By Lynne Cheney;  Lynne Cheney, former chairwoman of the National Endowment for the Humanities, is a senior fellow at the American Enterprise Institute.
 
 

For Stacy Christ, a fourth grader in Fairfax County, Va., a homework problem about pencils and packages was an exercise in frustration.

"The answer required division," her mother, Susan, explained to me, "but she'd never been taught to multiply."

Susan Christ saw this as one more sign of the miseducation of her child, but to advocates of what is sometimes called "whole math" (or "fuzzy math" or "new-new math"), Stacy's assignment was exactly right. Students don't need to know multiplication tables in order to divide, they say. Using objects and calculators, they can figure it out -- and thus begin to create their own mathematical knowledge.

The idea that knowledge is something to be constructed, rather than acquired, has been moving into American schools since the 1970's. This approach is obvious, for example, in language-arts teaching that encourages invented spellings.

But now "constructivism," as it is sometimes called, has become a force in teaching mathematics -- and the paradox is immense. In a field distinguished by reliance on proof, an unproven approach is being taken in thousands of schools.

The saga of whole math began in earnest in 1989, when the National Council of Teachers of Mathematics published standards that denounced a "longstanding preoccupation with computation and other traditional skills." According to the council, stressing addition, subtraction and, worst of all, memorization made students into "passive receivers of rules and procedures rather than active participants in creating knowledge."

The standards recommended that students get together with peers in cooperative learning groups to "construct" strategies for solving math problems, rather than sit in class with teachers instructing them. Calculators were a necessity from kindergarten on, the council said, because students liberated from "computational algorithms" could pursue higher-order activities, like inventing personal methods of long division.

Dr. Frank Allen, a former council president and whole-math opponent, has noted that as the standards were being developed, the council's research advisory committee expressed concern about the failure of the standards commission to provide research support for its recommendations. But the standards' writers were undeterred, and today their views drive the direction of curriculums and textbooks in both public and private schools.

Those who regard the council's recommendations as revealed truth have been rewarded: a panel named recently to oversee the development of President Clinton's national test in mathematics is composed entirely of supporters of the math teachers' council. Critics, meanwhile, have been shut out. In a recent speech, Prof. E. D. Hirsch of the University of Virginia noted that a leading journal, Educational Researcher, had refused to publish a section of an article debunking constructivist teaching even though its authors were "among the most distinguished cognitive scientists in the world."

The entry of whole math into the schools has angered many parents. Particularly in California, where schools have enthusiastically embraced the constructivist fad, parents have complained about students unable to do simple mental computations, about high school graduates who get A's and B's in whole-math classes and have to do remedial work in college.

A woman in Oceanside, Calif., wrote to The San Diego Union-Tribune that her child had been "used like a laboratory rat, experimented on with new, untested curricula." A parent whose child attended one of the overseas Defense Department schools, which have adopted two constructivist programs, MathLand and Interactive Mathematics, reported on a Web site, "We all feel our children are guinea pigs in a bad experiment."

Parental backlash has sent whole-math advocates scrambling for evidence to prove that what they do works. When American fourth graders did fairly well on an international test, a prominent whole-math advocate credited constructivist teaching. Her claim would have been more convincing had another leader in the movement not earlier explained away the dismal performance of eighth graders on the same test by saying that whole-math teaching had not sufficiently penetrated American classrooms.

Constructivist views were also undercut by survey data accompanying the international results. In high-performing countries like Singapore, Japan and Korea, teachers primarily teach the whole class rather than having students in small groups invent knowledge for themselves, and classroom calculators are extremely rare.

Creative Publications, publisher of the MathLand program, recently released an analysis of eight California districts purporting to show that at the least its curriculum does no harm: after one year, "when compared to students across the nation, MathLand students showed one year's growth in both computation and concepts and applications." The districts were not identified, however, nor the reason for choosing them rather than others. The analysis also failed to explain whether the test scores of all students within a district were considered.

Meanwhile, new evidence bears out the gloomy assessment of parents. The median percentile scores in mathematics on the Comprehensive Test of Basic Skills taken by more than 37,000 students one year after the Defense Department introduced whole math show that students gained little in conceptual understanding from being encouraged to construct their own knowledge. Scores in concepts and applications were roughly the same as the previous year. De-emphasizing computation, on the other hand, cost them dearly. Scores on that section of the exam dropped 9 points for third graders; 12 for fourth graders; 11 for fifth graders, 10 for sixth graders, 10 for seventh graders, and 4 for eighth graders.

After these results, the Pentagon decided to change its test to one "better aligned" with whole-math instruction. This move may produce better scores but at the price of masking student weaknesses in basic skills.

When medical researchers administering a protocol find it has negative consequences for human subjects, they do not ignore those results and change their test. They end the experiment to avoid imposing further harm.

Surely it is time for educators to realize that the same ethic should apply to them. In the face of strong evidence that constructivist mathematics does not help and even hurts, they should consider closing down the whole-math experiment. If we want our children to be mathematically competent and creative, we must give them a base of knowledge upon which they can build.