Seated on a couch in their house in Manokotak, in Alaska’s southwestern Bristol Bay region, Yup’ik elders Mike and Anecia Toyukak paged through a notebook of mathematics lessons based on traditional Yup’ik concepts. The couple is part of a team of elders, educators, curriculum writers and others, including University of Alaska Fairbanks (UAF) professor Jerry Lipka, who have collaborated for more than 30 years. During that time, the group has produced 10 culture-based mathematics lessons for elementary-school students.
In the Yup’ik view, the human body is the measure of the world, whether the item to be gauged is small, like one element of a hat pattern, or large, like the distance to be traveled between two features in the rugged Alaska landscape. “Here’s how we measure,” said Anecia, a retired teacher, as she jumped up to demonstrate computing lengths with a portion of the forefinger, the hand in open and closed configurations, one or both outstretched arms and more.
The U.S. Department of Education’s Alaska Native Educational Program and the National Science Foundation have supported the project, called Math in a Cultural Context. “All curricula are culturally based. The key question is, on whose culture is it based?” asks an article in the Journal of American Indian Education that was co-authored by Lipka, UAF professor Joan Webster and Evelyn Yanez, a Yup’ik educator and UAF adjunct professor.
Schools across Alaska have taught the curriculum. Research reveals that students from several Alaska tribes, as well as non-Native students, show improvement in test scores and outperform their peers when they use the system. This is according to scholarly papers in publications such as The Journal for Research in Mathematics Education by Lipka and co-authors including Dora Andrew-Ihrke, a Yup’ik educator and UAF adjunct professor. The curriculum is also “a small step in reversing power relations and what constitutes legitimate school knowledge,” the authors write.
Through the innovative lessons, children develop skills in measuring, which leads to understanding numbers, proportionality, geometry, algebra, data collection, graphing, probability, and more. The modules successfully cover in the earliest grades what is generally considered higher mathematics, according to Sassa Peterson, a Yup’ik educator and the project’s translator. “Both Evelyn and I have said we wished the curriculum had been available when we were young teachers,” Peterson said.
In the module “Patterns and Parkas,” the youngest students investigate the principals of geometry by folding an uneven item to create a symmetrical form, such as a square or circle. Practically speaking, this lesson can be used, for example, to make parka border patterns. It’s also conceptually important—critical for understanding symmetry, a basic idea of Yup’ik mathematical thinking. “You cannot have the whole without the half,” said Yanez.
In “Star Navigation,” fourth, fifth and sixth graders use cultural knowledge about angles and the stars to determine location, direction and distance. In “Salmon Fishing,” sixth and seventh graders integrate probability and environmental science, as they study salmon species and their life cycles.
The practical curriculum supports Yup’ik culture and values. The classroom is child-centered, with students working collaboratively. At home, the students see their parents and grandparents using similar approaches to make clothes, boots, snowshoes, kayaks, fish-drying racks and more, according to Anecia and Mike Toyukak. Peterson described traditional Yup’ik life as “rich in mathematics.”
The project has an international component, said the Toyukaks. In addition to working with partners in Alaska, the group has explored the relationship of culture and mathematics with Sami people in Sweden and Norway, Koryaks from Russia’s Kamchatka region, Yapese in Micronesia and Inuit in Greenland.
The work is ongoing, as the researchers continue to meet with elders and delve into the subtleties of the mathematics embedded in Yup’ik daily activities. “We’ve moved forward in just the last six months,” said Lipka. “We’re even learning from topics we first considered years ago.”
One recent realization has been that certain ideas are embedded in the language and used when referring to varied activities. Yanez explained: “We use the same words when making baskets, making parkas, navigating by boat and so on.” As a result, the team is working on supplemental learning modules that are currently in a pilot, testing phase in about a dozen schools.
Group members hope their work inspires other communities to work with their elders on their own curricula. Said Lipka: “We want to encourage others to see the beauty in this process.”
Here is a video on folding thirds: