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From Ethnomathematics to
    Ethnocomputing




       Ron Eglash, RPI
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
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.)
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.
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.
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.
Culturally Situated Design Tools
• www.csdt.rpi.edu – main site
Results and On-going research
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
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.
• 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.
On-going Research
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
Synthesizer Tool
        http://www.cs.rpi.edu/%7Elaut/MP/pcsdt.html
        Hit “run”
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.
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.
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.
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:

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From Ethnomathematics to Ethnocomputing

  • 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
  • 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.
  • 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: