Written: March 19, 1997
[Inspired by George Andrews's essay in the Notices of 4/97, v. 44, 458-462.]
Boys will be boys, and conservatives will be conservatives. Conservatives hate anything new, and believe that all we need is to go back to the good-old-days when only boys like Dick and George got an A in Math, and half of the class got C's and F's. Another good thing about the good-old-days was tons of homework, to shape your mind up and keep you off the streets. Since the good-old-days were so good, we should also keep teaching the same old stuff, or modify it to some extent, but no calculators and computers please!
Well, I agree that homework is good. I less agree about being a tough grader, but perhaps we need sharp sticks and sharp carrots. But, having old-time-discipline does not mean that we have to teach the old boring stuff. It is a myth the people a generation or two ago were better in math. Of course, every store-keeper had the algorithm for addition and subtraction programmed into them, but, conceptually, they were just as dumb, if not dumber, than today's Joe Average.
The computer is a wonderful tool, that already is making 95 percent of the old curriculum obsolete. We should teach our students how to use the computer. And, knowing how to press keys on the computer to get it to do meaningful stuff is analogous to playing a sonata on the piano, not playing a CD! There is nothing wrong in using a calculator to verify the identity 1/2=.5, as long as you do it correctly.
Most importantly, teach your children how to program! This will develop their minds much faster than any of the traditional curriculum, including, memorizing proofs in Euclidean Geometry, and being able to make minor variations, without really understanding the notion of proof.
I used to think that in order to understand a mathematical statement I needed a proof. Nonsense. While the top 10 percent of proofs do indeed give insight, most of them are just boring strings of assertions that lead from hypothesis to conclusion. Myself, when I want to understand something, I program it! Including proofs!
It is regrettable that with the advent of user-friendly software packages, the practical need to program is diminishing. Nevertheless, as a pedagogical tool, it beats anything else!
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