Average reading and mathematics test scores in Washington's public schools improved to 1980 for the second year in a row, following a decade of declining or stagnant achievement.

The year-to-year gains were slight, and most students entering District high schools remained far below the national norms on the standardized tests. But Supt. Vincent E. Reed said he was encouraged by the change in direction.

I'm not really satisfied," Reed said. "But I'm glad were moving now in the right direction. We still have a way to go to get to the national norms, but we're moving."

Reed said the gains were a "payoff" from the systems's new competency-based curriculum, a step-by-step program to teach specific skills, which Reed promoted. He also praised the hard work of students, teachers and administrators.

According to the new report, third graders in the school system were just one month behind the national norm in mathematics and five months behind in reading.

In the spring of 1978, before the upswing began, D.C. third graders were four months behind the norm in math and eight months behind in reading.

The sixth grade showed similar improvements, gaining an average of five months in both subjects in 1979 and another two months in 1980. The D.C. average for sixth-grade mathematics this spring was three months behind the national norm and one year behind the norm for reading.

For ninth graders, there was a three-month improvement this year in reading scores, but no change in math, following slight gains in both subjects in 1979. The scores remained very low, with District students near the end of ninth grade placing at the same level in math as students starting seventh grade across the nation. In reading, the ninth graders were a little better, placing at the same level as students nationwide who were three months into their seventh-grade year.

Looking at the ninth-grade figures another way, the District ninth grade is still 3 years behind the national average in math and nearly 2 1/2 years behind in reading.

The national grade-level norms are based on the scores of a representative national sample of about 130,000 students tested in 1973, and have not been revised since then. Thus, the scores do not reflect changes around the country since 1973, although they do provide a consistent measure of achievement in Washington. The scores are based on a 10-month school year.

The results released yesterday are from tests given in early May to all D.C. students in the third, sixth and ninth grades. The multiple-choice exam, called the Comprehensive Test of Basic Skills, was published by the California Testing Bureau, a division of McGraw-Hill Inc. It took about three hours to complete the tests.

In an interview, Judy Shoemaker, director of the test study group at the National Institute of Education, noted that the gains reported by Washington schools are still relatively small and should be interpreted cautiously. But she added: "Things look like they are getting better. It looks like they are beginning to catch up every year . . . The deficit in some areas is still pretty alarming. The math [score] in ninth grade is horrible. But at least the gap is decreasing, and that's a reason for the D.C. schools to feel good."

Several other big-city school systems throughout the country, including those in Newark, New Orleans and Detroit, also have shown gains in reading and math in the past two years, after slipping badly since the mid-1960s.

Jeanne S. Chall, a professor of education at Harvard, said that nationwide the improvement has been greatest in the early elementary grades, as it was in the District.

"There's been a real concentrated effort," she said, "and it's beginning to pay off. There's 'Sesame Street' on television. The children are being taught earlier [with Head Start and other prekindergarten classes.] And the schools are doing much heavier teaching of phonies in early grades."

Chall said it is more difficult to raise the scores in junior and senior high schools because their programs no longer concentrate on concrete skills and facts, and questions on standardized tests require more analytical ability.

"There may be some tendency [in the District] toward rote teaching [memorizing]," said D.C. Associate Superintendent James T. Guines, "and not enough concentration in mathematics to applying concepts to different situations. We'll have to work on that some more."

But Guines said the competency-based curriculum, which provides detailed lessons for reading, grammar, math and science from kindergarten through 12th grade, probably helped improve achievement by giving teachers a clear idea of what they are supposed to do. In each subject, children are supposed to move ahead to a new skill only after passing a test showing they have mastered the earlier skills.

After three years of development, Guines said, the curriculum was used for the first time in all the D.C. schools last year.

"Everybody out there knew what to do," he said, "as opposed to everybody out there shooting from the hip. It's a big difference, I think, and it's paying off."

Reed, who became superintendent in late 1975, said the higher test scores may also reflect his efforts to make students more serious about their studies by giving trophies and prizes for good attendance and high grades as well as for athletics.

At Reed's urging, the D.C. school board also has adopted a checklist of "critical skills" that all students will have to master before they can be promoted to the next semester's work. The plan will go into effect next fall in the first through third grades.

Even though the school system is facing major budget cuts -- including teacher layoffs -- for next year, Reed said he believed the competency-based curriculum could still be followed.

"The classes will be bigger, and we'll all have to work harder," Reed said, "but we'll try to do it."

Reed said a detailed report, showing test scores for each elementary and junior high school in the city, will be issued in about two weeks.

"It's very important to see how the individual schools are doing," Reed said. "Publishing the school-by-school results improves motivation. We've tried to create a competitive kind of atmosphere."