Saturday, February 21, 2009

Learning as a puzzle; pedagogical misdirection and Rube Goldberg devices

Related to the previous post, I don't like puzzles. That is to say, it seems to me that as a pedagogical principle, making people find puzzle pieces that are completely unrelated to the concepts on which you are trying to focus is not an especially helpful practice. Perhaps this goes to a question of mathematical "maturity" -- and I won't claim to be an especially mature mathematician -- but using exercises which rely upon picking up on cues unrelated to the subject material seems to be deliberate misdirection.

The artist Rube Goldberg provided the quintessential characterization of modern pedagogical practice in algebra, calculus, and real analysis in general. While Goldberg's devices are often thought of as engineering constructs, they capture perfectly the actual deductive practices and proof methods taught in modern mathematical texts. The proofs we are doing in Real Analysis certainly get from point A to point Z, but quite often they do so only by introducing an almost comically complicated and laboriously contrived sequence of facts. Certainly, the lack of real comical effect may make it difficult for people to see the connection of proofs to Rube Goldberg devices, but they are both systems of logical deduction.

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