Significados institucionales de la demostración. Implicaciones para la educación matemática

Referencias

BALACHEFF, N. (1987). Processus de preuve et situations de validation. Educational Studies in Mathematics, 18, pp. 147-176. BATTISTA, M.T. y CLEMENTS, D.H. (1995). Geometry and proof. The Mathematics Teacher, 88(1), pp. 48-54. BROUSSEAU, G. (1986). Fondements et méthodes de la didactique des mathématiques. Recherches en Didactique des Mathématiques, 7(2), pp. 33-115. CAÑÓN, C. (1993). La matemática: creación o descubrimiento. Madrid: Universidad Pontificia de Comillas. DUVAL, R. (1993). Argumenter, demontrer, expliquer: continuité ou rupture cognitive? Petit x, 31, pp. 37-61. FERNÁNDEZ, P. y CARRETERO, M. (1995). Perspectivas actuales en el estudio del razonamiento, en Carreter, M., Almaraz, J. y Fernández, P. (eds.). Razonamiento y comprensión. Madrid: Trotta. FISCHBEIN, E. (1982). Intuition and proof. For the learning of mathematics, 3(2), pp. 9-24. FRASCOLLA, (1994). Wittgenstein’s philosophy of mathematics. Londres: Routledge. GARRIDO, M. (1978). Lógica simbólica. Madrid: Tecnos. GARUTI, R., BOERO, P. y LEMUT. E. (1998). Cognitive units of theorems and dificulty of proof, en Olivier, A. y Newstead, K. (eds.). Proceedings of the 22nd Conference of the International Group for The Psychology of Mathematics Education, vol. 2, pp. 345-352. Stellenbosch (Suráfrica): University of Stellenbosch. GODINO, J.D. y BATANERO, C. (1994). Significado institucional y personal de los objetos matemáticos. Recherche en Didactique des Mathématiques, 14(3), pp. 325-355. GODINO, J.D. y BATANERO, C. (1998). Clarifying the meaning of mathematical objects as a priority area of research in mathematics education, en Sierpinska, A. y Kilpatrick, J. (eds.). Mathematics education as a research domain: A search for identity (pp. 177-195). Dordrecht: Kluwer, A.P. GRANGER, G.G. (1992). La vérification. París: Odile Jacob. HANNA, G. (1989). Proofs that prove and proofs that explain, en Vergnaud, G., Rogalski, J. y Artigue, M. (eds.). Proceedings of the 13th Conference of the International Group for the Psychology of Mathematics Education, pp. 45-54. París. HANNA, G. (1995). Challenges to the importance of proof. For the Learning of Mathematics, 15(3), pp. 42-49. HAREL, G. y SOWDER, L. (1996). Classifying processes of proving, en Puig, L. y Gutiérrez, A. (eds.). Proceedings of the 20th Conference of the International Group for the Psychology of Mathematics Education, vol. 3, pp. 59-65. Valencia: Universitat de València. HERBST, P. (1998). «What works as proof in the mathematics class?» Athens (EEUU): University of Georgia. Tesis doctoral. HERSH, R. (1993). Proving is convincing and explaining. Educational Studies in Mathematics 24, pp. 389-399. KLINE, M. (1980). Matemáticas. La pérdida de la certidumbre. Madrid: Siglo XXI [1985]. KRUMMEHEUER, G. (1995). The ethnography of argumentation, en Cobb, P. y Bauersfeld, H. (eds.). The emergence of mathematical meaning. Hillsdale, Nueva Jersey: Lawrence Erlbaum Associates. LESTER, F.K. (1975). Developmental aspects of children’s ability to understand mathematical proof. Journal for Research in Mathematics Education, pp. 14-25 LIVINGSTON (1987). The ethnomethodological foundations of mathematics. Londres: Routledge & Kegan Paul. MARTIN, W.G. y HAREL, G. (1989). Proof frames of preservice elementary teachers. Journal for Research in Mathematics Education, 20(1), pp. 41-51. OTTE, M. (1994). Mathematical knowledge and the problem of proof. Educational Studies in Mathematics 26, pp. 299-321. POINCARÉ, H. (1902). La science et l’hipothèse. Trad. De Besio, A.B. y Banfi, J. 1963. La ciencia y la hipótesis. Madrid: Espasa-Calpe. POLYA, G. (1944). How to solve it. Priceton: University Press. Trad. cast. 1985. Cómo plantear y resolver problemas. México: Trillas. RECIO, A.M. (1999). «Una aproximación epistemológica a la enseñanza y el aprendizaje de la demostración matemática». Granada: Departamento de Didáctica de la Matemática, Universidad de Granada. Tesis doctoral. RECIO, A.M. y GODINO, J.D. (1996). Assessment of university students’ mathematical generalization and symbolization capacities, en Puig, L. y Gutiérrez, A. (eds.). Proceedings of the 20th Conference of the International Group for the Psychology of Mathematics Education (pp. I-231). Valencia: Universitat de València. RESNICK, M.D. (1992). Proof as a source of truth, en Detlefsen, M. (ed.). Proof and knowledge in mathematics, pp. 6-32. Londres: Routledge. SCHOENFELD, A.H. (1994). What do we know about mathematics curricula? Journal for Mathematical Behaviour, 13, pp. 55-80 SENK, S.L. (1985). How well do students write geometry proofs? Mathematics Teacher. Sep. 1995, pp. 448-456. WILDER, R.W. (1981). Mathematics as a cultural system. Nueva York: Pergamon. WITTGENSTEIN, L. (1978). Remarks on the foundations of mathematics (3a. ed.). Oxford: Basil Blackwell. Trad. cast. 1987. Madrid: Alianza.