# Math Teaching That Adds Up

Concepts or memorization? Room for both in schools.

What's the best way to teach a child math? This simple question doesn't have a simple answer in an age when schools must teach more than "the basics" to students who face a 21st century that will demand higher levels of reasoning and computational skills.

A debate over math teaching has divided schools and upset parents. It is far more than just a question of using calculators in classrooms as a Monitor series, starting today, reveals. (See "Math Meltdown" on page 15.)

Rather, the drive to introduce new ways of teaching math is impelled by a need to keep the United States competitive in a technology-driven global economy. It's also spurred by new theories of how children learn and a desire to ensure that students in poor school districts aren't short-changed on math skills.

Unlike the "new math" of the Sputnik-era 1960s, when the aim was to produce more scientists and engineers, today's methods teach relevancy and reasoning. They try to equip students to cope with all the new ways that math comes into our lives, from tax accounting to software.

But one side of the debate warns that students aren't being taught the simplest math - such as multiplication tables - because teachers stress mainly an understanding of math concepts in "real life" problems. This "experiment" in teaching, opponents warn, still lacks confirmation that it produces math-savvy adults. A delegation of top mathematicians publicly decried the drift away from the rigor of learning basic calculating skills.

One answer to this debate, of course, is to somehow mingle the old and the new ways. But that can be impractical for many teachers and schools, which have tended to adopt complete sets of teaching materials fully steeped in only the new methods.

The bigger issue is whether national educators who are pushing the new math are correct, and whether they must change their methods.

Many schools feel pressure to respond to parents' concerns that students master the basics and internalize a core vocabulary of thinking in numbers. But they also want to instill an understanding of how math applies to daily life.

The National Council of Teachers of Mathematics moved at least a little way toward an amalgam of old math and new math when it recently revised its influential guidelines for instruction.

This group has long taken flak from critics who feel its latest guidelines (put out in 1989) sent the country spiraling toward "fuzzy math."

The council, clearly, has heard the critics. The revised guidelines acknowledge the importance of laying an early groundwork in the basics. But will teachers, many of whom have been hewing to the new math for years, readily alter their courses?

The evidence is mounting that students who never master fundamental algorithms, or systematic methods of doing calculations, will lose out in the workplace later on. High school students who have had nothing but "new math" approaches, where answers are often reasoned out in words, are sometimes tripped up by the intense numerical demands in college math.

Consider what's happened in the Los Angeles Unified School District. It has adhered to the new math for years, and its superintendent and many teachers believe that approach produces better results among the low-income, urban kids who are their main constituency. The state of California, however, is demanding a return to basics. For one thing, the state has moved to limits the use of calculators in classrooms.

The battle is hotly joined in Washington, too. Federal lawmakers have given speeches on how the new math is ruining our youth. The Department of Education drew sharp comment last year when it made math-instruction recommendations that favored the new, conceptual approaches. (The federal recommendations have been questioned because some of the people who helped shape them had professional or financial interests in the programs being evaluated.)

How should all this add up?

A reemphasis on basics is needed. All students should have sound math fundamentals, whether they move on to trigonometry, calculus, and so on - or whether their later math needs are limited to balancing checkbooks and figuring tips.

Having every student go at least as far as high school algebra makes sense for the children and the economy they'll have to participate in.

While strengthening the basics, however, schools should be flexible, adapting new-style math instruction that addresses students' abilities and their future needs for math.

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