Mapping Time, Space and the Body: Indigenous Knowledge and Mathematical Thinking in Brazil (New Directions in Mathematics and Science Education, 29)

"Mapping Time, Space and the Body: Indigenous Knowledge and Mathematical Thinking in Brazil brings people, land and numbers together in the fight for justice. On this extraordinary voyage through ancestral territories in central and southern Brazil, the Xavante, Suyá, Kayabi, and other local nations use mapping as a tool to protect their human rights to lands and resources they have traditionally owned and acquired. Mathematics activities inside the classroom and in everyday life help explain how Indigenous Peoples understand the cosmos and protect the living beings that helped create it. The book is a welcome contribution to a growing literature on the mathematical and scientific thinking of Indigenous Peoples around the globe. It makes mathematics alive and culturally relevant for students of all national backgrounds worldwide. 'A brilliant marriage of ethnography and mathematics written with deep understanding and obvious affection for the peoples she observed.' -- James A. Wiley, Ph. D. Professor, University of California at San Francisco, USA. 'This original and beautifully illustrated book offers a vivid study of Indigenous Peoples in Brazil. The author develops theoretical approaches and research methodologies to understand the way cultural groups deal with their natural and social environments.' -- Ubiratan D'Ambrosio, Ph. D. Emeritus Professor, Universidade Estadual de Campinas, Brazil. 'Mapping Time, Space and the Body is destined to create new and enlightened research in Ethnomathematics. It is an essential read for all of us working with culture and social justice in the realm of mathematics.' -- Daniel Clark Orey, Ph. D. Professor, Universidade Federal de Ouro Preto, Minas Gerais, Brazil. Emeritus Professor, California State University, Sacramento, USA. Cover photo by Mariana K. Leal Ferreira, 1998: Romdó Suyá, ceremonial leader of the Suyá people in the Xingu Indigenous Park."-- TABLE OF CONTENTS 6 FOREWORD 8 NOTE 10 FOREWORD 12 NOTE 15 INTRODUCTION: Mathematics and the Dream We Share of Inner Peace and Solidarity 16 MAPPING SPACE: COLONIAL MAP-MAKING AND THE FICTION OF TERRA NULLIUS 19 The Color Red: Naming the Newfound Land “Brasil” 22 Mapping Time: Before and After the Arrival of the “White Man” 25 Mapping the Body: The Body is the Guardian of the Guarani self 30 INDIGENOUS PEOPLES: A GLOBAL PERSPECTIVE 32 Who are Indigenous Peoples? 34 The Movement for Indigenous Rights 35 HOW THIS BOOK IS ORGANIZED 40 Part I: The Xingu Indigenous Park in Central Brazil 41 Part II: The Land-Without-Evil in Southern Brazil 41 Part III: People and Numbers in Xavante Land, Central Brazil 42 ACKNOWLEDGMENTS 43 NOTES 43 PART I: THE XINGU INDIGENOUS PARK IN CENTRAL BRAZIL 44 CHAPTER 1: WHEN 1 + 1 ≠ 2: Making Mathematics in Central Brazil 45 A WORLD OF NUMBERS: THE KAYABI, JURUNA, AND SUYÁ OF THE XINGU INDIGENOUS PARK 47 CAXIRI : THE OBLIGATION TO GIVE, TO RECEIVE, AND TO RECIPROCATE 51 BANG-BANG: CAPITALISM, CALCULUS, AND CASTLES OF DREAMS 53 THE DIAUARUM INDIGENOUS SCHOOL: MATHEMATICS IN PRACTICE 56 GIFTS, CURVES AND MACAW FEATHERS 64 FINAL THOUGHTS: MAP-MAKING AS A TOOL FOR LIBERATION 66 NOTES 66 CHAPTER 2: SHAMANIC MAP-MAKING IN THE BRAZILIAN AMAZON: The Suyá People of the Xingu Indigenous Park 69 SHAMANIC MAP-MAKING 71 Shamanic Mapping and Land Jurisprudence Experienced 73 Human and Animal Hybrids in Amazonian Map-Making 75 The Suyá People of the Xingu Indigenous Park 75 Fact, Fiction, and the Language of Jurisprudence 76 Cosmic Voyagers 77 Twelve Underwater Creatures of the Suyá Cosmos 80 Shamanic Map-Making and the Symbolic Order 83 PART II: THE LAND-WITHOUT-EVIL IN SOUTHERN BRAZIL 89 CHAPTER 3: TUPI-GUARANI APOCALYPTIC VISIONS OF TIME AND THE BODY 90 MAPPING TIME, SPACE AND THE BODY 92 THE GUARANI POPULATION IN BRAZIL 98 THE TERRA INDÍGENA GUARANI DE ITAÓCA 100 THE SINGER, THE COOK, AND THE TIN CAN GATHERER 102 THE DOCTOR, THE INDIAN AND THE AMBULANCE DRIVER 107 TRAVELERS, MISSIONARIES AND WARRIORS 110 LAND, RECIPROCITY AND NHANDE REKÓ 114 FINAL REMARKS: TURNING THE FUTURE INTO THE PRESENT 117 NOTES 121 CHAPTER 4; MAP-MAKING IN SOUTHERN BRAZIL: Self-Determination and Indigenous Peoples’ Rights 124 Mathematics Is Important for the Autonomy of Indigenous Peoples 126 WHO ARE WE TODAY AND WHERE ARE WE LOCATED? SOURCES OF INFORMATION 143 Is There Only One Mathematics? Or Are There Different Mathematics? 