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Identifying, Measuring, and Defining Equitable Mathematics Instruction

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Identifying, Measuring, and Defining Equitable Mathematics Instruction Identifying, Measuring, and Defining Equitable Mathematics Instruction by Imani Dominique Goffney A dissertation submitted in partial fulfillment of the requirement for the degree of Doctor of Philosophy (Education) in The University of Michigan 2010 Doctoral Committee: Professor Deborah Loewenberg Ball, Chair Professor Hyman Bass Professor Percy Bates Associate Professor Robert B. Bain Assistant Professor Vilma Mesa © Imani Masters Goffney 2010 DEDICATION My princesses Bria and Naima Remember that with faith, hard work, and God you can do anything! ii ACKNOWLEDGEMENTS This dissertation would not have been written without the tremendous support, guidance, encouragement, and friendship I received from my family, ―family‖, friends, and colleagues. I would first like to thank my family. To Brian for being everything I needed (co- parent, spades partner, dishwasher, editor, supportive shoulder) to help me get through this process. This process tested the boundaries of his patience, but he stepped up, learning to do bath, homework, cook, comb hair, and edit chapters. Thanks for being willing to both wipe away my tears and tell me when it was time to get over it. We celebrate this milestone together. Thanks to my beautiful and wonderful daughters, Bria and Naima, who have brought me more joy than I can say. Thanks Bria for being such an awesome daughter and for all of your patience and support. I know this was hard on you at times, and you handled my being busy with grace and love and I really appreciate it. To my little Naima who always makes me smile and is a perfect example of joy, love, patience, and friendship. I have learned so much from you even in just three years and look forward to a lifetime of learning with you! To my mom and dad for setting such high expectations and for always supporting me. No matter what, you have stood by me and behind me—loving me, praying for me, and supporting me in every way possible. I iii was able to accomplish this milestone because of the firm foundation of faith and hard work that you gave me. Next I would like to thank my dissertation committee: Deborah Loewenberg Ball, Percy Bates, Hyman Bass, Bob Bain, and Vilma Mesa. This dissertation builds on all of their work and has been shaped by their ideas, questions, and suggestions. I thank Vilma for her careful editing of my work and for continuing to push me to consider the difference between ―good‖ teaching and my definition of ―equitable instruction.‖ I would like to thank Bob for his support throughout my doctoral program and for his probing questions of my ideas, encouraging me to take risks, and helping me envision the next steps for my work. Hy has been an invaluable resource to me throughout my studies of mathematics education. His contributions, while usually humorous, taught me a great deal about the discipline and of mathematics and about learning in general. His ideas have shaped my work from the very beginning and I have been truly blessed to work so closely with such a brilliant person. His curiosity, generosity, and humor continue to inspire me. I would like to thank Percy for being my constant champion and advocate. From the very early stages of my graduate career, he has provided a listening ear, wise advice, a shoulder to cry on, and a safe space to learn and to grow. His feedback helped to focus, refine, and shape my ideas. I hope to build on his valuable contributions to studying equity and education throughout my career. I would like to especially thank my advisor and dissertation chair, Deborah Ball. She took me from being a curious, unfocused graduate student to a disciplined scholar. She has provided incredible opportunities that have changed my life. From making a cake for my daughter‘s birthday iv to having me re-write my dissertation proposal until it was right, her constant encouragement and support re-define what it means to be a good mentor. She took my passion and shaped it into a research agenda. She believed in me and pushed me until I could see the path myself. For helping shape each element of this dissertation, for keeping me focused and heading in the right direction, and for her friendship, I am eternally grateful. During my time at Michigan, I have valuable learning opportunities working on various research projects and committees. My work builds on the work produced by members of the Learning Mathematics for Teaching Project. Namely, I would like to thank Mark Hoover Thames, Laurie Sleep, Sean Delaney, and Yaa Cole for helping shape my ideas and helping me see new relationships between mathematics and equity. My extended ―family‖ and friends have been a tremendous support to my family and I during my time in graduate school, in particular during my dissertation writing. I would like to thank my friend Sean for reminding me to believe in myself, my friend Laurie for taking my ideas and always making them sound so much better, my friends Breda and Terri for always lending a helping hand or a friendly ear. Thanks to Orrin Murray who repaired my computer, found my lost data, and stopped asking me what happened, because I never knew! To Kristine and Kara, who also repaired my computer countless times, brought hard drives back from the dead, found lost data, taught me to text track a clip, and did it all quickly and with a smile—you two are amazing! To Lawrence Clark and R. L‘Heureux Lewis for being willing to read my work at the drop of a hat and give me immediate feedback. Thanks to Petrenia Davis and Monica Sosa for v allowing Bria to have permanent space in your apartments. To the members of the Programs for Educational Opportunity Staff for welcoming my girls in the office at all times. To my other friends, who either kept our girls, laughed with us, prayed with us, cried with us or reminded us that life is not only about research: Brit and Dave Caine, Stephanie Carter, Brighid Dwyer, Maggie and Chris Gelwix, Dana Gosen, Mark and Aurora Kamimura, Vicki and Bryon Lawrence, Neali and Brandon Lucas, Meghan Shaughnessy, Chris and Kieva Shults, and Alison and Ben Superfine, thank you for blessing our lives with your friendship. vi TABLE OF CONTENTS Dedication ............................................................................................................. ii Acknowledgements .............................................................................................. iii List of Appendices ................................................................................................ vi Abstract.. .............................................................................................................. xi CHAPTER ONE: THE RESEARCH PROBLEM ...........................................1 Introduction ............................................................................................................1 Studying Equity and Mathematics Education ........................................................1 Why Study Teaching? ............................................................................................6 Defining Equity and Equitable Instruction .............................................................7 Theoretical Framework: Cultural Considerations of Mathematical Knowledge for Teaching .........................................................................................13 Dissertation Study ................................................................................................20 Study Design ........................................................................................................20 Research Questions and Hypotheses ....................................................................21 Data Sources .........................................................................................................21 Measures of Mathematical Knoweldge for Teaching (MKT), Mathematical Quality of Instruction (MQI) and Mathematical Quality and Equity (MQE) ......................................................................................22 Cross Case Analysis .............................................................................................25 Organization of the Dissertation ...........................................................................26 Conclusions and Contributions ............................................................................26 CHAPTER TWO: CONSTRUCTING AND VALIDATING THE LEARNING MATHEMATICS FOR TEACHING PROJECT MATHEMATICAL QUALITY AND EQUITY (MQE) VIDEO CODES ..................................................................................27 Introduction ..........................................................................................................27 Study Description .................................................................................................30 Learning Mathematics for Teaching Project: Paper and Pencil Measures ..........30 Learning Mathematics for Teaching Project: Mathematical Quality of Instruction Observational Instrument ..................................................31 Dissertation Study Design ....................................................................................33 Research Questions and Hypotheses ....................................................................34 Teacher Sample ....................................................................................................34 Data Collection .....................................................................................................35 Developing the Mathematicval Quality and Equity (MQE)
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