The role of intuition in mathematics education

Document Type : Research Paper

Author

Tafresh University

Abstract

According to the views of some scientists and historians of science, the intuition and insight of mathematicians play a crucial role in the exploration of their field. Examples of these perspectives can be found in the works of some great mathematicians. The aim of this article is to delve deeper into this topic by examining the works and statements of mathematicians and then exploring the role of intuition in mathematics education.

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[1] J. S. Hadamard,An essay on the psychology of invention in the mathematical field, A. Mokhber, Tehran: Dana, 1988.
[2] L. Burton, Why is Intuition so Important to Mathematicians but Missing from Mathematics Education?, For the Learning of Math., 19 no. 3 (1999) 27–32.
[3] E. Fischbein, Intuition in Science and Mathematics: an Educational Approach, Mathematics Education Library, D. Reidel Publishing Co., Dordrecht, 1987.
[4] H. Hahn, The Crisis in Intuition, The World of Mathematics, 3 (1956) 1956–1976.
[5] R. Hersh, What is Mathematics, Really?, Oxford University Press, New York, 1998.
[6] V. John-Steiner, Notebooks of the Mind, Oxford University Press, Oxford, 1997.
[7] I. Lakatos, Proofs and Refutations: The Logic of Mathematical Discovery, Cambridge Philosophy Classics. Cambridge Uni-versity Press, Cambridge, 1976.
[8] J. Mackeman, What’s the point of proof?, Mathematics Teaching, 155 (1996) 14–20.
[9] G. Polya, Patterns of Plausible Inferno, 2, Princeton University Press, New Jersey, 1998.
[10] J. P. Smith and K. Hungwe, Conjecture and verification in research and teaching: conversations with young mathematicians, For the Learning of Math., 18 no. 3 (1998) 40–46.
[11] I. Stewart, Nature’s Numbers, The Unreal Reality Of Mathematics, Basic Books, New York, 1997.
[12] D. J. Struik, A Source Book in Mathematics (1200-1800), Harvard University Press, New York, Cambridge, Mass, 1969.
[13] R. L. Wilder, The role of intuition, in Campbell, D. M and Higgins J. C (eds), Mathematics: People, Problems, Results, 2, Belmont, CA, Wadsworth International, 1984.