For the first time since standardized testing began in Alexandria, black pupils in every elementary school scored above the national norm for all pupils last year, an achievement school officials said indicates that their extensive program to close the academic gap between middle-class white children and disadvantaged black children is working.

Test results released yesterday show that black pupils in Alexandria public schools still score an average of 33 percentile points lower than their white classmates but that, in the 1985-86 school year, blacks in grades one through eight made larger gains on the tests than whites, an increase of 3.1 percentage points versus 2.4 points.

In 1985, Alexandria recorded the widest gap -- as much as 48 points -- in the Washington area between black and white pupils in its standardized Science Research Associates tests measuring mathematics, reading and language arts skills. After calling attention to the problem, Superintendent Robert W. Peebles launched a major drive to improve pupils' performance.

The program, which has 21 components or strategies, includes computer-aided reading programs, peer counseling and tutoring, a special class to help disadvantaged kindergarteners catch up, and courses to help teachers better understand the needs of black pupils.

"What we are demonstrating is that schools make a difference, that we can't really accept low socio-economic backgrounds as being the factor that makes it impossible to make progress," Peebles said yesterday. "For too many years we have used that as an excuse . . . . We're dealing with a population that is getting more from school than they used to, and they should."

Along with the attention on blacks, the school system adopted a more rigorous, seldom-used method of tracking pupils' test scores. Alexandria is tracking the same set of pupils and comparing their scores from year to year as they advance in grade level.

Arlington schools also released their standardized test scores for kindergarten and grades two, four, six, eight and eleven. The scores of kindergartners and second and sixth graders improved in every category. The other grades either dropped slightly or stayed the same.

"Just maintaining last year's levels would have been an accomplishment," Arlington Superintendent Arthur W. Gosling said in a release.

The composite scores range from 70 among 11th graders to 92 for second graders. A racial breakdown of the Arlington scores will be available in the summer, school officials said.

Because the SRA scores are calculated in comparison with the scores of pupils nationwide, the gains for black pupils in Alexandria indicate that the pupils' ability to learn has increased under the local program, school officials said. Because all pupils are taught the same new subjects and skills each year, pupils' scores usually stay about the same.

The elementary scores ranged from 62 points for black third graders to 50 for black fourth graders.

The test scores of black secondary students also improved last year, but unlike in the elementary grades, they remained below the national norm, at 47 percentile points for seventh graders, 41 for eighth graders and 38 for 11th graders.

School officials said that it may be more difficult to affect older students because the curriculum is more difficult and the basic skills required are more numerous.

Some educators question the value of test results as an instrument to judge educational achievement, and some say that breaking down test scores into specific racial and age groups further exposes the achievement discrepancies.

"There is considerable worry about minimum competency exams aimed at {testing} fragmented knowledge," said Rexford Brown, spokesman for the Education Commission of the States, a policy think tank in Denver. "Are you teaching them thoughtful behavior, critical thinking, synthesis, all the hallmarks of a really educated person?"

The debate over black pupil achievement and its relationship to factors such as economic and social status has been a long one. Many educators still say that the schools are only a minor player in a child's ability to learn.

In areas such as Alexandria, where 47 percent of the public school pupils are black and the vast majority of those are poor, overcoming that doubt has been important to pupils and the community. Peebles said yesterday that he believed that societal, parental and pupil attitudes about making academic progress constitute the most important factor in accomplishing improvements.

James P. Akin, the school system's executive assistant for research, planning and evaluation, said persuading educators that progress can be made is a continuing struggle in Alexandria and elsewhere.

"Whenever I tell people this can be done, they say, 'You don't really believe this, do you?' There are doubters in the system and in the classroom. Not all of them are racist; some of them are blacks who doubt you can teach black children" from disadvantaged backgrounds, said Akin.

Systemwide, pupils in the nine Alexandria grades tested scored 10 or more percentile points above the national norm, which is 50. Third graders scored the highest, at 77. Grades four and eight made the greatest gains over last year. Eighth graders scored 7 points above last year at 60, and fourth graders were up 5 points to 69.

Test scores improved the most dramatically at the Cora Kelly Magnet School. Third graders there jumped 18 points from the previous year, and second graders scored 16 percentile points higher than they did when they were in first grade.