“Help me and let me help you.” Or in Ghana’s Twi language: “Boa me na me mmoa wo.”
The aphorism signifies cooperation and interdependence. And like many Twi expressions, it can be communicated with a symbol, or adinkra. This adinkra has two triangular halves that are almost, but not quite, symmetrical. One triangle has a circle sitting atop it and is missing a square from its interior, while the other triangle has a square attached to it and is missing a circle. Each half completes the other.
The symbol intrigues ethno-computing expert Ron Eglash. “There is no math concept in Europe for ‘complete me,’” says Eglash, of the University of Michigan in Ann Arbor.
Contemporary math has mostly Western origins, so ideas from non-Western cultures are often missing from the field, say Eglash and others who study ethno-mathematics, or the relationship between math and culture.
“It is useful to think of mathematics as a language,” says physicist Richard Taylor of the University of Oregon in Eugene. Some words and concepts will overlap across cultures but look different, while others will remain unique.
Efforts to identify those convergent and divergent math concepts — and add them to school curricula — can make math more culturally relevant, researchers say. Such research can also expand mathematical knowledge.
One way to detect math languages is through a given culture’s art, architecture and design. Eglash and his wife, graphic designer Audrey Bennett, have spent years teasing out the math hidden in these artefacts. That work has resulted in math models for cornrows, Native American bead work, henna designs, adinkras and others.
Over time, those models have transformed into free online coding tools. Users can learn about cultural concepts and math principles and then use that knowledge to generate their own designs, says Bennett, also of the University of Michigan.
The tools can increase math scores among students not traditionally represented in science, technology, engineering and mathematics fields, such as minority students in the United States or students in the Global South, Eglash’s research suggests (SN: 4/14/21). One study for example, showed that the adinkra model can help middle school students in Ghana understand logarithmic spirals.
Unlike linear spirals, where the space between each spiral revolution stays the same, log spirals grow as they extend outward. Snail shells follow this pattern. Many adinkra curves also derive from nature, such as those depicting a ram’s horns, chicken’s foot, bird’s neck and even a human fist. Ghanian artisans alter the tightness or looseness of a spiral to change the look of their adinkra designs. Students using the adinkra computing software can likewise change coil “strength” in their own designs.
In Eglash’s Ghana study, nine students in one class used the adinkra model to learn about log spirals while 10 students in another class learned the concept through conventional models. On a test of the material, the adinkra students scored higher, with an average test score of 45 percent, than the other students, who scored 14 percent on average, Eglash and colleagues reported in 2015 in the Multidisciplinary Journal of Education Research.
The experiment needs scaling up, but the team’s casual observations were striking. Students in the control group typically left immediately once class ended, while students in the adinkra group often stayed late to work on their computational designs.
Mavis Okyere, a math education researcher at the Catholic University of Ghana in Sunyani, has observed a similar phenomenon among middle and high school students in the Kumasi metro area who were learning about proportion, symmetry and other basic math concepts.
For instance, Ghanian students typically learn about rotational symmetry — the idea that a shape can maintain its form as it spins in space — by rotating triangles or squares (SN: 4/12/07). Okyere developed a curriculum that taught the concept through adinkras, such as Akoma Ntoasa, or “joining of the hearts.” This adinkra, a square connected to semicircles via four lines, can rotate 90 degrees in any direction and look the same.
Teaching math with adinkras proved immensely popular. The class was optional to join and initially only a handful of students showed up, Okyere says. “By the end of the fourth lesson, the class was full.”
Math education should give students both a window to a new world and a mirror reflecting their own world, says Rochelle Guttiérez, a mathematics education researcher at the University of Illinois Urbana-Champaign who was not involved in any of the research. “Too many times in math classrooms, people just look out and see lots of windows. They never get mirrors.” These tools provide that mirror, she says.
Besides adding cultural relevance to established concepts, learning new math languages has the potential to unearth previously unidentified patterns. That’s the case for the “complete me” adinkra. Eglash refers to this almost symmetry as “mutuality.”
Such discoveries can help students think through the math process from the ground up. Eglash’s thoughts on mutuality inspired seven U.S. geometry professors to develop a lesson around helping students define the concept. Students actively debated key theoretical questions, the professors wrote in a 2021 blog post for the American Mathematical Society. One student wondered if an exchange could be considered mutual if the corresponding shapes were of unequal size.
Unbeknownst to the student, that query captured the adinkra’s true significance, which Okyere, a native Twi speaker, describes as such: “We need each other, and we help each other in various ways even though … they are not the same. But I need you, and you also need me.”
Finding these sorts of links between math and cultural beliefs is at the root of ethno-mathematics, Eglash says. “There is a relationship between the geometric meaning and the social meaning.”