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Surviving Set Theory: a Pedagogical Game and Cooperative Learning Approach to Undergraduate Post-Tonal Music Theory

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Surviving Set Theory: a Pedagogical Game and Cooperative Learning Approach to Undergraduate Post-Tonal Music Theory Surviving Set Theory: A Pedagogical Game and Cooperative Learning Approach to Undergraduate Post-Tonal Music Theory DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Angela N. Ripley, M.M. Graduate Program in Music The Ohio State University 2015 Dissertation Committee: David Clampitt, Advisor Anna Gawboy Johanna Devaney Copyright by Angela N. Ripley 2015 Abstract Undergraduate music students often experience a high learning curve when they first encounter pitch-class set theory, an analytical system very different from those they have studied previously. Students sometimes find the abstractions of integer notation and the mathematical orientation of set theory foreign or even frightening (Kleppinger 2010), and the dissonance of the atonal repertoire studied often engenders their resistance (Root 2010). Pedagogical games can help mitigate student resistance and trepidation. Table games like Bingo (Gillespie 2000) and Poker (Gingerich 1991) have been adapted to suit college-level classes in music theory. Familiar television shows provide another source of pedagogical games; for example, Berry (2008; 2015) adapts the show Survivor to frame a unit on theory fundamentals. However, none of these pedagogical games engage pitch- class set theory during a multi-week unit of study. In my dissertation, I adapt the show Survivor to frame a four-week unit on pitch- class set theory (introducing topics ranging from pitch-class sets to twelve-tone rows) during a sophomore-level theory course. As on the show, students of different achievement levels work together in small groups, or “tribes,” to complete worksheets called “challenges”; however, in an important modification to the structure of the show, no students are voted out of their tribes. Challenges are graded individually, and these ii grades are averaged together to yield a score for each tribe. At the end of the unit, each member of the tribe that earned the highest cumulative average score on the challenges receives a modest gift card as a non-academic prize. While students’ grades are based solely on their own work, the game element promotes peer mentoring through cooperative learning (Johnson and Johnson 1999; Slavin 2012) and inspires constructive peer pressure that motivates all students to do their best. Aspects of the game designed to enhance student enjoyment and build tribe unity include tribe names, a customized logo, and an opening credits video. I present empirical results of implementing Set Theory Survivor in the classroom and discuss student responses to questionnaires exploring their attitudes toward post-tonal music, their self-perceived abilities to use set-theoretical analysis to study post-tonal music, and their views of Set Theory Survivor as a framework for studying pitch-class set theory. The self-reported ability of students to perform specific set-theoretical operations increased to a statistically significant extent during the unit, and the majority of students enjoyed the game-like format. By combining the peer support of cooperative learning with the motivational force of constructive competition and the fun of a pedagogical game, Set Theory Survivor provides an innovative approach to a subject that often sparks student resistance and presents a valuable tool with which to enhance the pedagogy of pitch-class set theory. iii To my students, the original Set Theory Survivors. iv Acknowledgments I would like to thank several people who have contributed significantly to the formation of my dissertation. First, I wish to thank my dissertation advisor, Dr. David Clampitt, for his wise counsel and prompt attention to my work throughout the writing process. I would like to thank Dr. Anna Gawboy and Dr. Johanna Devaney for serving on my dissertation committee and helping to shape my perspective on teaching. I am also grateful to Dr. Devaney for supporting my implementation of Set Theory Survivor in the classroom and to Nat Condit-Schultz for his assistance with the graphs in Chapter Five. I would like to thank my family and friends for their constant encouragement and support. And most of all, I thank God, without whose help this dissertation would not have been possible. v Vita 2009................................................................B.M. Church Music, Baylor University 2011................................................................M.M. Music Theory, Baylor University 2011................................................................Adjunct Instructor of Theory, Texas A&M University–Commerce 2012–2013......................................................University Fellow, Department of Music, The Ohio State University 2013–2015......................................................Graduate Teaching Associate, Department of Music, The Ohio State University 2015................................................................Lecturer, Department of Music, The Ohio State University Fields of Study Major Field: Music Music Theory vi Table of Contents Abstract ............................................................................................................................... ii Dedication .......................................................................................................................... iv Acknowledgments .............................................................................................................. v Vita ..................................................................................................................................... vi List of Tables ..................................................................................................................... ix List of Figures ..................................................................................................................... x Chapter 1: Introduction ....................................................................................................... 1 Chapter 2: Cooperation and Competition in the Classroom ............................................. 11 Chapter 3: Using Pedagogical Games to Facilitate Active Learning ............................... 35 Chapter 4: Methodology for Set Theory Survivor ............................................................ 60 Chapter 5: Results of Set Theory Survivor ....................................................................... 91 Chapter 6: Conclusion .................................................................................................... 118 Bibliography ................................................................................................................... 126 Appendix A: Challenges and Answer Keys ................................................................... 132 Appendix B: List of Set Classes ..................................................................................... 153 Appendix C: Selected Repertoire for In-Class Listening ............................................... 157 Appendix D: Pre-Test Questionnaire .............................................................................. 160 Appendix E: Post-Test Questionnaire ............................................................................. 164 vii Appendix F: IRB Approval Letter .................................................................................. 169 Appendix G: Online Informed Consent Form ................................................................ 171 viii List of Tables Table 4.1. Likert-type questions and motivations from pre-test and post-test questionnaires ................................................................................................................... 75 Table 4.2. Open-ended questions and motivations from pre-test and post-test questionnaires ................................................................................................................... 76 Table 4.3. Music played to celebrate leading tribes during Set Theory Survivor ............ 82 Table 4.4. Tasks for in-class challenges ........................................................................... 85 Table 5.1. Likert-type questions from pre-test questionnaire ........................................... 94 Table 5.2. Likert-type questions from post-test questionnaire ......................................... 97 Table 5.3. Tribe scores during Set Theory Survivor ....................................................... 104 Table 5.4. Cumulative tribe scores during Set Theory Survivor .................................... 104 ix List of Figures Figure 3.1. Sample card for theory bingo ......................................................................... 42 Figure 3.2. Survivor Math logo from Burks, p. 69 ........................................................... 53 Figure 4.1. Logo for Set Theory Survivor ........................................................................ 62 Figure 4.2. Sample scoreboard slide for Set Theory Survivor .......................................... 64 Figure 4.3. Challenge 3: Inversion and Prime Form ......................................................... 66 Figure 4.4. Treemail for Challenge 3 ................................................................................ 67 Figure 4.5. Repertoire list for three weeks prior to Set Theory Survivor ......................... 76 Figure 4.6. Final scoreboard for Set Theory Survivor ...................................................... 88 Figure 4.7. Questions
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