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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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