1. The vague idea of
“connection to cultural heritage” invites examples like “Rain Forest Mathematics,”
which merely replaces Dick and Jane counting marbles with Tatuk and Esteban
counting coconuts.
2. If examples are restricted
to lower primary school level, they are reinforcing primitivism (i.e. that
mathematical concepts from African culture are only child-like) rather than
opposing it.
3. If examples focus
only on the mathematics of “ancient empire” cultures (Chinese, Hindu, and
Muslim, and ancient Egypt examples) they merely reinforce the myth that small-scale
indigenous societies had no sophisticated math.
4. Vague notions of
“self-esteem” ignore the ways that students compensate by establishing a high-esteem,
oppositional identity-- eg researchers such as Fordham (1991) and Ogbu (1998),
document the ways in which African American students perceive a forced choice
between Black identity and high scholastic achievement.
B. Ethnomathematics
should pay close attention to the following four principles:
1)
Deep design themes.
When examined in their social context, indigneous mathematical practices are
not trivial or haphazard; they reflect deep design themes providing a cohesive
structure to many of the important knowledge systems for that society. Examples:
Fractals in African cultures, Cartesian organization in Native American cultures.
2)
Anti-primitivist and anti-racist representation. By showing sophisticated mathematical practices, not just
trivial examples (eg “African houses are shaped like a cylinder”), ethnomathematics
directly challenges the cultural stereotypes and genetic myths most damaging
to both minority and majority ethnic groups.
3)
Translation, not just modeling. Often indigenous designs are merely analyzed from a western
view. Ethnomathematics, in contrast, uses relations between the indigenous
conceptual framework and the mathematics embedded in related indigenous designs.
In effect, it uses modeling as a tool to provide a “translation” from indigenous
knowledge systems to western mathematics.
4)
Dynamic rather than static views of culture. While evidence for independent indigenous mathematics is
crucial in opposing primitivism, it is also important to avoid the stereotype of indigenous peoples as historically isolated,
alive only in a static past of museum displays. For this reason ethnomathematics
includes the vernacular practices of their contemporary descendents.
The bullet points above are not meant to be exhaustive, nor is it meant as a blanket condemnation of multicultural math. It is an attempt to examine some of the pitfalls of multicultural math in one particular context, which is the education of US under-represented minorities, and some potential solutions. Nonetheless, it is possible to take the underlying principles and apply them to any educational context. Indeed context is what its all about. For an African American student in the US, a lesson on the Korean board game "yut-nori" may merely be seen as a confirmation of pre-existing stereotypes (Asian kids as inherently superior in math). On the other hand Koreans form a low "caste" in Japan (Korea was colonized by Japan for 50 years), and children of Korean laborers have poor math performance there (Fischer et al 1996); using yut-nori to dispel myths about their inferiority in that context might be valuable.
In general, the problems stem from an "add culture and stir" approach. In general, the solutions stem from paying close attention to the political dimensions of social groups (which might include economic class, gender, sexual orientation, religion, profession, and many other markers of difference in addtion to ethnicity), and their current and historical interrelationships. That's not to say one need be infinetly immersed in idiosyncrasies: raising awareness of the myths of genetic determinism and the myths of cultural stereotype (whether that is race, gender, class, etc.) is one essential goal (for others see Eglash et al 2006). But conveying those concepts effectively depends on cultural specificity: you can't just "add culture and stir."
citations:
Eglash, Ron; Bennett, Audrey; O'Donnell, Casey; Jennings, Sybillyn; Cintorino, Margaret. "Culturally Situated Design Tools:. Ethnocomputing from Field Site to Classroom." American anthropologist 108:22, 347-362. 2006.
Fischer CS, Hout M, Sanchez Jankowski M, Lucas SR, Swidler A, and Voss K. 1996. Inequality by design: Cracking the Bell Curve myth. Princeton, NJ: Princeton University Press.