Ron Eglash

Dept. of STS, Sage Labs

Rensselaer Polytechnic Institute

110 8th Street

Troy, NY 12180-3590 USA



To appear in Information Technology and Indigenous People by Dr Laurel Evelyn Dyson, Max Hendriks and Stephen Grant: Idea Group 2006.


Ethnocomputing with Native American Design


The term “ethnomathematics” refers to mathematical concepts embedded in Indigenous practices. Examples range from purely numeric (eg counting systems) to geometric (sculpture, textiles) and even various uses of logical relations (such as Indigenous kinship diagrams). In discussing my previous work on fractal structures in African material culture (Eglash 1999), Matti Tedre of the University of Joensuu in Finland suggested the term “ethnocomputing,” which seems a better fit, given that many of the examples made use of computer simulations in order to “translate” between Indigenous practices and western technical concepts. My efforts are primarily focused on using these computer simulations of Indigenous designs to aid in mathematics education of secondary students (primarily those whose heritage are based in those traditions). In fall 2001 our team at RPI received funding from Housing and Urban Development, the Department of Education, and the National Science Foundation that allowed us to include some new efforts in Latino and Native American designs as well. We have titled this suite of simulations “Culturally Situated Design Tools” (CSDTs); they are available as free applets online at This paper will review the development and evaluation of CSDTs created in collaboration with Native American communities, and discuss how our activities attempt to navigate through the potential dangers and rewards of this potent hybrid of information technology, traditional culture and individual creativity.


1. The Virtual Bead Loom

In the summer of 2000 I was invited by professor James Barta at the University of Utah to discuss the ethnocomputing approach with the educational community on the Shoshone-Bannock reservation in southern Idaho. Key tribal members included Drusilla Gould, an instructor in American Indian Studies at Idaho State University, and Ed Galindo, science teacher at the reservation junior-senior high school. Our first attempt, the virtual bead loom, turned out to be one of the most successful tools in our entire repertoire.  


There were several aspects of the bead work that made it seem like an important candidate for one of the CSDTs. First, it offered a bridge between historic tradition and contemporary culture. All too often, components of what constitutes “tradition” have—whether by the colonial experience or neocolonial forces like tourism--become “museumified” into static forms that have little engagement with contemporary community members. But Native American bead work in general, and Shoshone-Bannock beadwork in particular, has not suffered this fate. It maintains direct ties from pre-contact practices, in which beading was an important form of personal adornment, to contemporary hybrids in which military insignia and other representations decorate everything from cigarette lighters to Wacom® digital stylus pens (Eglash 2004). Second, the rows and columns of the loom are analogous to the deep design theme of four-fold symmetry in Native American cultures (which will be explained momentarily). And third, the two axes of the loom offer an analog to the Cartesian Coordinate system, and thus provide a good match for standard school curricula.


The web page for this Virtual Bead Loom (VBL) begins by showing the four-fold symmetry theme that can be seen in a wide variety of native designs: Navajo sand paintings, Yupik parka decoration, Pawnee drum design, and other geometric manifestations of the “Four Winds” or “Four Directions” concept (which can also be seen in the prevalence of base four or sub-base four counting systems, temporal patterns of four in drumming rhythms, etc.). We then introduce the students to the analogy between the Cartesian coordinate system and these four-fold symmetries. This is a crucial step in ethnomathematics, and we initially gave a great deal of consideration to it. For example we show how the Yupik parka designers use a two-finger length to count over from left or right of the center line—in other words there is actually a quantitative grid employed here, so that it is not merely a metaphor to call it a Cartesian system. In contrast to our excitement in finding good evidence for an Indigenous Cartesian system, we have found that math teachers, even those at reservation schools, are typically far less interested in claims for Indigenous knowledge, and more focused on whether or not students can actually learn mathematics by using this software. The good news is that both goals seem to work in concert: the students not only express excitement in using it, but also show statistically significant increases in their performance on math evaluations.


The first prototype allowed creation of a pattern with only single beads added one by one. This was clearly too tedious, so we introduced shape tools: for example, you enter coordinate pairs for the two endpoints to make a line, or coordinate pairs for opposite corners to make a rectangle. Following the same logic, we created a triangle shape tool, in which the user enters the coordinates pairs for the three vertices to get a triangle. However, a problem arose because these virtual bead triangles often had uneven edges--the original Shoshone-Bannock beadwork always had perfectly regular edges (figure 1).


