Old math. New math. New-new math. And coming soon to a classroom near you . . . new-new math, modified.

For decades, math educators have tried to "fix" this often vexing school subject by revamping the content of lessons and methods of instruction.

Yet the record on math achievement remains mixed. On one hand, the math scores on the SAT college entrance exam have hit an all-time high. On the other, for all the reform efforts, the average 17-year-old today doesn't know math any better than his counterparts 20 years ago, according to the National Assessment of Educational Progress.

In the most recent chapter of math reform, educators have been guided by the 1989 standards of the National Council of Teachers of Mathematics. That document emphasized hands-on, real-world math. It sought to portray math as a thinking process rather than a body of facts to be memorized.

But critics of the new approach derided it as new-new math and said pondering real-world dilemmas didn't necessarily teach students much math.

Now, the council is modifying its original document. Part of the motivation for doing so was what it now says were misunderstandings of its efforts--such as the idea that correct answers and memorizing the multiplication tables are not important.

Leading the revision effort is Glenda Lappan, a Michigan State University education professor who has been council president since April. She says the goal remains the same as a decade ago.

"We continue to educate some very bright children very well indeed, but we were failing to educate even the kids in the bottom 80%," she said. "We were not engaging them in math in a way that was the least bit exciting."

The national council, she said, pushed "really hard to take an inert system and get it moving." In retrospect, she said, the organization's rhetoric may have been too extreme. But the point was to get a "conversation started."

Take the issue of correct answers. Lappan said the idea that the council was not interested in correct answers was a "gross misinterpretation" of its intent.

What the organization was trying to do, she said, was encourage teachers to listen to their students talk about how they solved problems, to gauge their understanding.

Most of the criticism of the standards has come from parents and mathematicians who thought the needs of students who wanted to pursue careers in science, medicine or mathematics were being neglected.

The draft of the new document acknowledges that, in emphasizing "mathematics for all," such students may have gotten short shrift. The rewrite "reaffirms NCTM's commitment to providing the highest-quality mathematics instructional programs for all students."

Consulting on the revisions are the leading professional mathematics groups. A first draft of the rewrite--due to be completed in 2000--is now available on the Internet at:

http://www.nctm.org/standards2000

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One outcome of the 1989 standards is the spread of calculators. The council's report advocated that all students have access to calculators at all times.

That proliferation led to perhaps apocryphal stories of college students turning to calculators to multiply 25 by 10 or divide 18 by six.

Now, the California State University system is joining the calculator crowd. Starting in January, incoming freshmen may use calculators on the state university's math placement exam. The goal, a university spokesman said, is to make the placement test more like college entrance exams, such as the SAT, which allow calculators.

But part of the test covers simple arithmetic, such as multiplying the fraction 7/16ths by 24. David Klein, a Cal State Northridge math professor who is an outspoken critic of current mathematics reforms, said allowing calculators "doesn't make any sense" given the content of the test and the fact that more than half of the incoming freshmen fail it.

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The national council's standards had another impact: They pushed states to write their own versions. The California Board of Education approved standards a year ago that have drawn widespread praise, most recently from the American Federation of Teachers.

The problem is the state still has not published those math standards. That means very few teachers have seen them. Nor do textbooks reflect them.

Even so, next spring, students in grades two through 11 will take tests to find out how well they have mastered the material. Material that, most likely, they have not been taught.