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Intuiting Mathematical Objects using Kinetigrams

John Pais

Teachers of mathematics have no consensus on answers to the questions: "What is mathematics?" and "How do you do it?" Too much emphasis has been placed on trying to answer the first, and not enough on addressing the second independently of the first.

John Pais  is Associate Professor of Mathematics at the St. Louis College of Pharmacy .

I have been developing a modeling approach to teaching calculus that emphasizes exploratory problem solving and visualization. In the process, I have developed several modeling situations that I will use in here to illustrate my ideas. These modeling situations are convenient fictions, and the degree to which they faithfully capture the processes they purport to model is not my point here.


This is a revised and expanded version of an article that appeared in the TALUM Newsletter Number 10, published by the Teaching and Learning Undergraduate Mathematics subcommittee of the Teaching Committee of the Mathematical Association of Great Britain, and edited by Dr. R. P. Burn.

I thank Bob Burn and Phillip Kent for several insightful and very helpful suggestions on previous versions of this article.

Published July 2001
© 2001 by John Pais. All rights reserved.


John Pais, "Intuiting Mathematical Objects using Kinetigrams," Convergence (October 2004)