Culturally Situated Design Tools

Our first design tool was developed for the "African Fractals" project (Eglash 1999). Mathematics teachers with large African American student populations reported that they could not use fractals -- there was too much pressure to conform to the standard curriculum -- and that they felt that many of the examples were too culturally distant from the students. They all felt that the examples of hairstyles would work well however. Thus our first tool focused on the hairstyles, and used the term "iterative transformational geometry" rather than "fractals." The graphic above shows the result, called "Cornrow Curves." Each braid is represented as multiple copies of a “Y” shaped plait. In each iteration, the plait is copied, and a transformation is applied. The series of transformed copies creates the braid. In the above example, we can see the original style at top right, and a series of braid simulations, each composed of plait copies that are successively scaled down, rotated, and translated (reflection is only applied to whole braids, as in the case where one side of the head is a mirror image of the other). One of the interesting research outcomes was that our students discovered which parameters need to remain the same and which would be changed in order to produce the entire series of braids (that is, how to iterate the iterations). The cultural background section of the website is divided into “how to” (for those unfamiliar with the actual process of creating cornrow hairstyles) and an extensive cultural history of cornrow hairstyles. We have found that many students, even those of African American heritage, will tell us that cornrows were “invented in the 1960s.” The history section was developed to provide students with a more accurate understanding of that history, starting with their original context in Africa (where they were used to signify age, religion, ethnic group, social status, kinship, and many other meanings), the use of cornrows in resistance to the attempt at cultural erasure during slavery, their revival during the civil rights era, and their renaissance in hip-hop. Most importantly, we want students to realize that the cornrows are part of a broader range of scaling designs from Africa (Eglash 1999), and that they represent a part of this African mathematical heritage that survived the middle passage. As noted previously, we have since developed a wide variety of design tools, ranging from simulations of Mayan pyramids (see image below) to virtual baskets. Our evaluations have been based on pre-test/post-test comparisons of mathematics performance, average grades in mathematics classes (comparing a year with the tools to the previous year without), and scores on a survey of interest or engagement with IT (specifically computing careers). All three measures show statistically significant increase (p < .05 or better) with use of these tools. In summary, we note that any attempts to re-value local or traditional knowledge in the face of oppressive histories will be challenging, and all the more so if the re-valuation has to compete with current mainstream global practices. But we feel that Culturally Situated Design Tools offer an important new position in which to engage that struggle.