Makin' Math Move

MAKIN’ MATH MOVE: A FULL BODY INTERACTIVE LEARNING ENVIRONMENT FOR PRE-ALGEBRAIC PRACTICE By TIFFANIE R. SMITH A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2019 © 2019 Tiffanie R. Smith I dedicate this to my entire support system of family, friends and loved ones. Without you all, I would not and could not have made it through. This is also dedicated to all of the future Black STEM scholars. It is possible. We can do it. ACKNOWLEDGMENTS First, I would like to give all glory and honor to God, because without Him none of this would have been possible. Secondly, I’d like to thank Yolanda D. Smith and Ollie S. Williams, my mother and grandmother, for instilling perseverance within me and their tremendous amount of love and support. I’d also like to thank my sister, brother, family members, New Light Baptist Church family, and friends for their constant prayers and support along this journey. Thank you to my committee members and advisor for helping to shape and reshape my ideas along the way. Thank you to the North Carolina A&T State University for my undergraduate career, foundation, and inspiration to pursue my doctoral degree. I’d also like to thank the National Science Foundation Graduate Research and Ford Dissertation Fellowship Programs for funding my education. I would also like to thank Mr. Curtis Peterson and the Caring and Sharing Learning School, as well as the Hopewell City Public Schools. Last, but certainly not least, I would like to thank the second family I’ve gained by way of the Human Experience Research Lab and at the University of Florida. I appreciate all of the support, friendship, laughs and memories. 4 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................... 4 LIST OF TABLES ...................................... 9 LIST OF FIGURES ..................................... 11 LIST OF SYMBOLS ..................................... 13 ABSTRACT ......................................... 14 CHAPTER 1 INTRODUCTION ................................... 16 Background ...................................... 16 Motivation ....................................... 17 Research Goals, Research Questions and Thesis ................... 18 Overview of Approach ................................. 19 Contributions ..................................... 20 Organization of the Dissertation ............................ 20 2 LITERATURE REVIEW ................................ 22 Algebraic Misconceptions ............................... 22 Culturally Relevant Pedagogy ............................. 24 Culturally Relevant Pedagogy in Math Education ................ 25 Nine Interrelated Dimensions of African-American Culture ........... 28 Embodied Cognition .................................. 29 Gestures in Education .............................. 30 Gesture Based Educational Technologies .................... 31 Interface Design .................................... 33 Natural User Interface Design .......................... 33 Designing of gesture sets ........................ 36 Gesture classification and taxonomies .................. 37 Designing for Culture .............................. 37 Designing for Children .............................. 39 Digital Game Based Learning and Gamification .................... 42 Math DGBL ................................... 46 Gesture Based DGBL .............................. 48 What’s Missing: Significance of Current Research .................. 50 3 DESIGN AND DEVELOPMENT OF Makin’ MATH MOVE: A CULTURALLY RELEVANT FULL BODY INTERACTIVE LEARNING ENVIRONMENT FOR PRE-ALGERBRAIC PRACTICE ....................................... 51 5 Use of System and Rationale ............................. 51 Content ........................................ 55 Interface Design .................................... 57 System Architecture and Implementation ....................... 60 4 GESTURE ELICITATION ............................... 64 Purpose ........................................ 64 Participants ...................................... 64 Instruments and Measures ............................... 64 Materials ........................................ 64 Procedure ....................................... 65 Results ......................................... 65 Gesture Taxonomy ................................ 65 Agreement .................................... 68 User Defined Gesture Set ............................ 71 Survey Results .................................. 72 Discussion and Next Steps ............................... 72 Predictions vs. Actual Gestures ......................... 72 Limitations .................................... 74 Next Steps .................................... 74 Summary and Conclusion ............................... 74 5 INITIAL EVALUATION OF MAKIN’ MATH MOVE’S USABILITY ......... 76 Purpose ........................................ 76 Participants ...................................... 76 Materials and Setup .................................. 77 Measures ........................................ 77 Procedure ....................................... 77 Results ......................................... 78 Task Completion and Gestural Accuracy .................... 78 Usability ..................................... 80 Cultural Relevance ................................ 80 Additional Results from Survey, Interview and Observations .......... 81 Discussion and Next Steps ............................... 82 Gestural Accuracy and Task Completion .................... 82 Usability ..................................... 82 Cultural Relevance ................................ 83 Conclusion ....................................... 83 6 COMPLETE USABILITY STUDY .......................... 85 Purpose ........................................ 85 Participants ...................................... 85 Hypotheses ....................................... 85 Results ......................................... 86 6 Usability ..................................... 86 Task Completion and Gestural Accuracy .................... 86 Cultural Relevance ................................ 88 Additional Results from Survey, Interview and Observations .......... 89 Revisiting the Hypotheses ............................... 90 Summary, Discussion and Next Steps ......................... 90 Gestural Accuracy and Task Completion .................... 90 Usability ..................................... 92 Cultural Relevance ................................ 93 Conclusion ....................................... 93 7 EVALUATION OF MAKIN’ MATH MOVE FOR IMPACT ON MOTIVATION AND ACADEMIC ACHIEVEMENT ............................. 95 Purpose ........................................ 95 Participants ...................................... 95 Materials and Study Set Up .............................. 97 Measures ........................................ 98 Hypotheses ....................................... 100 Procedure ....................................... 100 Before the Study ................................. 100 Study Logistics .................................. 100 Pre-Test and Post Test ............................. 101 The Experiment ................................. 101 Results ......................................... 102 Raw Score .................................... 103 Weighted Score ................................. 107 Motivation Score-Overall ............................ 107 Motivation: Attention .............................. 107 Motivation: Relevance .............................. 108 Motivation: Confidence ............................. 109 Motivation: Satisfaction ............................. 109 Makin’ Math Move Performance Data ........................ 109 Observations and Post-Survey Responses ....................... 111 Discussion ....................................... 114 Summary ........................................ 116 8 SUMMARY AND FUTURE WORK .......................... 117 Summary and Research Questions ........................... 117 Contributions ..................................... 118 Discussion, Limitations and Future Work ....................... 118 Conclusion ....................................... 122 APPENDIX A TAXONOMIC BREAKDOWN BY INDIVIDUAL REFERENTS ............ 124 7 B CULTURAL RELEVANCE ............................... 127 B.1 Questionnaire for Stimuli Preference (Verve) .................. 127 B.2 Child Activity Questionnaire : Movement and Music Subscale ......... 128 C MATH BENCHMARK ................................. 129 C.1 Course Motivation Survey ............................ 132 D ADDITIONAL SIGNIFICANT FINDINGS FROM EVALUATION ........... 138 REFERENCE LIST ..................................... 141 BIOGRAPHICAL SKETCH ................................. 161 8 LIST OF TABLES Table page 2-1 Gesture Conditions ................................... 30 2-2 Embodied Mapping Metaphors ............................ 32 2-3 Section of Mapping between Cultural Dimensions and Design Components ..... 39 2-4 Educational Design Principles ............................. 44 2-5 Types of Motivation and Corresponding Theories ................... 45 3-1 2017 FSA Performance by Predominantly African American Schools in Gainesville . 55 3-2 Strands Tested on SOLs by Grade Level and Percentage ............... 56 3-3 Strands Tested on FSA by Grade Level and Percentage ............... 57 3-4 Standards highlighted in Makin’ Math Move ..................... 57 4-1 Taxonomy of Full Body Gestures

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