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.
Die Geschichte der Mathematik des Abendlands mit ihren Quellen in China, Indien und im Islam
Author: Dietmar Herrmann
Der Band enthält zum ersten Mal in deutscher Sprache grundlegende Themen der chinesischen und indischen Mathematik, die den Nährboden für spätere Fragestellungen bereiten. Die nicht zu überschätzende Rolle, die islamische Gelehrte bei der Entwicklung der Algebra und der Verbreitung des Ziffernsystems gespielt haben, wird in exemplarischen Episoden veranschaulicht. Unterhaltsam wird geschildert, wie Fibonacci die orientalische Aufgabenkultur nach Italien bringt. Zahlreiche Beispiele demonstrieren das neue kaufmännische Rechnen, dessen Methoden sich in ganz Europa verbreiten. In Deutschland erwächst eine neue Generation von Rechenmeistern, die mit ihren erstmals im Druck verbreiteten Schriften eine ungeheure Popularisierung des Rechnens bewirken. Überraschende Einblicke in die Historie bieten die Kapitel über die Vermittlung mathematischen Wissens in Klöstern und Universitäten. Das Buch ist eine Fundgrube für historisch Interessierte; zahlreiche Aufgaben bieten vergnüglichen Stoff für Unterricht, Vorlesung und Selbststudium.
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
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.
Milton Rosa,Lawrence Shirley,Maria Elena Gavarrete,Wilfredo V. Alangui
Author: Milton Rosa,Lawrence Shirley,Maria Elena Gavarrete,Wilfredo V. Alangui
This book addresses numerous issues related to ethnomathematics and diverse approaches to it in the context of mathematics education. To help readers better understand the development of ethnomathematics, it discusses its objectives and assumptions with regard to promoting an ethics of respect, solidarity, and cooperation across and for all cultures. In turn, the book addresses a range of aspects including pedagogical action, culturally relevant pedagogy, innovative approaches to ethnomathematics, and the role of ethnomathematics in mathematics education. Ethnomathematics offers educators a valuable framework for transforming mathematics so that it can more actively contribute to realizing the dream of a just and humane society. As such, its primary goal is to forge mathematics into a powerful tool to help people create a society characterized by dignity for all, and in which iniquity, arrogance, violence, and bigotry have no place.
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.
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.
Building on historical and contemporary literature in anthropology and art theory, Lines That Connect treats pattern as a material form of thought that provokes connections between disparate things through processes of resemblance, memory, and transformation. Pattern is constantly in a state of motion as it traverses spatial and temporal divides and acts as an endless source for innovation through its inherent transformability. Graeme Were argues that it is the ideas carried by pattern's relational capacity that allows Pacific islanders to express their links to land, genealogy, and resources in the most economic ways. In doing so, his book is a timely and unique contribution to the analysis of pattern and decorative art in the Pacific amid growing debates in anthropology and art history. This striking and original study brings together objects and photographs, historical literature and contemporary ethnographic case studies to explore pattern in its logical workings. It presents the first-ever analysis of the well-known patterned shell valuable called kapkap as revealed in New Ireland mortuary feasts. Innovative research in the study of Christianity and the Baha'i faithful in the region shows how pattern has been appropriated in new religious communities. Were argues that pattern is used in various guises in performances, church architecture, and funerary images to contrasting effect. He explores the conditions under which pattern facilitates a connecting of old and new ideas and how missionary processes are implicated in this flow. He then considers the mechanisms under which pattern is internalized, paying particular attention to its embeddedness in spatial and numerical thinking. Finally, he examines how pattern carries new materials and technologies, which in turn provide new resources for sustaining old beliefs. Drawing on a multitude of fields (anthropology; art history; Pacific, museum, and religious studies; education; ethnomathematics), Lines That Connect raises key questions about the capacity of pattern across the Pacific to bind and sustain ideas about place, body, and genealogy in the most logical of ways.
From the Preface: "This book is addressed to all who are curious about the nature of mathematics and its role in society. It is neither a text book nor a specialists' book. It consists of a number of loosely linked essays that may be read independently and for which I have tried to provide a leitmotif by throwing light on the relationship between mathematics and common sense. In these essays I hope to foster a critical attitude towards both the existence of common sense in mathematics and the ambiguous role that it can play."