Figure 1: comparison of uneven steps in VBL triangle, and even steps in Shoshone-Bannock beadwork.


The original program used a standard “scanning algorithm” – filling in any specified polygon – for the task of generating these triangles. But somehow the traditional beadworkers had algorithms in their heads that were better. After a few conversations with them, we realized that they were using iterative rules—e.g. “subtract three beads from the left each time you move up one row.” We developed a second tool for creating triangles, this time using iteration (figure 2). We also retained the original triangle tool,

Figure 2: Triangle iteration example. This is actually several triangles overlaid to produce the change in colors.


so that students could see the contrast between the two. This has provided a powerful learning opportunity: claiming that there is such a thing as a “Shoshone algorithm” can evoke skepticism, but a comparison between the standard scanning algorithm with that used by the Shoshone bead workers makes the existence and strength of the Indigenous computing quite clear.


Art teacher, Mimi Thomas, working at a school serving the northern Ute reservation in Utah, has introduced new collaborative efforts between art and math instruction using the VBL. Figure 3 shows one of the examples from her classroom in which students created

virtual designs using the VBL, transferred the pattern to paper for use in math class, and then created physical beadwork in art class based on that same pattern.  

Figure 3: Ute students create physical bead work based on the VBL.


The most recent tribal connection has been with the Onondaga Nation in upstate New York. Following discussions with their school’s cultural counselor, Frieda Jacques, we began to develop additional historical material. An exciting contribution from their group was the important historical connections with the development of the US constitution. They also suggested creating an option to work with wampum, rather than spherical beads. Joyce Lewis, a tribal member and math teacher at a nearby high school serving the reservation population, investigated traditional wampum and found that their height to width ratio was about 2:1 – thus disrupting the one-to-one mapping of beads to integer coordinates which had made the current VBL work so well in math classrooms. We decided to offer two wampum choices, one with traditional dimensions and a modified bead with a 1:1 height to width ratio—a sort of hybrid bead whose reconstructed identity echoed the cultural hybridity inhabited by many of the students. See Barta et al 2003 for further discussion of the VBL.


2. SimShoBan: simulation of a cultural ecology

Back at the Shoshone-Bannock reservation in Idaho, discussions with science teacher Ed Galindo lead to a project the Shoshone students dubbed “SimShoBan” – a simulation of pre-colonial life, both social and biological. The development of the SimShoBan CSDT has been described elsewhere (see Eglash 2001). While the project began with a very broad scope, conversations with students and faculty at the reservation school eventually lead to a focus on simulations of four Indigenous technologies: the fish weir in the spring, the camus root gathering basket in the summer, the tipi in the fall, and the pine nut winnowing basket in the winter. The gathering basket simulations resulted in some particularly interesting creations by the students. Figure 4 for example shows two

Figure 4: “Munchie Basket” by 16 year old student at left, “Invincible” by 14 year old at right.


gathering basket simulations; the one at left was made by one of the older students (age 16). Younger students (age 12-14) tended to create simulations that look less recognizably “traditional,” such as the one on the right.  This was enabled by the particular software prototype used at the time, which allowed them to manipulate computer graphic parameters (such as resolution) as well as parameters that would correspond to physical features (such as basket depth). The age difference may have been due to the context of a science summer camp, in which the older students were constantly asked to set an example for the younger, but it also matches research that suggests that minority ethic/racial self-identity makes a dramatic (ie non-linear) shift in this age range (cf Forbes and Ashton 1998).   The names that students used to title their work also revealed playful creativity, including irony or parody, even for the older students who were more serious about the concepts of Indigenous knowledge (as the title “Munchie Basket” invokes). The basket simulation in figure 5, “The Black Bullet” is particularly interesting: this student tried to generate a basket with 1 million strands, causing the laptop to crash. He re-booted it and tried again at 900,000; gradually decreasing the number until he found the maximum it could tolerate. We had a striking sense that he felt he had mastered the machine in this process of discovering its limits.

