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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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Effective **mathematical** problem solvers are flexible and fluent thinkers.. **Problem-solving** habits of mind prepare individuals for real problems situations requiring effort and thought. proof). In the example of the four focus teachers, strong connections are observed among their reform-based goals...

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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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