Mathematics, Statistics, and Computer Science
mathematics, logic, mathematics education, proofs
If there is one aspect of mathematics education that frustrates both students and teachers alike, it has got to be learning how to do valid proofs. Students often feel they really know the mathematics they're studying but that their teachers place some unreasonably stringent demands upon their arguments. Teachers, on the other hand, can't understand where their students get some of the wacky arguments they come up with. They argue in circles, they end up proving a different result from what they claim, they make false statements, they draw invalid inferences - it can be quite exasperating at times! Unfortunately, constructing a genuine demonstration is not a side issue in mathematics; deduction forms the backbone and hygiene of mathematical intercourse and simply must be learned by mathematics majors. I'd like to focus attention on this topic in this paper first by sharing with you how we attack the problem at Dordt. I will then attempt to give the issue a bit of historical and philosophical depth by tracing some developments in mathematics and logic which seem to have had a strong influence upon contemporary approaches to teaching proof. I hope this will contribute to further discussion of the problem.
Jongsma, Calvin, "Logic and Proof for Mathematicians: A Twentieth Century Perspective" (1987). Faculty Work: Comprehensive List. 252.