An Exploration of Ideas Across Cultures
Author: Marcia Ascher
Publisher: Princeton University Press
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.
A Multicultural View of Mathematical Ideas
Author: Marcia Ascher
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.
Challenging Eurocentrism in Mathematics Education
Author: Arthur B. Powell,Marilyn Frankenstein
Publisher: SUNY Press
Presents the emerging field of ethnomathematics from a critical perspective, challenging particular ways in which Eurocentrism permeates mathematics education and mathematics in general.
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
Link Between Traditions and Modernity
Author: Ubiratan D'Ambrósio
Publisher: Sense Pub
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.
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.
What Makes a "Good" Rhythm Good?
Author: Godfried T. Toussaint
Publisher: CRC Press
The Geometry of Musical Rhythm: What Makes a "Good" Rhythm Good? is the first book to provide a systematic and accessible computational geometric analysis of the musical rhythms of the world. It explains how the study of the mathematical properties of musical rhythm generates common mathematical problems that arise in a variety of seemingly disparate fields. For the music community, the book also introduces the distance approach to phylogenetic analysis and illustrates its application to the study of musical rhythm. Accessible to both academics and musicians, the text requires a minimal set of prerequisites. Emphasizing a visual geometric treatment of musical rhythm and its underlying structures, the author—an eminent computer scientist and music theory researcher—presents new symbolic geometric approaches and often compares them to existing methods. He shows how distance geometry and phylogenetic analysis can be used in comparative musicology, ethnomusicology, and evolutionary musicology research. The book also strengthens the bridge between these disciplines and mathematical music theory. Many concepts are illustrated with examples using a group of six distinguished rhythms that feature prominently in world music, including the clave son. Exploring the mathematical properties of good rhythms, this book offers an original computational geometric approach for analyzing musical rhythm and its underlying structures. With numerous figures to complement the explanations, it is suitable for a wide audience, from musicians, composers, and electronic music programmers to music theorists and psychologists to computer scientists and mathematicians. It can also be used in an undergraduate course on music technology, music and computers, or music and mathematics.
Author: Francine F. Abeles,Mark E. Fuller
This book presents diverse topics in mathematical logic such as proof theory, meta-mathematics, and applications of logic to mathematical structures. The collection spans the first 100 years of modern logic and is dedicated to the memory of Irving Anellis, founder of the journal 'Modern Logic', whose academic work was essential in promoting the algebraic tradition of logic, as represented by Charles Sanders Peirce. Anellis’s association with the Russian logic community introduced their school of logic to a wider audience in the USA, Canada and Western Europe. In addition, the collection takes a historical perspective on proof theory and the development of logic and mathematics in Eastern Logic, the Soviet Union and Russia. The book will be of interest to historians and philosophers in logic and mathematics, and the more specialized papers will also appeal to mathematicians and logicians.
Code of the Quipu
Author: Marcia Ascher,Robert Ascher
Publisher: Courier Corporation
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.
Relocating Modernization and Technology
Author: Walter Goebel,Saskia Schabio
Category: Literary Criticism
Debates about the ‘Black Atlantic’ have alerted us to an experience of modernization that diverges from the dominant Western narratives of globalization and technological progress. This outstanding volume expands the concept of the Black Atlantic by reaching beyond the usual African-American focus of the field, presenting fresh perspectives on postcolonial experiences of technology and modernization. A team of renowned contributors come together in this volume in order to: redefine and expand ideas of Black Atlantic challenge unified concepts of modernization from a postcolonial perspective question fashionable concepts of the transnational by returning to the local and the national offer new approaches to cross-cultural mechanisms of exchange explore utopian uses of technology in the postcolonial sphere. Exploring a variety of national, diasporan and transnational counternarratives to Western modernization, Beyond the Black Atlantic makes a valuable contribution to the fields of postcolonial, literary and cultural studies.
Author: Michael P. Closs
Publisher: University of Texas Press
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.
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.
