Third-grade students in the D.C. public schools have achieved national norms on standardized reading, mathematics and science tests for the first time since the school system began testing all its students, school officials reported Friday.

School administrators hailed those results as the most encouraging news yet that their back-to-basics curriculum is slowly reversing a long-standing trend of low student achievement, especially in math and reading.

Scores also increased at grades six, nine and 11, but students in those grades still lagged behind norms by anywhere from two months to nearly three years. It was the fifth year in a row that reading and math test scores showed overall improvement in the school system.

The optimism over improved scores in math and reading was dampened somewhat by continued low achievement in social studies and science--two areas that the school system curriculum focuses on less.

The gap between D.C. students scores and the national norm was generally somewhat wider in science and social studies than in reading and math, although third graders exceeded the national norms in science.

"We in the public schools feel we are demonstrating on a daily basis that this is an educational system on the move," Schools Superintendent Floretta D. McKenzie said in releasing the results.

She said the fact that the majority of students continue to score below national norms provides "no cause to celebrate." But, she said, the improvement shown at every grade level is evidence that the system is "headed in the right direction."

School officials attributed the gains to stiffer promotion standards for elementary students, increased emphasis on reading and math at elementary and junior high levels and tougher math, science and social studies requirements for high school students.

The third graders, tested in the ninth month of third grade, scored 3.9 (third grade, ninth month) in science and mathematics, or one month above the 3.8 norm for all subjects, were exactly at the norm in reading and scored 3.6 in social studies.

Sixth graders fell somewhat short of the 6.8 norm, scoring 6.6 in mathematics, 6.2 in reading and science and 6.0 in social studies. Ninth graders scored 8.7 in math, 7.9 in reading, 7.8 in social studies and 7.4 in science. The 9th grade norm is 9.8.

Eleventh graders scored 9.7 in social studies, 9.2 in reading and 9.0 in mathematics and 8.1 in science. The national norm of 11th graders is 11.8.

Since 1976, the D.C. schools have been using a system of teaching known as the competency-based curriculum (CBC), first instituted by former superintendent Vincent E. Reed. The CBC method stresses reading and math and requires students to master skills at one level before moving on to the next.

In 1980, CBC was augmented by the implementation of a new promotions system for elementary students that tested students at midterm in an effort to identify those likely to have difficulty at year's end. Those who failed the midterm exams were given special tutoring.

School board vice president Nathaniel Bush (Ward 7) said that the test scores were "certainly quite a vindication of the decision the Board of Education made when it decided to implement a rigid promotions plan."

Schools that scored at or above national norms were spread throughout the city, crossing economic, ethnic and racial lines, according to preliminary data.

Green Elementary School on Stanton Road SE, for example, which serves a low-income section of the city, scored above the norms, as did Murch Elementary at 36th and Ellicott streets NW, in one of the city's more affluent communities.

McKenzie also praised principals and teachers in the system for their "seriousness of purpose and just plain hard work to insure students achieve to the best of their abilities."

Deal Junior High School at Fort Drive and Nebraska Avenue NW, one of the most racially and ethnically mixed junior highs, had the highest scores of any junior high. Its ninth graders scored 11.0 in reading and 11.7 in mathematics.

On the high school level, School Without Walls, a small, alternative school for outstanding students, and the Banneker Academic High School for college-bound students achieved the highest scores.

The 11th graders at School Without Walls scored 13.4 in reading and 12.2 in mathematics. At Banneker, the ninth grade, the only grade tested, scored 11.2 in reading and 13.0 in math. There were no 11th graders at Banneker, which just opened this school year.

Students at both schools scored higher than those at Wilson High School at Nebraska Avenue and Chesapeake Street NW, where the ninth graders scored 10.4 in reading, 10.6 in math, and the 11th graders scored 10.9 in reading and 11.9 in math.

The tests, called the Comprehensive Tests of Basic Skills, were given in May to all students in the appropriate grades. The system began testing all students in those grades in 1978. Before that, a 10 percent sampling had been tested in each grade, beginning about a decade ago, school officials said.