The author was invited by the organizers of the Benin symposium on the encounter between rationalities to contribute from the particular perspective of his research experience in ethno-mathematics – the study of mathematical ideas and practices as embedded in their cultural contexts. In this article he tries to contribute to the understanding of mathematical reasoning, as embedded in cultural practices, by means of illuminating some complementary aspects of geometrical exploration in diverse cultural contexts. He ends by offering a few comments on possible educational implications.
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References
1.
Ascher, Marcia (1991) Ethnomathematics: A Multicultural View of Mathematical Ideas. Pacific Grove, CA: Brooks Cole .
2.
Ascher, Marcia and Ascher, R.obert (1981) Code of the Quipu: A Study in Media, Mathematics, and Culture. Ann Arbor: University of Michigan Press .
3.
Bazin, Maurice (2001) Ensinar matemàtica e ciência indígena ou como aprendi do povo tuyuka (manuscript).
4.
Bishop, Alan (1988), Mathematical Enculturation: A Cultural Perspective on Mathematics Education. Dordrecht: Kluwer .
5.
Carraher, T., Carraher, D. and Schliemann, A. (1987) ‘ Written and Oral Mathematics ’, Journal of Research in Mathematics Education8: 83–97 .
6.
D’Ambrosio, Ubiratan (1985) ‘ Ethnomathematics and Its Place in the History and Pedagogy of Mathematics ’, For the Learning of Mathematics (Montreal) 5(1): 44–48 .
7.
D’Ambrosio, Ubiratan (1990) Etnomatemática: arte ou técnica de explicar e conhecer. São Paulo: Editora ¡tica .
8.
Eglash, Ron (1999) African Fractals: Modern Computing and Indigenous Design. Piscataway, NJ: Rutgers University Press .
9.
Gay, John and Cole, Michael (1967) The New Mathematics and an Old Culture, A Study of Learning among the Kpelle of Liberia. New York: Holt, Rinehart & Winston .
10.
Gerdes, Paulus (1990a) Ethnogeometrie. Kulturanthropologische Beiträge zur Genese und Didaktik der Geometrie. Bad Salzdetfurth: Verlag Franzbecker (2nd edn 2002).
11.
Gerdes, Paulus (1990b) Vivendo a matematica: desenhos da África. São Paulo: Editora Scipione .
12.
Gerdes, Paulus (1992a) Sobre o despertar do pensamento geométrico. Curitiba: Universidade Federal de Paraná (2nd edn 2003).
13.
Gerdes, Paulus (1992b) Etnomatemática: Cultura, Matemática, Educacao. Maputo: Instituto Superior Pedagógico .
14.
Gerdes, Paulus (1993) L’ethnomathématique comme nouveau domaine de recherche en Afrique: quelques réflexions et experiences du Mozambique. Maputo: Instituto Superior Pedagógico .
15.
Gerdes, Paulus (1993/4) Geometria Sona: Reflexões sobre uma tradição de desenho em povos da África ao Sul do Equador. Maputo: Instituto Superior Pedagógico (3 vols).
16.
Gerdes, Paulus (1995a) Ethnomathematics and Education in Africa. Stockholm: University of Stockholm Institute of International Education .
17.
Gerdes, Paulus (1995b) Une tradition géométrique en Afrique. Les dessins sur le sable. Paris: L’Harmattan (3 vols: Analyse et reconstruction, Exploration éducative et mathématique, Analyse comparative).
18.
Gerdes, Paulus (1996) Femmes et géométrie en Afrique Australe. Paris: L’Harmattan .
19.
Gerdes, Paulus (1997a) Ethnomathematik dargestellt am Beispiel der Sona Geometrie. Heidelberg: Spektrum Verlag .
20.
Gerdes, Paulus (1997b) Recréations géométriques d’Afrique – Lusona – Geometrical Recreations of Africa. Paris: L’Harmattan .
21.
Gerdes, Paulus (1998a) Women, Art and Geometry in Southern Africa. Lawrenceville, NJ: Africa World Press .
22.
Gerdes, Paulus (1998b) ‘ Culture and Mathematics Teacher Education ’, Journal of Mathematics Teacher Education1(1): 33–53 .
