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A 50-year debate on math shows no sign of slowing changes have met with resistance and prompted alternative approaches and the issue is by no means settled

Sunday, August 23, 1998

Jane BLotzer, Associate Editor, Post-Gazette

OK, class. To fully appreciate the current state of play of math education, you may need a history lesson. And don't forget, history tends to repeat itself.

The traditional American approach to math finds a teacher in front of a room, demonstrating how to solve a problem. She works a few with the class to make sure they get it. Then she assigns many more to be solved precisely the same way.

The trouble is this: While many of the students can follow the leader, they don't know where they're going or how to make the connections between past and present lessons to get there. Most will be clueless if confronted with a variation.

The result is a nation of individuals with only the most rudimentary mathematical skills and sense.

There is nothing new about this situation. The U.S. Army was alarmed during World War II when it discovered the level of mathematical incompetence among draftees. That concern deepened in the post-war years as it became clear that scientific and technological superiority were key to Cold War dominance.

The government created the National Science Foundation in the early 1950s; a math education reform movement was born.

When the U.S.S.R. launched sputnik in 1957, concern turned to panic as many feared that the balance of scientific and military power had tipped. A cadre of engineers, scientists and mathematicians was needed to make those commie heads spin.

The math education reform movement grew up in a hurry.

New Math was created in universities around the country to deepen the

understanding of those students who already were mathematically agile and to enlighten others of the beauty and power of math.

New Math differed from Old Math in its focus on the theory behind the numbers - set theory, associative, distributive and commutative properties, all were taught in New Math classrooms.

Fueled by federal dollars, the new math curriculum swept through classrooms in record time. By the 1970s it was the standard in nearly half the schools across the country.

Back to basics

But parents hated it. They didn't get it and couldn't help their children. Teachers - particularly those in elementary and middle schools with limited math understanding themselves - were uncomfortable with it, and in their discomfort, some became ridiculous in their adherence to its principles. Others actively tried to sabotage the effort.

A few students understood the theory, but many more were lost. And simple computational skills also were lost in the process.

Shaken by this strange curriculum, parents and teachers sought out the tried-and-true, back-to-basics approach. Well it was tried, but it was hardly true.

All of the problems that were identified by the reformers were no less corrosive simply because they applied the wrong medicine, or applied the right medicine badly.

But back-to-basics triumphed, and students for three more decades have mostly been learning math as an alphabet soup of formulas and operations with little emphasis on what it means or how it actually pertains to life.

Then in the 1980s, U.S. students did badly in international math comparisons. At the same time, the economy was in a recession, suggesting we were being left behind in the race for technological competence. Industrial jobs no longer relied on brawn but on an ability to operate computerized equipment.

Pressure to change math education, grew and in 1989 the National Council of Teachers of Mathematics issued a set of 54 standards for kindergarten through 12th-grade education.

The standards were designed to meet five fundamental goals: that students learn to value mathematics; that they become confident in their ability to do math; that they become mathematical problem solvers; that they learn to communicate mathematically; and that they learn to reason mathematically.

The NSF applauded the standards, but realized that more needed to be done if they were to be applied. And so it got back into the math-curriculum development business. In the early 1990s, it offered $50 million to help develop programs for elementary, middle and high school math that reflect the standards.

Only a minority of students are in schools using the science foundation's funded programs, although some mainstream publishers have incorporated the ideas.

Combat grinds on

But no change is painless. Many teachers, particularly in elementary and middle schools, remain uneasy with math and especially uncomfortable with a technique that asks them to have deep and flexible understanding of the topic. Some have looked at the suggestion that reason be emphasized and drill de-emphasized; they decided that there need be no drill or memorization.

Concerned parents worried that their children weren't going to be taught the basics anymore, that they'd need a calculator to add 6 and 3. A backlash began.

Its tremors were first felt in California in the mid-1990s, as parents, teachers and mathematicians lined up on both sides of new math offerings and the proposed state standards. Anti-reformers dubbed the changes New New Math, despite profound differences between the two approaches.

When the Third International Math and Science Study results came out in 1996 and 1997, again ranking American eighth- and 12th-graders at or near the bottom in math achievement, anti-reformers claimed it was the "fuzzy math" that had led to the poor performance. Reformers believe that America's long-standing emphasis on simple arithmetical basics through eighth-grade was a prime culprit.

In truth, the two sides seek the same goals: a mathematically literate population - one comfortable with both problem-solving and computation, and one able to work their way through basic algebraic, geometric and statistical mazes.

That common ground would seem a reasonable basis for a truce in the ongoing math wars.

The problem, however, is that the battle is precisely about defining what the proper balance is, and on that there is no agreement.

And so the combat grinds on.

A math war, echoing the bitter debate that occurred between advocates of

whole language and advocates of phonics-based reading programs, is exactly what this country does not need, according to Edward Silver, a University of Pittsburgh professor of math education and cognitive studies, who also has helped distill the lessons of TIMSS, the international math survey.

Rather than moving in steady and consistent steps forward, education in the United States experiences enormous, and enormously counterproductive swings. Fundamental change in math education will take a generation at a minimum, Silver predicts. But traditionally impatient Americans expect immediate turnarounds. That tendency leads to ill-prepared implementation of reforms and an immediate backlash and retreat when miracles don't occur.

Silver understands that no one wants his child to be the subject of experimentation, so curriculum changes must be made carefully. "A lot of bad can be done in the name of a good idea," he said.

But before rejecting every new approach, he says parents should honestly evaluate their own math history. "Many people have very fond memories of this experience they hated to death."


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