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I learned all mathematicians in the study considered proofs valuable for students because they offer students new methods, important concepts and exercise in logical reasoning needed in problem solving. The study shows that some mathematicians consider proving and problem solving almost as the same kind of activities.
Written proofs are a record of your understanding, and a way to communicate mathematical ideas with others. ... And real life has a lot to do with “doing” mathematics, even if it doesn't look that way very often.
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