Test scores of Alexandria school children have climbed sharply, approaching the level of most other Northern Virginia schools, according to results released yesterday by the State Department of Education.

Alexandria, which traditionally has had among the lowest test scores in the Virginia suburbs, recorded strong gains in both mathematics and reading in standardized tests given to students in grades four, eight and 11 last November.

"I'm very pleased," said Alexandria's assistant superintendent for pupil services, Donald Dearborn. "We'd have to say our program, with its emphasis on basic skills, is paying off."

Overall, Northern Virginia students' scores remained the same as last year or improved slightly, with Northern Virginia continuing to lead the state in standardized test results.

The smallest improvement in test results this year occurred in Fairfax County, where scores in math and reading increased by only four percentage points.

"We are pleased our students continued to score well above the national averages and . . . again led all school systems in the state," Fairfax County School Superintendent Linton Deck said yesterday.

In Arlington, where reading scores in the three grades tested remained the same as last year and math scores increased by six percentage points, School Superintendent Larry Cuban called the results "an extraordinary achievement on the part of Arlington teachers and administrators."

While school were required by Virginia to test students in three grades, all area schools voluntarily tested sixth graders. Arlington saw a dramatic improvement in sixth grade results with scores in five subject areas jumping by a total of 40 points over last year's tests.

Scores in Prince William and Loudoun counties, which have in the past lagged behind Arlington and Fairfax, rose by 20 and 15 percent, respectively coming within a few percentage points of the front-runners in the fourth grade scores.

"We're pleased to see the scores come up like they did," said Arthur Welch, Loudoun's assistant superintendant for pupil services. "The lower grades are especially important because that's where they learn to read and acquire other basic skills."

In the tiny Falls Church school system, where most grades have only about 100 students enrolled, test scores jumped among fourth and 11th graders and fell in the eighth grade results.

"In a large system you don't see big fluctuations in classes but we do with our small system," said Nancy Sprague, assistant principal at George Mason High School. "We want our students to be at or above their ability level and educational ability tests indicate our students are right where they should be."