COME WEDNESDAY morning there will be a new school board.The political bluster about a mayor's slate of candidates, attacks on incumbents for past sins and talk about candidates who want to use the board to start campaigning for city council will all be stale tidbits of yesterday's news. The future -- for students, parents, teachers and school administrators -- will lie with a school board that will remain in office for at least two years. Tuesday's election could add six new members -- a majority of the 11-member board. And the board's conduct is crucial to any hope of improving public schools. The key will be a school board that strengthens Superintendent Vincent Reed's authority and capacity to do the job he has set out to do.

Accordingly, the first responsibility for the fate of the schools rests with District voters. In the past the turnout for school board elections has been low. The winners were the candidates who had enough cars to drive people to the polls. This time there needs to be more participation. The election is a chance to act on the simmering frustion people feel about some board members and to support those who have done better by the schools. The choices may not be spectacular, but they are real and can make a difference.

What needs to be done to provide the city's public school children with a good education? Five obligations come to mind: 1) end social promotions, by which students are passed from grade to grade without having done passing schoolwork; 2) make sure that public school teachers are competent and recruit the best available; 3) give students and teachers a school setting in which to work that includes reasonable class sizes and protection from intruders, and get class-cutters out of the halls; 4) fight for a budget-large enough to give students and teachers adequate textbooks and supplies; and 5) give Supertendent Reed and his principals undivided support for the Competency Based Curriculum, a step-by-step teaching method that Mr. Reed says will raise test scores and guarantee that there will no longer be seniors in high school who can't read.

Throughout its tenure, the new school board will also have to deal with the increasingly unfriendly relations between the teachers' union and the school system. This will mean tough, sometimes unpopular stands that make demands on teachers. But even more than toughness, relations with the teachers' union will call for cool, creative thought and action -- in a word, diplomacy -- by a school board famous in the past for its hotheadedness and divisiveness.

Voters could keep an eye out for candidates who show willingness to work with others. Eugene Kinlow, seeking re-election at large, has demonstrated this quality. It is a characteristic that will serve all new school board members well in dealing with the growing -- and not always reasonable -- pressure from city politicians to make immediate and vast improvements in the schools. It would be good if the new board members were capable of converting that pressure into public concern and more money for the school budget without feeling threatened by other politicians' interest in the schools. That new attitude might also be a step toward ending the school board's image as an object of laughter, especially for some District Building politicians. You might not think so to judge from much of its behavior in the past, but the school board is a serious and important body, and no public task is more serious and important than trying to make it work.