Mathematics Elsewhere is a fascinating and important contribution to a global view of mathematics. Presenting mathematical ideas of peoples from a variety of small-scale and traditional cultures, it humanizes our view of mathematics and expands our conception of what is mathematical. Through engaging examples of how particular societies structure time, reach decisions about the future, make models and maps, systematize relationships, and create intriguing figures, Marcia Ascher demonstrates that traditional cultures have mathematical ideas that are far more substantial and sophisticated than is generally acknowledged. Malagasy divination rituals, for example, rely on complex algebraic algorithms. And some cultures use calendars far more abstract and elegant than our own. Ascher also shows that certain concepts assumed to be universal--that time is a single progression, for instance, or that equality is a static relationship--are not. The Basque notion of equivalence, for example, is a dynamic and temporal one not adequately captured by the familiar equal sign. Other ideas taken to be the exclusive province of professionally trained Western mathematicians are, in fact, shared by people in many societies. The ideas discussed come from geographically varied cultures, including the Borana and Malagasy of Africa, the Tongans and Marshall Islanders of Oceania, the Tamil of South India, the Basques of Western Europe, and the Balinese and Kodi of Indonesia. This book belongs on the shelves of mathematicians, math students, and math educators, and in the hands of anyone interested in traditional societies or how people think. Illustrating how mathematical ideas play a vital role in diverse human endeavors from navigation to social interaction to religion, it offers--through the vehicle of mathematics--unique cultural encounters to any reader.
In this truly one-of-a-kind book, Ascher introduces the mathematical ideas of people in traditional, or "small-scale", cultures often omitted from discussion of mathematics. Topics such as "Numbers: Words and Symbols", "Tracing Graphs in the Sand", "The Logic of Kin Relations", "Chance and Strategy in Games and Puzzles", and "The Organization and Modeling of Space" are traced in various cultures including the Inuit, Navajo, and Iroquois of North America; the Inca of South America; the Malekula, Warlpiri, Maori, and Caroline Islanders of Oceania, and the Tshokwe, Bushoong, and Kpelle of Africa. As Ascher explores mathematical ideas involving numbers, logic, spatial configuration, and the organization of these into systems and structures, readers gain both a broader understanding and anappreciation for the idease of other peoples.
This fascinating study of mathematical thinking among sub-Saharan African peoples covers counting in words and in gestures; measuring time, distance, weight, and other quantities; manipulating money and keeping accounts; number systems; patterns in music, poetry, art, and architecture; and number magic and taboos. African games such as mankala and elaborate versions of tic-tac-toe show how complex this thinking can be. An invaluable resource for students, teachers, and others interested in African cultures and multiculturalism, this third edition is updated with an introduction covering two decades of new research in the ethnomathematics of Africa.
Indigenous Knowledge and Mathematical Thinking in Brazil
Author: Mariana Kawall Leal Ferreira
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
In this book, Ubiratan D'Ambrosio presents his most recent thoughts on ethnomathematics - a sub-field of mathematics history and mathematics education for which he is widely recognized to be one of the founding fathers. In a clear, concise format, he outlines the aim of the Program Ethnomathematics, which is to understand mathematical knowing/doing throughout history, within the context of different groups, communities, peoples and nations, focusing on the cycle of mathematical knowledge: its generation, its intellectual and social organization, and its diffusion. While not rejecting the importance of modern academic mathematics, it is viewed as but one among many existing ethnomathematics. Offering concrete examples and ideas for mathematics teachers and researchers, D'Ambrosio makes an eloquent appeal for an entirely new approach to conceptualizing mathematics knowledge and education that embraces diversity and addresses the urgent need to provide youth with the necessary tools to become ethical, creative, critical individuals prepared to participate in the emerging planetary society.
Bill Atweh,Angela Calabrese Barton,Marcelo C. Borba,Noel Gough,Christine Keitel-Kreidt,Catherine Vistro-Yu,Renuka Vithal
Author: Bill Atweh,Angela Calabrese Barton,Marcelo C. Borba,Noel Gough,Christine Keitel-Kreidt,Catherine Vistro-Yu,Renuka Vithal
Publisher: Springer Science & Business Media
This book aims to develop theoretical frameworks of the phenomena of internationalisation and globalisation and identify related ethical, moral, political and economic issues facing mathematics and science educators. It provides a wide representation of views some of which are not often represented in international publications. This is the first book to deal with issues of globalisation and internationalisation in mathematics and science education.
