David Dennis's Math History Papers

(for high school teachers, math education researchers, mathematicians, and other fans of mathematics)

Historical Perspectives for the Reform of Mathematics Curriculum: Geometric Curve Drawing Devices and Their Role in the Transition to an Algebraic Description of Functions. Ph.D. Dissertation, Cornell University, 1995.
(Note: This is a pdf file over 300 pages long, so it may take a while to download.)

Functions of a Curve: Leibniz's Original Notion of Functions and its Meaning for the Parabola.
Originally published in The College Mathematics Journal, March 1995, Vol. 26, #2, p.124-130.

The Creation of Continuous Exponents: A Study of the Methods and Epistemology of Alhazen and Wallis. 
Originally published in J. Kaput & E. Dubinsky (Eds.), Research in Collegiate Mathematics II.   CBMS Vol 6, pp. 33-60, 1996. Providence, RI: American Mathematical Society.

Appendix to "The Creation of Continuous Exponents" (previously unpublished).

Project-Based Mathematical Investigation For Prospective K-8 Teachers: Students Produce Original Approaches to the Generation of Pythagorean Triples
Presented at The Joint Mathematics Meetings, A.M.S - M.A.A. January 1997, San Diego, CA

Rene Descartes' Curve-Drawing Devices: Experiments in the Relations Between Mechanical Motion and Symbolic Language.
Originally published in Mathematics Magazine, Vol. 70, No. 3, June 1997, pp. 163-174.

Drawing Logarithmic and Exponential Curves with the Computer Software Geometer's Sketchpad: A Method Inspired by Historical Sources.
Originally published in J. King & D. Schatschneider (Eds.), Geometry Turned On: Dynamic Software in Learning, Teaching and Research. pp. 147-156, 1997.  Washington D.C.: Mathematical Association of America.

Geometric Curve Drawing Devices as an Alternative Approach to Analytic Geometry:  An Analysis of the Methods, Voice, and Epistemology of a High School Senior.
Originally published in R. Lehrer and D. Chazan (Eds.), Designing Learning Environments for Developing Understanding of Geometry and Space, pp. 297-318, 1998.  Hillsdale, NJ: Lawrence Erlbaum Associates.

Dennis, D. & Kreinovich, V. & Rump, S. Intervals and the Origins of Calculus. 
Originally published in Reliable Computing 4: 191-197, 1998. Dordrecht, Netherlands: Kluwer.

The Role of Historical Studies in Mathematics and Science Educational Research.
Originally published in  Kelly and Lesh (Eds.),  Research Design in Mathematics and Science Education, 2000. Mahwah, NJ: Lawrence Erlbaum.