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Students Getting a Wrong Number

Researcher Says Children's Computational Skills Are Slipping

By Jay Mathews
Washington Post Staff Writer
Tuesday, September 3, 2002; Page A01

The Bethesda-Chevy Chase High School team was on a roll in the first round of the Saturday morning television quiz competition "It's Academic." The students knew the title character in Gabriel Garcia Marquez's "The General in his Labyrinth" (Simon Bolivar). The first name of Winston Churchill's wife (Clementine) was no problem. They identified the 11th U.S. president (James K. Polk) in a second.

But although they won that day last winter, the Bethesda-Chevy Chase scholars had an embarrassing moment when host Mac McGarry asked what seemed like a fourth-grade question: "How much is a 4 percent sales tax if the purchase price is $90?" There was an awkward silence, and as time ran out, team captain Ann Horwitz made a guess: "$3.50?"

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Close, but no points -- another sign of American students' problems with practical arithmetic, which many educators say is vital for daily life as well as school. And now a Brookings Institution researcher is saying that computation test scores are stagnating or declining in the United States and the government has covered it up.

In a report released today, Tom Loveless, director of the Brown Center on Education Policy at Brookings, said the federally funded National Assessment of Educational Progress has presented a cheery picture of rising math scores in the last decade, even while arithmetic scores have languished. NAEP often is called the nation's report card.

Loveless has a high-profile supporter in Vice President Cheney's wife, Lynne Cheney, who invited him to present his research at an education forum this year.

"For the past several years, there has been a growing groundswell of opposition to the new methods of teaching mathematics," Lynne Cheney said. "Parents have known intuitively that it makes no sense to deemphasize skills such as addition, subtraction, multiplication and division. Tom Loveless has done us all a favor by disentangling, from the available statistics, data showing that parents have been right to be concerned."

In his report, Loveless laments a decision by the federal board that oversees NAEP. The decision relegated the test of students' basic math skills without the aid of calculators -- derided by some experts as "shopkeeper arithmetic" -- to a part of a larger test. As a result, the computation scores are not reported separately.

"So we arrived where we are today: a federally endorsed state of ignorance on the computation skills of American students," said Loveless, a former elementary school teacher and Harvard professor who writes extensively on education policy.

In the meantime, he said, the fraction of 17-year-olds correctly answering NAEP questions requiring basic arithmetic skills has declined from 76.3 percent in 1990 to 71.9 percent in 1999, on the test given every four years or so. The drop was particularly noticeable in fraction problems.

Larry Feinberg, spokesman for the National Assessment Governing Board, which oversees the $111 million-a-year testing system, said Loveless's analysis of NAEP data was "selective and distorted." He said Loveless excluded some percentage questions that would have shown arithmetic achievement unchanged for 17-year-olds and improving for 13-year-olds during the 1990s.

Loveless, in response, said that however the arithmetic scores are presented, they are too low.

Sharif Shakrani, deputy executive director of the governing board, acknowledged a problem with 17-year-olds' computation skills but said it was part of an overall weakness in mathematics at that age, which the NAEP results had identified.

Shakrani said computation skills are important not only in the parts of the NAEP tests designed to measure them, but throughout the federal mathematics assessment. If test-takers were as bad at arithmetic as Loveless suggests, he said, they would not have shown improvement on other parts of the NAEP tests over the past decade.

He also noted that SAT math scores have been going up, with the national average reaching a 32-year high this year.

Nonetheless, Shakrani strongly endorsed the importance of testing computation skills. "It is an indication of whether the student understands our number system," he said. That is why the federal board rejected a recommendation from the Reston-based National Council of Teachers of Mathematics to allow calculators on all NAEP tests; the board restricted calculator use to one-third of the main NAEP math tests.

Several math and science teachers said they had noticed a decline in practical math skills but wondered if there was anything that could be done, or needed to be done, in an age of calculators.

"The change I noticed in student computation ability over 17 years of teaching was no different than the change I noticed in their everyday lives," said Marcia Weinhold, a former high school math teacher now studying at Western Michigan University. "Why walk or ride a bike when you can drive? Why climb stairs when you can take an elevator? Why write anything by hand, especially mail? Students are very close observers of their culture, and they know where it is headed."

George Bond, a mathematics teacher at Woodbridge High School in Prince William County, said: "Technology is making so much simpler while at the same time letting many do far more than they could do without it. It's a trade-off. Basic math is the loser."

Loveless believes it is shortsighted to shrug off the decline.

Computation scores reveal understanding of arithmetic, he said, and that leads to success in higher math, in college and in the workplace. "There are large numbers of kids at the bottom of the achievement distribution -- the non-SAT takers -- who are going in the wrong direction," he said.

He said the taxpayers who fund the NAEP tests deserve to have computation scores reported as a separate category and not buried in the "Number Properties and Operations" section, where they are only 40 percent of the test.

"Number Properties and Operations? What parent is worried about that?" Loveless said. "Why is it that the NAEP, the federal government's primary tool for evaluating American education, cannot tell whether fourth-graders know how to compute accurately?" Officials say there are plans for a federal initiative, backed by Lynne Cheney, to reemphasize basic math.

In his report, Loveless contrasted a strong climb in fourth-grade math scores on the main NAEP test from 1990 to 1999 with little change in computation scores over the same period. Computation scores for eighth-graders in Iowa, one of the few states that allow separate scrutiny of paper-and-pencil math skills, dropped sharply after 1992. "Iowa may be the canary in the coal mine, warning the nation that there are consequences to deemphasizing computation skills in the elementary grades," he said.

Loveless said he blames math reformers, including the National Council of Teachers of Mathematics, for turning away from basic skills in the 1990s.

The new thinking, he said, was that "calculators would free students from the drudgery of memorizing multiplication tables and practicing long division. Rather than learning standard algorithms through direct instruction, arithmetic could be learned while solving real-world problems that piqued children's interest. The federal government . . . enthusiastically embraced this position. Unfortunately, official support preceded any practical experience with the [National Council of Teachers of Mathematics] standards or independent research on their effects."

Johnny W. Lott, a mathematics professor at the University of Montana and president of the math teachers group, said there is widespread evidence, including the recent NAEP results, of the positive effect of the changes in instruction. Computational fluency is essential, he said, but students also "have to understand the meaning of these operations." He said that "to try to concentrate only on computation would be comparable to trying to concentrate only on the alphabet while learning to read."

Sophie Altman, who created the "It's Academic" TV competitions for high schools in 1961, said she has noticed very bright students having trouble with basic math questions, although usually in those portions of the show in which they can only hear and not see the questions.

Jonathan Raviv, the math expert on the Bethesda-Chevy Chase team, has just begun his freshman year at Johns Hopkins University. He had a near-perfect 790 score on his SAT math test and got the top grade, a 5, on the Advanced Placement Calculus BC test.

He said that when the sales tax question came up, he froze for a moment under the lights and the time pressure. He said he would have succeeded if he had had a few more seconds to think, but he does not rule out the possibility that lack of computation practice hurt him. He tried to estimate the answer -- a tactic strongly encouraged by the math teachers group -- but his method gave him a 5 percent, not a 4 percent, tax. Hearing nothing from him, Horwitz tried her desperate guess. The correct answer was $3.60.

Raviv said he knows the slip-up was trivial, but he still felt bad. "I blew it," he said. "I was very disappointed in myself."


© 2002 The Washington Post Company


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