FROM FORMAL PROOFS TO INFORMAL PROOFS-TEACHING MATHEMATICAL PROOFS WITH THE HELP OF FORMAL PROOFS

This paper introduces a way to teach mathematical proofs with the help of formal proofs and technology. The most challenging task in theoretical mathematics is writing a proof. A proof is a step-by-step demonstration that a statement is valid. Students’ ability to write a valid proof is crucial to their success in mathematics. Students’ inability to write a proof is often a major obstacle in their mastering advanced topics in mathematics. Mathematicians have long recognized that logic plays an important role in mathematical thinking processes, and logic is taught before students are exposed to proofs. However, it appears that some students are unable to apply logic skills and techniques when they write a proof. With the help of a visualization tutorial, the instructor is able to embed meaning into the laws of logic. This approach enables students to write proofs with confidence. The process of constructing formal proofs helps student set proof strategy, justify each argument, and gain confidence in writing proofs.