                                                                                                                                                          Figure 5: the black bullet

3. Yupik Simulations

Native researcher Claudette Engbloom-Bradley has been working on Yupik star navigation for a number of years (Bradley 2002), and developed a board game for the purpose of teaching both the skill (much needed for survival when snow mobiles or Global Positioning System  fails) and the mathematics embedded in its practice. With her help we created an online version of this game, with the hope that although it is not really “design” per se it might open the door to the development of other Yupik CSDTs. In March 2003 I accompanied Engbloom-Bradley on a trip to the village of Akiachak in the Kuskokwim delta, near the Bearing sea. The children at the local school greatly enjoyed reading the cultural background section, which named Fred George, the Yupik navigator, with whom they were all familiar. They were happy to engage in the game once or twice, but soon grew tired of it. That is partly because we only finished the first “level” of the game; presumably adding on additional levels will allow us to extend their interest. But it is also a drawback of the lack of creativity involved in playing a game as opposed to the act of design:  the design tools often engage the children for a much greater span of time.


Fred George and his family generously invited us to a dinner one night, and afterwards I showed them the simulations from SimShoBan. Fred did not speak much English, but was excited about the Shoshone fish weir, and showed us a traditional Yupik weir that he made for catching blackfish (Dallia pectoralis). Although there were considerable differences between the two, we created a new version of the webpage on the spot, substituting an image of Fred with his weir for the Shoshone image. The following day we tried it at the school, and the children were delighted—it had both the name recognition of Fred George and a more creative component in its design capabilities (figure 6). Adults we spoke to suggested that we develop a Yupik-specific


Figure 6: One of Fred George’s granddaughters creating a 3D simulation of her grandfather’s fish weir.


design, and expressed interest in the possibility of a cross-cultural exchange between the Shoshone and the Yupik.


4. Evaluation

There are several advantages to the use of Culturally Situated Design Tools, but one of the most important is the possibility of boosting children’s mathematics achievement. Our best quantitative data to date comes from evaluations of the VBL. Middle school teacher Adriana Magallanes, who has both Native American and Latina heritage, ran a quasi-experimental study of the VBL for her master’s thesis.  She compared the performance of Latino students in two of her pre-algebra classes, one using the beadloom, and the other using conventional teaching materials. She found a statistically significant improvement (p<.01) in the math test scores of students using the beadloom.  Other teachers have used pre-test/post-test comparisions on a single classroom, and also found statistically significant improvement using the VBL. We expect to find similar positive results with the other design tools. We have also examined the impact of design tools on attitudes towards information technological careers with minority students, using the Bath County Computer Attitudes Survey. Using workshops with Latino and African American students, we found statistically significant (p<.05) increases over baseline values for that local population. This indicates that it may also be possible to raise interest in technological careers for Native American students using the design tools.



CSDTs offer an exciting convergence of both pedagogical and cultural advantages. Unlike many other ethnomathematics examples, we can modify the interface to allow a  close fit to the math curriculum, which makes it easy for teachers to incorporate into their class. At the same time their ability to move between virtual and physical implementations allows use in the arts; and their historical connections provide teaching opportunities in history and social science. Most importantly they allow for a flexible, creative space in which students can reconfigure their relations between culture, mathematics, and technology.


Acknowledgment: This material is based upon work supported by the National Science Foundation under Grant No. 0119880.




Barta, J., Jette’, C., & Wiseman, D.  (2003). Dancing Numbers: Cultural, Cognitive, and Technical Instructional Perspectives on the Development of Native American Mathematical and Scientific Pedagogy. Educational Technology Research and Development, 51(2), 87-97.


Bradley, Claudette. (2002). “Travelling with Fred George: The Changing Ways of Yup’ik Star Navigation in Akiachak, Western Alaska.” In Krupnik, Igor, and Jolly, Dyanna (eds.).  The Earth is Faster Now: Indigenous Observations of Arctic Environmental Change. Fairbanks Alaska: Arctic Research Consortium of the United States,.


Eglash, R. (1999). African Fractals: modern computing and Indigenous design.  New Brunswick: Rutgers University Press.


Eglash, R. (2001) “SimShoBan: Computer simulation of Indigenous knowledge at the Shoshone-Bannock School.” Online at


Eglash, R. (2004). “The American Indian Computer Art Project: an Interview with Turtle Heart.”pp. 181-206 in Eglash, R., Croissant, J., Di Chiro, G., and Fouché, R. (ed)  Appropriating Technology: Vernacular Science and Social Power, University of Minnesota Press.


Forbes, Sean and Ashton, Patricia.” (1998). The identity status of African Americans in middle adolescence: a reexamination of Watson and Protinsky - 1991 - response to M.F. Watson and H. Protinsky, Adolescence, vol. 26, p. 963.” Adolescence Winter.