Alexandria schools have begun to narrow the gap between the scores of black and white students on standardized math and reading tests, school officials said yesterday.

Results of Science Research Associates tests show the average difference between blacks' and whites' composite scores for reading, math and language arts this year is 33.3 percentile points, down from 37 points last year.

"Last year, when we decided to break out the test scores [by racial group], it was a very tough thing to do," said Superintendent Robert Peebles. "It revealed the gap between the blacks' and whites' scores in particular. That gap has narrowed."

Overall, student scores in Alexandria rose or remained steady in eight of the nine grades tested, and the scores of black students showed gains of as much as 13 percentile points. The scores of Hispanic students also showed some significant gains, rising 15 percentile points on the third grade reading test and 14 points on the sixth grade language arts test.

The results show that "despite the advantages that come from middle-class backgrounds, minority children can achieve better than they have in the past . . . the schools can make a difference," Peebles said yesterday.

After releasing test results by race last year, Alexandria educators made improving minority achievement a top priority.

This year, the average scores of black students rose above the national norm of 50 for the first time in four of the nine grades tested. The disparity between the scores of blacks and whites ranged from 21 points on the third grade language arts test to 48 points on the 11th grade reading test.

"I can see just on the surface that there have been some gains made," said Charlotte Northern, chairman of the schools' Task Force on Minority Achievement. "But we cannot consider it a signal to abandon our efforts toward improving minority achievement in Alexandria . . . . I think we have a long way to go."

The School Board agreed in January to launch several new programs in the 1986-87 school year aimed at closing the gap between blacks' and whites' scores, including one that uses computer software to teach reading to kindergartners and another that will emphasize study skills to help sixth graders prepare for junior high school.

Virginia requires schools to administer skills and ability tests to fourth, eighth and 11th graders. Alexandria also tests students in first, second, third, fifth, sixth and seventh grades.

Overall, the scores of third and 11th graders showed the most improvement, while those of eighth graders generally fell. Peebles said the difficulties some students experience in adjusting to junior high school may account for that decrease.

As in other Northern Virginia school districts, Alexandria students generally scored better on the math tests than on reading and language arts. James P. Akin, executive assistant for research, planning and evaluation, said one explanation may be that "math is an area that is not as sensitive to socioeconomic differences. Math seems to be a skill that is almost totally acquired in school" rather than at home.