# Mathematical thinking problem-solving and proofs

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My early problem-solving courses focused on problems amenable to solutions by Polya-type heuristics: draw a diagram, examine special cases or analogies, specialize. Classroom instruction that fosters mathematical thinking and problem solving: connections between theory and practice.

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Reversibility: Successful problem solvers are able to reverse trains of thought or reproduce these in reverse.. Mathematical problem-solving competences are thus acquired through the promotion of manifestations of mental agility (reduction, reversibility, minding of aspects and change of aspects).

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The teacher plays an important role in school. He is not simply to impart knowledge but also mould the habits, traits and character of pupils. He is to achieve educational objectives through the curriculum of...

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