Collaborative Group for Research in Mathematics Education


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Psychology of Experimental Mathematics

Experimental mathematics has been a part of mathematics for as long as mathematics has existed. The standards of rigour established by, among others, Archimedes, should not detract from the fact that many of the earliest mathematical results were discovered empirically. More recently, Gauss was a confirmed experimentalist in mathematics, although he only ever published his conjectures, or findings for which he had mathematical proofs.

What has changed in recent years is the respectablity of experimental mathematics. There is even an academic journal for Experimental Mathematics, an Institute for Experimental Mathematics at the University of Essen, Germany, a Centre for Experimental and Constructive Mathematics at Simon Fraser University, British Columbia, Canada, and the 1995 Kemeny Lecture was on the experimental mathematics of complex spatial systems.

The reason for this change is principally the availability of electronic computers. This has made experimentation in mathematics possible on a scale previously unknown, and so increased the pressure to report on experimental findings in mathematics prior to rigorous proofs being available. Good experimental mathematics is distinguished by the depths of its experimental results and the extent to which such results provide fertile ground for other mathematical investigations.

The aim of this project was to consider the implications of the rise of experimental mathematics for learners and teachers of mathematics. Over time, the changes are likely to be profound. The techniques used in this project were those of individual cognition - both for learners and for teachers - from a constructivist point of view, and social constructivist methods aimed at describing and analysing the ways in which mathematics is built-up by mathematically active learners and teachers.

Gary Davis and Keith Jones led a discussion group on the psychology of experimental mathematics at the 20th annual conference of the International Group for the Psychology of Mathematics Education, Universitat de Valencia, July 8 -12, 1996. These pages provide links to some preliminary material used in that meeting.

Publications

Davis, G. and Jones, K. (1996), The Psychology of Experimental Mathematics. In: L. Puig and A. Gutiérrez (Eds), Proceedings of the 20th Conference of the International Group for the Psychology of Mathematics Education. University of Valencia, Volume 1, 149 [extended abstract].
Click here for full article in pdf format.

Related CRME Projects

CalGeo: teaching calculus using dynamic geometric tools
The project is supported by a grant from the EU, award: 11892-CP-1-2004-1-GR-COMENIUS-C21

The School-University Transition in Mathematics
The project was supported by a British Council 'Treaty of Windsor' Grant.

The Metacognitive Behaviour of Mathematics Undergraduates when Solving Calculus Problems
This project was supported by ESRC research award R00429524142

Students' Conceptions of Proof


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