The national test of student math skills is filled with easy questions, raising doubts about recent gains in achievement tests, a study contends.

On the eighth-grade version of the test, almost 40 percent of the questions address skills taught in first or second grade, according to the report by Tom Loveless, director of the Brown Center on Education Policy at The Brookings Institution (search), a Washington think tank.

The test for fourth-graders also has "false rigor," Loveless says: More than 40 percent of questions gauge first- and second-grade skills, two levels below the students tested.

The central fault, Loveless contends, is that too many problem-solving questions rely on whole numbers, with too few challenges involving fractions, decimals and percentages. Such instruction sets students up for trouble in more advanced high school classes and in daily life, where tasks such as shopping and measuring rarely involve neat, round numbers, he said.

"If we want kids to be sophisticated problem solvers, they've got to be able to think beyond whole numbers," Loveless said. "That's just not good enough."

Known as the nation's report card, the National Assessment of Educational Progress (search) is the most widely respected measure of the skill levels of U.S. students. Given to representative samples of students, it is offered periodically in many subjects, including math in 2003.

A leader of the National Assessment Governing Board (search), which sets the test content, strongly disagreed with the findings, saying the study is flawed because it is based on a questionable formula of what kids should know when.

The study, being released Thursday, analyzed questions from the 2003 math tests, and then determined a grade level for those questions based on the Singapore math textbook program. Loveless said he chose that program because of its clarity and strong international reputation, and he said it compared well to the math-class sequences used in states such as California and North Carolina.

But using Singapore as a model presents skewed results, said Sharif Shakrani, deputy executive director of the assessment governing board. Math is taught differently in that country, with heavy concentration on computation early before other topics are introduced. U.S. schools go for breadth, he said, with more math skills to cover each year.

Overall, he said, the questions on the national in fourth grade and eighth grade are commensurate with what's being taught in those grades.

"I contend that if we do what he suggests, moving to much more complex skills, it would be akin to giving a test in Russian," Shakrani said. "We already are not doing well. If you increase the cognitive function of the math concepts and the way you test them, you will end up with scores so low you will not be able to make sense of the results."

Some questions — about 20 percent of them — are intentionally the same on the fourth-grade and eighth-grade tests to help track growth in achievement over grades, Shakrani said.

A fair number of questions, he said, involve percentages and fractions. But others avoid them to isolate whether students have problem-solving skills regardless of the complexity of the numbers. Loveless said that approach is shortsighted.

"Boosting students' competency in arithmetic and the ability to solve problems are not contradictory goals," he wrote. "Neither one need be denigrated in the pursuit of the other."

Scale scores on the math tests have risen sharply for fourth-graders and eighth-graders since 1990. Loveless said it is not clear whether that reflects true gains in math knowledge, particularly since the gains have not translated into more enrollment in high-level classes.

Overall, more than seven in 10 fourth-graders and almost as many eighth-graders are now achieving at a basic level or better on math, according to the latest federal scores. But more than two-thirds can't do math at the more challenging "proficient" level they should.