Abstract
I will analyse the individual and collective activities of fourth grade students while trying to explain a schoolfellow's mistake in the use of a geometrical schema (shared by the class) of the sunshadows phenomenon. The study aims at detecting productive links between context-related argumentation, mathematical modelling (here concerning sunshadows) and conceptualization (inclination of a straight line to a plane), as well as discussing their relevance for mathematics education.
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References
Bartolini Bussi, M.: 1996, 'Mathematical discussion and perspective drawing in primary school', Educational Studies in Mathematics 31, 11–41.
Berthelot, R. and Salin, M.H.: 1992, L'enseignement de l'espace et de la géométrie dans la scolarité obligatoire, Thèse, L.A.D.I.S.T., Université de Bordeaux-I.
Blum, W. and Niss, M.: 1989, 'Mathematical problem solving, modelling, applications and links to other subjects', in W. Blum, M. Niss and I. Huntley (eds.), Modelling, Applications and Applied Problem Solving, 1–22, E. Horwood, Chichester.
Boero, P.: 1994, 'Experience fields as a tool to plan mathematics teaching from 6 to 11', in L. Bazzini and H.G. Steiner (eds.), Proceedings of the Second Italian German Bilateral Symposium on Didactics of Mathematics, 45–62, IDM Bielefeld.
Boero, P., Dapueto, C., Ferrari, P., Ferrero, E., Garuti, R., Lemut, E., Parenti, L. and Scali, E.: 1995, 'Aspects of the mathematics-culture relationship in mathematics teaching-learning in compulsory school', Proceedings of PME-XIX, Vol. 1, Recife, pp. 151–156.
Brousseau, G.: 1986, 'Fondements et méthodes de la didactique des mathématiques', Recherches en didactique des mathématiques 7, 33–115.
Brown, T.: 1997, Mathematics Education and Language, Kluwer Academic Publishers, Dordrecht.
Douek, N.: 1998, 'Analysis of a long term construction of the angle concept in the field of experience of sunshadows', Proceeding of PME-XXII, Vol. 2, Stellenbosch, pp. 264–271.
Duval, R.: 1991, 'Structure du raisonnement déductif et apprentissage de la démonstration', Educational Studies in Mathematics 22, 233–261.
French, L.: 1985, 'Acquiring and using words to express logical relationships', in S.A. Kuczai and M.D. Barrett (eds.), The Development of Word Meaning, 303–338, Springer-Verlag, New York.
Freudenthal, H.: 1983, Didactical Phenomenology of Mathematical Structures, D. Reidel Publ. Co., Dordrecht.
Heath, T.L.: 1908, The Thirteen Books of Euclid's Elements, University Press, Cambridge.
Lakatos, I.: 1985, Preuves et réfutations, Hermann, Paris.
Lakoff, G. and Nunez, R.: 1997, 'The metaphorical structure of mathematics', in L. English (ed.), Mathematical Reasoning: Analogies, Metaphors and Images, 21–89, L.E.A., Hillsdale, NJ.
Scali, E.: 1997, 'Choix des taches et organisation des intéractions dans la classe pour l'appropriation des signes de la géométrie dans les activités de modélisation', Proceedings of CIEAEM-49, Setubal (to appear).
Serres, M.: 1993, Les origines de la géométrie, Flammarion, Paris.
Simon, M.: 1996, 'Beyond inductive and deductive reasoning: the search for a sense of knowing', Educational Studies in Mathematics 30, 197–210.
Thurston, W.: 1994, 'On proof and progress in mathematics', Bulletin of the A. M. S., 30, 161–177.
Vergnaud, G.: 1990, 'La théorie des champs conceptuels', Recherches en Didactique des Mathématiques 10, 133–170.
Vygotsky, L.S.: 1985, Pensée et langage, Editions Sociales, Paris.
Vygotsky, L.S.: 1978, Mind in Society, Harvard University Press, Cambridge, MA.
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Douek, N. Argumentation and Conceptualization in Context: a Case Study on Sunshadows in Primary School. Educational Studies in Mathematics 39, 89–110 (1999). https://doi.org/10.1023/A:1003800814251
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DOI: https://doi.org/10.1023/A:1003800814251