Dan very succinctly and clearly lays out the case for what I call ‘removing the scaffolding’.
‘Problem Solving’ has been a phrase I have heard lauded ever since I began teaching (not so short and not so long ago.) And yet the methods proposed and the rationale presented have never seemed quite complete.
Far too often maths curricula have interpreted this to mean inserting some, all too often, spurious context or introducing more puzzles and games into each or some lessons. At best there seems to be a very prescriptive approach to how you solve a problem and questions designed to lead to a very clear and algebraically perfect answer. Collect the data – put it in a table – find the pattern….