Mining and Crafting Mathematics: Designing a Model for Embedding Educational Tasks in Video Games DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Heather McCreery Kellert, M.A. Graduate Program in Education Teaching & Learning The Ohio State University 2018 Dissertation Committee: Dr. Patricia A. Brosnan, Advisor Dr. Theodore Chao Dr. Sarah Gallo Dr. Karen E. Irving Copyright by Heather McCreery Kellert 2018 Abstract The purpose of this study is to investigate the design and modification of a rich mathematical task embedded in an educational video game Minecraft through analysis of observations of student engagement in mathematical practices. Student engagement in both the game and the overarching task is framed using the application of Self-Determination Theory to video games (Przybylsky, Ryan & Rigby, 2010) while analysis of the researcher-teacher’s design, implementation, and modification is framed through an iterative design process. Results of this qualitative study include multiple modifications of the researcher-teacher in attempt to enhance engagement in the Standards of Mathematical Practice (Common Core Standards State Initiative, 2018). The design and modifications of the task were then fit into a model to depict the relationships between four categories of student engagement including (1) engagement with the game, (2) engagement with mathematics, (3) engagement possibly motivated by factors of Self-Determination Theory, and (4) the task’s ability to provide opportunities for students to engage in Standards for Mathematical Practice (Common Core State Standards Initiative, 2018). Key terms: educational video games, design cycle, design process, rich mathematics tasks, student engagement, mathematics task design i Acknowledgements First and foremost, I would like to thank my advisor, Dr. Patti Brosnan. You have been an inspiration from the time of our first meeting, and have spent countless hours with me through my doctoral journey. I am eternally grateful for my experiences in the Mathematics Coaching Program, which not only solidified my educational philosophies, but also evolved my own practices and goals for influencing how children might learn and love mathematics. You have truly been a wonderful thinking partner throughout my messy research processes, and my researcher and educator identities would not be what they are without your guidance. I am also emphatically grateful to Dr. Azita Manouchehri, who spent a myriad of her time providing me with thoughtful and critical feedback throughout my final writing process. It was in your final course that I reached many of my “a-ha” moments due to your careful questioning and thought-provoking challenges. I truly appreciate the time you spent with me reviewing my analysis, and instilling in me the passion you carry for mathematics education research. I would also like to thank my committee members Dr. Teddy Chao, Dr. Sarah Gallo, and Dr. Karen Irving. Your collective expertise has been overwhelmingly helpful throughout the refinement of my study from a “stadium of squirrels” to (just about) “one squirrel.” I am grateful for the time you set aside to meet with me to detail your insight throughout the multiple stages of my writing process and articulation of ideas, as well as the time and energy you invested in me in your classes and during conferences. Dr. Annalies Corbin and Dr. Sheli O. Smith: Words cannot describe how grateful I am for the opportunity to work and thrive within the PAST family, but I will try. Thank you for bringing ii me onto the team, listening to my ideas, and entertaining my well-intentioned mischief. The two of you exemplify strong, non-nonsense, female leaders who believe in what is right for children, and you know no boundaries. To the PAST Team (in alphabetical order): Alyssa, Andy, Ashley, Diana, Jim, Kat, Kayla, Lori, Maria, Monica, Pam, Ruth, and Sam. You saw and heard it all, uncut and unfiltered. Thank you for listening and supporting me through one of the most intellectually challenging times in my life. You are truly a thinking partner collective and I will forever be in your debt for the ongoing support you provided me during my face-to-face time with you. To James Ross and the fine folks at Nodecraft: Thank you for the generous scholarship you provided to the Minecraft Mathematics program. Your server helped immensely with classroom management and task delivery to students. The students were so excited to have their “own” server that they could enjoy together, and the ability to backup our worlds was invaluable! Finally, I would like to thank my life partner and love Brian: You and our sweet daughter Finley Brooke are my light and inspiration for life-long learning. I would not be where I am without you and your support along every step of the way. We are the captains of our ship, and I am looking forward to many more voyages to come, including our second daughter on the way! iii Vita August 2005 ………………………………………………….……….B.A. Mathematics, University of Washington Seattle, Washington Winter 2008 - Summer 2008 ………………………………….Teacher of Mathematics, Nathan Hale High School, Seattle, Washington June 2008 ……………………………………………….……………..M.A. Education, University of Washington Seattle, Washington Autumn 2008 - Summer 2011 …………………………..……Teacher of Mathematics, Garfield High School, Seattle, Washington June 2010 – Winter 2012……………………………….…….…Textbook Co-Author and Production Coordinator, Kinetic Books Company, Inc. January 2013 – August 2014……………………………………Academic Advisor, Department of Mathematics, The Ohio State University August 2014 – May 2015………………………………………..Graduate Research Associate, The Ohio State University August 2014 – May 2015………………………………………..Mathematics Tutor Supervisor, The Ohio State University May 2015 – Present….………………………………………..….STEM Innovator and Hybrid Teacher, PAST Foundation, Columbus, Ohio Fields of Study Major Field: Education: Teaching & Learning iv Table of Contents Abstract ........................................................................................................................................... i Acknowledgements ........................................................................................................................ ii Vita ................................................................................................................................................ iv Table of Contents ........................................................................................................................... v Table of Tables ............................................................................................................................ viii Table of Figures .............................................................................................................................. x Chapter 1: Introduction .................................................................................................................. 1 Minecraft as an Educational Video Game .................................................................................. 3 Background of Minecraft Mathematics Workshop .................................................................... 7 Research Questions .................................................................................................................... 8 Definition of Terms ..................................................................................................................... 9 Chapter 2: Literature Review ........................................................................................................ 11 Research on Educational Video Games .................................................................................... 11 Research on Engagement with Video Games ........................................................................... 21 Research on Engagement with Mathematical Practices .......................................................... 31 Research on Design Cycles ....................................................................................................... 37 Theoretical Framework ............................................................................................................ 40 Chapter 3: Methodology .............................................................................................................. 51 Characteristics of Minecraft Mathematics Workshop Setting ................................................. 52 Procedure and Timeline of Study ............................................................................................. 59 The Task .................................................................................................................................... 61 v Participants ............................................................................................................................... 64 Instrumentation ....................................................................................................................... 65 Analysis ..................................................................................................................................... 74 Researcher-Teacher Beliefs and Biases .................................................................................... 80 Credibility ................................................................................................................................