# In math education, who decides what works best?

THE MATH MELTDOWN

PALO ALTO, CALIF. — Ever since William Hewlett and David Packard launched Silicon Valley out of a Palo Alto garage in 1939, math has counted for a lot in this town. Knowing your way around an algorithm is the sure way into the hottest high-tech market.

That's why parents - many of whom were top math professionals at Stanford University or local software companies - took note when plans surfaced to revamp math in the middle schools. They didn't like this new approach, especially after test scores plummeted. They also didn't like being told that they'd have no say in how math was taught.

"Some of the best mathematicians in the country, if not the world, found it incredibly difficult to make any kind of an impression or get other programs for their kids," says R. James Milgram, a math professor at Stanford.

At stake in the ensuing debate were competing visions of what creates capable thinkers in a high-tech age. Should math classes prepare all students for New Economy jobs? Can American teachers teach to that level?

Or is it enough to have an appreciation of mathematical thinking? And does it require a higher level of competence for teachers to teach "discovery" modes than it does to drill students in basics?

In many Asian and European nations, it's national policy to ensure that all children have access to a curriculum that leaves open a career in professional mathematics. In France, all students study the same math until about age 15, then are sorted into career tracks largely on the basis of how well they handle math.

But even France is facing a battle to make math more responsive to those who won't become mathematicians. "We're trying to get more practical problem solving into the curriculum," says Jean-Michel Kantor, a math professor at the University of Paris 7 who edits Cosinus, a new math magazine for children.

But he and others say that the fight is a formidable one. Former Education Minister Claude Allegre was lambasted for urging a lighter math program, and was recently forced to resign. Math associations strenuously oppose efforts to introduce statistics, interdisciplinary classes, or more open-ended problem solving.

In the United States, the issue is nearly reversed. Many US teachers support teaching to all levels in a classroom, but are often not as well grounded as European or Asian counterparts in content. Professionals complain new texts have errors.

For Silicon Valley professionals, the concern was that kids needed a more solid math content in their K-12 years to be on track for advanced math in college. Colleges, after all, weren't adjusting to "new new math" by changing their standards.

By the mid-'90s, Palo Alto parents lobbied Sacramento for stronger math standards. Most critically, they moved their research and protest onto the Web. Finally, they won the option of traditional math classes.

Math teaching is best understood as pendulum swings between professional mathematicians and math educators. It's an important distinction: Professional mathematicians are the first to point out that math educators do not do math for a living. They worry that current courses aren't up to levels that will train mathematicians.

Many math teachers studied theories about how to teach math, not math itself. They note that knowing math doesn't ensure you'll be able to teach it.

The "new math" of the 1960s and '70s was a pure product of professional mathematicians. Spurred by Russian space successes, they wanted advanced math early. US math students found themselves puzzling out abstract issues, such as set theory, at a tender age. Content was often over teachers' heads.

"New new math" would be hands-on. Students would learn math in the context of real-life problems, in groups.

This had as little to do with professional mathematicians as the old "new math" had to do with the classroom. In 1989, the National Council of Teachers of Mathematics issued standards that encouraged "discovering" routes to the answer. Memorizing tables was out; calculators, open-ended problems were in.

In the end, a handful of people on a state standards board, textbook panel, or education school can give a powerful nudge to a math camp. Other factors, too, come into play. After the NCTM standards came out, the Education Department and the National Science Foundation threw funding their way.

"The 'new new math' came in response to real problems. Students haven't been doing well," says Ralph Cohen, director of the education program for Teachers of Mathematics at Stanford. But "by this [1989] document, they implemented a national doctrine. The education division of the NSF has funded almost exclusively math programs that fit that definition."

(c) Copyright 2000. The Christian Science Publishing Society