A History of Walking
Author: Rebecca Solnit
Category: Social Science
A passionate, thought provoking exploration of walking as a political and cultural activity, from the author of Men Explain Things to Me Drawing together many histories--of anatomical evolution and city design, of treadmills and labyrinths, of walking clubs and sexual mores--Rebecca Solnit creates a fascinating portrait of the range of possibilities presented by walking. Arguing that the history of walking includes walking for pleasure as well as for political, aesthetic, and social meaning, Solnit focuses on the walkers whose everyday and extreme acts have shaped our culture, from philosophers to poets to mountaineers. She profiles some of the most significant walkers in history and fiction--from Wordsworth to Gary Snyder, from Jane Austen's Elizabeth Bennet to Andre Breton's Nadja--finding a profound relationship between walking and thinking and walking and culture. Solnit argues for the necessity of preserving the time and space in which to walk in our ever more car-dependent and accelerated world.
Author: Joyce Appleby
Publisher: W. W. Norton & Company
“Uncommonly good . . . makes a compelling case that . . . intellectual curiosity not only changed Europe, but launched modernity.” —Cleveland Plain Dealer When Columbus first returned to Spain from the Caribbean, he dazzled King Ferdinand and Queen Isabella with exotic parrots, tropical flowers, and bits of gold. Inspired by the promise of riches, countless seafarers poured out of the Iberian Peninsula and wider Europe in search of spices, treasure, and land. Many returned with strange tales of the New World. Curiosity began to percolate through Europe as the New World’s people, animals, and plants ruptured prior assumptions about the biblical description of creation. The Church, long fearful of challenges to its authority, could no longer suppress the mantra “Dare to know!” Noblemen began collecting cabinets of curiosities; soon others went from collecting to examining natural objects with fresh eyes. Observation led to experiments; competing conclusions triggered debates. The foundations for the natural sciences were laid as questions became more multifaceted and answers became more complex. Carl Linneaus developed a classification system and sent students around the globe looking for specimens. Museums, botanical gardens, and philosophical societies turned their attention to nature. National governments undertook explorations of the Pacific. Eminent historian Joyce Appleby vividly recounts the explorers’ triumphs and mishaps, including Magellan’s violent death in the Philippines; the miserable trek of the “new Argonauts” across the Andes on their mission to determine the true shape of the earth; and how two brilliant scientists, Alexander Humboldt and Charles Darwin, traveled to the Americas for evidence to confirm their hypotheses about the earth and its inhabitants. Drawing on detailed eyewitness accounts, Appleby also tells of the turmoil created in the all societies touched by the explorations. This sweeping, global story imbues the Age of Discovery with fresh meaning, elegantly charting its stimulation of the natural sciences, which ultimately propelled Western Europe toward modernity.
Author: Victor J. Katz
Publisher: Addison-Wesley Longman
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.
Nature, Exploration and Exploitation
Author: John McCannon
Publisher: Reaktion Books
Bitter cold and constant snow. Polar bears, seals, and killer whales. Victor Frankenstein chasing his monstrous creation across icy terrain in a dogsled. The arctic calls to mind a myriad different images. Consisting of the Arctic Ocean and parts of Canada, the United States, Russia, Greenland, Finland, Norway and Sweden, the arctic possesses a unique ecosystem—temperatures average negative 29 degrees Fahrenheit in winter and rarely rise above freezing in summer—and the indigenous peoples and cultures that live in the region have had to adapt to the harsh weather conditions. As global temperatures rise, the arctic is facing an environmental crisis, with melting glaciers causing grave concern around the world. But for all the renown of this frozen region, the arctic remains far from perfectly understood. In A History of the Arctic, award-winning polar historian John McCannon provides an engaging overview of the region that spans from the Stone Age to the present. McCannon discusses polar exploration and science, nation-building, diplomacy, environmental issues, and climate change, and the role indigenous populations have played in the arctic’s story. Chronicling the history of each arctic nation, he details the many failed searches for a Northwest Passage and the territorial claims that hamper use of these waterways. He also explores the resources found in the arctic—oil, natural gas, minerals, fresh water, and fish—and describes the importance they hold as these resources are depleted elsewhere, as well as the challenges we face in extracting them. A timely assessment of current diplomatic and environmental realities, as well as the dire risks the region now faces, A History of the Arctic is a thoroughly engrossing book on the past—and future—of the top of the world.