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The implementation of local mathematical practices into the mathematics curriculum

Workshop of the Project ETKnoS


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May 26, 2017

University Paris Diderot,
Room Kandinsky, 631B*,
9.30 am – 6 pm


1) Jerry Lipka & David Koester (Fairbanks University)

  • The Project “Math in a Cultural Context” (Yup’ik/Yupiaq, Alaska)
    We situate the development of curriculum materials and a pedagogical approach within a long-term collaborative relationship with Yupiaq elders and expert Yupiaq teachers. Joint analyses of everyday activities revealed an underlying set of mathematical principles that guides those activities. The key concepts of qukaq (center), halving, symmetry, measuring, and verifying are the cultural and mathematical generative concepts. We also share our evolving understanding with examples of curriculum development at different stages of our work as well as an appreciation of our insider/outsider research group and how Yupiaq knowledge emerged from discussions, demonstrations, visual representation and translation, and how this knowledge continues to evolve and grow.
    • References :
    • Lipka, J. (1991). Toward a culturally based pedagogy : A case study of one Yup’ik Eskimo teacher. Anthropology & Education Quarterly, 22(3), 203-223.
    • Lipka, J., with Mohatt, G. V, and the Ciulistet group. (1998). Transforming the culture of schools : Yup’ik Eskimo examples. New York : Routledge.

2) Eric Vandendriessche & Céline Petit (SPHERE, University Paris Diderot)

  • Yup’ik string figures
    Several string games traditionally known among Yup’ik people (Yupiit) will be presented, with the view of shedding light on the mathematical ideas that have seemingly been involved in the creation of these procedural games. Epistemological and didactical issues raised by the potential use of string games as tools for teaching mathematics will then be discussed, both within a local perspective (cf. "culturally embedded mathematics") and at a larger level (string games as pedagogical support for teaching mathematics in various cultural contexts).
    • References :
    • Nicolai, D. (2002). Yup’ik string figures, Bulletin of the international string figure association, vol. 9, 202-234.
    • Video extracts showing Yup’ik elder Gregory Kapatak “Kokwak” (from Koliganek, Southwestern Alaska, 1930-1995) making string figures in Anchorage, Alaska, in the 1980s-90s (Alaska Bilingual/Multicultural Materials Development Center)

3) Alban Da Silva (doctorant, SPHERE / PRAG, University of New Caledonia)

  • Sand drawing from Vanuatu
    In Vanuatu (ex New-Hebrides), a cultural practice consists in drawing geometrical figures (mostly symmetric) in the sand (or in the ashes), tracing a continuous line with a finger, without lifting it from the ground and by ending the drawing at the starting point. The analysis of ethnographic datas leads us to make hypotheses about the mathematical concepts that underlie the creation and the practice of these geometrical drawings. First, we will make some of these « sand drawings » of which a computer modeling (written in Python) will thereafter be presented. Then, we will discuss the sand-drawing educational perspectives. In particular, we will give evidence of some mathematical skills that this activity could bring into the classroom.
    • References :
    • Ascher, M. (1994). Ethnomathematics : A multicultural view of mathematical ideas. CRC Press.
    • Ascher, M. (1988). Graphs in Cultures : A Study in Ethnomathematics. Historia Mathematica, 15, 201-227.
    • Deacon, A. B., & Wedgwood, C. H. (1934). Geometrical drawings from Malekula and other islands of the New Hebrides. Journal of the Royal Anthropological Institute of Great Britain and Ireland, 64, 129-175.
    • Gerdes, P. (1988). On possible uses of traditional angolan sand drawings in the mathematics classroom. Educational Studies in Mathematics, 19(1), 3–22.

4) Sophie Desrosiers (EHESS)

  • Weaving dualism in the Andes
    In some areas of the Bolivian and Peruvian highlands, weaving processes in use since more than two millennia involve the use of logical and counting rules that shape textile designs and texture. Yet these logics grounded on symmetries and secondary on substitution are used in several domains of social organisation and life where they show a dualist, sometimes tripartite, way of thinking. We will break down the weaving process in order to make these logics understandable and connect them with the woven result (with two symmetrical faces), and then we will compare them with other more accessible expressions of Andean dualism. The learning method applied in a community of the Cuzco valley shows the important role of symmetries in the construction of knowledge. I have not found yet any pedagogical experience using these ways of knowing. Still looking for them.
    • References :
    • Henri Stobart et Rosaleen Howard (eds), Knowledge and Learning in the Andes. Ethnographic Perspectives, Liverpool Univ. Press, 2002.
    • E.M. Franquemont et C.R. Franquemont, « Tanka, Chongo, Kutij. Structure of the World through cloth », In Dorothy K. Washburn et Donald W. Crowe, Symmetry Comes of Age. The role of Pattern in Culture (pp. 177-214), Univ. of Washington Press, 2004.
    • S. Desrosiers, “Retour sur “Les techniques de tissage ont-elles un sens ?”” et “Les techniques de tissage ont-elles un sens ? Un mode de lecture des tissus andins”, Techniques & culture 54-55 (1), 2010 (publié en 2011) : 260-262, 263-285.

* Room Kandinsky (631B), University Paris Diderot, Building Condorcet (Site B), 4, rue Elsa Morante, 75013 PARIS. Campus map with access.

N° ANR-16-CE27-0005-01, 2016–2020