Abstract
Although studies on students’ difficulties in producing mathematical proofs have been carried out in different countries, few research workers have focussed their attention on the identification of mathematical proof schemes in university students. This information is potentially useful for secondary school teachers and university lecturers. In this article, we study mathematical proof schemes of students starting their studies at the University of Córdoba (Spain) and we relate these schemes to the meanings of mathematical proof in different institutional contexts: daily life, experimental sciences, professional mathematics, logic and foundations of mathematics. The main conclusion of our research is the difficulty of the deductive mathematical proof for these students. Moreover, we suggest that the different institutional meanings of proof might help to explain this difficulty.
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REFERENCES
Balacheff N.: 1987, ‘Processus de preuve et situations de validation’, Educational Studies in Mathematics 18, 147–176.
Battista, M.T. and Clements, D.H.: 1995, ‘Geometry and proof’, The Mathematics Teacher 88(1), 48–54.
Chazan, D.: 1993, ‘High school geometry students' justification for their views of empirical evidence and mathematical proof’, Educational Studies in Mathematics 24, 359–387.
Chevallard, Y.: 1992, ‘Concepts fondamentaux de la didactique: Perspectives apportées par une approche anthropologique’, Recherches en Didactique des Mathématiques 12(1), 73–112.
Dieudonné, J.: 1987, ‘The concept of “rigorous proof”’, The Mathematical Gazette 80, 204–206.
Ernest P.: 1994, Constructing Mathematical Knowledge: Epistemology and Mathematics Education, The Falmer Press, London.
Fernández P. and Carretero, M.: 1995, ‘Perspectivas actuales en el estudio del razonamiento’, in M. Carretero, J. Almaraz and P. Fernández (eds.), Razonamiento y comprensió n, Trotta, Madrid.
Fischbein, E.: 1982, ‘Intuition and proof’, For theLearning of Mathematics 3(2), 9–24.
Fourez, G.: 1994, La construcció n del conocimiento científico, Narcea, Madrid.
Galbraith, P.L.: 1981, ‘Aspects of proving: A clinical investigation of process’, Educational Studies in Mathematics 12, 1–28.
Garnier, R. and Taylor, J.: 1996, 100% Mathematical Proof, John Wiley and Sons, New York.
Garuti, R., Boero, P. and Lemut, E.: 1998, ‘Cognitive units of theorems and dificulty of proof’, in A. Olivier and K. Newstead (eds.), Proceedings of the 22th International Conference of PME (Vol. 2), Stellenbosch, South Africa, pp. 345–352.
Godino, J.D. and Batanero, C.: 1998, ‘Clarifying the meaning of mathematical objects as a priority area of research in mathematics education’, in A. Sierpinska and J. Kilpatrick (eds.), Mathematics Education as a Research Domain: A Search for Identity, KluwerAcademic Publishers, Dordrecht, pp. 177–195.
Godino, J.D. and Recio A.M.: 1997, ‘Meanings of proof in mathematics education’, in E. Pehkonen (ed.), Proceedings of the 21th International Conference of PME (Vol. 2), Lahti, Finland, pp. 313–321.
Hanna, G.: 1989, ‘More than formal proof’, For the Learning of Mathematics 9(1), 20–23.
Hanna, G.: 1995, ‘Challenges to the importance of proof’, For the Learning of Mathematics 15(3), 42–49
Harel, G. and Sowder, L.: 1998, ‘students' Proof Schemes’, in E. Dubinsky, A. Schoenfeld and J. Kaput (eds.), Research on Collegiate Mathematics Education, Vol. III, American Mathematical Association, pp. 234–283.
Healy L. and Hoyles, C.: 2000, ‘A study of proof conceptions in Algebra’, Journal for Research in Mathematics Education 31(4), 396–428.
Kline, M.: 1980, Matemáticas. La pérdida de la certidumbre, Siglo XXI, Madrid [1985].
Livingston, E.: 1987, The Ethnomethodological Foundations of Mathematics. Routledge, London.
Martin, W.G. and Harel, G.: 1989, ‘Proof frames of preservice elementary teachers’, Journal for Research in Mathematics Education 20(1), 41–51.
Miller-Jones, D.: 1991, ‘Informal reasoning in inner-city children’, in J.F. Voss, D.N. Perkins and J.W. Segal (eds.), Informal Reasoning and Education, Lawrence Erlbaum, A.P., Hillsdale, N.Y.
Polya G.: 1944, Có mo plantear y resolver problemas. Mexico. Trillas [1985].
Polya, G.: 1953, Matemáticas y razonamiento plausible, Tecnos, Madrid [1966].
Popper, K.: 1972, Conocimiento objetivo, Tecnos, Madrid [1974].
Recio, A.M.: 2000, Una aproximació n epistemoló gica a la enseñ anza y el aprendizaje de la demostració n matemática. Servicio de Publicaciones. Universidad de Có rdoba, Spain.
Recio, A.M. and Godino, J.D.: 1996, Assessment of University Students' mathematical generalization and symbolization capacities, in L. Puig y A. Gutiérrez (eds), Proceeding of the 20th Conference of PME, Valencia, p. 1–231.
Resnick, M.D.: 1992, ‘Proof as a source of truth’, in M. Detlefsen (ed.), Proof and knowledge in mathematics Routledge, London, pp. 6–32.
Senk, S.L.: 1985, ‘How well do students write geometry proofs?’, Mathematics Teacher 78, 448–456.
Wilder, R.W.: 1981, Mathematics as a Cultural System, Pergamon, New York.
Zaslavsky, O. and Ron, G.: 1998, ‘students' understanding of the role of counterexamples’, in A. Olivier and K. Newstead (eds.), Proceedings of the 22nd International Conference of PME, Stellenbosch, South Africa, Vol. 4, pp. 225–232.
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Recio, A.M., Godino, J.D. Institutional and personal meanings of mathematical proof. Educational Studies in Mathematics 48, 83–99 (2001). https://doi.org/10.1023/A:1015553100103
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DOI: https://doi.org/10.1023/A:1015553100103