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TEACHERS’ USE OF INSTRUCTIONAL MOVES DURING TECHNOLOGY-BASED MATHEMATICAL ACTIVITIES by Susan B. Miller B.S. Chemical Engineering, Bucknell University, 1989 M.B.A., University of Denver, 2000 A dissertation submitted to the Faculty of the Graduate School of the University of Colorado in partial fulfillment of the requirement for the degree of Doctor of Philosophy School of Education 2017 This dissertation entitled: Teachers’ Use of Instructional Moves During Technology-Based Mathematical Activities written by Susan B. Miller has been approved for the School of Education __________________________________ David C. Webb __________________________________ Daniel Liston __________________________________ Joseph Polman __________________________________ Edd V. Taylor __________________________________ Ben Shapiro Date_______________ The final copy of this thesis has been examined by the signatories, and we find that both the content and the form meet acceptable presentation standards of scholarly work in the above mentioned discipline. IRB protocol # 13-0182 ii Miller, Susan B. (Ph.D., Curriculum and Instruction [Mathematics], School of Education) Teachers’ Use of Instructional Moves During Technology-Based Mathematical Activities Dissertation directed by Associate Professor David C. Webb ABSTRACT This study investigates instructional moves by teachers in mathematics classrooms in which technology-based activities (i.e., student-oriented simulations) and features of those simulations influence classroom practices. Four teachers were studied over the course of a year as an exploratory study to build interpretive cases that described instructional practices in technology- based lessons. Teachers developed lessons using PhET simulations designed to support algebraic reasoning. Data sources included teachers’ process of selecting and designing lessons, observations of teachers’ non-technology and technology-based mathematical activities, and teacher interviews and reflections. This work was based on a conceptual framework blending the ideas of Mathematical Tasks (Stein, Smith, Henningsen, & Silver, 1998), Mathematical Pedagogical Content Knowledge (Ball, Thames, & Phelps, 2008), and Technological Pedagogical Content Knowledge (Mishra & Koehler, 2006), in which teachers’ instructional practices are determined by teachers’ mathematical pedagogical content knowledge, task selection and design, and use of technology. Results indicated that teachers see simulations as having significant benefits in the classroom. Teachers leveraged these opportunities by increasing class discussions, engaging in higher levels of thinking and reasoning, and focusing on mathematical representations. When teachers used simulations, the teachers spent less time in direct instruction, focused more on the mathematics, and focused more on investigations rather than drill-oriented tasks. iii Technology in the classroom, however, was problematic for some teachers. The very nature of students working independently with their own devices meant that student-student interactions decreased in some lessons. Furthermore, teachers’ discomfort in managing technology seems to limit ongoing use. Specific features of the simulations that prompted instructional moves included the ability to support conceptual understanding and build student engagement. Simulations also provided a ‘low floor, high ceiling,’ supporting differentiation, and a dynamic responsiveness, facilitating connections between representations. On the other hand, teachers raised concerns that some features of the simulation could do the math for the students. Furthermore, the perception of simulations as being a game may impact how and when simulations are used. The emergent use of technology in math classrooms is under-supported. For simulations to be used in a more extensive fashion in mathematics classes, professional development and curricular materials are needed to support implementation. iv ACKNOWLEDGEMENTS There are many people to thank, who supported me in this journey from math teacher to math researcher. First, I offer my love and gratitude to my husband, Eric. You are my cheerleader, my biggest supporter, and the love of my life! Your patience in taking care of the house, kids, and more dinners than I can count, so that I could pursue my passion is a debt I can never repay. I promise this is my last degree. To my children, Amanda, Katherine, Daniel and Alexander. You’ve watched your mom read, study, and write papers at all hours of the day and night. You cheered me on, and nagged me to keep going when I needed it. You read my papers, corrected my grammar, and pushed me to be excellent. I hope I’ve made you half as proud of me as I am of all of you! To my parents, Bob and Pat Miller, I offer my gratitude, love and admiration. You read all my papers, shared the latest educational news, discussed all my ideas, and always told me I could do anything I wanted to do! You were my inspiration! To my brother, Rob Miller – you told me over and over again that I could do this. Your support meant the world to me. And to my sister, Laura Miller Cozean, you cheered me on, celebrated every small victory, and most importantly, read and proofed every single word of this dissertation. Thank you for all your love and support! To my former students and their families who regularly checked in with me to see if I was “done yet” and to cheer me on. You sent me cards, emails and texts to keep me going. You were the original inspiration for me to pursue this degree, and I’m so very grateful for all your support. To my committee, who supported me throughout this process, and throughout my years at the University of Colorado – Boulder; Dan Liston, who challenged me to think critically about teacher education, while reminding me that there was a place for spirituality in the classroom; Joe v Polman, who introduced me to the work of Larry Cuban, and whose research inspired me to think critically about the use of technology in new ways; Edd Taylor, who helped me consider the impact of instructional practices on student learning, and pushed me to think about rigor in my research; and Ben Shapiro, who shared key research that significantly influenced my final research direction. I owe you all a huge debt of gratitude. To my advisor, David Webb. You’ve been instrumental in my growth from a teacher, to a teacher educator, to a mathematics researcher. You taught me to be a critical reader of research, and bring that critical thought into my own research. You taught me how to step back and see education from a much broader perspective than I ever realized possible. You read draft after draft of this study, never showing even an ounce of impatience. You are my teacher, my mentor, my advisor, and my friend. Words just simply can’t describe my appreciation for you. Finally, to the four teachers who opened their classrooms and shared all that they are as teachers – I could not have done this study without you. You are all wonderful, inspiring teachers who love their students and work tirelessly to ensure that you are doing the very best job you can. Thank you for the gift of your time and friendship. vi TABLE OF CONTENTS 1 CHAPTER 1: THE RESEARCH PROBLEM .................................................................. 1 1.1 TECHNOLOGY IN THE CLASSROOM ...................................................................... 2 1.2 MATH SIMULATIONS ................................................................................................. 6 1.3 PURPOSE OF THE STUDY .......................................................................................... 7 1.4 RESEARCH QUESTIONS ............................................................................................ 8 1.5 SIGNIFICANCE OF THE STUDY................................................................................ 8 2 CHAPTER 2: CONCEPTUAL FRAMEWORK ............................................................... 9 2.1 MATHEMATICAL PEDAGOGICAL AND CONTENT KNOWLEDGE ................... 9 2.2 MATHEMATICAL TASKS ........................................................................................ 10 2.3 TECHNOLOGICAL PEDAGOGICAL CONTENT KNOWLEDGE ......................... 13 2.4 CONCEPTUAL MODEL ............................................................................................. 16 3 CHAPTER 3: LITERATURE REVIEW ......................................................................... 17 3.1 MATHEMATICAL TASKS IN MATHEMATICAL CLASSROOMS ...................... 17 3.1.1 Group-Worthy Tasks ................................................................................................ 21 3.1.2 Rich Discussion of Mathematical Tasks ................................................................... 24 3.1.3 Other instructional practices ..................................................................................... 27 3.1.4 Summary ................................................................................................................... 29 3.2 TECHNOLOGY ........................................................................................................... 29 3.2.1 Benefits of use........................................................................................................... 30 3.2.2 Barriers to use ........................................................................................................... 30 3.2.3 Location of the technology ......................................................................................
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