Abstract
This text starts with the legacy of Polya (1945), highlighting the importance of problem solving in school and from the mathematical point of view. It presents, afterwards, a summary and a reflection on what was written in CERME 2015 about problem solving. It makes an incursion on the relevance of the discovery of a key solution idea, by the solver, associated with the attention and its change. There are identified good features of the solvers of non-routine problems and also it is referred the mediating role played by the teacher, namely in the analysis and comparison of others resolutions, promoting self-regulatory capacity in students.
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