Mathematics Elsewhere: An Exploration of Ideas Across Cultures, Marcia Ascher, 2002. x + 203 pp., $24.95 hardbound. ISBN 0-691-07020-2. Princeton University Press, 41 Williams Street, Princeton, New Jersey 08540, www.pup.princeton.edu.
Marcia Ascher has been a noted scholar of ethnomathematics for many years, blending anthropology and mathematics at least since her studies of the Inca quipu, and especially in her book, Ethnomathematics: A Multicultural View of Mathematical Ideas (1991). This latest effort is essentially a continuation of her earlier book. In both, she discusses the ways mathematical ideas—which often may not resemble the formal Western notions of mathematics—can appear in non-European cultures. Also, in both books she gives detailed examples of this mathematical thought in action.
Sometimes ethnomathematics has been criticized as being limited to examples of low-level mathematics such as exotic systems of counting words or symmetries in art of various cultures. Ascher goes well beyond these kinds of examples to discuss rather sophisticated mathematics and the complex relationships between the mathematics and aspects of culture. Her examples are not trivial. The topics include modular systems in divination, complexities of calendars and other human chronological cycles, physical models of South Pacific ocean currents, algebraic structures of family and social relationships, and cross-cultural similarities in recursive, fractal-like art patterns. These discussions offer interesting reading and she provides lucid explanations, but most are too complicated for teachers to include as brief classroom anecdotes, other than noting that high-level mathematical thinking supports these cultural situations. Rather, they might provide source material for long-term class projects or math club programs. Social studies teachers may also find them valuable for classroom use.
Lawrence Shirley, Professor of Mathematics, Towson University