EVER SINCE VINCENT E. REED took office as superintendent of the District of Columbia public schools, we have been applauding improvements in the management of the system and efforts to make good things happen in the classrooms. And today we continue to believe that the District's school system is getting better, though progress is slow and uneven -- depending heavily on the tone set in each school by its principal. Across the city there are schools that parents and teachers are proud of, just as there are schools where breakdowns of discipline and weak administrators are wreaking havoc. Still, as you may have read in a report last week by staff writer Juan Williams, many middle-class black parents have been shifting their children from public to private schools.

We can't tell how much of this movement is due to greater efforts by private schools to attract black students, and how much to deep disappointment with the public schools or simply to social pressures on parents. But clearly Superintendent Reed, along with the school board, the new city administration, teachers and others who care about the state of public education in this city should be looking for additional ways to attract and challenge good students.

One way was proposed nearly three years ago -- by Mr. Reed. He endorsed the creation of an academically rigorous four-year high school, with higher requirements for graducation. But the plan drew criticism from a number of directions. Some parents feared that the new school would drain the best teachers, students and programs from their neighborhood high schools; others were concerned that the school would serve only an elite group of students. What Mr. Reed tried to get across then was that a successful academic program need not be unique or exclusive -- but that a general improvement in systemwide standards had to begin somewhere.

So true. But just one such school is not necessarily the answer. There should be rigorous academic programs for bright students in every school, especially in the high schools, so that these students will have strong reason to stay in the public schools and prepare for college. Isn't this preferable to a middle-class exodus to private schools that would leave the bright students from poor families trapped in a mediocre system?

Existing specialized facilities, such as schools for the arts, math and science, marine science and vocational skills, need to be brought to the attention of more parents and students, too. And as the people of the Anacostia school community chose to do on their own last year, there should be tougher standards for promotions and graduations -- tests of "everyday skills" before students are promoted.

Right now, though, any proposals to improve the schools face a more immediate threat -- namely, a deadline next Tuesday, when a 90-day teachers' contract extension expires. Both the school board and the union are saying that a settlement by then is unlikely. If that is so, another temporary extension would be far preferable to a strike in the middle of the school year, just when a new administration under Mayor Barry has pledged to work with all parties to improve teacher performance and classroom conditions.