Mapping Mathematical Imaginaries for Apache Education

• In Event: (Re)Mapping Sovereign Imaginaries for Indigenous Publics: Examples of School and Community Education

Abstract

Mathematics is a social construct (Bishop, 1988). In the pursuit to better define and classify the world in which we live, humans have relied upon their intellect to develop ways in which we can see the world. Unfortunately, we do have a bias that identifies aspects that make sense in our own social and cultural perspectives. Essentially, as we experience our life through the interpretations of our senses and these interpretations are based on socio-cultural perspective (Fleck, 1979; Foucault, 2005; Freire, 2007; Gee, 2005; Ladson-Billings, 1995, Radford, 2006). The mathematics taught within most public schools is heavily situated within a Eurocentric cultural perspective (Lipka et al., 2005; Lunney & Wagner, 2006; Orey & Rosa, 2004; Sfard 1995). Coupling the prevalence of Eurocentric mathematics with the fallacy of mathematics as acultural, leads to current disconnects in the education of minoritized communities, specifically indigenous communities’ perspectives (Castagno & Brayboy, 2008; Lomawaima & McCarty, 2006). Such communities unjustly become identified as under-performing, emergent, falling far behind or simply not smart (Sternberg, 2007; Urrieta, 2006). As a purported democratic endeavor, public education must incorporate (or at least allow the meaningful use of) the socio-cultural perspectives of minoritized communities within schools. As a means to document possible socio-cultural differences in perspective, this research analyzes mathematical understanding within the San Carlos Apache culture, against the backdrop of the hegemony of mathematics as presented in public schools. The desired dual outcome for the inclusion of Apache mathematical discourse and socio-cultural perspectives within public school pedagogy is 1) access to school success for Apache communities along with 2) an expanded and further developed inclusive perspective of mathematics in general.
Apache mathematics, that is the mathematical concepts that are utilized by Apache community members but misidentified as non-mathematical in practice, has the potential to not only provide Apache students with the opportunity to access success within schools, but also expands what is imaginable within the field of mathematics in general. As an Apache researcher and community member, I draw upon interviews with fellow community members to illustrate how mathematics is initially identified as limited to arithmetic concepts (i.e. adding, subtracting, counting etc.). However, through further discussions, more Apache notions of mathematics are complex and seen as part of the overall engaged events (i.e. physics regarding trajectory, the computation of essential force needed within wood cutting). The phenomena of identifying and naming individual concepts embedded within the whole, quite common within Eurocentric perspectives, runs counter to Apache perspectives of valuing the whole over the part, as Apache values reflect a contextual and relational view of the world (i.e. family and clan allegiances, a sense of belonging to a place). As democratic imaginaries seek to encompass diversity and inclusion, I present the notion of Apache mathematics as a vital relational and contextual knowledge system which not only validates Apache ways of seeing the world, but offers benefits to all learners by surfacing learning as connected ecologies of situated knowledge, and (re)imagines whose knowledge counts in the context of schooling.

Author

• Philip Stevens, The University of Arizona