Математическое образование в США

[leblon]

Познакомился с одним интересным человеком - профессором в местном университете. Долго говорили с ним о проблемах преподавания математики в школах, а под конец он признался, что написал книгу по истории этого вопроса. Очень информативно, a must read.

Comments

[chaource.livejournal.com]

I found another book on his web site. The book has a very interesting statement: rote memorization and drill in arithmetic/algebraic calculations is vital for further mathematical learning because the brain needs to activate nonverbal thinking that will be impossible unless simple arithmetic and algebraic operations are completely automatic.

[chaource.livejournal.com]

The link is here:

ftp://math.stanford.edu/pub/papers/milgram/what-is-mathematical-proficiency.pdf

I also found Milgram's text on why long division is important.

http://www.csun.edu/~vcmth00m/longdivision.pdf
http://www.shearonforschools.com/why_long_division.htm

There are people arguing against teaching long division, mainly on the grounds of this being a practically useless and difficult skill. I can sympathize: for example, school kids used to learn the decimal square root algorithm, which is even more difficult and also practically useless. I used to feel good that I didn't have to learn that at school. But actually I am now getting second thoughts about it. Maybe at least Newton's method for square root should have been taught, to minimize the trauma that comes with the realization that square roots cannot be computed easily.

[posic.livejournal.com]

I regretted not knowing the decimal square root algorithm ever since I heard about its existence. Once I tried to ask my granmother, who learned it in school, but she was unable to explain the thing to me; apparently she had forgotten it. Having reread this comment of yours today, I started to write this reply, and then it occured to me to look for this algorithm in the Internet. And of course, I found it on a web resource for homeschooling parents -- http://www.homeschoolmath.net/teaching/square-root-algorithm.php . The exposition is good, and the thing itself is quite understandable. Learning is still alive, and it is the homeschoolers who keep the fire burning!

[chaource.livejournal.com]

I think the Newton method is superior; but I'm not sure.

[posic.livejournal.com]

It likely is, particularly when one needs great precision. But it is not for the sake of efficiency that I am interested in such algorithms. I am satisfied with just having an algorithm for the square root resembling the division algorithm that I know. The most efficient algorithms are rarely the most interesting ones from a mathematician's point of view. E.g., there are beautiful algorithms for computing quantities like \pi and e based on the Euler-MacLaurin formula. They are fast enough to be used for demonstrative purposes in a classroom, but I've never heard about them being used for actual computations by the contemporary programmers or numerical analysts.