The Cultural Development of Mathematical Ideas


2015 Eleanor E. Maccoby Book Award (Developmental Psychology). American Psychological Association

2014 Stirling Prize for Best Published Book in Psychological Anthropology. Society for Psychological Anthropology, American Anthropological Association.

2013 Best Authored Book Award from the Cognitive Development Society




Drawing upon field studies conducted in 1978, 1980, and 2001 with the Oksapmin, a remote Papua New Guinea group, I trace 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 my focus is on the fascinating case of Oksapmin communities, the insights and general framework I provide can be useful for understanding shifting representational forms and emerging cognitive functions in any human community.





From Cambridge University Press;  From

BOOK REVIEWS (excerpts from published reviews). Read full reviews by clicking on some titles (bolded).
Glick, J.  (2013). Cultural-historical analysis done right: Review of Cultural Development of Mathematical ideas. Human Development. 56:213-216. DOI: 10.1159/000348338.  From the review:  "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." --Joseph Glick, The Graduate Center, City University of New York
Dasen, P. R. (2013). Cultural development of mathematical ideas [note de lecture]. Alterstice, 3(1), 93-96. [in French]  from the review:  "...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 
Forman, E. A. (2014). Cultural development of mathematical ideas: Papua New Guinea Studies, by Geoffrey Saxe. Mathematical Thinking and Learning, 16:2, 175-180, DOI: 10.1080/10986065.2014.893718. From the review: "Cultural anthropologist Clifford Geertz proposed that “small facts speak to large issues” (1973, p. 23). 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 30 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 at the beginning of this review 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, Dept. of Learning & Instruction, University of Pittsburgh
Maynard, A.E. (2014). Cultural Development of mathematical ideas: Papua New Guiinea Studies. Journal of Cognition and Development, 15(3), 524-525. From the review: Saxe is a master of theory and method in human development, and he provides a model for how to conduct contextually grounded, theoretically useful, path-breaking research that moves the field forward. -- Ashley E. Maynard, Professor and Chair, Dept. of Psychology, University of Hawaii. 
Beller, S. (2014). Cultural development of mathematical ideas: the Papua New Guinea studies by Geoffrey B. Saxe.  Ethos, 42:2, E3-E5. DOI: 10.1111/etho. 12050.  from the review:  " … [Saxe] highlights what the Cognitive Sciences can gain from anthropologically informed cognitive studies [] such as deep insights into the construction and alteration of cognitive representations within the sociocultural context and its changing demands.... the synopsis presented in this volume condenses a profound and impressive collection of about 25 years of research in a way that allows for deeper insights to be gained than the single papers could have done alone. … A striking commonality in the chapters throughout this book is Saxe’s focus on the tool-like character of the body-part system and how this tool is used and adapted purposefully to serve new functions. No matter whether or not one shares the theoretical framework on cognition and culture with Geoffrey Saxe, his detailed analyses and the broad contextualization open a fascinating window into the cultural development of numerical cognition. " - Sieghard Beller, Department of Psychosocial Science, University of Bergen, Norway
Sfard, A. (2015). When Oksapmin number system met Western arithmetic - Answering the question of how cognitive and cultural change induce each other. Educational Studies in Mathematics,  88:283–290.  DOI 10.1007/s10649-014-9586-7.  From the review: "Saxe’s Papuan expeditions were much more than ethnographic adventures, and the story of body parts turned numbers is much more than a curiosity. Cultural Development of Mathematical Ideas makes all this abundantly clear. The main contribution of the Oksapmin study, as I see it, is in the opportunity it creates for tackling the question of how it happens thatindividual “cognitive leaps” propagate in space and time, amounting to cultural changes, visible on the societal-historical scale. This question is of paramount importance, because the capacity for transforming our “forms of life” from one generation to another may well be this one feature that captures the essence of humanness and makes it possible to distinguish between people and other species in an unequivocal manner.  [...]  I can see at least three reasons why this book is a must read for every mathematics education researcher. First, as an inexhaustible source of insights about numerical thinking and its development and also about human thinking in general, it can be trusted to provide the interested reader with a hearty serving of food for thought. Second, it is not every day that one sees a longitudinal study capturing a historical change in the making. This turns Saxe’s story into something truly unique and precious. Finally, these 330 pages of the well-written text are too enjoyable a read to be missed.--Anna Sfard, University of Haifa
Owens, K. (2013). Cultural Development of Mathematical Ideas: Papua New Guinea Studies. ISBN: 9780521761666. Journal of Pacific Rim Psychology, 7(01), 50-52. oi:10.1017/prp.2013.5  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, Austraila