WITH THE ELECTION yesterday of a new school board president to join a top-flight superintendent, a serious majority of board members and a cooperative mayor, Washington's public schools--and the children in them--may at last get the time, attention and understanding they deserve. While no miracles will suddenly send reading and math scores skyrocketing or costs of education plummeting, there is good reason to be believe that the community has spoken for, and is serious about, accentuating the positive and eliminating the negative from the classroom to the board room.

No, the election of the Rev. David H. Eaton as president was not all sweetness and light yesterday; some of the old, too familiar holdovers on the board still prefer factional carping and warfare with city hall to low-profile, high-result public service. One complaint from this noisy corner, in fact, was that Mr. Eaton and other newer members of the board get along too well with Mayor Marion Barry to fight city hall on behalf of the schools. This assumes, of course, that fighting is a prerequisite to service on the board--and unfortunately until now it has been.

But you do get a feeling from students, teachers, administrators, voters in the last school board election and Superintendent Floretta D. McKenzie that people who care about the public schools are fed up with petty factionalism and showboating on the board. And if Mayor Barry's close ties with Mr. Eaton, Mrs. McKenzie and a new majority of board members are too "political" for the unsilent minority on the new board, long live politics--at least as long as it delivers for the schools.

If Mayor Barry, Superintendent McKenzie and other school officials can meet and agree on a reasonable, realistic budget for the schools for the coming fiscal year--as they just have--that, too, is politics at work constructively. Sure, it's a campaign year; but isn't that attention one of the best reasons for holding elected officials responsible?

Just as there is room for serious debate about exactly how many dollars it takes to make an "adequate" school budget, there are grounds for some understandable concern about how best to make money available for schools. Mayor Barry's increase in the amount agreed to for the schools includes what was to have been an installment in a series of annual payments to eliminate the city's accumulated debt. Symbolically as well as fiscally, the debt retirement is as important as Mayor Barry had been saying it was before he decided to postpone this payment.

Still, there is symbolic and genuine importance as well in Mayor Barry's interest in the school system. Though the last of the school board's hell-raising minority is complaining about "power grabs," control of the school board by the mayor and/or "his pastor" (which Mr. Eaton happens to be), many more people are much more concerned about the ability of this city to educate its young.

With a serious board and a talented and imaginative superintendent, these important supporters can concentrate on strengthening the curriculum; on moving students into jobs they are prepared for; on evaluating teachers and encouraging the very best from all of them; on strengthening the hands of competent principals and getting rid of the hand- wringers who cannot set a tone in their buildings for learning, discipline and school spirit.

Only then--and now is already late--will confidence in the District's schools, fed by results that count, return as it must if publicly supported, quality education for all children is to exist in the capital city.