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Cultural Development of Mathematical Ideas
Papua New Guinea Studies

$103.00 (C)

Part of Learning in Doing: Social, Cognitive and Computational Perspectives

  • Date Published: September 2012
  • availability: In stock
  • format: Hardback
  • isbn: 9780521761666

$103.00 (C)
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About the Authors
  • Drawing upon field studies conducted in 1978, 1980, and 2001 with the Oksapmin, a remote Papua New Guinea group, Geoffrey B. Saxe traces the emergence of new forms of numerical representations and ideas in the social history of the community. In traditional life, the Oksapmin used a counting system that makes use of twenty-seven parts of the body; there is no evidence that the group used arithmetic in prehistory. As practices of economic exchange and schooling have shifted, children and adults unwittingly reproduced and altered the system in order to solve new kinds of numerical and arithmetical problems, a process that has led to new forms of collective representations in the community. While Dr. Saxe’s focus is on the Oksapmin, the insights and general framework he provides are useful for understanding shifting representational forms and emerging cognitive functions in any human community. Video and visual supports for the book, the Cultural Development of Mathematical Ideas: Papua New Guinea Studies, which are key to a deeper understanding of this ground-breaking project are available online at http://www.culturecognition.com

    • Roots analyses of the social history of representations and ideas in methods of the behavioral and cognitive sciences through three periods of fieldwork (1978, 1980, 2001)
    • The book is richly illustrated with photographs and helpful diagrams, including photographs of first Western contact with the Oksapmin
    • Includes studies of child development as well as the shifting structure of numerical and arithmetical thought over time in the cultural history of the community
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    Reviews & endorsements

    "...This book is a tour de force in moving theory toward a fully historical, social and activity based account of cultural and developmental change. The case presented is particular to an “exotic” (to us) group, but the theoretical apparatus developed has wide-ranging application. This book isn’t about “them” it is about “us” as well. It is an important contribution to developmental theory."
    --Joseph Glick, The Graduate Center, City University of New York, Human Development

    "...comprehensive and well documented.... should appeal to a wide audience beyond cultural anthropology and cultural psychology.... it will delight.... this book should be of interest worldwide...."
    --Pierre R. Dasen, University of Geneva, Alterstices

    "deeply impressed with its contributions to our understanding of cognitive development."
    -- Book Award from the Cognitive Development Society

    "...Saxe’s background chapters on his personal journey and his visits to Oksapmin and the historical background of currency changes in Papua New Guinea together with the carefully developed reports of each study and the overall linkage with his theoretical perspective make this an important contribution to psychology especially within the Pacific Rim region, and a crucial reference for those in Papua New Guinea interested in mathematics, education, cognition, psychology, anthropology and/or sociology."
    --Kay Owens, Charles Sturt University, Journal of Pacific Rim Psychology

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    Product details

    • Date Published: September 2012
    • format: Hardback
    • isbn: 9780521761666
    • length: 393 pages
    • dimensions: 234 x 160 x 22 mm
    • weight: 0.67kg
    • contains: 120 b/w illus. 4 maps 24 tables
    • availability: In stock
  • Table of Contents

    Introduction
    Part I. The Origins of Number-Enduring Questions:
    1. Culture-cognition relations
    2. Cultural forms of number representation used in Oksapmin communities
    Part II. Economic Exchange:
    3. Collective practices of economic exchange: a brief social history
    4. Reproduction and alteration of numerical representations
    5. Reproduction and alteration in currency token representations
    6. Representational forms, functions, collective practices, and fu: a microcosm
    Part III. Schooling:
    7. A brief history: collective practices of schooling in Oksapmin
    8. Unschooled children's developing uses of the body system
    9. Children's adaptations of the body system in school in 1980: an unintended consequence of postcolonial schooling
    10. About twenty years later: schooling and number
    11. Teachers and students as (unintentional) agents of change
    Part IV. Towards an Integrated Treatment of Socio-Historical and Cognitive Developmental Processes:
    12. What develops? A focus on form-function relations
    13. How do quantification practices develop?
    14. Why do form-function relations shift?
    Epilogue.

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    These resources are provided free of charge by Cambridge University Press with permission of the author of the corresponding work, but are subject to copyright. You are permitted to view, print and download these resources for your own personal use only, provided any copyright lines on the resources are not removed or altered in any way. Any other use, including but not limited to distribution of the resources in modified form, or via electronic or other media, is strictly prohibited unless you have permission from the author of the corresponding work and provided you give appropriate acknowledgement of the source.

    If you are having problems accessing these resources please email cflack@cambridge.org

  • Author

    Geoffrey B. Saxe, University of California, Berkeley
    Dr Geoffrey Saxe has conducted research on mathematical cognition and culture in a variety of settings, including remote parts of Papua New Guinea, urban and rural areas of northeastern Brazil and elementary and middle school classrooms in the United States. His prior books include Culture and Cognitive Development: Studies in Mathematical Understanding (1991) and Social Processes in Early Number Development (with S. Guberman and M. Gearhart, 1987). He is currently a professor at the Graduate School of Education, University of California, Berkeley.

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