Skip to main navigation menu Skip to main content Skip to site footer

Artículos

Vol. 16 No. 3 (2013): Noviembre

CONFIGURAL REASONING AND VERIFICATION PROCEDURES IN GEOMETRIC CONTEXT

DOI
https://doi.org/10.12802/relime.13.1633
Submitted
July 13, 2023
Published
2023-07-13

Abstract

The goal of this study is to characterize the processes involved in mathematical proof, in the context of geometry, from a cognitive perspective. In particular, the focus of this study is the characterization of the interaction between reasoning processes and verification procedures that secondary students use when solving geometry problems in a pencil-and-paper environment. The results show that the different ways of using alternative verification procedures to validate a proposition are related to the different outcomes of the reasoning in problems that require a proof.

References

  1. Bishop, A. J. (1983). Space and geometry. In R. Lesh & M. Landau (Eds.), Acquisition of mathematics concepts and processes (pp. 125-203). Nueva York, USA: Academic Press.
  2. Bishop, A. J. (1989). Review of research on visualization in mathematics education. Focus on Learning Problems in mathematics, 11(1), 7-16.
  3. Balacheff, N. (1988). Aspects of proof in pupils’ practice of school mathematics. In D. Pimm (Ed.), Mathematics, Teachers and Children, (pp. 216-235). London, UK: Kodder & Stoughton.
  4. Dreyfus, T. (1999). Why Johnny can’t prove? Educational Studies in Mathematics, 38(1/3), 85-109.
  5. Duval, R. (1998). Geometry from a cognitive point a view. In C. Mammana & V. Villani (Eds.), Perspective on the Teaching of Geometry for the 21st Century. Dordrecht/ Boston: Kluwer Academic Publishers.
  6. Duval, R. (2007). Cognitive functioning and the understanding of mathematical processes of proof. In P. Boero (Ed.), Theorems in schools: from history and cognition to classroom practice, (pp. 137-161). Rotterdam, Netherland: Sense Publishers.
  7. Fischbein, E. (1987). Intuition in science and mathematics: an educational approach. Dordrecht, Netherland: Reidel.
  8. Fischbein, E. (1993). The theory of figural concepts. Educational Studies in Mathematics, 24 (2), 139-162.
  9. Gutiérrez, A. (1996). Visualization in 3-dimensional geometry: In search of a framework. In A. Gutiérrez & L. Puig (Eds.), Proceedings of the 20th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 3-19). Valencia, España. University of Valencia
  10. Harel, G. (2007). Students’ proof schemes revisited. In P. Boero (Ed.), Theorems in school: From history, epistemology and cognition to classroom practice (pp. 65-78). Rotterdam, The Netherlands: Sense Publishers.
  11. Harel, G. y Sowder, L. (1998). Student’s Proof Schemes: Results from exploratory studies. In E. Dubinsky, A. Schoenfeld & J. Kaput (Eds.), Research on Collegiate Mathematics Education (Vol. 3, pp. 234-283). Providence, RI: American Mathematical Society.
  12. Harel, G. y Sowder, L. (2007). Toward comprehensive perspective on the learning and teaching of proof. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 805-842). Greenwich, CT: Information Age Publishing.
  13. Hanna, G. y Jahnke, H.N. (1996). Proof and proving. In A. J. Bishop; M. A. Clements; C. Keitel; J. Kilpatrick & C. Laborde (Eds.), International Handbook on Mathematics Educations (Vol. 2, pp.877-908). Dordrecht, Netherland: Kluwer Academic Publishers.
  14. Hershkowitz, R., Parzysz, B.,Van Dermolen, J. (1996). Space and Shape. In A.J. Bishop; M.A. Clements; C. Keitel; J. Kilpatrick & C. Laborde (Eds.), International handbook of Mathematics Education (Vol. 1, pp. 161-204). Dordrecht, Netherland: Kluwer Academic Publishers.
  15. Houdement C., Kuzniak A. (2006). Paradigmes géométriques et enseignement de la géométrie. Annales de didactique et de sciences cognitives, 11, 175-193.
  16. Ley Orgánica de Educación. (2006). Ley Orgánica 2/2006 – Boletín Oficial del Estado. Recuperado el 12 de febrero de 2013 de http://www.boe.es/boe/dias/2006/05/04/pdfs/A17158-17207.pdf
  17. Mesquita, A. (1989). L’influence des aspects figuratifs dans l’argumentation des élèves en géométrie: Éléments pour une typologie. Thèse d’université non publiée, Université Louis Pasteur. France.
  18. NCTM - National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
  19. Nelson, R. (1993). Proofs without word: Exercises in visual thinking. Washington D.C., EE.UU.: The Mathematical Association of America.
  20. Padilla, V. (1990). L’influence d’une acquisition de traitements purement figuraux sur l’apprentissage des mathématiques. Thèse d’université non publiée, Université Louis Pasteur. France.
  21. Presmeg, N.C. (1986). Visualisation and mathematical giftedness. Educational Studies in Mathematics, 17(3), 297-311.
  22. RAE - Real Academia Española, (2001). Diccionario de la lengua española. Vigésima segunda edición. Madrid, España: Espasa Calpe S.A.
  23. Torregrosa, G. y Quesada, H. (2007). Coordinación de procesos cognitivos en geometría. Revista Latinoamericana de investigación en Matemática Educativa, 10(2), 275-300.
  24. Torregrosa, G. y Quesada, H. (2010). Razonamiento configural como coordinación de procesos de visualización. Enseñanza de las Ciencias, 28 (3), 327-340.
  25. Zazkis, R., Dubinsky, E. y Dautermann, J. (1996). Coordinating visual and analytic strategies: a study of students’ understanding of the group D4. Journal for Research in Mathematics Education, 27 (4), 435-457.

Downloads

Download data is not yet available.

Similar Articles

<< < 1 2 3 4 5 6 7 8 9 > >> 

You may also start an advanced similarity search for this article.