151 Xavante Mathematics: “The Two of Us Together” 152 Palikur Mathematics: Geometry Is Everywhere 155 The Palikur Numerical System 157 Mathematics, Justice, and Respect for Human Rights 169 ACKNOWLEDGEMENTS FOR CHAPTER 4 172 NOTES 172 PART III: PEOPLE AND NUMBERS IN XAVANTE LAND, CENTRAL BRAZIL 174 CHAPTER 5: THE TWO OF US TOGETHER: Xavante Mathematics in Central Brazil Today 175 THE XAVANTE WARRIORS OF THE BRAZILIAN CERRADO 175 BACK TO THE RESERVA INDÍGENA KULUENE IN 1978 179 THE XAVANTE IN HISTORY: MAPPING TIME, SPACE, AND THE BODY 183 THE XAVANTE SOCIONUMERICAL SYSTEM 187 The Expropriation of the Xavante Socionumerical System 192 A Totality is the Sum of its Parts 192 Xavante Cyclical Laws of Numerical Succession 194 The Reciprocal System of Gift-Giving 198 Final remarks 199 NOTES 200 CHAPTER 6: THE COLOR RED: Mapping Flowers and Fruits in the Brazilian Savannah 201 The Principles and Language of Human Rights in Xavante Thought and Daily Life 211 EPILOGUE: THE RIGHT TO FREE, PRIOR, AND INFORMED CONSENT (FPIC) IN THE UN DRIP 220 NOTES 221 EPILOGUE: Successes of Indigenous Mathematics Education 223 MULTICULTURAL MATHEMATICS: CRITICAL THINKING AND REAL-LIFE SITUATIONS 229 NOTES 231 REFERENCES 232 ABOUT THE AUTHOR 242 "Mapping Time, Space and the Body: Indigenous Knowledge and Mathematical Thinking in Brazil brings people, land and numbers together in the fight for justice. On this extraordinary voyage through ancestral territories in central and southern Brazil, the Xavante, Suyá, Kayabi, and other local nations use mapping as a tool to protect their human rights to lands and resources they have traditionally owned and acquired. Mathematics activities inside the classroom and in everyday life help explain how Indigenous Peoples understand the cosmos and protect the living beings that helped create it. The book is a welcome contribution to a growing literature on the mathematical and scientific thinking of Indigenous Peoples around the globe. It makes mathematics alive and culturally relevant for students of all national backgrounds worldwide. 'A brilliant marriage of ethnography and mathematics written with deep understanding and obvious affection for the peoples she observed.' -- James A. Wiley, Ph. D. Professor, University of California at San Francisco, USA. 'This original and beautifully illustrated book offers a vivid study of Indigenous Peoples in Brazil. The author develops theoretical approaches and research methodologies to understand the way cultural groups deal with their natural and social environments.' -- Ubiratan D'Ambrosio, Ph. D. Emeritus Professor, Universidade Estadual de Campinas, Brazil. 'Mapping Time, Space and the Body is destined to create new and enlightened research in Ethnomathematics. It is an essential read for all of us working with culture and social justice in the realm of mathematics.' -- Daniel Clark Orey, Ph. D. Professor, Universidade Federal de Ouro Preto, Minas Gerais, Brazil. Emeritus Professor, California State University, Sacramento, USA. Cover photo by Mariana K. Leal Ferreira, 1998: Romdó Suyá, ceremonial leader of the Suyá people in the Xingu Indigenous Park."-- Provided by publisher Introduction Part I: the Xingu Indigenous Park in Central Brazil WHEN 1 + 1 ≠ 2: Making mathematics in Central Brazil Shamanic map-making in the Brazilian Amazon: The Suyá people of the Xingu Indegenous Park Part II: The land-without-evil in Southern Brazil Tupi-Guarani apocalyptic visions of time and the body Map-making in Southern Brazil: Self-determination and indigenous peoples' rights Part III: People and numbers in Xavante Land, Central Brazil The two of us together: Xavante mathematics in Central Brazil today The color red: Mapping flowers and fruits in the Brazilian Savannah Epilogue: Successes of indigenous mathematics education.