Magazine article Teaching Children Mathematics

# Elastic Geometry and Storyknifing: A Yup'ik Eskimo Example

Magazine article Teaching Children Mathematics

# Elastic Geometry and Storyknifing: A Yup'ik Eskimo Example

## Article excerpt

On sunny days, when the tide ebbed low enough, we would walk along the soft, dry, grainy shoreline and along the eroded, grassy, willow embankments. We searched for claylike, grayish brown mud that stuck together like putty, more prominent on the edges of the fallen earth....When we found the desired mud, we anxiously smoothed away a flattened area with our homemade storyknives, spitting on the mud continuously to moisten it until a creamy yet firm rectangular spot was cleared away, then the first storyknifer etched out a scene and some figures, and began her story.

Jerry Lipka and Nastasia Wahlberg (1998)

Storytelling occurs across cultures but is not generally thought of as having a mathematical component; nor are other everyday activities, such as shopping for groceries, packing for a trip, or making a quilt. Each of these informal activities, however, contains embedded mathematics; in Yup'ik Eskimo storyknifing, the forms etched illustrate a relationship between mathematics and ethnomathematics (see fig. 1). Children usually do not see the relationship between their surroundings and activities and mathematics. Connecting the intuitive, visual, anti spatial components of storyknifing, as well as other everyday and ethnomathematical activities, with mathematical reasoning is a way to adapt, enrich, and enlarge the types of problems and processes that elementary school students face when learning mathematics.

In Adapting Yup'ik Eskimo Elders' Knowledge, a development project funded by a National Science Foundation grant to create a supplementary elementary school mathematics curriculum, we are bridging the knowledge contained in everyday situations in southwest Alaska with the spatial abilities required for geometry. We have worked collaboratively in Alaska with Yup'ik Eskimo elders, teachers, mathematicians, and mathematics educators to transform the curriculum by incorporating local knowledge into culturally based mathematics lessons (Lipka 1998).

Two-Way Curriculum Development

Using embedded and culturally specific mathematics found in a certain context requires adapting everyday and cultural knowledge to school activities. The original purpose of the activities revolves around solving real everyday problems rather than hypothetical mathematical problems. Two competing and sometimes conflicting criteria guide this two-way process of developing curriculum: (1) ensuring cultural and contextual authenticity and (2) meeting mathematics standards.

In our project, the process begins with cultural documentation and analysis of the elders' knowledge. We first learn about activities and how they are performed by the elders in the context of their daily lives. We then engage in joint analysis until local conceptions and practices are at least partially understood by the curriculum developers. To accomplish the curriculum development, Yup'ik teachers, educators, mathematicians, and elders may jointly or individually propose activities. The activities are reviewed with participating teachers and elders, who provide feedback for further revisions and adaptations in the curriculum. After the activities have been revised several times, they are prepared for piloting and field testing in the classroom. Ultimately, teachers in other settings may use these methods to incorporate everyday and cross-cultural knowledge into school mathematics curricula for their students.

Storyknifing

Storyknifing is a way of telling a story to an audience while using a storyknife--a tool not unlike a butter knife--to etch symbols in the mud to illustrate and enhance the presentation. As the story proceeds, each scene is wiped away and the mud is smoothed over to allow another scene to be etched. The scenes incorporate the actions and movements of the symbolic characters and are transformed fairly quickly (see fig. 2).

Each scene etched by a storyknifer creates a map, describing interior spaces and natural landscapes. …

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