Volume
22
Issue
3
Abstract
In this set of four articles, we invite Calculus teachers to encounter some of the ideas that shaped and motivated the innovation of the subject, presented in story form. We find that in traditional treatments of these topics, the dramatic tension between ways of thinking, representations, and phenomena in the world can be lost in a sea of calculations, procedures, and partially-understood formal proofs. However, the fundamental ideas and insights can be identified in nascent form in students’ ways-of-thinking about Calculus, and in their struggles to connect Calculus with their prior mathematical experiences.
We are honored to contribute these Stories of Calculus to this number of The Mathematics Enthusiast, honoring the life and thinking of David Tall. David’s work with technology in Calculus learning brought him into close contact with Jim Kaput, the SimCalc Projects, and the Kaput Center. He and Jim discussed ideas that came to represent his “three worlds” of mathematics, a story he tells in part in his contribution to the volume, The SimCalc Vision and Contributions (Hegedus & Roschelle, 2013). His ideas, and his sense of both the challenges of learning Calculus and the potential transformations offered by digital and executable representations, are coherent with the approach we are advocating in these articles.
First Page
185
Last Page
218
Recommended Citation
Brady, Corey and Moreno-Armella, Luis
(2025)
"Part 1: Mathematical Alchemy,"
The Mathematics Enthusiast: Vol. 22
:
No.
3
, Article 2.
DOI: https://doi.org/10.54870/1551-3440.1658
Available at:
https://scholarworks.umt.edu/tme/vol22/iss3/2
Digital Object Identifier (DOI)
10.54870/1551-3440.1658
Publisher
University of Montana, Maureen and Mike Mansfield Library
