AFTER 13 ballots, 5 days, 3 candidates and an endless supply of personal hang-ups, Washington's 11 school board members have come up with a president for the year. He is R. Calvin Lockridge, who has the distinction of being the only current board member who voted against renewing Superintendent Vincent E. Reed's contract in 1978 and who was part of the board majority that forced a showdown with the teachers' union that led to a 3 1/2-week strike last year. While neither of these actions can be linked to the advancement of public education in this city, Mr. Lockridge now says he'll work for harmony all around -- and in this he deserves public encouragement and board support.

For that matter, the whole board deserves a break -- one long enough to let Superintendent Reed go about the business of improving things in the classroom. That, after all, is where parents, teachers and administrators would prefer to see the spotlight -- rather than on the antics and infighting of a bunch of self-indulgent politicians jockeying for status.

But reconciling old differences and backing off enough to let the superintendent, administrators and teachers get down to business come as a challenge yet unmet by the holdover members of the board. If these members continue their preoccupation with "preserving the school board's autonomy" (and each member's as well), sentiment could grow for doing away with the elected board entirely.

The effort to improve District of Columbia public schools should focus on better recruiting, testing and evaluations of teachers; assigning principals who can establish and maintain the order and spirit that a school must have to be a good one; keeping classrooms reasonable in size and secure; insisting on the finances necessary to provide textbooks and supplies; and creating new academic opportunities to attract those students and parents who have been abandoning the public schools. This is a tall order, and Vincent Reed still needs all the help he can find to fill it.