Intuiting Mathematical Objects
Using Diagrams and Kinetigrams


Acknowledgements

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. In addition, I am grateful to David Smith for suggesting that I submit this article to JOMA, and to the editors and referees for many improvements to its structure and navigation.  

References

[1] R. Hersh (1997). What is Mathematics, Really? New York: Oxford University Press, Inc.

[2] M. Kline (1967). Calculus: An Intuitive and Physical Approach. New York: John Wiley & Sons, Inc.

[3] M. Kline (1977). Why the Professor Can't Teach: Mathematics and the Dilemma of University Education. New York: St. Martin's Press.

[4] J. Pais (in preparation). Intuiting the Objects of a Mathematical Theory.

[5] J. Pais (1997-2001). Calculus for Kinetic Modeling. St. Louis: Interactive MathVision.

[6] W. V. Quine (1981). Theories and Things. Cambridge: Harvard University Press.

[7] M. D. Resnik (1997). Mathematics as a Science of Patterns. New York: Oxford University Press, Inc.

[8] E. Spitznagel (1992). Two-Compartment Pharmacokinetic Models. C-ODE-E, Harvey Mudd College.

[9] D. Tall (1991). Intuition and Rigour: The Role of Visualization in the Calculus. In W. Zimmermann and S. Cunningham (eds.), Visualization in Teaching and Learning Mathematics. MAA Notes Number 19, Washington: The Mathematical Association of America.

[10] W. P. Thurston (1994). On Proof and Progress in Mathematics. Bulletin of the American Mathematical Society 30 (2), 161-177.

[11] R. Tieszen (1998). Gödel's Path from the Incompleteness Theorems (1931) to Phenomenology (1961). Bulletin of Symbolic Logic 4 (2), 181-203.

[12] E. K. Yeargers, R. W. Shonkwiler, and J. V. Herod (1996). An Introduction to the Mathematics of Biology. Boston: Birkhauser.
 

John Pais is Associate Professor of Mathematics in the Division of Pharmaceutical Sciences, St. Louis College of Pharmacy, 4588 Parkview Place, St. Louis, MO 63110
pais@kinetigram.com