The Hanover Collaboration

You’ve all been in class where the guy up at the board screws something up. You, being as sharp as you are, notice immediately. Then you have to decide whether or not you should correct him. I’m curious what your policies are here since I’m thinking about changing mine… Which is:

First, I don’t want to be a show-off. I hate those kids. I always want to give the prof an opportunity to catch it himself. So if the mistake is someplace unimportant, I just let it go. If it is running derivation, watch to see if the mistake propagates. Often it willl get spontaneously corrected on the next line. Other times it will simply persist until it makes its presence felt later. If I think that will be soon and it won’t undergo any growth or change (like most sign flips), I still let it go. Otherwise, for instance if an incorrect minus sign undergoes exponentiation, or it is going to be 10 lines before the guy sees it, it is probably in everybody’s interest that you get it fixed.

But now I’m in this proofs class. It isn’t so much like derivations where each line depends on the line above, instead there are about a dozen statements all numbered, asterixed and daggered any several of which can be called upon to make a new statement. At each of these steps, we depend gravely on the absolute veracity of the previous steps. This is in contrast to algebra where you are mostly just writing stuff down to so you don’t lose track of things. This means that the mistakes have a lurkier character in the context of proofs. Nonetheless, about half the time, the guy just wrote it wrong and will use it later as if he had written it right. All you need to do is write it correctly in your notes and it is a non-issue.

But the strange thing is that if the prof catches it himself later and changes it, even if it was the most obvious typo you’ve ever seen, even if he said the thing he meant to write while writing it wrong, pretty much every kid in the class is correcting his or her notes. I look around and think that maybe I should have said something.

The only worse case than that is the whispering. Sometimes kids are paying enough attention to see it (say, if it is early in the lecture), then over the ensuing minute or two, people decide it is important to confer with their neighbors whether or not there is, in fact, an error on the board. I find this infuriorating. If you’re unsure, don’t be a wimp and raise your hand. If you are sure, don’t be a show-off and shut up.

note: I don’t mean to imply that I am catching all of the prof’s mistakes. I’m not. I’m struggling a lot more than some. I do make more of an effort to follow the lecture than most (owing to the fact that I write far less of it down). I ask myself, had I not noticed this error, would I be grateful if someone else pointed it out? I often think, “no, I wouldn’t”, but upon this further reflection, it is more subtle than that. When you’re falling off the back, as they say in bike racing, perhaps those little mistakes can be the short hills that finish you off. Conversely, the break in tempo plus the slight improvement in clarity due to the correction might be just what the other kids need to rejoin the group. Then again, I’m not sure everyone wants to keep the pack together.