Wednesday, July 21, 2004

Take Notice

The August issue of the Notices showed up in my mailbox today. Very interesting this month.

One of the letters to the editor is about mathematics education. The author appears to be saying that mathematicians should stop that wacky NCTM before they ruin K-12 math education. He seems to be focusing on algorithms, noting that, "Mastery of addition and the other algorithms of basic arithmetic act as a flashlight, allowing the young student to move freely about in the world of numbers and basic numeric operations." This strikes me as optimistic. I would say that for many students algorithms act as a flat-head screwdriver: conveniently at hand and used for many things that they were not designed for (and dangerously at times!). I wonder how he'd feel if he asked his students, "What's a derivative?" and they answered, "It's that thing where you multiply by the exponent and then lower it by one." [Aside: Do your students use d/dx as a verb? I hate that.]

The NCTM definitely does some provocative things. Their 1998 Yearbook contains an article entitled "The Harmful Effects of Algorithms in Grades 1-4." Many of the good points in the article are probably missed by people shocked by its title.

The idea of a systematic approach which will take the inputs to a specific problem and generate the correct outputs is an important idea, and I believe it should be taught. However, I am much more flexible about which algorithms should be taught. And if given a choice, I'd much rather that my freshmen knew that if you divide a by b and get a quotient q and remainder r (with r greater than or equal to 0 and less than b), then a = bq + r (and to realize that a - r is divisible by b) than for them to know how to do long division by hand.