In mathematical research, the purpose of proof is to convince. The test of whether something is a proof is whether it convinces qualified judges. In the classroom, on the other hand, the purpose of proof is to explain. Enlightened use of proofs in the mathematics classroom aims to stimulate the students' understanding, not to meet abstract standards of “rigor” or “honesty.”
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Hersh, R. Proving is convincing and explaining. Educ Stud Math 24, 389–399 (1993). https://doi.org/10.1007/BF01273372
- Mathematics Classroom
- Mathematical Research
- Abstract Standard
- Qualified Judge