Much like solving everyday problems, we normally approach textbook math problems rather informally, haphazardly, unscientifically, mostly a mental exercise, with a few tentative scribblings for a solution documented in whatever piece of paper is handy, with hardly any reflections on the actual process of problem solving. It is usually a one-go affair, usually unsuccessful, never to be visited again due to a resigned attitude of not being able to solve the problem.
Mason scrutinized the problem solving process in explicit detail, and suggested the twin approach of specializing and generalizing, plus the sub-strategies of entry, attack and review. The rubric that follows is helpful, for instance, how to introduce images and representations to represent the information you've already classified as needing a specialized skill, attempting a conjecture, framing a tentative resolution, checking and later, generalizing and even extending to accomodate various flavors of the original problem.
Mason gets very emphatic in recommending that you doggedly document your thinking and feelings, with all the false starts, detours, pitfalls, promising leads, frustration, the inevitable STUCK moments, and the delightful AHA moments. I thinks that's how great problems are solved by great mathematicians, as they religiously keep field notes of their thinking, and follow through their insights in a determined way.
Most definitely, we can use Mason's approach to our advantage, in Math classrooms and the larger room of life-long learning. Surely, I will adapt some of his ideas in my actual teaching.
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