Experimentation and Proof in Mathematics

  • Michael de Villiers


This paper examines the role and function of experimentation in mathematics with reference to some historical examples and some of my own, in order to provide a conceptual frame of reference for educational practise. I identify, illustrate, and discuss the following functions: conjecturing, verification, global refutation, heuristic refutation, and understanding. After pointing out some fundamental limitations of experimentation, I argue that in genuine mathematical practise experimentation and more logically rigorous methods complement each other. The challenge for curriculum designers is therefore to develop meaningful activities that not only illustrate the above functions of experimentation but also accurately reflect the complex, interrelated nature of experimentation and deductive reasoning.


Mathematics Education Deductive Reasoning Interior Angle Dynamic Geometry Software Deductive Proof 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



Reprinted adaptation of article by permission from CJSMTE, 4(3), July 2004, pp. 397–418, , © 2004 Canadian Journal of Science, Mathematics and Technology Education (CJSMTE).


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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.School of Science, Mathematics & Technology EducationUniversity of KwaZulu-NatalDurbanSouth Africa

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