Is Mathematical Logic Really Necessary in Teaching Mathematical Proofs?

Abstract

As it is already observed by mathematicians and educators, there is a discrepancy between the formal techniques of mathematical logic and the informal techniques of mathematics in regards to proof. We examine some of the reasons behind this discrepancy and to what degree it affects doing, teaching and learning mathematics in college. We also present some college students’ opinions about proofs, and we briefly observe the situation in Greek and Greek-Cypriot high schools in which mathematical logic is part of the curriculum. Finally, we argue that even though mathematical logic is central in mathematics, its formal methods are not really necessary in doing and teaching mathematical proofs and the role of those formalities has been, in general, overestimated by some educators.

Keywords

• formal
• logic
• proof
• student
• teacher