Ron Eglash

When Math Worlds Collide: Intention and Invention in Ethnomathematics

Ethnomathematics is a relatively new discipline that investigates mathematical knowl edge in small-scale, indigenous cultures. This essay locates ethnomathematics as one of five distinct subfields within a general anthropology of mathematics and describes interactions between cultural and epistemological features that have created these divisions. It reviews the political and pedagogical issues in which ethnomathematics research and practice is immersed and examines the possibilities for both conflict and collaboration with the goals, theories, and methods of social constructivism.

Toward culturally responsive computing education

Improving academic success and social development by merging computational thinking with cultural practices.

Culturally Responsive Computing in Urban, After-School Contexts Two Approaches

The academic performance and engagement of youth from under-represented ethnic groups (African American, Latino, and Indigenous) in science, technology, engineering, and mathematics (STEM) show statistically large gaps in comparison with their White and Asian peers. Some of these differences can be attributed to the direct impact of economic forces. But cultural factors also play a role. This essay will examine two culturally responsive math education technologies and report on evaluations of the technologies in urban out-of-school settings that suggest both approaches can be effective for integrating math education into urban, after-school contexts.

Fractal Simulations of African Design in Pre-College Computing Education

This article describes the use of fractal simulations of African design in a high school computing class. Fractal patterns---repetitions of shape at multiple scales---are a common feature in many aspects of African design. In African architecture we often see circular houses grouped in circular complexes, or rectangular houses in rectangular complexes. Typically the accompanying ceremonies, cosmologies, and other traditions make use of scaling and recursion in their conceptual models. African scaling designs include textiles, sculpture, adornment, and other forms; in many cases there are explicit geometric algorithms and other formal aspects (e.g., pseudorandom number generation in divination systems) embedded in the associated indigenous knowledge system. Thus African fractals provide a strong counter to stereotypes of African culture as primitive or simplistic. Following this fieldwork, we developed a Web site which uses Java simulations of these African designs to teach computational perspectives on fractals to high school students.1 We hypothesized that this combination of anti-primitivist “ethnocomputing” and design-based creative learning would enhance both the engagement and performance of under-represented students in computing. A quasi-experimental study used two 10th grade computing classes, both taught by the same instructor, and both including more than 50% under-represented students (Latino and African American). The control class received six days of instruction using a popular Web site (with Java applets but no cultural content or design activities) for high school fractal lessons; the experimental class received the same amount of instruction using our Web site. Pre/post differences on both achievement and attitude tests indicate statistically significant improvement for the students in the experimental class. Potential implications for improving participation and achievement of under-represented students in computing education are discussed.

The Race For Cyberspace: Information Technology in the Black Diaspora

Barbara Christian’s (1987) seminal essay, ‘The race for theory’, analyzed the ways in which the academic competition to create a theory of black women’s writing had overshadowed the potent theoretical content of the writing itself. Similarly, this essay examines how the hype over the application of new information technologies to racialized social problems has overshadowed the potent technological content of the communities themselves. Focusing on the black diaspora, we broaden the category of ‘information technology’ to show how traditions of coding and computation from indigenous African practices and black appropriations of Euro-American technologies have supported, resisted, and fused with the cybernetic histories of the West: a potential source for changes in reconstructing identity, social position and access to power in communities of the black diaspora. j ANTI-RACIST TECHNOPHILIA

From Ethnomathematics to Ethnocomputing

Ethnomathematics faces two challenges: first, it must investigate the mathematical ideas in cultural practices that are often assumed to be unrelated to mathematics. Second, even if we are successful in finding this previously unrecognized mathematics, applying this to children’s education may be difficult. In this essay, we will describe the use of computational media to help address both of these challenges.

The African Heritage of Benjamin Banneker

Benjamin Banneker is well known for his accomplishments in early American applied science, as well as for his seminal role in African-American science history. Historical and linguistic evidence suggests that his grandfather was of Wolof origin, and that his father was from the area between what is now Ghana and Nigeria. This cultural heritage may have emerged in some of his mathematical thinking.

CYBERNETICS AND AMERICAN YOUTH SUBCULTURE

Similar shifts can be seen in the use of cybernetic modelling across a wide variety of scientific disciplines. This article will categorize these shifts in terms of three historical phases: (1) modern cybernetics, focused on digital hierarchical systems, which reached its high point in the late 1960s; (2) transitional postmodern cybernetics, focused on analogue decentralized systems, which started in the late 1970s; and (3) stable postmodern cybernetics, based on a synthesis between the analogue/digital and centralized/decentralized oppositions, which started in the late 1980s. While the shifts themselves can be explained by internalist narratives, the ways in which youth subculture closely parallels these changes suggests that there are causal links between cybernetics and popular culture which work in both directions.

Experimental and credentialing capital: an adaptable framework for facilitating science outreach for underrepresented youth.

Increasing the numbers of black, latino and native youth in STEM careers is both an important way to reduce poverty in low income communities, and a contribution to the diversity of thought and experience that drives STEM research. But underrepresented youth are often alienated from STEM. Two new forms of social capital have been identified that can be combined to create a learning environment in which students and researchers can meet and explore an area of shared interest. Experimental capital refers to the intrinsic motivation that students can develop when they learn inquiry techniques for exploring topics that they feel ownership over. Credentialing capital denotes a shared interest and ability between all parties engaged in the experimental endeavor. These two forms of social capital form an adaptable framework for researchers to use to create effective outreach programs. In this case study sports biomechanics was utilized as the area of shared interest and understanding the slam dunk was used as experimental capital.

Basins of Attraction for Generative Justice

It has long been known that dynamic systems typically tend towards some state – an “attractor” – into which they finally settle. The introduction of chaos theory has modified our understanding of these attractors: we no longer think of the final “resting state” as necessarily being at rest. In this essay we consider the attractors of social ecologies: the networks of people, technologies and natural resources that makeup our built environments. Following the work of “communitarians” we posit that basins of attraction could be created for social ecologies that foster both environmental sustainability and social justice. We refer to this confluence as “generative justice”; a phrase which references both the “bottom-up”, self-generating source of its adaptive meta stability, as well as its grounding in the ethics of egalitarian political theory.