23.
Gerdes, Paulus (1999) Geometry from Africa: Mathematical and Educational Explorations. Washington DC: The Mathematical Association of America .
24.
Gerdes, Paulus (2000) Le cercle et le carré: Créativité géométrique, artistique, et symbolique de vannières et vanniers d’Afrique, d’Amérique, d’Asie et d’Océanie. Paris: L’Harmattan .
25.
Gerdes, Paulus (2002a) Lusona: recreações geométricas de África. Maputo: Moçambique Editora; Lisboa: Texto Editora .
Gerdes, Paulus (2003a) Sipatsi: Cestaria e Geometria na Cultura Tonga de Inhambane. Maputo: Moçambique Editora (in press).
31.
Gerdes, Paulus (2003b) ‘Plaited Strip Patterns on Tonga Handbags in Inhambane (Mozambique) – An Update’, Visual Mathematics, Belgrade (in press).
32.
Gerdes, Paulus (2003c) ‘ Exploring Plaited Plane Patterns among the Tonga in Inhambane (Mozambique) ’, Symmetry: Culture and Science (in press).
33.
Gerdes, Paulus (2003d) Awakening of Geometrical Thought in Early Culture, Foreword by Dirk Struik. Minneapolis, MN: MEP Press .
34.
Gerdes, Paulus (2003e) ‘ Níjtyubane – Sobre alguns aspectos geométricos da cestaria Bora na Amazónia peruana’ , Revista Brasileira de História da Matemática, Rio Claro (in press).
35.
Gerdes, Paulus and Bulafo, Gildo (1994) Sipatsi: Technology, Art and Geometry in Inhambane. Maputo: Universidade Pedagógica .
36.
Hountondji, Paulin, ed. (1994) Les savoirs endogènes: pistes pour une recherche. Dakar: CODESRIA .
37.
Kane, Abdoulaye (1987) Les systèmes de numération parlée des groupes ouest-atlantiques et Mande. Contribution à la recherche sur les fondaments et l’histoire de la pensée logique et mathématique en Afrique de l’Ouest, Lille (unpublished doctoral thesis).
38.
Ki-Zerbo, Joseph (1990) Educate or Perish: Africa’s Impasse and Prospects. Dakar: UNESCO-UNICEF .
39.
Kubik, Gerhard (1988) Tusona-Luchazi Ideographs: A Graphic Tradition as Practised by a People of West-Central Africa. Fohrenau:Verlag Stiglmayr .
40.
Lancy, David, ed. (1978) ‘ The Indigenous Mathematics Project ’, Papua New Guinea Journal of Education14: 1–217 .
41.
Luquet, G. (1929) ‘ Sur l’origine des notions mathématiques: remarques psychologiques et ethnographiques ’, Journal de psychologie: 733–761 .
42.
Njock, George (1985) Mathématiques et environnement socio-culturel en Afrique Noire , Présence Africaine135: 3–21 .
43.
Posner, J. (1982) ‘ The Development of Mathematical Knowledge in Two West African Societies ’, Child Development53: 200–208 .
44.
Powell, Arthur B. and Frankenstein, Marilyn, eds (1997) Ethnomathematics: Challenging Eurocentrism in Mathematics Education. New York: State University of New York Press .
45.
Santos, Eduardo (1960) ‘ Sobre a matemática dos Ouiocos de Angola ’, Garcia da Orta3(2): 257–271 .
46.
Santos, Eduardo (1961) ‘ Contribuição para o estudo das pictografias e ideogramas dos Quiocos ’, Estudos sobre a etnologia do ultramar português2: 17–131 .
47.
Zaslavsky, Claudia (1973) Africa Counts: Number and Pattern in African Culture. Boston, MA: Prindle, Weber and Schmidt [paperback edition Brooklyn, NY: Lawrence Hill Books, 1999].
48.
Zaslavsky, Claudia (1994) ‘Mathematics in Africa: Explicit and Implicit’, in I. Grattan-Guinness (ed.), Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences, pp. 85–92. London: Routledge .
