From the complex to the simple, so many of the daily, tradition-based activities of the Yup’ik are accomplished through the use and knowledge of symmetry.
This unusual connection is the focus of a National Science Foundation-supported project to study traditional everyday activities—from fashioning clothing out of raw irregular material to navigating on land and sea—and their potential contributions to math classes in Alaska and elsewhere.
The project is called The Potential Contribution of Indigenous Knowledge to Teaching and Learning Mathematics. It stems from Math in a Cultural Context (MCC), a larger and decades-old related body of work. Jerry Lipka, an education professor at the University of Alaska, Fairbanks, heads both.
This concept fascinates Lipka. He points out that Yup’ik elders were the first to discover that the principles of symmetry could be used in measuring and constructing a wide variety of everyday artifacts.
“We believe that there are underlying core embedded mathematical processes that enable Yup’ik elders to precisely construct their artifacts. These ways of thinking and constructing will be transformed into teaching and learning tools that Native students can relate to at many levels,” Lipka said.
Math in a Cultural Context
MCC has a long history of developing math modules that cover specific topics by relating mathematics content with Yupik cultural content (i.e., designing parka patterns) through curriculum guides, posters, storybooks and other instructional aids.
A recent randomized control study conducted in Alaska reported that students using two second grade MCC’s modules outperformed their peers who used their “regular” school math curriculum at statistically significant levels (see Kisker, Lipka et al. 2012 in the Journal of Research in Mathematics in Education).
Other research conducted by Lipka and his colleagues also revealed similar findings.
The Potential Contribution of Indigenous Knowledge to Teaching and Learning Mathematics is now in its first year. Over the three-year study period, Lipka and team hope it will present additional opportunities to understand everyday Yup’ik activities and how they relate to the foundations of mathematical thinking.
Traditions Rooted in Mathematics
To tap the wealth of indigenous knowledge, Lipka is once again teaming with two of his former students turned fellow educators and colleagues, Dora Andrew-Ihrke and Evelyn Yanez.
Andrew-Ihrke and Yanez are both Yup’ik community members and retired teachers with more than 70 years of teaching experience between them. Both women are involved in MCC and other projects, so the collaboration for this latest effort was a natural fit.
“They [Andrew-Ihrke and Yanez] have a marvelous knowledge of their culture; a really deep knowledge of cultural activities and how to produce all kinds of things,” Lipka said. “And as we’ve been working together, slowly over the years, we noticed a pattern within the knowledge and began to see the mathematical nature of the knowledge.”
What is Traditional Knowledge?
“Tradition knowledge encompasses very useful information that can be passed on to the young people,” Andre-Ihrke explained. “Some of it might include how to make materials for living—for example, a coat. The process of making that coat includes mathematics and a precise way of measuring. We must not ever waste materials and the byproduct has to fit the person you are making it for. You use your body parts [i.e., a finger] as a unit of measurement. … You can’t just estimate.”
For Yanez the same is true about indigenous knowledge. “Indigenous knowledge, to me, is what I have learned outside of the Western classroom; what I learned from my parents and from the elders that I lived with,” she said. Yanez has talked extensively about how she learned to navigate without instrumentation. This knowledge relates well to the concept of a coordinate grid.
Addressing a Disconnect
Although traditional knowledge is passed down through stories and activities in the home and surrounding community, it is often not represented within schools. In fact, this disconnect is what started the group’s journey.
“I always believed that schools should reflect the community,” Lipka said. “I moved to Alaska and saw the schools and said, ‘Hmmm. What is being reflected here?’ And that got us launched on this crazy ride!”
Lipka, Andrew-Ihrke and Yanez are working with their partners across Arctic Alaska, Norway and Sweden, Greenland and Kamchatka, as well as Micronesia to determine if indigenous groups in a different geographical, cultural, and linguistic spaces share similarities in the ways they construct their everyday artifacts.
Teaming with Yup’ik Elders
The project team will work within the participating communities to capture video data of elders performing daily activities like preparing food and making headbands. The researchers will also collect audio data of the elders explaining their actions in their own language to help them understand how concepts are expressed.
“I may use the word symmetry when elders fold material in half to see if one side is equal to the other side, but the Yup’ik people won’t use the word symmetry. So, what word will they use and what does it mean to them?” Lipka said. Together the video and audio data let the team analyze and compare concepts and ways of thinking across all five groups. From there, they will begin to transform and apply elders’ knowledge to classroom math-oriented activities.
Even though the project is in its early stages, Lipka and his team are not wasting any time. Lipka, Andrew-Ihrke and Yanez have already begun to build some of the activities that can be used in the classroom.
“These include things like geometrical construction, the development of measuring tools, using techniques based on indigenous knowledge versus store-bought, already constructed rulers,” Lipka said.
Ultimately, studying and bringing indigenous knowledge into the classroom ensures it will live on in future generations. After seeing some of the teams' earlier learning activities developed for the classroom one Yup’ik elder told Andrew-Ihrke that, “If you use this knowledge in the classroom, then the knowledge goes well into the future.” “She was very poetic,” Andrew-Ihrke recalled.
For more information about this project and Lipka’s other research on teaching math in a cultural context, visit: http://www.uaf.edu/mcc/. --Alicia Clarke