Problem solving: the legacy of Pólya and a reading of CERME 2015

Abstract

This text starts with the legacy of Pólya (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.