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I don't buy the sports analogy with which he argues that it is "self-serving nonsense" if people state that mathematics education trains your general problem so

by ar0 10y ago

I don't buy the sports analogy with which he argues that it is "self-serving nonsense" if people state that mathematics education trains your general problem solving skills. His argument that soccer players should only play soccer seems not to be anchored in reality: Of course professional soccer players spend a lot of time in the weights room or go running to enhance their general strength and stamina [1]! They do not only train their bodies by playing soccer... I do think that learning math does help you to think more clearly and to analyze problems in a more systematic matter. Now, he does not define well what he means by "higher mathematics": I agree that (as with almost all learning) there is diminishing marginal utility in mathematics education. While I would argue that learning how to work with percentages and also basic calculus (to get a feeling for the difference between a change in position and a change in velocity, for example) increase your general problem solving skills by a lot, if you have been through all this then learning about Ricci flow will probably not do that much to your general problem solving anymore. [1]: http://well.blogs.nytimes.com/2014/07/16/train-like-a-german-soccer-star/?_r=0 http://well.blogs.nytimes.com/2014/07/16/train-like-a-german...

Ologn 10y ago
I agree. I used to do IT work at a company where playing chess was popular among the techs and I decided to improve my skill. The ways to improve: * Study tactics and strategy books * Study grandmaster games * Do two-to-mate or tactical chess problems * Review your own games and look for mistakes * Study openings (once you're more advanced) Some of these things are straightforward, some not. If I study openings and know e5 is a good response to e4, I know my study did that. I am following an opening I memorized from a book. If I spend months carefully studying the games of Kasparov, Fischer, Karpov etc., and my playing begins improving - how do I prove studying the greats carefully has improved my game? It might be "self-serving nonsense", as I can't draw a line between a move I do to some game I studied, like I can for an opening I memorized from a book. All I know is my general problem solving skills have somehow increased. I now see patterns I did not see before, and the correct path forward where before it was muddled, although I can't fully explain why. The only test is a sample comparison of those who do it versus a sample of those who don't.
rm445 10y ago
Allegedly (association) football coaches seventy years ago would make players train without the ball all week, on the grounds that they would be keener to actually play football come Saturday. Of course they ended up under-skilled. My point is that one should find the combination of training that gets best results. In my engineering career, successfully solving technical problems has generally consisted of working out what basic techniques solve an approximation of the problem and leaving it at that. I would say first-year undergrad level rather than 8th-grade, but definitely not the most complex mathematics I've ever looked at. Apparently being able to put together any sort of solution from scratch is relatively rare. I do think problem-solving could be better taught. And schoolkids should definitely learn more about finance and statistics. Going on, the OP's stance seems fairly objectionable, but it's hard to disagree that employers use success in maths-heavy degrees as a proxy for selecting who may be best at a technical job. It seems like a fairly good filter, but it probably leads to injustice in certain cases, and the credential-chasing and learning less-necessary things may be inefficient.
lordnacho 10y ago
You're right. In particular, when we train for something, we tend not to train things in the proportion that they occur in during the game. For instance modern coaching has the kids run around with the ball a lot more than in a real 11-a-side match. That's because it matters a heck of a lot that the kids are comfortable on the ball, and only one of 22 people has the ball during the game. The same goes for math. You may not have to solve PDEs very often, but if you never do it, you will be stuck when it comes time to do so. I recall writing a Bessel function for an option valuation routine once, and if I hadn't come across it in uni, I'd have been struggling with it.

by ar0 10y ago

Ologn 10y ago

I agree. I used to do IT work at a company where playing chess was popular among the techs and I decided to improve my skill. The ways to improve: * Study tactics and strategy books * Study grandmaster games * Do two-to-mate or tactical chess problems * Review your own games and look for mistakes * Study openings (once you're more advanced) Some of these things are straightforward, some not. If I study openings and know e5 is a good response to e4, I know my study did that. I am following an opening I memorized from a book. If I spend months carefully studying the games of Kasparov, Fischer, Karpov etc., and my playing begins improving - how do I prove studying the greats carefully has improved my game? It might be "self-serving nonsense", as I can't draw a line between a move I do to some game I studied, like I can for an opening I memorized from a book. All I know is my general problem solving skills have somehow increased. I now see patterns I did not see before, and the correct path forward where before it was muddled, although I can't fully explain why. The only test is a sample comparison of those who do it versus a sample of those who don't.

rm445 10y ago

Allegedly (association) football coaches seventy years ago would make players train without the ball all week, on the grounds that they would be keener to actually play football come Saturday. Of course they ended up under-skilled. My point is that one should find the combination of training that gets best results. In my engineering career, successfully solving technical problems has generally consisted of working out what basic techniques solve an approximation of the problem and leaving it at that. I would say first-year undergrad level rather than 8th-grade, but definitely not the most complex mathematics I've ever looked at. Apparently being able to put together any sort of solution from scratch is relatively rare. I do think problem-solving could be better taught. And schoolkids should definitely learn more about finance and statistics. Going on, the OP's stance seems fairly objectionable, but it's hard to disagree that employers use success in maths-heavy degrees as a proxy for selecting who may be best at a technical job. It seems like a fairly good filter, but it probably leads to injustice in certain cases, and the credential-chasing and learning less-necessary things may be inefficient.

lordnacho 10y ago

You're right. In particular, when we train for something, we tend not to train things in the proportion that they occur in during the game. For instance modern coaching has the kids run around with the ball a lot more than in a real 11-a-side match. That's because it matters a heck of a lot that the kids are comfortable on the ball, and only one of 22 people has the ball during the game. The same goes for math. You may not have to solve PDEs very often, but if you never do it, you will be stuck when it comes time to do so. I recall writing a Bessel function for an option valuation routine once, and if I hadn't come across it in uni, I'd have been struggling with it.