STUDENT MODELING OF PHYSICAL PHENOMENA AS THEY DERIVE STANDARD INTEGRAL FORMULAE: ONE WAY TO REDUCE PROOF PHOBIA

Abstract

ABSTRACT Students in a freshmen calculus course should become fluent in the modeling of physical phenomena that are represented by integrals, in particular, geometric formulas for volumes and arc length and physical formulas for work. This paper describes how I successfully trained my students to became fluent in such modeling and derivation of standard integral formulas. These lessons also greatly reduced the students' proof phobias. An appendix provides my lecture notes, which include simple (student level) derivations of integrals for geometric and physical phenomena.