Geometry through Beadwork Designs
Barkley, Cathy A., Cruz, Sandra, Teaching Children Mathematics
The fifth-grade children eagerly picked out envelopes containing brightly colored, geometric shapes to begin making their Ute Indian beadwork designs. Each child had a strip of construction paper simulating a tanned hide, or buckskin, to decorate with shapes traditionally used in Ute designs. Much excitement was evident as the students discussed how they wanted their patterns to look and what colors they wanted to use. The colorful geometry pieces were traded back and forth as the designs began to emerge on their papers.
The everyday activities of people, both past and present, involve many mathematical applications. Many of these applications have not been considered to be mathematics because they do not fit the traditional definition of mathematics as a rigid set of complicated rules and algorithmic procedures. The field of study known as ethnomathematics seeks to correct this misconception by studying mathematics within the context of culture (Ascher 1991). This study often involves a reexamination of artifacts from indigenous peoples.
One practice shared by all people is that of using geometry to decorate everyday objects. Native American beadwork exhibits a high degree of sophistication when it is examined in light of specific symmetrical patterns. Native American languages have no word for art; the notion of art as a separate idea had no meaning for Native people because it was incorporated into their everyday lives.
Before the arrival of European traders, Native Americans sewed such decorative objects as seeds, shells, and animal teeth to their tanned leather garments and objects. None of these objects added much color to the tanned goods, so a major advancement was made when someone realized the usefulness of decorating with porcupine quills. The quills were dyed with extracts from native plants, thus resulting in colorful articles of clothing, cooking utensils, and storage containers. When traders arrived with beautifully colored glass beads, the porcupine designs were adapted for use with these beads. Elegant isosceles and equilateral triangles, stepped mountains, and square and rectangular bundles were adapted from the quill designs to designs with the finer beads. The resulting designs were rich in the use of transformational geometry.
Children can gain an appreciation for Native American cultures as they study the geometry inherent in the beadwork designs. Swetz (1997) likens mathematics to a singular object in a painting with an otherwise bare canvas. The object may be interesting by itself, but without a background, it has limited meaning and no context. The use of a context in which to study mathematics is one of the central goals of the NCTM's Principles and Standards for School Mathematics (2000). Native American children can develop a sense of personal pride in the accomplishments of their ancestors by viewing geometry through beadwork designs. Girls may be especially intrigued to learn that the beadwork was designed and sewn by the women in the tribe.
The designs made by the Utes were used to communicate their feeling of harmony with the natural world in which they lived. The patterns became a rich story of events, places, or objects found in their natural world: mountains, pony tracks, feathers, tipis, medicine bundles, whirlwinds, and rabbit ears became a part of their beaded records. Each pattern is a unique creation of the artist, who expresses the natural world and her relationship to it through colors, figures, symmetry, and spaces. An essential element of all beadwork is its symmetry, which symbolizes the balance in, and the harmony of the people with, the environment.
Fourth-grade students in Colorado study the history of their state and the Native people who lived there before European exploration took place. The Ute Indian people were a small group indigenous to Colorado and Utah. Students expand their knowledge gained from social studies to include mathematics and art from this same historical perspective. …