Niagara Falls, December 2 - 5, 2016
Contrary to their high school careers where many admit that memorization played a major role in their success, we are obliged to train students how to study productively while encouraging life long learning. With this idea in mind, we will discuss a few methods for combatting the memorization method in favour of strong problem solving skills, and the ability to apply knowledge outside of in-class problems.
This talk is a plea for returning to the once universally accepted axiom that learning is improved when students are offered a deep understanding of the material that they are supposed to master; that language makes more sense when we know what the words mean and that geometric facts become clear when we can look at the right picture. We focus on slight changes to a standard calculus course that introduce the Fundamental Theorem of Calculus early and often, resulting in the communication of its essential meaning. This summarizes work with Darlene Olsen* and Rob Poodiack** at Norwich University, as well as many years of experimenting with calculus teaching going back to last century.
*A Truly Beautiful Theorem: Demonstrating the Magnificence of the Fundamental Theorem of Calculus, D. McQuillan and D. Olsen, Journal of Humanistic Mathematics, Vol. 6, No 2, July 2016, pp. 148-160.
**On the Differentiation Formulae for Sine, Tangent and Inverse Tangent, D. McQuillan and R. Poodiack, College Mathematics Journal, Vol. 45, No. 2, March 2014, pp. 140-142.