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Miller comments on Making Reasoning Obviously Locally Correct - Less Wrong
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For someone that didn't spend much time in school, you've identified one of my chief ways of guessing the teacher's password. It's often the case that one can essentially perform this kind of hack to narrow down the options without otherwise understanding the problem as it was intended.
In this case for instance, one can imagine a multiple choice where the answers are the line that was the error. Your solution would rule out lines after a certain point. You might get lucky as a student and have 3 of the 4 answers ruled out this way. Voila! You've won and know almost nothing.
Speaking as a mathematican(ok, grad student but close enough for this purpose), this isn't learning almost nothing. Once one has gone through an example and can see where an attempted proof breaks down one can then look at that part in more detail. Of course one won't learn much if one only cares about identifying the problematic line, whether in a school setting or another setting; one always needs to generalize and integrate knowledge. Don't blame the teacher if one isn't going to take steps to do that.