## Ethnomathematics

• In mathematics education, ethnomathematics is the study of the relationship between mathematics and culture. Often associated with "cultures without written expression", it may also be defined as "the mathematics which is practised among identifiable cultural groups". It refers to a broad cluster of ideas ranging from distinct numerical and mathematical systems to multicultural mathematics education. The goal of ethnomathematics is to contribute both to the understanding of culture and the understanding of mathematics, and mainly to lead to an appreciation of the connections between the two.

The term "ethnomathematics" was introduced by the Brazilian educator and mathematician Ubiratan D'Ambrosio in 1977 during a presentation for the American Association for the Advancement of Science. Since D'Ambrosio put forth the term, people - D'Ambrosio included - have struggled with its meaning ("An etymological abuse leads me to use the words, respectively, ethno and mathema for their categories of analysis and tics from (from techne)".).

The following is a sampling of some of the definitions of ethnomathematics proposed between 1985 and 2006:

Some of the systems for representing numbers in previous and present cultures are well known. Roman numerals use a few letters of the alphabet to represent numbers up to the thousands, but are not intended for arbitrarily large numbers and can only represent positive integers. Arabic numerals are a family of systems, originating in India and passing to medieval Islamic civilization, then to Europe, and now standard in global culture—and having undergone many curious changes with time and geography—can represent arbitrarily large numbers and have been adapted to negative numbers, fractions, and real numbers.

Less well known systems include some that are written and can be read today, such as the Hebrew and Greek method of using the letters of the alphabet, in order, for digits 1–9, tens 10–90, and hundreds 100–900.

A completely different system is that of the quipu, which recorded numbers on knotted strings.

• "The mathematics which is practiced among identifiable cultural groups such as national-tribe societies, labour groups, children of certain age brackets and professional classes".
• "The mathematics implicit in each practice".
• "The study of mathematical ideas of a non-literate culture".
• "The codification which allows a cultural group to describe, manage and understand reality".
• "Mathematics…is conceived as a cultural product which has developed as a result of various activities".
• "The study and presentation of mathematical ideas of traditional peoples".
• "Any form of cultural knowledge or social activity characteristic of a social group and/or cultural group that can be recognized by other groups such as Western anthropologists, but not necessarily by the group of origin, as mathematical knowledge or mathematical activity".
• "The mathematics of cultural practice".
• "The investigation of the traditions, practices and mathematical concepts of a subordinated social group".
• "I have been using the word ethnomathematics as modes, styles, and techniques (tics) of explanation, of understanding, and of coping with the natural and cultural environment (mathema) in distinct cultural systems (ethnos)".
• "What is the difference between ethnomathematics and the general practice of creating a mathematical model of a cultural phenomenon (e.g., the "mathematical anthropology" of Paul Kay [1971] and others)? The essential issue is the relation between intentionality and epistemological status. A single drop of water issuing from a watering can, for example, can be modeled mathematically, but we would not attribute knowledge of that mathematics to the average gardener. Estimating the increase in seeds required for an increased garden plot, on the other hand, would qualify".
• Ascher, Marcia (1991). Ethnomathematics: A Multicultural View of Mathematical Ideas Pacific Grove, Calif.: Brooks/Cole.
• D'Ambrosio. (1985). Ethnomathematics and its place in the history and pedagogy of mathematics. For the Learning of Mathematics, 5, 44-8.
• D'Ambrosio. (1997). "Foreword", Ethnomathematics, p.xv and xx. .
• D'Ambrosio. (1999). Literacy, Matheracy, and Technoracy: A Trivium for Today. Mathematical Thinking and Learning 1(2), 131-153.
• Berczi, Sz. (2000): Katachi U Symmetry in the Ornamental Art of the Last Thousands Years of Eurasia. FORMA, 15/1. 11-28. Tokyo
• Closs, M. P. (ed.) (1986). Native American Mathematics. Austin, TX: University of Texas Press.
• Crowe, Donald W. (1973). Geometric symmetries in African art. Section 5, Part II, in Zaslavsky (1973).
• Eglash, Ron (1999). African Fractals: Modern Computing and Indigenous Design. New Brunswick, New Jersey, and London: Rutgers University Press. , paperback
• Eglash, R., Bennett, A., O'Donnell, C., Jennings, S., and Cintorino, M. "Culturally Situated Design Tools: Ethnocomputing from Field Site to Classroom." American Anthropologist, Vol. 108, No. 2. (2006), pp. 347–362.
• Goetzfridt, Nicholas J. (2008) Pacific Ethnomathematics: A Bibliographic Study. Honolulu: University of Hawai'i Press. .
• Harrison, K. David. (2007) When Languages Die: The Extinction of the World's Languages and the Erosion of Human Knowledge. New York and London: Oxford University Press.
• Joseph, George Gheverghese (2000). The Crest of the Peacock: Non-European Roots of Mathematics. 2nd. ed. London: Penguin Books.
• Menninger, Karl (1934), Zahlwort und Ziffer. Revised edition (1958). Göttingen: Vandenhoeck and Ruprecht.
• Menninger, Karl (1969), Number Words and Number Symbols. Cambridge, Mass.: The M.I.T. Press.
• Luitel, Bal Chandra and Taylor, Peter. (2007). The shanai, the pseudosphere and other imaginings: Envisioning culturally contextualised mathematics education. Cultural Studies of Science Education 2(3).
• Powell, Arthur B., and Marilyn Frankenstein (eds.) (1997). Ethnomathematics: Challenging Eurocentrism in Mathematics Education, p. 7. Albany, NY: State University of New York Press.
• Situngkir, H., Surya Y. (2007). Fisika Batik (The Physics of Batik). Gramedia Pustaka Utama.
• Zaslavsky, Claudia (1973). Africa Counts: Number and Pattern in African Culture. Third revised ed., 1999. Chicago: Lawrence Hill Books.
• Zaslavsky, Claudia (1980). Count On Your Fingers African Style. New York: Thomas Y. Crowell. Revised with new illustrations, New York: Black Butterfly Books.
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