Proofs: Teaching and testing-a tragedy in three acts

Abstract

Student in examination: 'This theorem is proved in three tragic steps.' (Lecture notes: 'This theorem is proved in three strategic steps.') This article discusses the nature of mathematical proof, the problems of communicating and teaching proofs and the important part played by the methods of assessment in students' choice of learning strategies. The traditional method of asking students to reproduce theorems and proofs in examinations simply encourages rote learning. Examples are given of alternative methods of assessment within the confines of the traditional examination system.