This document discusses the advantages and challenges of ethnomathematics and introduces culturally situated design tools (CSDTs). The key advantages of ethnomathematics include defeating myths of genetic and cultural determinism, using math to bridge cultural gaps, and contributions to mathematics. Challenges include issues of authenticity, ownership, and ensuring CSDTs do not ghettoize students but instead spread knowledge. The document then describes several CSDT projects including on African fractals, a synthesizer tool for polynomials, and designs from Navajo students. It concludes by discussing plans for programmable CSDTs and a CSDT community site.

1. From Ethnomathematics to
Ethnocomputing
Ron Eglash, RPI

2. 7 Advantages of Ethnomathematics
• Defeating myths of genetic determinism (“race limits
intelligence”)
• Defeating myths of cultural determinism (if you do well
in math you are “acting white”)
• Using math to bridge cultural gaps (eg connecting
African Americans to Africa)
• Making cultural capital more available to its owners for
new purposes (new forms of hybrid identity, conversion
to other forms of capital, etc.).
• Peace and social justice efforts.
• Environmental sustainability efforts
• Contributions to mathematics, and inspiration for
similar endeavors in other disciplines

3. 7 Challenges of Ethnomathematics
1. Not all mathematical modeling of culture is
ethnomath.
• The more evidence that a model provides the emic
view (not etic), the better case for ethnomath.
• Evidence includes:
– Explanatory narratives by informants
– Variant use of a specific “design theme” (not rote
memorization)
– Correlations across different domains (eg linguistic etc.)

4. Challenges of Ethnomathematics
2. Professional, academic math is just as “cultural” as
any other type.
• If ethnomath cannot show the cultural aspects of
professional math, it has failed its mission.
– Examples include Mandelbrot’s critique of the exclusion
of illustrations, Forman’s study of arly quantum physics
in Germany, Bloor’s study of the history of Euler’s
formula for polyhedra, etc.

5. Challenges of Ethnomathematics
3. “Ownership” issues with cultural images and
practices must be negotiated with legitimate
cultural representatives.
4. The “Bantu Education” problem: how to avoid
ghettoizing students? How to show sophisticated,
world-class mathematics, spread ethnomath to
dominant groups, use multicultural rather than
monocultural approach?
5. Authenticity: how to support identity hybridity and
innovation rather than reify or freeze ethnic
identity.

6. Challenges of Ethnomathematics
6. The end of ethnomath “innocence”– how to
encourage recognition of the politics of race in
science/technology, the distinctions of indigenous,
vernacular, and state societies, “copping to” our
own race, class and gender positions, etc.
7. Using ethnomath to replace rote learning with
discovery learning and inquiry learning: to support
student agency in their creative development of
their own projects, skills and identity. From
consumers to producers.

7. Culturally Situated Design Tools
• www.csdt.rpi.edu – main site

8. Results and On-going research

9. African Fractals with Andrew Woodbridge
(Grover Cleveland High School NYC)
•10th grade computer science class, two sections.
•About 75% minority, over 50% female.
•Control class has 6 days on fractal instruction websites with
java applets.
•Intervention class has 6 days on the African fractals website.
•Post-test shows higher scores in intervention group;
•statistically significant at .001 level

10. 1. Attitudes towards careers in information
technology: Baseline data was generated by
175 randomly selected eighth grade students
from low-income families. We found
statistically significant (p<.05) higher
aspirations for careers in IT in minority
students exposed to CSDTs in comparison to
our baseline data. A similar intervention with
90% white students did not show a statistically
significant difference from the baseline data.

11. • 2. Quasi-experimental evaluation in
mathematics class: Torch middle school in
California, compared the performance of two
pre-algebra classes, one with the Virtual Bead
Loom, and one without. Found statistically
significant higher scores (p < .05) in the class
using the VBL. The study was subsequently
accepted for a master’s thesis.

12. On-going Research

13. Bill and Melinda Gates STEM initiative in
Cleveland Ohio
Grade 9-10 teachers from 2 schools in Ohio came to RPI for
training for project-based learning; CSDTs one of several
technologies presented.
Math and music teacher wanted to work together on
Polynomials
We proposed new CSDT: Synthesizer tool
—cultural focus on electronic music (Moog,
Jimi Hendrix, etc.).
— math focus on Visualization and
“audio-zation” of polynomials

14. Synthesizer Tool
http://www.cs.rpi.edu/%7Elaut/MP/pcsdt.html
Hit “run”

15. Dine college, Navajo Nation
Designs from a workshop with Navajo
high school students. We used this
opportunity to build better relations
with the educators and get feedback
on the software. Everyone seems to
agree that adding non-traditional
colors was culturally acceptable so
we did that.

16. Dine college, Navajo Nation
When asked about this particular angle (about 36 degrees), weaver said it is create by an
“up one over one” pattern (up one weft over one warp). But she said she could do lots of other
patterns (up one over 2, over 3, etc.). Why is this one used so commonly? She explained that
other angles gave a more jagged edge. In other words they were concerned about the aliasing
problem, a common feature in early computer graphics (and still a concern in certain situations
such as bitmaps). Do some rugs show anti-aliasing techniques? This implies a whole new realm
of research in which children could be involved.

17. programable CSDTs (pCSDTs)
Eventually we hope to have all CSDTs in this scratch-like programable interface. Some
progress was made this summer but it will not launch until December.

18. CSDTs community site
A prototype for the site is now up and running at http://community.csdt.rpi.edu/
Here is a prototype logo for the community site: