The conceptual fields theory and its role in Mathematics Education

  • Cristian Alfaro-Carvajal Escuela de Matemática Universidad Nacional Heredia, Costa Rica
  • Jennifer Fonseca-Castro Escuela de Matemática Universidad Nacional Heredia, Costa Rica
Keywords: conceptual fields, mathematics education, scheme

Abstract

This article refers to the theory of Vergnaud’s conceptual fields and its implications in teaching mathematics. Fundamental concepts of this theory are discussed in light of teaching and learning mathematics; providing specific examples in the discipline and establishing relationship with other related references; for example, Polya problem-solving and Brousseau didactic situations, among others.

References

Brousseau, G. (1986). Fondements et méthodes de la didactiques des mathématiques. Recherches en Didactique des Mathématiques, 7(2), 33–115. Recuperado de http://cimate.uagro.mx/ivanlopez/seminario/archivos/Brousseau_Fondements.pdf

Chevallard, Y. (1991). La transposición didáctica, Del saber sabio al saber enseñado. Buenos Aires: Aique Grupo Editor.

Murillo, M.; Soto, A.; y Araya, J. (2003). Matemática básica con aplicaciones. San José: Editorial Universidad Estatal a Distancia.

Piaget, J.; Inhelder, B.; Sinclair-de Zwart, H.; Cheret, M.; Revello, A. (1978). Memoria e intelligencia. Buenos Aires: El Alteneo.

Polya, G. (1965). Cómo plantear y resolver problemas. México: Editorial Trillas.

Ruiz, A. (2000). El desafío de las matemáticas. Heredia, Costa Rica: Editorial de la Universidad Nacional.

Vergnaud, G. (1982). A classification of cognitive tasks and operations of thought involved in addition and subtraction problems. En Carpenter, T., Moser, J. y Romberg, T. (edits.), Addition and subtraction: A cognitive perspective, pp. 39-59. Hillsdale, N. J.: Lawrence Erlbaum.

Vergnaud, G. (1983). Quelques problèmes theóriques de la didactique a propos d'un example: les structures additives. Atelier International d'Eté: Récherche en Didactique de la Physique. La Londe les Maures, Francia.

Vergnaud. G. (1990). La théorie des champs conceptuels. Récherches en Didactique des Mathématiques, 10(23), 133-170. Recuperado de http://www.fundesuperior.org/Articulos/Pedagogia/Teoria_campos_conceptuales.pdf

Vergnaud, G. (1994). Multiplicative conceptual field: what and why? En H. Guershon y J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics, pp. 41- 59. Albany, N.Y.: State University of New York Press.

Published
2016-01-01
How to Cite
Alfaro-Carvajal, C., & Fonseca-Castro, J. (2016). The conceptual fields theory and its role in Mathematics Education. Uniciencia, 30(1), 17-30. https://doi.org/10.15359/ru.30-1.2
Section
Original scientific papers (evaluated by academic peers)

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