Audrey BennettRon Eglash is a professor of science and technology studies at Rensselaer Polytechnic Institute.
Around 1987, I noticed a funny thing about aerial photos of African villages: they look a lot like fractals, the repetitive shapes from computer graphics. Rectangular architecture had nested rectangles within; circular houses were in circles of circles, sometimes down to very small scales. A Fulbright fellowship gave me a year of travel in west and central Africa, where I found these recursive patterns-within-patterns in African sculpture, textiles, hairstyles and all sorts of things. Moreover, these were not just intuition; some of the artisans actually had procedures or recipes; a sort of geometric algorithm.
I published “African Fractals,” thinking that we could now have African math in inner-city classrooms, but teachers told me they did not know how to teach this material. With support from the National Science Foundation, we started online computer simulations called culturally situated design tools. Kids could now use the mathematics of scaling and recursion to design their own African village, sculpture and cornrow hairstyles. Over time, we branched out to use these tools for Native American beadwork, Latino percussion rhythms, and even graffiti and break-dancing.
Flash forward to 2010: Now we are broadening our approach with a new grant from the science foundation’s GK-12 program, which places graduate science and technology students as assistants in elementary and secondary schools. Our project, Triple Helix, creates these graduate fellowships in fields like nanotechnology and biomedical research. We challenge these graduate fellows to not only help teach middle-school students from low-income backgrounds, but also to think about how to redirect their own research to become more relevant to developing the resources and meeting the needs of these low-income communities. Our hypothesis is that kids will be more interested in science and technology when they see its relevance to their own lives.
The GK-12 folks kindly include an international component, which explains why I am writing this from Ghana. My job here is to create research opportunities, so that next year grad fellows can come with me and explore connections to their research and teaching in the United States.
We have three potential areas. First, since two of the grad fellows are in computer science, the existing cultural design research seems like a good starting point. But will African kids also be interested in mixing math with culture? We are about to find out. There are also opportunities for the grad fellows in biomedical research: my co-principal investigator, Audrey Bennett, has been working on H.I.V. prevention, and will be conducting some initial research to examine how college students here think about AIDS.
Finally, I have also brought with me five outstanding undergrad engineering students. They are not actually part of the GK-12 grant; coincidentally, Rensselaer Polytechnic Institute started an exchange program with an engineering college here. But their project, converting biomass waste to useful energy, seemed like something our graduate students in nanotechnology or chemical engineering might want to be involved with, so I volunteered to chaperon them on this journey as well. Add in our graceful hosts from Kwame Nkrumah University of Science and Technology, and Ghana’s early success in the World Cup, and it’s hard to imagine a better way to spend a summer break.
Our first challenge for testing the cultural design tools with African children was that none of the local middle schools had a computer lab. So before leaving the United States I purchased eight small netbooks: vastly cheaper than trying to buy computers there. Unfortunately, carrying eight netbooks meant that I could be mistaken for an unscrupulous vendor trying to skirt the import fees. So I began distributing one netbook to each of my traveling companions, including my children. I know, I sound like a drug smuggler — but it gets worse. One of the R.P.I. undergrads on our team caught our flight with minutes to spare, and left his bag with me for a restroom run. In the rush to board the plane I forgot to tell him that I had stashed another netbook in his bag. I’m like that guy they warn you about in the airport announcements.
We did clear customs in Accra, and a couple of days later found ourselves at Ayeduase junior high school in Kumasi. Our first question to the students: What math comes from Africa? “Addition and subtraction” and “90-degree angles” were the most common answers. I asked them if there were other angles, and they looked at me blankly. One of the teachers had on a shirt with Adinkra patterns, so I pointed out that source of indigenous geometric design. Now we had some smiles and nodding.
At that point, we introduced the idea that there is math in traditional Ghanaian music. It took some prompting, but we finally got them to sing — it was a joyful, soulful noise mixing African sensibilities with Christian lyrics. Finally we opened up the Rhythm Wheels software. This Web applet lets you attach percussion sounds (traditional drumbeats and hip-hop effects like scratching) to rotating wheels of various sizes. Because the wheels rotate at the same speed, a wheel with three beats will finish before a wheel with four beats. So the first thing we did was challenge the students to change the number of loops so that the wheels finish simultaneously.
Working the mouse was difficult for them. But my children were terrific assistants, and soon had everyone creating rhythms. Eventually, all the students reported the right answer: If the three-beat wheel goes around four times, and the four-beat wheel goes around three times, they will both stop at 12 beats. They had discovered the least common multiple for themselves, and they had used music to do it.
About this time I lost my assistants, because a monkey had shown up, and they wanted to help the younger kids in the yard chase the monkey (which, surprisingly, seemed to enjoy the attention).
After some more least common multiple exercises, and a final post test (which did show considerable improvement), I let them experiment: They seemed especially excited about the hip-hop sounds. Next on the agenda will be working with our cornrows and fractal geometry tools, and — thanks to the inspiration from that shirt — perhaps some experiments with simulating Adinkra.