Florida Summer Term 2014 Major Professor: Juli K. Dixon © 2014 Lisa A Brooks ii ABSTRACT This qualitative study documents the establishment of new social and sociomathematical norms in a second grade classroom. The teacher allowed students to speak directly to one another without having to raise their hands first during whole group mathematics instruction. Reform efforts in mathematics and the standards for mathematical practice contained in the Common Core State Standards call for students to discuss their reasoning with each other. Data were collected through interviews with the teacher and students, field notes, and video-recorded lessons over the course of 23 days. An online survey tool was utilized to share selected video of the teacher’s instruction. Initial professional development topics were chosen from research in mathematics education related to the social construction of understanding. Ongoing professional development was responsive to what occurred during instruction. The literature suggests that teachers often utilize traditional teaching methods and struggle to deviate from established patterns regardless of their desire to implement change. The teacher in this study learned that allowing students to talk openly provided him with insight into their mathematical conceptions and misconceptions. The students initially viewed mathematics as a set of rules to follow and exhibited the role of passive recipients of information. This changed as students were provided opportunities to participate in discussions and in doing so developed a new understanding of their role during mathematics lessons. Mathematical errors became a catalyst for communication and were viewed by students as opportunities for assisting their peers. iii This is dedicated to my mom and dad. Thank you for always believing in me. I did it! iv ACKNOWLEDGMENTS I would like to thank the teacher I worked with on my research. I appreciate him opening his classroom to me. The students in the class were a joy to work with. I am so thankful for the endless support of the people who surround me. My colleagues at UCF have encouraged and inspired me throughout my career. I would like to thank my dissertation chair, Dr. Juli K. Dixon, for being an amazing mentor. Her support throughout this process has meant the world to me. I appreciate her dedication and ability to always know what I needed to stay motivated. I consider myself fortunate to have had the opportunity to work with my committee: Dr. Janet Andreasen, for her thoughtful attention to detail and personal support; Dr. David Boote, for sharing his expertise throughout my program and for his insightful perspective; and Dr. Enrique Ortiz, for his thought provoking questions which helped me gain a deeper understanding of the topics I studied. I would also like to thank Dr. Michael Hynes, for always providing meaningful advice and support. My family and friends have listened tirelessly, cheered me on, and kept me moving forward. I would like to thank my brothers, sisters, and my in-laws for all their encouragement. I am so thankful for my children for being incredibly patient and supportive throughout the years. Finally, I have a special thank you for my wonderful husband, John for everything he has done to support me. I am blessed beyond measure to have had his support and love throughout this journey. v TABLE OF CONTENTS LIST OF FIGURES ....................................................................................................................................................... x LIST OF TABLES........................................................................................................................................................xi CHAPTER ONE: INTRODUCTION ............................................................................................................................ 1 CHAPTER TWO: LITERATURE REVIEW ................................................................................................................ 6 Introduction ................................................................................................................................................................................................. 6 The Current Paradigm ............................................................................................................................................................................. 8 Classroom Discourse .............................................................................................................................................................................. 10 IRE and IDE Discourse Patterns .................................................................................................................................................. 12 Reform in Elementary Mathematics ............................................................................................................................................... 15 The Learning Environment ........................................................................................................................................................... 16 The Role of the Teacher .................................................................................................................................................................. 18 The Role of the Students................................................................................................................................................................. 18 Social Norms .............................................................................................................................................................................................. 19 Sociomathematical Norms .................................................................................................................................................................. 19 Teacher Practice ...................................................................................................................................................................................... 24 Task Selection ..................................................................................................................................................................................... 26 The Need for Increased Discourse ................................................................................................................................................... 27 Standards for Mathematical Practice ....................................................................................................................................... 27 Sociolinguistics ................................................................................................................................................................................... 28 Summary ..................................................................................................................................................................................................... 32 CHAPTER THREE: METHODOLOGY .................................................................................................................... 34 Introduction ............................................................................................................................................................................................... 34 vi Research Design ....................................................................................................................................................................................... 35 Setting ........................................................................................................................................................................................................... 37 School and Class Demographics .................................................................................................................................................. 37 Consent Process ......................................................................................................................................................................................
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