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May. 29th, 2012 (UTC)

I think of statistical knowledge as one of the lowest forms of knowledge, what you use to describe a phenomenon when you do not have or cannot trust more specific insights. A Gaussian error is often just a sum of a moderate number of specific effects, most or all of which can be comprehended. Peter Thiel recently made some related observations in his Startups class.

Thinking of my mistakes as bugs has been second nature for me for as long as I can remember; it did not occur to me that this was unusual. I wonder how common this actually is. "Maybe nobody's actually stupid" strikes me as literally false but usefully provocative; a teacher should calibrate the speed of teaching to the student's abilities--so that systematic debugging is possible--and then work with the student on the actual debugging. Ideally, the student learns to and gets in the habit of debugging their own mistakes most of the time.

I wonder about practical considerations. I've seen a lot of pushback against the "small class sizes = good" conventional wisdom, but this approach does seem to require a small class size, and good teachers of course.

Edit: The debugging model has wide application, but there are quite a few educational problems outside its scope. E.g. if someone is performing poorly in a foreign language class, a teacher might be able to suggest a few study habit adjustments, but there's a significant amount of raw memorization that has to occur, and it's often rational for the student to spend that time on something else even if the foreign language class is required. It's also only partially applicable to creative endeavors like English composition and arguably mathematical proofs. Still, it's a big step forward from what we have now.

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