Educational Studies in Mathematics

, Volume 39, Issue 1–3, pp 89–110 | Cite as

Argumentation and Conceptualization in Context: a Case Study on Sunshadows in Primary School

  • Nadia Douek

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.

argumentation conceptualization context geometrical modelling primary school sunshadows 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bartolini Bussi, M.: 1996, 'Mathematical discussion and perspective drawing in primary school', Educational Studies in Mathematics 31, 11–41.CrossRefGoogle Scholar
  2. 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.Google Scholar
  3. 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.Google Scholar
  4. 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.Google Scholar
  5. 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.Google Scholar
  6. Brousseau, G.: 1986, 'Fondements et méthodes de la didactique des mathématiques', Recherches en didactique des mathématiques 7, 33–115.Google Scholar
  7. Brown, T.: 1997, Mathematics Education and Language, Kluwer Academic Publishers, Dordrecht.Google Scholar
  8. 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.Google Scholar
  9. Duval, R.: 1991, 'Structure du raisonnement déductif et apprentissage de la démonstration', Educational Studies in Mathematics 22, 233–261.CrossRefGoogle Scholar
  10. 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.Google Scholar
  11. Freudenthal, H.: 1983, Didactical Phenomenology of Mathematical Structures, D. Reidel Publ. Co., Dordrecht.Google Scholar
  12. Heath, T.L.: 1908, The Thirteen Books of Euclid's Elements, University Press, Cambridge.Google Scholar
  13. Lakatos, I.: 1985, Preuves et réfutations, Hermann, Paris.Google Scholar
  14. 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.Google Scholar
  15. 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).Google Scholar
  16. Serres, M.: 1993, Les origines de la géométrie, Flammarion, Paris.Google Scholar
  17. Simon, M.: 1996, 'Beyond inductive and deductive reasoning: the search for a sense of knowing', Educational Studies in Mathematics 30, 197–210.CrossRefGoogle Scholar
  18. Thurston, W.: 1994, 'On proof and progress in mathematics', Bulletin of the A. M. S., 30, 161–177.Google Scholar
  19. Vergnaud, G.: 1990, 'La théorie des champs conceptuels', Recherches en Didactique des Mathématiques 10, 133–170.Google Scholar
  20. Vygotsky, L.S.: 1985, Pensée et langage, Editions Sociales, Paris.Google Scholar
  21. Vygotsky, L.S.: 1978, Mind in Society, Harvard University Press, Cambridge, MA.Google Scholar

Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • Nadia Douek
    • 1
  1. 1.MontreuilFrance

Personalised recommendations