FOR THE LAST several years, standardized test scores in the District's public elementary schools have reached and exceeded national norms. That has come to be expected. A strong school superintendent, a more effective school board, better teaching and a back-to-basics curriculum have been the reasons for the success. But the greater challenge has been in the city's junior and senior high schools, where students continued to test well below their counterparts nationally.

On this point, D.C. parents have been considerably less confident. They have been more inclined to leave their children in the relatively effective elementaries, but have looked elsewhere -- to the suburbs and to private and parochial schools -- as the children got older. The school system installed its competency-based curriculum in 1978 and began its Student Progress Plan, a prescribed set of skills to be mastered every semester, for grades one through three, in the fall of 1981. Grades four through six were added the next year. The plan moved into the secondary schools, for seventh graders, in the 1984-85 school year. Eighth graders were added last fall, and the plan will include ninth and 10th graders for the first time next fall. What has been happening to test scores at the secondary level as a result?

The progress has been less dramatic than earlier successes, but there is improvement nonetheless. D.C. ninth graders, who surpassed the 50th-percentile national norm on the math section of the test for the first time last year with a 51, matched that again this year. For the first time, they also equaled the national norm in language skills and surpassed it in the category measuring their abilities to use a library. Eighth graders pulled closer to the national norms, outscoring the previous year's eighth graders in all parts of the test.

Nowhere was the progress more dramatic than at Cardozo High School, where test scores have been consistently poor. This year, Cardozo's 11th graders scored grade-level equivalents that were as much as two years higher than last year's class. Cardozo seemed to do much that could be duplicated in other schools. There were tutorial sessions on test skills for the lowest-scoring students, and teachers gave students sample test questions every day.

Although more progress is needed, these citywide scores show that the schools are heading in the right direction. The kinds of efforts made at Cardozo need to be pressed throughout the city's high schools.