Originally published in the International Study Group on Ethnomathematics (ISGEm) Newsletter, Volume 13, Number 2, May 1998. Located at: http://web.nmsu.edu/~pscott/isgem132.htm. Article reproduced 2003 with permission of the ISGEm Newsletter editor for use in the Ethnomathematics Digital Library (www.ethnomath.org) developed by Pacific Resources for Education and Learning (www.prel.org).

Hairstyles Talk a Hit at NCTM!

Gloria Gilmer and Mary Porter

Gloria Gilmer and Ron Eglash presented the 1998 ISGEm talk at the NCTM Annual Conference to an overflow crowd at the Convention Center in Washington, DC. Even ISGEm's editor, Rick Scott, was turned away from the crowded room. The popular talk was on Hairstyles in African American Communities. In an Oprah Winfrey-like fashion, Gilmer highlighted styles worn by participants in the audience, many of whom were African American. She noted that these styles are seen in schools and communities but not in mathematics textbooks, and this must be changed.

In preparation for the talk, Dr. Gilmer and Ms. Mary Porter, the presider, interviewed a master hairbraider from Nigeria and one of her American-born students in their respective shops. Their customers and operators were also interviewed. The idea was to determine what the hairbraiding and hairweaving enterprise can contribute to mathematics teaching and learning and what mathematics can contribute to the enterprise.

The observations and interviews provided insight into some of the cultural values that form the basis of hairbraiding and weaving traditions in African American communities and the creative use of geometrical patterns in the design of hairstyles. For generations, African Americans were told that "nappy" hair was bad and were made to feel that the only way to attain "good" hair was to straighten it. The chemicals and heat treatments used to straighten the hair often resulted in damaged, unhealthy hair that would not grow. The customers we interviewed, however, felt good about having a beautiful hairstyle without altering the natural texture of their hair. We were told that some styles required sixteen or more hours to complete. Often this is done in a single sitting. Beyond beauty, the enterprise is also an important source of income for African Americans. At the age of eleven, one stylist said she was the neighborhood braider and could always make money. Therefore, concepts of time use and value, cost of supplies and equipment, and establishing workers' salaries and customer fees are important sources of mathematical problems for the classroom.

Gilmer displayed a sequence of hairstyles using male and female models. Some styles involved tessellations of the scalp with triangles, rectangles, and pentagons. Cornrows, both in concentric circles and in spirals, were seen on the scalp; spirals were also seen in planes orthogonal to the scalp. Self-similarity, symmetry, and fractal patterns were also shown. Eglash showed that these aspects of the hair styles are part of a much broader fractal design theme in African material culture, ranging from architecture and craft production to symbolic and quantitative systems. The storyboard for a computer-based math lab showed how students can use simulations of these designs to support learning in geometry, algebra and trigonometry.

The two presentations demonstrated the first two steps in Gilmer's Five Step Model for Concept Development. These steps examined the importance of the concept intuitively and its occurrence in nature or in culture. Hence, they drew heavily upon the visual aspects of mathematics and one's own experiences. The last three steps, which treat the concept with mathematical rigor, were alluded to. This model was used successfully to engage students in mathematical studies at all levels. We used it to motivate the study of Euclidean and fractal geometry. In this way, the relevance of the study was made clear.

Feedback from the session has been quite encouraging. A Harcourt representative wrote of her interest in including photos similar to those shown in the presentation in their math textbooks. Jim Barta, ISGEm treasurer, commented, "The feeling in that room was so wonderful!" Shirley Burkes, a mathematics and science support teacher in the Baltimore Public Schools, said, "Your part on the program was excellent! I find myself looking at everybody's hair and thinking of how I can use the design in class because all the girls braid each other's hair." Another participant said, "I heard people talking about this session on the train. I was here forty minutes before the session began, and the room was already full."

Our experience suggests that if we are to increase African American appreciation for mathematics, as the Standards state, then the curriculum content must be extended to include a range of activities that African American communities engage in naturally and from which mathematics is derived. Our experience also suggests that it is beneficial for mathematics educators to subject a familiar thing to detailed study for this is, after all, one of the outstanding educational values of mathematics.

Next year, Gilmer and Eglash hope to demonstrate how the quality of learning can be enhanced by manipulating computer simulations of these hairstyles. They also hope to extend the time of the session and maybe even get a larger room.

References

Sagay, Esi. (1983). African Hairstyles, Portsmouth NH: Heinemann Educational Books.
Oliveras Contreras, Maria Luisa. (1997). Mathematics and crafts in Andalusia. ISGEm Newsletter; 13(1), 3-5.

Gerdes, Paulus. (1997). On Culture, Geometrical Thinking and Mathematics Education in Ethnomathematics: Challenging Eurocentrism in Mathematics Education. Arthur B. Powell and Marilyn Frankenstein (editors), State University of New York Press.