It was before the strike.

Schools Superintenden t Vincent E. Reed stood in his office overlooking Pennsylvania Avenue and the almost 200 public schools he is charged with running. The night before he had been in another battle with the school board trying to get support for having one of his pricipals tenured. "You know," he said, "I travel around the country a good deal and everywhere I go I hear people talking about what to do with school boards. I mean, what purpose do they really serve anymore?"

After the strike the same question was raised by a member of the Washington Teachers' Union, the union that fought the board through a nearly four-week-long strike. "School boards," said a teacher walking out of the auditorium at Mckinley High School after voting to obey a judge's order that sent teachers back to work-"They've got no use anymore. They didn't settle the strike, the judge did. They don't run the schools, Vince Reed does that. The name school board even sounds like something out of the 1800s."

This questioning of their reason-for-being comes at a very bad time for the D.C. School Board. For the one person with power to change the talk from idle renderings to serious debate is Mayor Marion Barry. And Barry appears also to be considering the question of what purpost the school board serves. Even worse for the board, there have been two high-visibility battles between it and the mayor in the first three months of the Barry adminstration, leaving the mayor with no warm feelings for the board he once led as president.

The most recent battle between Barry and the board centered on the strike. During the strike he and the board harangued each other publicly. The board said Barry was working for the union and did not care about improving city schools. They said he was a politician who was endorsed by the union during last year's mayoral campaign and he was paying back a political debt. Barry's aides, in turn, called the board "amateur politiicans" and accused them of being out of touch because they were talking about improving schools when they should have been moving quickly to settle a crisis-the strike-that was affecting the whole city.

"Virtually everyone in this city," said former school board president Conrad Smith, who is still on the board, "understands that the school system has reached the point where we have students who can't read, who can't do math and most people in the city want to improve the schools but they don't know how to go about it. The school board knows that. If Barry doesn't know that.

That did not mean, however, that Barry was unaware of the need to do something about city public schools where ninth graders are doing sixth-grade work. His awareness of the problems in the city schools had led him into a fight with the board in the first month of his adminstration. During his mayoral campaign he had made an issue of the poor quality of the city schools. And after he won the election, the task force he established to look at the problems of education in the city recommended that Barry name a commissioner of education for the District, establis a District Office of Education and convene a 1979 Mayor's Conference on Education.

Those recommendations rankled with the Board of Education and sent them to City Hall to tell the mayor that as an independent city agency they did not want a commissioner of education (who would be working for the mayor) looking over their shoulder.

The board's angry response got Barry to limit his adoption of his task force's recommendation. Instead of naming an education commissioner, Barry named a special assistant for education. And so far that is all that he had done. But aides to Barry say the new mayor plans to do more in the area of education.

At the heart of those changes, the mayor's aides say, would be a referendum -sponsored by the mayor-on the question of whether he should have the authority to take charge of the city's troubled public schools. In effect, it would be a referendum on whether there should be an elected school board at all.