We describe some classic experiments on the Möbius strip, the projective plane band, and the Klein bottle band. We present our experience with freshmen college students, college teachers, high school students, and Mathematics Education graduate students. These experiments are designed to encourage readers to learn more about the properties of the…

An experiment was conducted over three recent semesters of an introductory calculus course to test whether it was possible to quantify the effect that difficulty with basic algebraic and arithmetic computation had on individual performance. Points lost during the term were classified as being due to either algebraic and arithmetic mistakes…

We study situations in introductory analysis in which students affirmed false statements as true, despite simple counterexamples that they easily recognized afterwards. The study draws attention to how simple counterexamples can become hidden in plain sight, even in an active learning atmosphere where students proposed simple (as well as more…

This paper integrates technology, in the form of a physics simulation; science concepts, via image formation by lenses; and a mathematics apparatus, in the form of rational functions. All constituents merge into an instructional unit that can be embedded into a high school or undergraduate mathematics or physics course. The cognitive purpose of…

To help students understand the real-world applications of calculus, our calculus students all take part in a lab. This is not another "computer lab" but a lab where the students perform experiments and then collect and analyze the data. The students are able to verify for themselves many of physical claims that are left as theory in…

Described is a Monte-Carlo method for modeling physical systems with a computer. Also discussed are ways to incorporate Monte-Carlo simulation techniques for introductory science and mathematics teaching and also for enriching computer and simulation courses. (RH)