Mathematical Proofs 101: How Proofs Should Be Read, Written, and Taught

TL;DR

This paper explores effective methods for teaching, understanding, and writing mathematical proofs, emphasizing student perceptions, instructional strategies, peer review, and skill development to improve proof literacy.

Contribution

It offers a comprehensive overview of pedagogical approaches and emphasizes peer review and skill-building for better proof comprehension and writing.

Findings

Students' perceptions influence proof learning

Peer review enhances proof critical reading skills

Instructional strategies impact proof writing effectiveness

Abstract

A significant amount of research has considered mathematical proofs, the students who learn them, and the instructors that teach them, from a variety of perspectives. This paper considers this topic from four main perspectives: students' perceptions of mathematical proofs, instructors' presentations of mathematical proofs, using peer review to develop students' abilities to read proofs more critically and write proofs more convincingly, and providing students with the skills required to independently read and write proofs.