Fuzzy memory on fuzzy math

Posted: Sep 14, 2006 12:01 PM

The National Council of Teachers of Mathematics released new guidelines that, for example, call on fourth graders to know multiplication tables and division.

Oddly, it's big news when math teachers call for students to learn math skills. So The Wall Street Journal and The New York Times reported that the guidelines signaled a return to emphasizing ''basics" in math education.

Stanford University math professor James Milgram, who advised the NCTM on the new guidelines, told Education Week that the new guidelines represent "an end to the math wars." Milgram was referring to the ideological battle between educators who believe that students should memorize multiplication tables and master long-division and educrats who believe teachers should encourage students to discover math for themselves and master estimating numbers.

In 1989, the NCTM was on the fuzzy side. The council argued that kids did not need to memorize math facts because, "The calculator renders obsolete much of the complex pencil-and-paper proficiency traditionally emphasized in mathematics courses."

State agencies compounded the folly. California educators argued that memorization of number facts was "a hindrance rather than a help in developing mathematical understanding."

In keeping with the NCTM's emphasis on children writing about math, developers of a California assessment test told graders to give more credit to students who got the wrong answer to a math question (but wrote a better essay) than students who gave the right answer without the right prose. California elementary schools scarfed up MathLand, a trendy program that pooh-poohed exercises with "predetermined numerical results."

The unofficial slogan for new-new math: There is no right answer. Trendy programs recommended that students work in groups so that they could discover the answers. Instead of memorizing 5+4=9, students would look for creative ways to solve the equation, such as that 5+5=10 but since 4 is 1 less 5, the answer is 9. In the name of creativity, new-new math was both time-consuming and boring.

No surprise, students suffered. Milgram found that the number of California State University students -- that is, the top 30 percent of high school graduates -- who needed remedial math more than doubled, from 23 percent in 1989 to 55 percent some 10 years later.

So I was thrilled to see the NCTM actually concentrating on math skills. Until I talked to NCTM executive director Jim Rubillo, who said the new guidelines were a "continuation" of the 1989 standards, and there is no "change in philosophy."

Don't blame the NCTM for bad trendy textbooks, Rubillo added: "In theater, I've seen Shakespeare done very well and very poorly."

Forsooth: Fuzzy math doth not equal Shakespeare. Before I called Rubillo, I told Cal State L.A. math professor Wayne Bishop that the NCTM was really coming around, but Bishop was skeptical. I chided him. After all, I noted, the guidelines may not call for third-graders to memorize multiplication tables, as California's substantive standards do, but at least they support "quick recall of multiplication facts" in the fourth grade. At least they deal with math now.

Bishop responded, "I would be surprised if behind the scenes they've moved at all." Now I wonder, too. It is not a good sign that, when I cited Milgram's quote about the end of the math wars, Rubillo responded, "The math wars are just an invention in the last few years of just a couple of people."

This mess started when true believers turned math into a faith-based folly. When angry parents and teachers rebelled, the faddists denied that they had moved away from the basics. After years of clashes within curriculum commissions and fierce textbook battles, they now deny there was a curriculum war. Then they wonder why no one believes them.

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