Constant Perimeter, Varying Area: A Case Study of Teaching and Learning Mathematics to Design a Fish Rack
This paper describes Math in a Cultural Context: Lessons Learned from Yupik Eskimo Elders (MCC modules), a series of modules designed to supplement K-6 mathematics curriculum. The MCC modules are meant to connect mathematics with Yupik culture and knowledge in a way that is consistent with constructivist practice. The author focuses on one particular module: Building a Fish Rack: Investigations into Proof, Properties, Perimeter, and Area (Adams & Lipka, 2003). Included in this module is an overview of the geography and ecology of southwestern Alaska, and the role of fish racks in the subsistence lifestyle of the Yupik people. The module is designed to connect cultural knowledge (building a fish rack using traditional Yupik techniques) to formal mathematics (shape, determining the length of diagonals). In this case study of a teacher and her sixth-grade class using the Building a Fish Rack module, the author conducted and analyzed teacher interviews, classroom observation records, and video of the classroom. As part of analysis, the author examines student achievement, comparing that of Alaska Native students to non-Alaska Native students, as well as compares achievement to students who studied the same mathematical concepts with commercially available textbooks. Based on pre- and post-tests, students who were taught with the Building a Fish Rack module made substantial gains, particularly compared to the growth of students who had been taught with commercially available textbooks. While the sample size for both control and treatment groups are small, the author does suggest that this analysis provides informative insights, particularly in terms of improving the performance of Alaska Native students.
This case study of one specific mathematics lesson presented through a cultural context is focused on developing reasoning through exploration of “inquiry-oriented, problem-centered” challenges. The study reports findings that this approach has led to higher student achievement in one classroom that included Alaska Native students. While the study is limited in its scope, it provides value in demonstrating how mathematical problems can guide students in exploration and learning through culturally relevant engagements. It is likely to be of most interest and use for those interested in inquiry based mathematical curricula with a specific focus on engaging the cultural interest of native Alaskan students.