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KINESTHETIC MATHEMATICS: MEANINGFUL APPLICATIONS IN THE CLASSROOM MEGAN JOHNSTON A THESIS SUBMITTED TO THE FACULTY OF GRADUATE STUDIES IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS GRADUATE PROGRAMME IN INTERDISCIPLINARY STUDIES YORK UNIVERSITY TORONTO, ONTARIO OCTOBER 2010 Library and Archives Bibliotheque et 1*1 Canada Archives Canada Published Heritage Direction du Branch Patrimoine de I'edition 395 Wellington Street 395, rue Wellington OttawaONK1A0N4 OttawaONK1A0N4 Canada Canada Your file Votre rGterence ISBN: 978-0-494-80625-8 Our file Notre reference ISBN: 978-0-494-80625-8 NOTICE: AVIS: The author has granted a non L'auteur a accorde une licence non exclusive exclusive license allowing Library and permettant a la Bibliotheque et Archives Archives Canada to reproduce, Canada de reproduire, publier, archiver, publish, archive, preserve, conserve, sauvegarder, conserver, transmettre au public communicate to the public by par telecommunication ou par I'lnternet, preter, telecommunication or on the Internet, distribuer et vendre des theses partout dans le loan, distribute and sell theses monde, a des fins commerciales ou autres, sur worldwide, for commercial or non support microforme, papier, electronique et/ou commercial purposes, in microform, autres formats. paper, electronic and/or any other formats. The author retains copyright L'auteur conserve la propriete du droit d'auteur ownership and moral rights in this et des droits moraux qui protege cette these. Ni thesis. Neither the thesis nor la these ni des extraits substantiels de celle-ci substantial extracts from it may be ne doivent etre imprimes ou autrement printed or otherwise reproduced reproduits sans son autorisation. without the author's permission. In compliance with the Canadian Conformement a la loi canadienne sur la Privacy Act some supporting forms protection de la vie privee, quelques may have been removed from this formulaires secondaires ont ete enleves de thesis. cette these. While these forms may be included Bien que ces formulaires aient inclus dans in the document page count, their la pagination, il n'y aura aucun contenu removal does not represent any loss manquant. of content from the thesis. 1*1 Canada IV Abstract Kinesthetic mathematics: Meaningful applications in the elementary classroom examines kinesthetic ways to enhance the elementary Ontario Mathematics Curriculum through the use of the Ontario Drama and Dance Curriculum. I accomplish this within the context of a case study in a primary classroom in a public school in the Greater Toronto Area. I designed creative movement/creative dance activities to create ways to enhance the Ontario Mathematics Curriculum and then collected evidence that supports the effectiveness of those ideas. It is my aim to make my research available for use by all teachers, regardless of their creative movement and/or creative dance training. V Acknowledgments "Be the change you wish to see in the world." Mahatma Gandhi With all my heart, I give thanks to the following: • The Great Spirit, my center, strength and inspiration on this journey. • Mary-Elizabeth Manley, Margaret Sinclair and Walter Whiteley, my guides through this learning process. Your investment, guidance and kindness will always be remembered. • Ms. T. for offering your perspective and your class for this study. • The students, for participating in this study. • All my teachers, past and present, I have learned so much from you. • Kathleen McCann Johnston and Edward Johnston, my parents and great examples on this journey. Thank you for your love and support through this process. • Jake, Molly, Jesse, Rose, Claire and Elizabeth, my siblings. I am very fortunate to have you in my life. Thank you for your love and support. • Francis Douthwright, my husband. Your love, support and encouragement has helped me more than words can express. Thank you. • This work is dedicated to the memory of my mother in law, Anna Douthwright. The torch still burns and is carried on. vi Table of Contents Abstract iv Acknowledgments v Table of Figures x Chapter One: Introduction 1 Rationale 1 Study Questions 2 Chapter Two: Literature Review 4 Teaching Mathematics through a Kinesthetic Approach 4 Family Math for Young Children 4 Math in Motion 5 Methods of Teaching Dance 6 Creative Dance Classes 9 Dance in the Schools 10 Laban's Movement Theories 12 The Ontario Kindergarten Program 16 Kindergarten Mathematics 17 Kindergarten Dance 18 Teaching Movement in Alternative Schools 18 Montessori Education 19 vii Waldorf Education 20 Arrowsmith School 22 Roger Williams Middle School 22 Linwood A+ Elementary School 24 Whittier Community School for the Arts 24 Learning Theories 25 Piaget's Cognitive-Developmental Theory 25 Multiple Intelligences 27 Brain Plasticity 28 Chapter Three: Methodology and Methods 31 Aboriginal Research Methodology 31 Case Study 32 Study Overview 33 Participant Observation 35 Participants 36 Setting 38 Scheduling 38 Materials 39 Curriculum 41 Data Collection 43 Photographs 44 viii Student Journals 44 Data Analysis 44 Ethics 45 Chapter Four: The Study 46 Lesson One 46 Lesson Two 50 Lesson Three 54 Lesson Four 61 Lesson Five 66 Lesson Six 71 Lesson Seven 75 Chapter Five: Emergent Themes 81 A Special Case 81 Creativity 84 Diverse Representations 88 Emerging Competence 92 Chapter Six: Answers to Questions and Conclusions 102 First Question 102 Second Question 107 Third Question Ill Fourth Question 113 ix References 125 Appendix A: Lesson Plans 1-7 129 Appendix B: Checklists 148 Appendix C: Post Survey for Students 150 X Table of Figures Figure 1 14 Figure 2 48 Figure 3 49 Figure 4 52 Figure 5 53 Figure 6 54 Figure 7 57 Figure 8 58 Figure 9 60 Figure 10 60 Figure 11 61 Figure 12 62 Figure 13 65 Figure 14 65 Figure 15 66 Figure 16 68 Figure 17 70 Figure 18 71 Figure 19 76 Figure 20 77 xi Figure 21 78 Figure 22 79 Figure 23 79 Figure 24 82 Figure 25 82 Figure 26 83 Figure 27 83 Figure 28 85 Figure 29 89 Figure 30 90 Figure 31 91 Figure 32 91 Figure 33 92 Figure 34 94 Figure 35 109 Figure 36 110 Figure 37 110 1 Chapter One: Introduction My connections to dancing and teaching have always been important to me. My secondary education led me to study for a BFA in contemporary dance at Concordia University in Montreal, Quebec, followed by a BEd at York University in Toronto, Ontario. The seed of integrating the arts into traditional curriculum subjects was planted by my BEd Course Director, Kathy Gould Lundy. I explored dance integration in my practicum placements as well as in my first two years of teaching in the Toronto District School Board. As a teacher in the public system it became impossible to ignore the persistent feeling within—a feeling that the way the curriculum is taught by teachers and learned by students was not reaching its fullest potential. I surmised that by integrating movement into the traditional curriculum subjects, student learning would improve. At this time, I decided to write a proposal to York University's Interdisciplinary Department in Graduate Studies. I wanted to further explore the linking of kinesthetic learning with the core curriculum. I hoped to do this by bringing together the disciplines of education, dance, and mathematics. Rationale It was my intention to create ways to enhance the Ontario Mathematics Curriculum and collect evidence to see if my ideas would work. It was also my intention to make my research applicable for use by all teachers regardless of their creative movement/creative dance training. The purpose of my research was to investigate how to increase integration of kinesthetic activities in the mathematics curriculum. The case study was done in the context of a case study in a Junior Kindergarten/Kindergarten 2 classroom. This research is relevant and valuable to education because it focuses on movement, the first modality that young children use to communicate feelings about themselves, the environment, and other people. I was investigating the impact of activities that may help diverse learners within the classroom. This research was also an attempt to develop students' potential for creative communication. It was my hope that the students in the study would benefit from learning mathematics with movement and that my research would help teachers understand what kinds of activities are interesting to students and what activities help students learn best. Study Questions The following are the four study questions that I posed for this study: 1. Are the students engaged in the learning of mathematics when it is learned through creative movement/creative dance? • I hypothesized that students would become more engaged in the learning of mathematics, especially when learning with their bodies (part or whole). 2. How might student attitudes and feelings towards mathematics change when learned through creative movement/creative dance activities? • I hypothesized that student attitudes and feelings would be positively affected when creative movement/creative dance activities were integrated into learning mathematics. Attitudes and feelings towards mathematics would be shown by increased enjoyment of learning mathematics. 3. Will students' self confidence in mathematics class be improved when it is learned through creative movement/creative dance? 3 • I hypothesized that students would feel more confident about themselves during math class. I also hypothesized that the self-confidence developed in math class would filter into other curriculum subjects and interactions with others. 4. What sequence of activities supports students'learning? • I hypothesized that the way I sequenced the lessons would support the students' learning of the material presented. By answering these questions, it is anticipated that the research which focuses on creating and teaching meaningful learning experiences for students will be furthered. 4 Chapter Two: Literature Review In this chapter, I will discuss the literature around the themes of teaching mathematics via a kinesthetic approach, methods of teaching dance, the Ontario Kindergarten Program, alternative schools and their approaches to teaching mathematics and dance, and learning theories.