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Special Article

Vol. 13 No. 4(I) (2010): Número Especial /Diciembre

FIGURAL AND EPISTEMIC FUNCTIONS OF DRAWINGS

Submitted
January 4, 2024
Published
2010-03-25

Abstract

It has been said that figural representations, or geometrical drawing, ought to be interpreted in terms of their properties in order to establish certain relations given beforehand, after which is possible to arrive to deductive treatment of geometry. This viewpoint does not acknowledge the epistemic nor figural function of drawings. Recognizing geometrical properties and linking them casually isn' t enough to have a wholesome understanding of geometry. The referent is just as important as the reference. This paper focuses on the figural and epistemic functions of drawings through the use of geometry.

References

  1. Acuña, C. (2006). Tratamientos como dibujo y como figura de la grafica en tareas de construcción e interpretación por estudiantes de bachillerato el caso de los ejes cartesianos. En E. Filloy (Ed.), Matemática Educativa, treinta años. Una mirada fugaz, una mirada externa y comprensiva, una mirada actual (pp. 215-236), México: Fondo de Cultura Económica.
  2. Acuña, C. (2009). Gestalt configurations in geometry learning. [Electronic version]. CERME 6 Conference of the European Society for Research in Mathematics Education. Lyon, France.
  3. Acuña, C. & Larios V. (2008). Prototypes and Learning of geometry, a reflection on its pertinence and its causes, [Electronic version]. Visualization in the Teaching and Learning of Mathematics ICME Topic Study Group 20 (TSG 20). Monterrey, México.
  4. Aspinwall, L. Kenneth S. and Presmeg N. (1997). Uncontrollable mental imagery: graphical connections between a function and its derivate. Educational Studies in Mathematics. 33 (2), 301-317
  5. Capponi, B. & Laborde C. (1994). Cabri-géomètre constituant d'un milieu l'apprentissage de la notion de figure géométrique, Recherches en Didactique des Mathématiques, 14 (1.2). 165-210.
  6. Duval, R. (1995). Geometrical pictures of representation and specific processing. In R. Sutherland and J. Mason (Eds.), Exploiting Mental Imagery with computes Education (pp. 142-157). NATO ASI Series.
  7. Duval, R. (2003), «Voir» en mathématiques. In E. Filloy (Ed.), Matemática educativa. Aspectos de la investigación actual (pp. 41-76). México: Cinvestav y Fondo de Cultura Económica.
  8. Duval, R. (2007). Cognitive functioning and the understanding of mathematical processes of proof. In Paolo Boero (Ed.), Theorems in School from history, epistemological and cognition to Classroom practice (pp. 137-161). Sense Publishers.
  9. Fischbein, E. (1993). The theory of figural concepts. Educational Studies in Mathematics. 24 (2), 139-162.
  10. Galperin P. & Georgiev L. (1969). The formation of elementary Mathematical Notions. In J. Kilpatrick & Wirszup (Eds.), Soviet Studiesin the Psychology of learning and teaching Mathematics: The Learning of Mathematical Concepts, 1, 189-216. Chicago, USA: University of Chicago.
  11. Gobert, S. (2007). Ways of thinking about the uses of imagen in learning and teaching geometry: more thorough investigation of links between drawing and figures, [Electronic version]. 3a Conference of the European Society for Research in Mathematics Education. Larnaca Cyprus. Recuperado de http://ermeweb.free.fr/
  12. Hershkowitz, R. (1989). Visualization in geometry- two sides of the coin, Focus on Learning Problems in Mathematics, 11 (1), 63-75.
  13. Houdement, C. & Kuzniak. A. (1999). Un exemple de cadre conceptuel pour l'étude de l'enseignement de la géométrie en formation des maitres. Educational Studies in Mathematics, 44 (3), 283-312.
  14. Kospentaris G. & Spyrou P. (2007). Assessing the attainment of analytic descriptive geometrical thinking with new tools. Working group 7, 5th Conference of the European Society for Research on Mathematics Education. Larnaca, Cyprus
  15. Larios, V. (2003). Geometrical rigidity: An obstacle in using dynamic geometry software in a geometry course. [Electronic version]. Third Conference of the European Society for Research on Mathematics Education. Bellaria, Italy
  16. Larios, V. (2005). Fenómenos cognitivos presentes en la construcción de argumentos en un ambiente de Geometria Dinámica. (Tesis de doctorado). Cinvestav, México D.F.
  17. Laborde, C. (2005). Hidden role of diagrams in students' construction of meaning in geometry. In J. Kilpatrick (Ed.) Meaning in Mathematics Education (pp.159-179) USA: Springer.
  18. Maracci, M. (2001). Drawing in the problem solving process. [Electronic version]. 2nd Conference of the European Society for Research in Mathematics Education (pp. 478-488).
  19. Mesquita, A. (1998). On conceptual obstacles linked with external representation in geometry. The Journal of Mathematical Behavior, 17 (2), 183-195.
  20. Mesquita, A., & Padilla P. (1990). Point D'ancrage en Geometrie. L'ouvert 58, 30-35.
  21. Parzysz, B. (1988). Knowing vs seeing: Problems of the plane representation of space geometry figures. Educational Studies in Mathematics, 19(1), 79-92.
  22. Richard, P. (2004). L'inférence figurale: un pas de raisonnement discursive-graphique. Educational Studies in Mathematics, 57 (2), 229-263.
  23. Vygotski, L. (1979). El desarrollo de los procesos psicológicos superiores. Barcelona, España: Editorial Critica

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