We distinguish four “moves” that a skilled problem-solver repeats, not always in a linear order, when facing a new problem: understanding the data and the unknown, searching for a route to tackle it, carrying out the calculations or the proof, and finally reviewing to check and to learn something.
The four moves of the problem-solver: the solid arrows are the “ideal” flow, the dashed ones remind you that you can always go back.
The solid arrows represent the “ideal” flow; the dashed ones remind you that — always — you can go back when something does not add up. It is not a failure: it is part of the method.
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Topics: Working method
Concepts: Problem solving · Solution strategy
Skills: Modelling · Reasoning by cases
People: Polya