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While Arizona elementary and middle school students have maintained or improved their math and reading skills, their abilities lag behind national averages, test results released Tuesday show.

Students in fourth and eighth grades showed the greatest improvement in mathematics, while gains in reading were modest, according to the National Assessment of Educational Progress test, also called "The Nation's Report Card."

The state scores mirrored national results, which showed increases in math competence with slower gains in reading. Results are based on test scores from the 2006-07 school year.

The test, which samples students from classrooms across the nation, shows that 31 percent of Arizona fourth-graders were proficient or better at math problems such as finding the perimeter of a shape.

In eighth grade, 26 percent of students in the state were proficient or better at math problems such as computing the measure of an angle.

Both marks were lower than the national average, although the state's top education official said the test isn't reliable at measuring how Arizona students stack up against others across the country.

Still, Arizona students continued to improve from past math tests. The percentages of both fourth- and eighth-grade students who achieved a basic level — considered the minimum level of competence — or better on the test increased for the fourth test in a row.

Math scores for fourth-graders have increased 30 percent — or 17 percentage points — since 2000, while scores for eighth-graders have increased 10 percent — or 6 percentage points — during the same period, results show.

Statewide reading gains for both grades were less pronounced, with 25 percent of fourth-graders and 24 percent of eighth-graders labeled proficient or better. Both marks were below the national average.

The national test shows that Arizona students are headed in the right direction, although the state needs to do more to teach skills that are assessed on the national test, said Tom Horne, the state superintendent of public instruction.

Local education leaders, including Superintendent Roger Pfeuffer of the Tucson Unified School District, said the national test doesn't match state standards. The dichotomy can cause problems, Vail School District Superintendent Calvin Baker said.

"One of the difficulties here is that they're almost asking schools to shoot at two targets at the same time," Baker said.

Students in Arizona learn skills that the national test doesn't assess, Horne said. Conversely, he said, some skills that the national test measures — such as solid geometry — aren't taught at the same grade levels.

The state is reviewing math curricula to determine how to bring state standards more in line with the national test.

"As we bring our standards closer to theirs, you'll see them falling in line," Horne said.

Vail officials plan to incorporate the national test's standards, which are more rigorous than state standards, into their curriculum, Baker said.

"We hope that if we can bring students up to the NAEP (national) standards, they'll also be proficient at the state standards," he said.

Horne said the national test is unreliable at gauging how Arizona students compare with students in other states, citing other national tests that have shown Arizona students are above the national average in reading and math. Those tests include the Terra Nova and SAT, he said.

The test showed that students nationally are making across-the-board gains in math and more modest progress in reading. The test scores 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 students performing math and reading at their proper grade levels 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.