added a research item
Students' lives, both in and out of school, are full of different forms of value. Wealthy students enjoy value in the form of financial capital; their fit to hegemonic social practices; excellent health care and so on. Low-income students, especially those from African American, Native American, and Latinx communities, often lack access to those resources. But there are other forms of value that low-income students do possess. Most examples of what we will call Counter-Hegemonic Practice (CHP) in the African American community involve some mixture of Indigenous African heritage, contemporary innovation in the Black community, and other influences. Moving between these value forms and the computing classroom is a non-trivial task, especially if we are to avoid merely using the appearance of culture to attract students. Our objective in this paper is to provide a framework for deeper investigations into the computational potentials for CHP; its potential as a link between education and community development; and a more dignified role for its utilization in the CS classroom. We report on a series of collaborative engagements with CHP, largely focused on African American communities.
Every society exhibits one or more "design themes"-geometric abstractions that are manifested in myriad concrete forms. Four-fold symmetry is a deep design theme in many Native American cultures. This essay will describe how four-fold (and related bi-fold) symmetry is used as an organizing principle for religion, society, and technology in many Native American cultures. It will explore the ways in which this design theme has emerged through native structures analogous to the Cartesian coordinate system, and describe some software applications that help teachers make use of this ethnomathematics in the classroom.
Research in the knowledge systems of indigenous societies can be hampered by both cultural and technological assumptions. We see these assumptions at work in many popular television documentaries, where one hears of the " vanishing native " who " lived at one with nature. " Such portraits come from good intentions; but they only serve to further the stereotype of indigenous peoples as historically isolated, alive only in a static past. The idea of " living close to nature " implies concrete rather than abstract thinking, a simplistic " primitive " society taking only the first steps up a supposed ladder of progress. We need to take special efforts to open our eyes to the dynamic histories and technological sophistication of indigenous cultures-for example, to think about active indigenous ecological knowledge rather than the passive portraits we so often hear, e.g. " Indians lived as part of the ecosystem. " Rather than the illusion of a frozen pre-colonial tradition, we need to see indigenous societies as having always been in a state of change, and to understand more recent features of Native American life as part of that history. Steven J. Gould (1981) describes how biological evolution  used to be thought of as a single ladder of progress, but is now seen as a " copiously branching bush. " In the same way, contemporary anthropologists now see cultural evolution as a branching diversity of forms. While European societies may have followed one particular sequence in the development of mathematics, other cultures might have developed mathematical ideas along very different lines. Rather than assuming that Native American mathematics must be restricted to simple counting systems or geometric forms, we should be open to any mathematical pattern that appears, including those which are embedded, emergent, or obscured by difficulties in translation to their western counterparts. Equally important, we should strive to show the interrelationships among such culturally embedded mathematical concepts. This essay will attempt to show how such an approach can open new possibilities through computation, complexity and coding in Native American knowledge systems.