El legado de Piaget a la didáctica de la Geometría
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Lista de autores
Camargo-Uribe, Leonor
Resumen
Como contribución al homenaje que se le rinde a Jean Piaget, a los treinta años de su fallecimiento, presentamos una revisión, que no pretende ser exhaustiva, de algunas de sus ideas y de cómo estas han sido germen de estudios posteriores relacionados con la enseñanza y el aprendizaje de la Geometría. Exponemos dos hipótesis centrales de los estudios de Piaget sobre el desarrollo de la concepción del espacio en los niños. Mostramos el punto de vista de Piaget acerca de la competencia que tienen los niños en tareas de: discriminar figuras geométricas, representar figuras geométricas, construir sistemas de referencia bi o tridimensionales y justificar afirmaciones sobre hechos geométricos. Al respecto de cada tarea, hacemos referencia a estudios posteriores, la mayoría hechos en el contexto escolar, que confirman las ideas de Piaget o sugieren una revisión de las mismas.
Fecha
2011
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Referencias
Balacheff, N. (1999). Is argumentation an obstacle? Invitation to a debate... Newsletter on proof, Mai/Juin. http://www.lettre-delapreuve.it/ Bishop, A (1980). Spatial abilities and mathematics achievement- a review. Educational Studies in Mathematics, 11, 257-269.Boero, P., Garuti, R., Lemut, E., y Mariotti, A. (1996). Challenging the traditional school approach to the theorems: a hypoth-esis about the cognitive unity of theorems. Proceedings of the 20th PME International Conference,2, 113 - 120.Camargo, L. (2010). Descripción y análisis de un caso de ense-ñanza y aprendizaje de la demostración en una comunidad de práctica de futuros profesores de matemáticas de educa-ción secundaria. Disertación doctoral. España: Universidad de Valencia.Clements, D.H y Battista, M.T. (1992). Geometry and spatial reasoning. En D.A. Grouws (ed). Handbook of research on mathematics teaching and learning. New York: MacMillan 420-464. Darke, I. (1982). A review of research related to the topologi-cal primacy thesis. Educational Studies in Mathematics. 13, 119-142.de Villiers, M. (1986). The role of axiomatization in mathematics and mathematics teaching. http://mzone.mweb.co.za/resi-dents/profmd/axiom.pdf.Del Grande, J. (1990) Spatial Sense. Arithmetic Teacher. 14-20Douek, N. (2007). Some remarks about argumentation and proof. En P. Boero (Ed.), Theorems in school. From history, epistemology and cognition to classroom practice. Rotter-dam: Sense Publishers. (pp. 249 - 264).Duval, R. (1991). Structure du raisonnement deductif et appren-tissage de la demonstration. Educational Studies in Math-ematics. 22, 233 - 261.Gal, H. y Linchevski, L. (2010). To see or not to see: analyzing difficulties in geometry. Educational Studies in Mathematics, 74(2), 163 – 183. Geeslin, W. E. y Shar, A.O. (1979). An alternative model describ-ing children’s spatial prefer-ences. Journal for research in mathematics education. 10, 57-68.Hoffer, A. (1981). Geometry is more than proof. Mathematics Teacher. 74, 11-18. Ibbotson, A. y Bryant. P.E. (1976). The perpendicular error and the vertical effect in children’s drawing.Perception. 5, 319 – 326. Krutetstkii, V. A. (1976). The psy-chology of mathematical abili-ties in schoolchildren. Chicago: University of Chicaago Press.Laurendeau, M. y Pinard. A. (1970). The development of the con-cept of space in the child. New York: International Iniversity Press. Mariotti, M. A. (1997). Justifying and proving in geometry: the mediation of a microworld. Proceedings of the European Conference on Mathematical Education. 21 - 26.Mariotti, M. A. (2005). La geo-metria in classe. Riflessioni sull’insegnamento e apprendi-miento della geometría (prime-ra ed.). Bologna: Pitagora.Mariotti, M. A. (2006). Proof and proving in Mathematics Educa-tion. In A. Gutiérrez y P. Boero (Eds.). Handbook of Research on the Psychology of Mathemat-ics Education. Rotterdam: Sense Publishers. (pp. 173 - 204).Martin, J. L. (1976). An analysis of some of Piaget’s topological task from a mathematical point of view. Journal for research in mathematics education. 7, 8-24.Newcombe, N. (1989). The devel-opment of spatial perspective taking. En H.W. Advances in child development and behav-ior. New York: Academic Press. Reese (Ed.) Parzysz, B (1988) “Knowing” vs “Seeing”. Problems of the plane representation of space geometry figures. Educational Studies on mathematics. 19, 79-92. Pedemonte, B. (2007). How can the relationship between argumen-tation and proof be analysed? Educational Studies in Math-ematics. 66, 23 - 41.Piaget, J. y Inhelder, B. (1967). The child’s conception of space. Norton y Co. New York.Piaget, J. (1987). Possibility and necessity. Vol. 2. The role of necessity in cognitive develop-ment. Minneapolis: University of Minnesota Press. Presmeg, N. (1986). Visualization in high school mathematics.For the learning of mathemtics. 6(3), 42-46. Saads, S, y Davis, G. (1997). Spatial abilities, van Hiele levels & lan-guage use in three dimensional geometry. U.K.: University of Southampton. Somerville, S.C. y Bryant, P.E. (1985). Young children’s use of spatial coordinates. Child Development. 56, 604-613. van Hiele, P.M. (1986). Structure and insight. Orlando: Academ-ic Press.Vinner, S. y Hershkowitz, R. (1980). Concept images and com-mon cognitive paths in the development of some simple geo-metrical concepts. Proceedings of the fourth International. Concerence for the Psychology of Mathematics Education. 177-184.Zazkis, R; Leikin, R. (2008). Exemplifying definitions: a case of a square. Educational Studies in Mathematics. vol 69, 131-148.