Recently, there has been a growing awareness of the inadequacies of American elementary and secondary mathematics education in comparison to many other nations around the world. Studies such as those presented in The Underachieving Curriculum show the disparity between United States mathematics education and the rest of the world. The NCTM Curriculum and Evaluation Standards for School Mathematics advocates "mathematics for all" as a central idea in education reform, but this slogan can be used to champion two very different views of mathematics and how it should be taught: 1) mathematics as a culture in and of itself into which the student is to be "enculturated" (as mentioned by Robert Davis in "The Culture of Mathematics and the Culture of Schools") or 2) mathematics as an invention of the student who is inextricably linked to his or her own culture. Although the first has certain aesthetic appeal, the latter view will provide the most effective vision for raising the level of mathematics education in this country.
It is easy to say that there exists a culture of mathematics and it is a common belief that mathematics is somehow "culture-free, " in that it is somehow independent of external cultural influences. But what kind of mathematics are we teaching that lacks cultural context. Furthermore, should we enculturate students into a field that is essentially divorced from the everyday realities they face. Damerow and Westbury, in "Mathematics for All -- Problems and Implications," point to this fundamental question in mathematics education: what is the better alternative in teaching mathematics -- "ideology or reality?" (p. 177).
In the ideological sense, educators could conceivably enculturate all students into the theoretical world of mathematics, but how would this serve either the student or society? Essentially, only the few who eventually "specialize in some way or other in the subject" (Damerow and Westbury, p. 177) would benefit from such a goal, betraying the purpose and spirit of "mathematics for all."
What good is mathematics for all if only an elite few actually have use for it in the future? By focusing upon the theoretical and ideological aspects of the mathematics culture, the subject becomes separated from the very reality it is used to explain. It is no longer a tool, but instead it is an aesthetic work (which is not without its own merit, but does not provide valid motivation for the vast majority of students).
The culture of mathematics has been derived from many cultures throughout the ages, yet in most of those cultures it has been used to define the elite, to maintain class structures, to give and take power. These inherently divisive aspects that have been integrated into the culture of mathematics make the subject, by definition, not for all. Hence, educators and students must work to reinvent the culture. Ethnomathematics works from this assumption and builds upon the "reality" alternative suggested by Damerow and Westbury.
By looking for everyday mathematics within a given culture (culture is associated with but not synonymous with race, ethnicity, and gender), ethnomathematics moves from the commonplace to the theoretical. It starts by looking at specific reality and generalizes those ideas to be applied in new and different situations. Inherently, this process is grounded in reality. It accepts the fact that students bring with them a certain amount of intuitive knowledge of mathematics through their everyday interaction with their culture. By using these interactions as a base, it expands the problem solving techniques already used by the student and adapts them to new situations. This is very much in keeping with Freudenthal's theory that "the students applies certain new rules unconsciously until at a certain movement he becomes conscious about them" (Keitel, p. 402), except here the rules are not new, they are rules that are familiar (yet, unanalyzed by the student).
By focusing upon individual cultures' interpretations of mathematical concepts, the curriculum can build upon the pre-existing foundation of knowledge owned by the student. The student can then develop their understand of mathematics within their culture (the culture which will mold the rest of their lives) and make the field of mathematics truly for all.
Davis, R. B. (1989). The culture of mathematics and the culture of schools. Journal of Mathematical Behavior, 8, 143-160.
Keitel, C. (1987). What are the goals of mathematics for all? Journal of Curriculum Studies, 19(5), 393-407.
McKnight, C.C., McKnight, C.C., F.J. Crosswhite, J.A. Dossey, E. Kifer, J.O. Swafford, K.J. Travers, and T.J. Cooney (1989). The Underachieving Curriculum. Champaign, IL: Stripes Publishing.
NCTM. (1993). Curriculum and Evaluation Standards for School Mathematics. Reston, VA: NCTM.
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