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

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.