Ethnomathematics: Exploring Cultural Diversity in Mathematics

Abstract

This thesis provides a new conceptualisation of ethnomathematics which avoids some of the difficulties which emerge in the literature. In particular, work has been started on a philosophic basis for the field. There is no consistent view of ethnomathematics in the literature. The relationship with mathematics itself has been ignored, and the philosophical and theoretical background is missing. The literature also reveals the ethnocentricity implied by ethnomathematics as a field of study based in a culture which has mathematics as a knowledge category. Two strategies to over come this problem are identified: universalising the referent of ‘mathematics’ so that it is the same as “knowledge-making”; or using methodological techniques to minimise it. The position of ethnomathematics in relationship to anthropology, sociology, history, and politics is characterised on a matrix. A place for ethnomathematics is found close the anthropology of mathematics, but the aim of anthropology is to better understand culture in general, while ethnomathematics aims to better understand mathematics. Anthropology, however, contributes its well-established methodologies for overcoming ethnocentricity. The search for a philosophical base finds a Wittgensteinian orientation which enables culturally based ‘systems of meaning’ to gain credibility in mathematics. A definition is proposed for ethnomathematics as the study of mathematical practices within context. Four types of ethnomathematical activity are identified: descriptive, archaeological, mathematising, and analytical activity. The definition also gives rise to a categorisation of ethnomathematical work along three dimensions: the closeness to conventional mathematics; the historical time; and the type of host culture. The mechanisms of interaction between mathematical practices are identified, and the imperialistic growth of mathematics is explained. Particular features of ethnomathematical theory are brought out in a four examples. By admitting the legitimacy of other viewpoints, ethnomathematics opens mathematics to new creative forces. Within education, ethnomathematics provides new choices, and turns cultural conflict into a useful tool for teaching. Mathematical activity exists in a variety of contexts. Learning mathematics involves being aware of, and integrating, diverse concepts. Ethnomathematics expands mathematical horizons, so that cultural diversity becomes a richer contributor to the cultural structures which humans use to understand their world.