Mathematical Proof and Proving (MPP) - Design and Implementation of a Special Undergraduate Course

New York University, New York NY

Investigators

Abstract

This project stems from two common assumptions: 1) mathematical proof and proving are at the heart of mathematics; and 2) the notion of formal proof and the activity of mathematically proving are dauntingly difficult even for most good undergraduate students. It follows that there is a need for undergraduate courses that focus on mathematical proofs in ways that attend to students' difficulties. The project addresses this need. Included in the project is a proof based freshman level course. Course material includes approximately 50 carefully constructed case-problems that create the need to prove in an investigative and engaging way. For each of five central methods of proof there are 6-10 problems that can be proved by this method. For each method, the problems vary in terms of the mathematical topic. A particular problem may serve to illustrate more than one type of proof. This is a collaboration between mathematics educators and mathematicians at NYU. The mathematics educators bring their expertise on effective teaching and learning and knowledge of the research literature on teaching proofs, while the mathematicians bring their expertise in the discipline of mathematics and can ensure that the course meets the requirements of undergraduate majors in mathematics. This unique collaboration between mathematicians and mathematics educators strengthens the quality and impact of the course. Professional development resources and activities are developed and implemented. The faculty development resources allow future courses to be taught by a single faculty member who is either a mathematician or a mathematics educator.