New data from a national math test show that U.S. fourth- and eighth-graders have made slight gains since 2009, but only 35 to 40 percent of the students tested showed proficiency in math.

The federally run National Assessment of Educational Progress (NAEP), often known as "the Nation's Report Card," periodically tests students on several subjects to gauge their progress over time. The National Center for Education Statistics (NCES) released the results of the 2011 assessments in mathematics and reading on November 1.

The new math results continue two trends: a history of overall improvement since 1990, and a series of small but continual gains since 2003, when biennial testing began. Both the fourth- and eighth-grade groups increased their average scores on the 500-point test by a single point between 2009 and 2011, and both groups are now testing six points higher than they were in 2003. "In grades four and eight, in mathematics we actually see the highest scores to date," NCES commissioner Jack Buckley said in an October 31 conference call with reporters.

The math test is designed to gauge the status of the entire U.S. student population by taking a representative sample of pupils at public, private and religious schools. Some 209,000 fourth-graders from 8,500 schools and 175,200 eighth-graders from 7,610 schools participated in the 2011 test.

But when it comes to how many of those students meet proficiency standards, the picture is hardly rosy. The National Assessment Governing Board, an independent committee that sets policy for the test, defines proficiency as "solid academic performance" with "demonstrated competency over challenging subject matter." In the 2011 test, 40 percent of fourth-graders were assessed as proficient or better in math; among eighth-graders only 35 percent qualified as proficient. The latest figures each represent an increase of one percentage point from 2009 levels.

The new numbers are a far cry from the goals of No Child Left Behind (NCLB), the ambitious education law signed by President George W. Bush in 2002. That policy set a target of 100 percent academic proficiency across the board—not just in math—by 2014. If the pace of improvement that has held steady since the passage of NCLB does not change, it will be two decades or so before a mere 50 percent of U.S. eighth-graders reach math proficiency. President Barack Obama recently enacted changes that allow states to request waivers for some of the legal requirements of NCLB, including the 2014 deadline, stating that the strictures of the law were hampering academic progress in some schools.

Buckley acknowledged that the gains from 2009 to 2011 were modest, taking as an example the one-point rise in math scores among fourth-graders. "While it is statistically significant, it is not an enormous increase substantively in terms of, 'What can students really do?'" Buckley said. "They're a little bit more likely to get some particular types of items right—they have made some small improvements, but it's not an enormous change."

The NAEP statistics on mathematical proficiency are in broad agreement with international assessments that show U.S. students trailing their peers in industrialized nations in math and science. In a 2009 survey of 15-year-olds in the member countries of the Organization for Economic Cooperation and Development, U.S. students placed in the bottom third in terms of mathematical literacy.

Nevertheless, some observers are encouraged. "I think you have to take a step back and look at the longer trend line," says Russ Whitehurst, director of the Brown Center on Education Policy at The Brookings Institution. Scores have increased steadily for two decades, raising nationwide averages by 28 points for fourth-graders and by 21 points for eighth-graders since 1990. "I don't view the gains as subtle in mathematics," Whitehurst says. "They are very large."

"We should understand that the size of any year-to-year change isn't the important thing," agrees Jeremy Kilpatrick, a professor of mathematics education at the University of Georgia. "What's important is that the movement in average scores over time has been consistently in the right direction."

Some bright spots did emerge from the latest assessment. Hawaii, New Mexico, Rhode Island and Washington, D.C., all posted significant score increases at both grade levels, compared with 2009. And nationwide scores for students classified as Hispanic rose in both grade levels; the score gap between white and Hispanic eighth-graders shrunk by three points between 2009 and 2011. Average test scores for girls increased slightly in both grade levels, drawing to within one point of the average scores for boys.

The new NAEP figures do not include an explanation of which education policies or practices are working or not. That analysis falls to the individual states, which are left to provide context for the data on their own school systems. "NAEP is very good at telling us where we stand...but data of the sort that we collect are not as useful in making causal inferences," Buckley said. "We're not very good at telling you why the scores are what they are."

Many have tried to ascribe gains to specific policies or practices, such as No Child Left Behind, but Whitehurst dismisses such connections as "guesswork," noting that there are simply too many moving parts to make clear inferences. "So to attribute this [gain] to any particular policy initiative, whether it's a federal policy, a state policy or a policy of the National Council of Teachers of Mathematics, is very perilous," he says.

# Arithmetic Progression: U.S. Education Assessment Shows Modest but Steady Gains in Math Scores

The so-called Nation's Report Card shows some progress in bringing U.S. students up to speed in mathematics