District public school students increased their scores dramatically on comprehensive standardized tests this spring, indicating a continuing improvement in the six skills that were tested, school officials said yesterday.

Sixth grade students surpassed national norms in five of six skill areas for the first time since the schools began systemwide testing five years ago, officials said yesterday.

Third grade students, who surpassed national norms in math, science, language and reference skills for the first time last year, continued to improve this year, exceeding national norms in those areas and also in reading and social studies.

In the past, test scores in the District have fallen far below national standards. Ninth and 11th grade students still fell short of the national norms this year but showed substantial improvement over last year in each of the six skills tested: reading, math, language, reference skills, science and social studies. Eleventh graders showed the most dramatic improvement, although their scores were still below the national norms.

Only students in grades 3, 6, 9 and 11 were tested.

"These test data indicate the continued academic progress of all of our students," D.C. School Superintendent Floretta D. McKenzie said at a press conference announcing the scores yesterday. "The results are very gratifying." School board president David Eaton added: "I'm tremendously pleased with this report."

Saying that the improved scores were "a direct reflection of the determination and concerted efforts of our students and teachers," McKenzie said that there were also other reasons for the results.

Among them, she cited the current school year budget that reduced class sizes, expanded numbers of volunteer tutors and classroom teacher aides, and standardized test-taking instruction that teachers have given to students.

Since 1981, the school system has circulated books on test-taking skills to the city's schools. Those handbooks cover a variety of areas including sample questions, how to eliminate obviously wrong answers in multiple choice questions, and how best to prepare for them.

"It does make a difference," said James Guines, associate superintendent for instruction. "We have also allowed students to practice on other kinds of standardized tests. Coaching and practicing does improve test scores."

National norms for the Comprehensive Test of Basic Skills used by the District schools are based on grade level equivalents. For third graders it is 3.8 (eighth month of the third grade year). For sixth graders it is 6.8, for ninth graders, 9.8, and for 11th graders, 11.8.

D.C.'s third graders, who matched the national norm for the first time two years ago, surpassed national norms in all six skill categories this year, scoring a 3.9 in reading or one month above the national norm, 4.0 in social studies, 4.1 in language, 4.3 in math and 4.6 in science and reference skills.

Sixth graders, who last year exceeded national norms only in reference skills, this year scored above the national norm in every skill area except social studies, with grade level equivalents of 6.9 in reading, 7.3 in math and science, and as high as 8.6 in reference skills. They scored 6.2 in social studies.

Ninth and 11th graders, while falling below national norms in all categories, showed improvement over last year in each skill area. Ninth grade reading scores went up from 7.9 in 1982 to 8.4 this year, while science scores improved from 7.4 to 8.0. Eleventh graders showed the greatest improvement over last year of any grade. For example, in reading, 11th grade scores went from 9.2 to 10.1, from 9.0 to 9.9 in math, and from 8.1 to 9.3 in science.

Comparing the D.C. results and its level of improvement with other jurisdictions is difficult because of the wide array of standardized tests used by other localities. But Mike Casserly, a legislative and research associate with the Council of Great City Schools, a research and lobbying group for a coalition of 32 of the nation's largest urban school systems, said the scores show that D.C. students "are joining the ranks of other major urban school districts who have begun to match and surpass national norms in the last four years."

School board vice president Nathaniel Bush (Ward 7) said the challenge now would be to bring the city's secondary schools to the national norm level, while other board members present heaped praise on McKenzie's work as superintendent and the community at large for volunteering to help the students.

"You have turned a spear of frustration into a shaft of hope," said Eaton of McKenzie.