Abstract
Pattern is a key element in both the esthetics of design and mathematics, one definition of which is “the study of all possible patterns”. Thus, the geometric patterns that adorn cultural artifacts manifest mathematical thinking in the artisans who create them, albeit their lack of “formal” mathematics learning. In describing human constructions, Franz Boas affirmed that people, regardless of their economic conditions, always have been engaged in activities that reveal their deeply held esthetic sense. The Tlingit Indians from Sitka, Alaska, are known for their artistic endeavors. Art aficionados and museum collectors revere their baskets and other artifacts. Taking the approach of ethnomathematics, I report my analysis of the complex geometrical patterns in Tlingit basketry.
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Notes
Twining is a basketry technique in which two wefts cross over each other between warps. There are variations to twining that result in different surface features of the weave. For an illustration, see http://www.washington.edu/burkemuseum/baskets/Teachersguideforbasketry.htm
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False embroidery (the inappropriateness of this term is indicative of ethnocentrism) is a weaving technique of overlaying to introduce different colors in the design. Usually a third color as a weft is introduced and twined in such a way that the design only appears on the outer surface of the object. In contrast to embroidery, which is done after completing an object, false embroidery is a part of making the object and continues as the weaving of the object progresses. A characteristic of false embroidery is that it is at a slant angle and opposite orientation to the twining. The Tlingit basket makers used moss, maidenhair fern, grass, etc. in their false embroidering of designs.
Emmons wrote that often the Tlingit women would take a European textile and boil it to extract dyes, then steep the material in the resulting liquid (Emmons, 1903/1993, p. 238). However, in later days when aniline dyes were available, the use of colors in baskets was radically impacted.
The Tlingit mat had a painted motif, similar to the wood-carved items. One Tsimshian basket had the word SISTER woven on it, the other had two stylized faces of a bear.
This phenomenon, common all over the world, has made the knowledge of ethnobotany and dye chemistry vulnerable and gradually disappear.
References
Apple, M. W., & Buras, K. L. (Eds.). (2006). The subaltern speak: Curriculum, power, and educational struggles. New York: Routledge.
Arnheim, R. (1986). New essays on the psychology of art. Berkeley: University of California Press.
Bishop, A. J. (1988). Mathematical enculturation. A cultural perspective on mathematics. Dordrecht: Kluwer.
Boas, F. (1927/1955). Primitive art. New York: Dover
Emmons, G. T. (1903/1993). The basketry of the Tlingit and the Chilkat blanket. Sitka, AS: Sheldon Jackson Museum. (Originally published in July, 1903, Memoirs of the American Museum of Natural History, volume III)
D’Ambrosio, U. (1985). Ethnomathematics and its place in the history and pedagogy of mathematics. For the Learning of Mathematics, 5, 44–48.
D’Ambrosio, U. (2001a). Ethnomathematics. Link between traditions and modernity. Rotterdam: Sense Publishers.
D’Ambrosio, U. (2001b). What is ethnomathematics and how can it help children in schools? Teaching Children Mathematics, 7, 308–310.
Deloria, V., Jr. (1969). Custer died for your sins: An Indian manifesto. New York: MacMillan.
Freire, P., & Macedo, D. (1987). Literacy: Reading the word and the world. South Hadley: Bergin & Garvey.
Gerdes, P. (1985). Conditions and strategies for emancipatory mathematics education in undeveloped countries. For the Learning of Mathematics, 5, 15–20.
Gerdes, P. (1988). On possible uses of traditional Angolan sand drawings in the mathematics classroom. Educational Studies in Mathematics, 19, 3–22.
Gerdes, P. (1998). Women, art and geometry in Southern Africa. Trenton: Africa World Press.
Gerdes, P. (1999). Geometry from Africa: Mathematical and educational explorations. Washington, DC: The Mathematical Association of America.
Gerdes, P. (2007). African basketry: A gallery of twill-plaited designs and patterns. http://www.lulu.com
Gerdes, P., & Bufalo, G. (1994). Sipatsi. Technology, art and geometry. Maputo: Instituto Superior Pedagogico.
Gombrich, E. H. (1979). The sense of order. Oxford: Phaidon.
Hargittai, I., & Hargttai, M. (1994). Symmetry: A unifying concept. Bolinas: Shelter Publications Inc.
Joseph, G. G. (2000). The crest of the peacock: Non-European roots of mathematics (2nd ed.). London: Princeton University Press.
Lave, J. (1988). Cognition in practice. Cambridge: Cambridge University Press.
Lave, J., & Wenger, E. (1991). Situated learning. Legitimate peripheral participation. Cambridge: Cambridge University Press.
Lipka, J., Yanez, E, Andrew-Ihrke, & Adam, S. (2008). A two way process for developing effective culturally based math: Examples from Math in a Cultural Context. In B. Greer, S. Mukhopadhyay, S. Nelson-Barber & A. B. Powell (Eds.), Culturally Responsive Mathematics Education. London: Routledge (in press)
Lipka, J., Mohatt, G., the Ciulistet group (1998). Transforming the culture of schools: Yup’ik Eskimo examples. Mahwah: Lawrence Erlbaum Associates
Lomawaima, K. T. (1999). The un-natural history of American Indian education. In K. G. Swisher & J. Tippeconnic III (Eds.), Next steps: Research and practice to advance Indian education (pp. 3–31). Charleston: ERIC Clearinghouse on rural education and small schools.
McManus, I. C. (2005). Symmetry and asymmetry in aesthetics and the arts. European Review, 13, 157–180.
Mukhopadhyay S. & Best, K. (2008). Ethnomathematics: Learning mathematics through cultural artifacts (in preparation)
Paul, F. (1944). Spruce root basketry of the Alaska Tlingit. Sitka: Sheldon Jackson Museum.
Powell, A. B., & Frankenstein, M. (Eds.). (1997). Ethnomathematics. Challenging Eurocentrisn in mathematics education. Albany: SUNY Press.
Sawyer, W. W. (1955). Prelude to mathematics. London: Penguin.
Smith, L. T. (1999). Decolonizing methodologies: Research and indigenous people. London: Zed Books.
Spivak, G. C. (1988). Can the subaltern speak? In C. Nelson & L. Grossberg (Eds.), Marxism and the interpretation of culture (pp. 271–313). Urbana: University of Illinois Press.
Washburn, D. K. (1999). The cultural salience of symmetry. American Anthropologist, 101, 547–562.
Washburn, D. K., & Crowe, D. W. (1988). Symmetries of culture. Theory and practice of plane pattern analysis. Seattle: University of Washington Press.
Willoughby, C. C. (1905). Textile fabrics of New England Indians. American Anthropologist, 7(New Series), 85–93.
Wynn, T. (2004). Evolutionary developments in the cognition and symmetry. In D. K. Washburn (Ed.), Embedded symmetries. Natural and cultural (pp. 27–47). Albuquerque: University of New Mexico Press.
Zaslavsky, C. (2005). Multicultural math: One road to the goal of mathematics for all. In E. Gutstein & B. Peterson (Eds.), Rethinking mathematics: Teaching social justice by the numbers (pp. 124–129). Milwaukee: Rethinking Schools.
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This research was supported by Portland State University’s Diversity Action Council Faculty Mini-grant 2003.
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Mukhopadhyay, S. The decorative impulse: ethnomathematics and Tlingit basketry. ZDM Mathematics Education 41, 117–130 (2009). https://doi.org/10.1007/s11858-008-0151-7
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DOI: https://doi.org/10.1007/s11858-008-0151-7