BRATTLEBORO -- In national standardized test results released this week, Vermont students scored higher -- on average -- than their counterparts around the nation, but the state failed to show improvement over previous tests, or make gains in the achievement gap between low income students and their classmates.

And while Vermont students generally outperform the rest of the nation, test scores in the state still show that fewer than 50 percent of the students taking the test are at or above grade level proficiency in math and reading.

Results from the 2013 National Assessment of Educational Progress, or NAEP, also known as the Nation's Report Card, were released Tuesday and Vermont students scored within the top seven of all states and the District of Columbia in all four categories.

The tests in math and English, which are administered every other year, were given to students in fourth and eighth grades in Vermont, and across the nation.

Vermont's fourth graders had the fifth highest average score in math, and the seventh highest score in reading.

And the state's eighth graders showed the fourth highest math scores, and the fifth highest reading scores, on average.

But while the state stacked up well compared to the rest of the nation, only about half of Vermont students are showing proficiency on the grade level exams.

In fourth grade about 52 percent of the students in Vermont were proficient on the math test, compared to a national average of 41 percent, while those same students only showed 42 percent proficiency in reading, compared to a national average of 34 percent.

In eighth grade 47 percent of Vermont students were proficient in math, compared to a 34 percent national average, and in reading 45 percent of the eighth graders in Vermont were proficient compared to a 34 percent national average.

"It's similar to what we have seen the past. It's gratifying the see Vermont kids doing so well," said Windham Southeast Supervisory Union Curriculum and Assessment Coordinator Paul Smith.

Smith says the national test scores show that Vermont students are among the highest scoring.

But as the same time the same stubborn achievement gap that shows up on the New England Common Assessment Program, the state's standardized test, shows up in the national test.

In fourth grade there was a 20 point difference on the math test between students on the national free lunch program and their peers in Vermont, and in eighth grade students receiving free lunch in Vermont had scores about 26 points below the students who are not eligible for the free lunch program on the math test.

Many schools in WSESU are shrinking that gap, Smith said, and more work needs to be done to help those students from low income households.

"We're working as hard as we can to reach those kids and it is starting to show," Smith said. "But it is slow and incremental. We want to get everybody to proficiency. That is the whole idea. It is just going to take time."

Vermont Agency of Education Director of Educational Assessment Michael Hock said that while the national test results are not as valuable to educators as the state tests , NAEP is the only way to compare Vermont to the rest of the nation.

"You don't get grade level results and so the average classroom teacher probably doesn't pay close attention," said Hock. "But we see that same gap based on income level and so it confirms for us what we see on the state tests."

Nationally, education officials highlighted the steady progress many states have been making since the tests were first given in the 1990s.

Tests scores, on average, inched up one or two points in both reading and math at both grade levels since 2011.

"Every two years, the gains tend to be small, but over the long run they stack up," said Jack Buckley, commissioner of the Education Department's National Center for Education Statistics.

Buckley said he was "heartened" by some of the results, "but there are also some areas where I'd hoped to see improvement where we didn't."

Vermont showed virtually no change in test results between 2011 and 2013.

The test was given this year to about 377,000 fourth graders and 342,000 eighth graders across the country. It was taken by students from public and private schools, but state-specific numbers are only from public schools.

The Associated Press contributed to this report.

Howard Weiss-Tisman can be reached at hwtisman@reformer.com; or 802-254-2311, ext. 279. You can follow Howard on Twitter @HowardReformer.