SteveH, a frequent commenter at this blog, has made some cogent observations about the transferability of problem solving skills, and about “understanding” in general. Like me and others I know, he feels that far too much importance is placed on understanding in math in K-6 than is necessary. He also posits that mastery of procedural skills in the early grades and even high school, doth not a “math zombie” maketh. I’ve taken two of his recent comments and placed them here for general interest.
I. Problem solving and transference
I want to say more about problem solving and transference. Polya is worthless, so what problem solving skills are transferable? You can draw pictures, label variables, and write equations to look for m=n. Everybody does that, but still, it’s difficult. You can study governing equations and their variations. This is classic homework p-set work. However, does D=RT problems and variations easily…
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