Thursday, October 15, 2009

This initially began as a response to Brian's latest post on education: http://adeadhamster.blogspot.com/2009/10/information-is-not-knowledge.html

However, it overflowed so here it is:

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The post discusses incorrect learning, not lack of motivation, so we'll stick with the premise that people can be motivated. Given this, is your problem primarily that people aren't stopping to examine their learning more deeply? Certainly this would make their experience more worthwhile. However, I feel that the issue is even simpler than this. Perhaps I'm not qualified to comment (after all, those faulty red moppers are certifiably better than me =P), but it seems that its misconception about what needs to be learned in the first place. Here's an example: in complex, Dr Osborne would have test reviews, and during the reviews, the most common questions was "Are there gonna be proofs? What proofs might be on there?" and he would tell us, and most of the class would go home and memorize the damn proofs. So it's no surprise that when you ask a student to prove the thing a month later, they can't do it. People don't understand that they're supposed to be learning different approaches to proving certain kinds of results and, more generally and more usefully, how to think about different problems. You might think that massive proof based classes in college cure this. False. For the most part, what happens is a few students who like math and have grasped the concepts do the problems and explain the proofs to the others, who write the proofs down, are told what proofs are on the tests, and never take a math class again. The kids who continue to take math are those who have grasped the concepts anyway, so effectively the problem hasn't been cut down at all. In fact, the problem here in particular seems 10 times worse than at TJ. The problem is most visible in math, but it's actually present everywhere. The kind of thinking we need in doing math is in fact the kind of thinking that creates progress in all fields, and yet only in math and physics is there even an attempt being made to promote it.

All in all, I feel that while this is a huge problem, it's not all that hard to tackle. However, this post has gone on for a while, so I'll stop now and finish my HUM paper (whatever MIT might call these terrible classes, certain things don't change in my book =P).

~jnub

6 comments:

  1. To me, it's just a difference between memorization and understanding. I think everyone realizes that there is in fact a difference - I don't think everyone realizes that memorization as opposed to learning will hurt them in the long run. Or if they do, they lack the motivation to put in the extra effort that understanding requires.

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  2. Heh. Massive proof-based math classes in college. I'm guilty.

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  3. Massive proof-based math classes - yeah...every single problem we do in analysis is a proof...

    Though I think it's unfair to say that proof-based classes aren't any better than "normal" classes. It might be an exceptional case, but if the the majority of a class is able to grasp the concepts, you really can't help but feel required to put in more effort if you don't (or maybe that's just me >_>).

    Take my analysis class for example. I swear most of the 50 or so people are extremely proficient at proof-based math. On the other hand, I'm certainly below average, getting points docked off for clarity, vagueness, and not making the correct insights all the time. It really sucks, but still I'm finding myself working on a less-than-ten-problems problem set from 5 PM to 5 AM (like last night XP).

    So I agree with Ved that for some people, the extra effort that understanding requires can be a dissuading factor, and can sometimes be downright huge as I'm discovering about pure math.

    Last night was the first time I had to write up a 7 page proof for just one question using 6 induction proofs. >_>;;

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  4. That actually sounds really nice. I wasn't attacking proof-based classes in general: they've certainly got the right idea, at least to a point. I'm just saying that even those have failed, at least here, because of the problem I outlined. Just curious, how many people are in your analysis class?

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  5. 2 classes, about 70 people total.

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  6. i agree with arvind. Memorization was complex analysis for me (other than cauchy-riemann formulas...b/c it was easy). I just wish they would offer classes where you can learn but are not overwhelmed with proofs

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