The National Assessment of Educational Progress (NAEP) is often referred to as the "nation’s report card" and is held up a tool for comparing learning by American students with those in other countries. A new study (we haven’t had one of those in a long time), however, says that the math questions on the test are too easy. For example, researchers claim that 40% of the questions asked of eighth graders test skills that are taught in first or second grade, the same percentage of questions at that level on the fourth grade test.

The central fault, Loveless [director of the think tank that wrote the report] 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."

The NAEP people disagree with the study, of course, questioning the formula of what students should know by any particular grade. A fair criticism. However, I have to agree with one of the central concepts of the report, that goes beyond what is tested to what is taught. Students in most elementary and middle schools rarely face problems that have "messy" answers. Too many have nice, neat integer results, unlike those people face in their daily lives.

I found it interesting that, while we are told almost daily how schools are doing a bad job, the math scores on this "national report card" have shown a large increase over more than a decade. As always, however, the numbers don’t tell the whole story.

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.

Bottom line, just knowing the mechanical process of arithmetic doesn’t necessarily mean students understand mathematics and how to apply it to actual problem solving.