An Anthropological Approach to String Figure-making in Oral Tradition Societies
Author: Eric Vandendriessche
This book addresses the mathematical rationality contained in the making of string figures. It does so by using interdisciplinary methods borrowed from anthropology, mathematics, history and philosophy of mathematics. The practice of string figure-making has long been carried out in many societies, and particularly in those of oral tradition. It consists in applying a succession of operations to a string (knotted into a loop), mostly using the fingers and sometimes the feet, the wrists or the mouth. This succession of operations is intended to generate a final figure. The book explores different modes of conceptualization of the practice of string figure-making and analyses various source material through these conceptual tools: it looks at research by mathematicians, as well as ethnographical publications, and personal fieldwork findings in the Chaco, Paraguay, and in the Trobriand Islands, Papua New Guinea, which all give evidence of the rationality that underlies this activity. It concludes that the creation of string figures may be seen as the result of intellectual processes, involving the elaboration of algorithms, and concepts such as operation, sub-procedure, iteration, and transformation.
Celebrations of Diversity of Mathematical Practices
Author: Swapna Mukhopadhyay,Wolff-Michael Roth
Publisher: Springer Science & Business Media
This book grew out of a public lecture series, Alternative forms of knowledge construction in mathematics, conceived and organized by the first editor, and held annually at Portland State University from 2006. Starting from the position that mathematics is a human construction, implying that it cannot be separated from its historical, cultural, social, and political contexts, the purpose of these lectures was to provide a public intellectual space to interrogate conceptions of mathematics and mathematics education, particularly by looking at mathematical practices that are not considered relevant to mainstream mathematics education. One of the main thrusts was to contemplate the fundamental question of whose mathematics is to be valorized in a multicultural world, a world in which, as Paolo Freire said, “The intellectual activity of those without power is always characterized asnon-intellectual”. To date, nineteen scholars (including the second editor) have participated in the series. All of the lectures have been streamed for global dissemination at:http://www.media.pdx.edu/dlcmedia/events/AFK/. Most of the speakers contributed a chapter to this book, based either on their original talk or on a related topic. The book is divided into four sections dealing with: • Mathematics and the politics of knowledge • Ethnomathematics • Learning to see mathematically • Mathematics education for social justice.
An Ecocultural Perspective for Space, Geometry and Measurement Education
Author: Kay Owens
This book develops the theoretical perspective on visuospatial reasoning in ecocultural contexts, granting insights on how the language, gestures, and representations of different cultures reflect visuospatial reasoning in context. For a number of years, two themes in the field of mathematics education have run parallel with each other with only a passing acquaintance. These two areas are the psychological perspective on visuospatial reasoning and ecocultural perspectives on mathematics education. This volume examines both areas of research and explores the intersection of these powerful ideas. In addition, there has been a growing interest in sociocultural aspects of education and in particular that of Indigenous education in the field of mathematics education. There has not, however, been a sound analysis of how environmental and cultural contexts impact visuospatial reasoning, although it was noted as far back as the 1980s when Alan Bishop developed his duality of visual processing and interpreting visual information. This book provides this analysis and in so doing not only articulates new and worthwhile lines of research, but also uncovers and makes real a variety of useful professional approaches in teaching school mathematics. With a renewed interest in visuospatial reasoning in the mathematics education community, this volume is extremely timely and adds significantly to current literature on the topic.
Culture, Place and Personhood in the Southern Amazon, AD 1000–2000
Author: Michael J. Heckenberger
In 1884 a community of Brazilians was "discovered" by the Western world. The Ecology of Power examines these indigenous people from the Upper Xingu region, a group who even today are one of the strongest examples of long-term cultural continuity. Drawing upon written and oral history, ethnography, and archaeology, Heckenberger addresses the difficult issues facing anthropologists today as they "uncover" the muted voices of indigenous peoples and provides a fascinating portrait of a unique community of people who have in a way become living cultural artifacts.
Unique, thought-provoking study discusses quipu, an accounting system employing knotted, colored cords, used by Incas. Cultural context, mathematics involved, and even how to make a quipu. Over 125 illustrations.
