Cultural Development of Mathematical Ideas

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.

'Cultural anthropologist Clifford Geertz proposed that 'small facts speak to large issues' … In many ways, Geoffrey Saxe's new book echoes the Geertz quote. By gathering together the many small facts of numerical reasoning practices he has collected over a thirty-year period in a community in the Oksapmin region of Papua New Guinea, Saxe has assembled a dynamic documentary report of answers to the question: how are culture and cognition related? … At the end of this book, Saxe returns us to the Geertz quote … by suggesting that this culmination of thirty years of field work in Oksapmin mathematics makes three distinct contributions to the literature: thick description of a vanishing cultural community; little theory; and big theory … I would like to add that this important book provides a window into the professional career of a remarkable researcher and scholar.' Ellice A. Forman, Mathematical Thinking and Learning

• 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.