Reading and mathematics performance by students in Washington's public schools remained steady last year at averages far below the national norms but achievement at particular schools varieted widely.

The results of standardized tests, released yesterday, showed the scores for individual schools for the first time since 1972. In general, the scores followed the income and educational level of neighborhoods, wit most schools in low-income areas doing poorly despite extra federal aid, and those in well-off areas - both white and black - doing well.

But officials said that many schools that were near each other and whose pupils were similar had significantly different levels of achievement, indicating that school programs can have a strong impact regardless of children's background.

For example, at Lovejoy Elementary School, 12th and D streets NE, whose enrollment was mostly low-income, third grade achievement was above national norms in both reading and mathematics. Most nearby schools with similar children did poorly, however, and throughout the District of Columbia only 31 of the city's 130 elementary schools scored at the national norms or above them in either reading or math.

Only one junior high school out of 32 - Deal in upper Northwest Washington - reached the national norms. Two others came close: Backus, at South Dakota Avenue and Hamilton Street NE; and Francis, at 24th and N streets NW.

The results released yesterday are based on tests given last spring to all third, sixth, and ninth graders throughout the city. The exams, called the Comprehensive Tests of Basic Skills, were written and scored by the California Testing Bureau, a division of McGraw Hill publishers.

For the past six years, the same tests were given to a 10 percent sample of students in all grades to show system-wide performance. But because of the small sample tested, comparisons between individual schools could not be made.

The citywide averages were about the same as the 10 percent sample tested in 1977, except for a slight improvement in third-grade math and a decline in ninth-grade scores have been exceptionally low in Washington for many years. On the other hand, third-grade achievement has shown a generally upward trend.

In a press release accompanying the new scores, Superintendent Vincent Reed warned against using the results "as the sole measure for evaluating schools because of the many variable factors that tend to influence (them, such as) class size, socioeconomic level, and student and teacher attendance."

But Reed said the scores would be a useful "benchmark" to measure future progress.

"Naturally, we are not happy with many of the scores," Reed said. "It is evident we must continue to work hard and we accept the challenge this report presents to us."

Overall, the new report shows District third-graders averaging four months below the national norms in mathematics and eight months below in reading.

By sixth grade, students were a year behind the norms for math and 1.7 years behind in reading.

Ninth graders, the report said, averaged about three years behind the norms in both subjects, indicating that high school freshmen here perform as well on average as sixth graders throughout the country.

Yesterday Assistant Superintendent James T. Guines said, "We've always known we've had a problem in the ninth grade and we'll just have to do better."