Although there are arguments about the exact processes involved and the exact competencies required, there is universal agreement that problem solving is what we do when we don’t know what to do. That is, problem solving is not the precise application of a known procedure. It is not the implementation of a taught algorithm. And it is not the smooth execution of a formula. Problem solving is a messy, non-linear, and idiosyncratic process. Students will get stuck. They will think. And they will get unstuck. And when they do, they will learn—they will learn about mathematics, they will learn
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