Elementary and middle-school students are making across-the-board gains in math and more modest progress in reading, national test results out Tuesday show.

The scores on the National Assessment of Educational Progress will be scrutinized by policymakers and educators looking for signs of whether the No Child Left Behind education law is working. The goal of that five-year-old law is to get all kids doing math and reading at their proper grade level by 2014.

"We're making slow and steady progress in reading, and we're doing much better in math," Mark Schneider, the commissioner of the Education Department's research arm, said after reviewing the scores.

The national assessments, sometimes referred to as the nation's report card, provide a uniform way to compare student progress across state lines.

Overall, math scores were up for fourth- and eighth-graders at every step on the achievement ladder. The results show:

—Thirty-nine percent of fourth-graders are proficient or better in math, up from 36 percent two years ago when the test was last given. Hitting the proficient mark is the goal, policymakers say.

—Nearly a fifth of the fourth-graders tested still can't do basic-level work, such as subtracting a three-digit number from a four-digit one. But scores are up in that part of the achievement spectrum since 2005.

—Among eighth-graders, 32 percent are proficient or better in math, up 2 percentage points from last time.

—Seventy-one percent performed at the basic level or better, up from 69 percent two years ago.

In reading, fourth-grade scores are higher than they were two years ago. But eighth-grade reading scores only moved up a little. The results show:

—A third of fourth-graders were proficient or better at reading — up 2 percentage points from 2005. Kids working at that level could identify a literary character's problem and describe how it was solved.

—Sixty-seven percent of fourth-graders can do a minimum of basic-level work, up from 64 percent last time.

—There was no increase in eighth-graders working at proficient or advanced levels. About a third can do that level of work, meaning they can identify the literary genre of a story, for example.

—Seventy-four percent of eighth-graders can read at a basic level, up just 1 percentage point from 2005.

Darvin Winick, chair of the National Assessment Governing Board, which oversees the tests, said it was discouraging that there wasn't more progress in eighth-grade reading. The results come on the heels of flat reading scores for high-school seniors.

"We need to look into reading deficiencies in middle and high schools in depth. That should be the next national imperative," Winick said.

The math scores have generally been on a steady upward trajectory since the early 1990s. Some educators say it's easier for teachers to affect math scores, because math is almost entirely a school-based subject while some children get extra exposure to reading in their homes.

One goal of the No Child Left Behind law is to shrink the gap in math and reading scores between racial and ethnic minorities and their white peers.

The reading achievement gap between black and white fourth-graders narrowed this year, as did the gap between black and white eighth-graders in math. The gaps in other grades, as well as those between whites and Hispanics, held steady.

Students in the District of Columbia and the following states posted gains in math in both grades: Delaware, Hawaii, Indiana, Kentucky, Massachusetts, Missouri, New Hampshire, New Mexico, New Jersey, North Dakota, Oklahoma, Pennsylvania, Vermont and Virginia.

In reading, students in the District of Columbia, Florida, Hawaii and Maryland saw their scores go up in both fourth and eighth grade.

The states set their own policies regarding the percentage of special education and limited English speakers who participate in the national assessments.

Overall nationally, however, more kids with disabilities and limited English skills have been taking the tests in recent years.