There is no question that native cultures in the New World exhibit many forms of mathematical development. This Native American mathematics can best be described by considering the nature of the concepts found in a variety of individual New World cultures. Unlike modern mathematics in which numbers and concepts are expressed in a universal mathematical notation, the numbers and concepts found in native cultures occur and are expressed in many distinctive ways. Native American Mathematics, edited by Michael P. Closs, is the first book to focus on mathematical development indigenous to the New World. Spanning time from the prehistoric to the present, the thirteen essays in this volume attest to the variety of mathematical development present in the Americas. The data are drawn from cultures as diverse as the Ojibway, the Inuit (Eskimo), and the Nootka in the north; the Chumash of Southern California; the Aztec and the Maya in Mesoamerica; and the Inca and Jibaro of South America. Among the strengths of this collection are this diversity and the multidisciplinary approaches employed to extract different kinds of information. The distinguished contributors include mathematicians, linguists, psychologists, anthropologists, and archaeologists.
Key Message: A History of Mathematics, Third Edition, provides a solid background in the history of mathematics, helping readers gain a deeper understanding of mathematical concepts in their historical context. This book's global perspective covers how contributions from Chinese, Indian, and Islamic mathematicians shaped our modern understanding of mathematics. This book also includes discussions of important historical textbooks and primary sources to help readers further understand the development of modern mathematics. Key Topics: Ancient Mathematics: Egypt and Mesopotamia, The Beginnings of Mathematics in Greece, Euclid, Archimedes and Apollonius, Mathematical Methods in Hellenistic Times, The Final Chapter of Greek Mathematics; Medieval Mathematics: Ancient and Medieval China, Ancient and Medieval India, The Mathematics of Islam, Medieval Europe, Mathematics Elsewhere; Early Modern Mathematics: Algebra in the Renaissance, Mathematical Methods in the Renaissance, Geometry, Algebra and Probability in the Seventeenth Century, The Beginnings of Calculus, Newton and Leibniz; Modern Mathematics: Analysis in the Eighteenth Century, Probability and Statistics in the Eighteenth Century, Algebra and Number Theory in the Eighteenth Century, Geometry in the Eighteenth Century, Algebra and Number Theory in the Nineteenth Century, Analysis in the Nineteenth Century, Probability and Statistics in the Nineteenth Century, Geometry in the Nineteenth Century, Aspects of the Twentieth Century Market: For all readers interested in the history of mathematics.
The Mathematical Archetypes of Nature, Art, and Science
Author: Michael S. Schneider
Publisher: Harper Collins
The Universe May Be a Mystery, But It's No Secret Michael Schneider leads us on a spectacular, lavishly illustrated journey along the numbers one through ten to explore the mathematical principles made visible in flowers, shells, crystals, plants, and the human body, expressed in the symbolic language of folk sayings and fairy tales, myth and religion, art and architecture. This is a new view of mathematics, not the one we learned at school but a comprehensive guide to the patterns that recur through the universe and underlie human affairs. A Beginner's Guide to Constructing, the Universe shows you: Why cans, pizza, and manhole covers are round. Why one and two weren't considered numbers by the ancient Greeks. Why squares show up so often in goddess art and board games. What property makes the spiral the most widespread shape in nature, from embryos and hair curls to hurricanes and galaxies. How the human body shares the design of a bean plant and the solar system. How a snowflake is like Stonehenge, and a beehive like a calendar. How our ten fingers hold the secrets of both a lobster and a cathedral. And much more.
Author: John Wallace Nunley,Cara McCarty,John Emigh,Lesley Ferris,St. Louis Art Museum,Field Museum of Natural History,Museum of Fine Arts, Houston
Publisher: Harry N. Abrams
From Paleolithic times to have to present, people used masks to add power and mystery to religious rituals, warfare, and entertainment. This lavishly illustrated book, the companion volume to an exhibition opening at The Saint Louis Art Museum, provides a stunning and comprehensive cultural history of these universal human artifacts.Transporting readers across centuries and continents, the authors compare and contrast the use of masks in initiation rites and Mardi Gras, Greek tragedy and commedia dell'arte, warfare and football. The 200 colorplates, illustrating such fascinating examples as African ceremonial masks, the Apollo 15 space helmet, and an Egyptian death mask, make this landmark study as visually spectacular as it is thought-provoking.
Haraldur Sigurdsson,Professor in the Graduate School of Oceanography Haraldur Sigurdsson