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Using geometrical models in a process of reflective thinking in learning and teaching mathematics

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Abstract

In this paper we investigate how geometrical models can be used in learning and teaching mathematics, in connection with the development of a process of reflective thinking, which we study first in general. Some more specific questions — arising from the use of geometrical models in the classroom — have led us to an experimental study, the results of which are presented and discussed in the paper.

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References

  • BillingtonJ. and EvansP.: 1987, ‘Levels of knowing 2’, Mathematics Teaching 120, 12–19.

    Google Scholar 

  • Bouligand, G.: 1962, ‘Intuitive approaches toward some vital organs of mathematics’, in F. le Lionnais (ed.), Great Currents of Mathematical Thought, Dover Publ., 1971, Vol. I, pp. 57–66.

  • BrousseauG.: 1983, ‘Les obstacles épistémologiques et les problèmes en Mathématiques’, Recherches en Didactique des Mathématiques 4, No 2, 165–198.

    Google Scholar 

  • BrousseauG.: 1986, Fondements et méthodes de la Didactique de Mathématiques’, Recherches en Didactique des Mathématiques 7, No 2, 33–115.

    Google Scholar 

  • Castelnuovo E.: 1972, Documenti di un'esposizione de Matematica, Boringhieri, pp. 35–42.

  • FischbeinE.: 1972, ‘Les modèles génératifs et le développement intellectuel’, Activités-recherches pédagogiques 5, 10–14.

    Google Scholar 

  • Freudenthal, H.: 1978, Weeding and Sowing, Reidel Publ. Co.

  • GattegnoC.: 1987, ‘Parts and wholes’, Mathematics Teaching 119, 26–27.

    Google Scholar 

  • GriffithsH. B.: 1971, ‘Mathematical insight and mathematical curricula’, Educational Studies in Mathematics 4, 153–165.

    Google Scholar 

  • Hadamard, J.: 1949, The Psychology of Invention in the Mathematical Field, Dover Publ., pp. 14–77.

  • HewittD.: 1986, ‘H.S.M. Coxeter is a geometer’, Mathematics Teaching 117, 34–35.

    Google Scholar 

  • Hinton, C. H.: Speculations on the Fourth Dimension, R. V. B. Rucher (ed.), Dover Publ.

  • Kaldrimidou, M.: 1987, ‘Images mentales et representations en Mathématiques chez des mathématiciens et des étudiants en Mathématiques’, Thèse, Université Paris VII.

  • KilpatrickJ.: 1985, ‘Reflection and recursion’, Educational Studies in Mathematics 16, 1–26.

    Google Scholar 

  • O'Daffer, P. G. and Clemens, S. R.: 1976, Geometry — An Investigative Approach, Addison-Wesley Publ.

  • Piaget, J. and Inhelder, B.: 1981, La représentation de l'espace chez l'enfant, Presses Universitaires de France, 4e edition, pp. 351–398 (original work published 1947).

  • PiagetJ.: 1971, Science of Education and the Psychology of the Child, Viking, New York (original work published 1969).

    Google Scholar 

  • Polya, G.: 1957, How to Solve It, Princeton Univ. Press (original edition 1945).

  • Polya, G.: 1962, Mathematical Discovery — On Understanding, Learning and Teaching Problem Solving, Wiley.

  • Robertson, S. A.: 1984, Polytopes and Symmetry, London Math. Society Lecture Note Series, Cambridge Univ. Press.

  • Robert, A. and Tenaud, I.: 1987, ‘Travail en petits groupes’, Cahiers de didactique No 40, IREM Paris 7.

  • Skemp, R. R.: 1971, The Psychology of Learning Mathematics, Pelican Books, pp. 54–67.

  • SkovsmoseO.: 1985, ‘Mathematical education versus critical education’, Educational Studies in Mathematics 16, 337–354.

    Google Scholar 

  • Stamatis, E.: 1969, ‘Polygonal numbers considered geometrically’, Eucleidis 1969, periodical of the Greek Math. Society (in Greek).

  • Thom, R.: 1982, ‘Mathématique et théorisation scientifique’, in Penser les Mathématiques, Ed. du Seuil, pp. 252–273 (original work published 1979).

  • Toeplitz, O.: 1963, The Calculus — A Genetic Approach, Phoenix Science Series, pp. 52–53.

  • WirszupI.: 1976, ‘Breakthroughs in the psychology of learning and teaching geometry’, in J. L.Martin (ed.), Space and Geometry — Papers from a Research Workshop, ERIC Center for Science, Mathematics and Environmental Education, Ohio.

    Google Scholar 

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Gagatsis, A., Patronis, T. Using geometrical models in a process of reflective thinking in learning and teaching mathematics. Educ Stud Math 21, 29–54 (1990). https://doi.org/10.1007/BF00311014

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