MAYOR BARRY does have a point: the D.C. school budget is a mystery that does not tell him or the public enough about how the hundreds of millions of dollars given to the schools are spent. From the mayor's point of view, it would be crazy to give the school system more money when it is unclear what the school board is doing with the money it already has. Even parents' groups fighting to get more do not know how the school system spends its money.

But the parents do know what happened this year when the school board's budget request was cut $3 million from last year's budget and $35 million from the amount the board requested for this year. What happened is that there were 700 fewer teachers. In some classrooms, there were no teachers for about two weeks at the beginning of the school year; the classes that did have teachers were larger, the official student-teacher ratio going up from about 26 to 1 to 28 to ; and many good young teachers had to be fired because older teachers and administrators used their civil service rights to claim jobs held by less senior personnel.

The result, then, was confusiion in the schools that has yet really to be settled. The progress being made by Superintendent Vincent Reed in both curriculum and student test scores is in danger as a result. Worse may be yet to come: Mr. Reed is proposing that all school system personnel be furloughed for a 10-day period sometime in the spring to save more money.

Last year's budge cut created a shock wave for parents and students who had just begun to have faith again in the city's public schools after years of decline. Mayor Barry is aware of this, but he argues that the school board made spending cuts that hurt children when it could have made cuts in its bureaucracy. The school system's administration has been found by independent analysts to be overpopulated; one study released in April found the District schools to have 80 percent more employees than the Prince George's County school system, which has 22,000 more students than the District's.

The school board and Superintendent Reed say they did eliminate some administrative positions as a result of last year's budget cut. In a letter on this page today, the superintendent says that 10 percent of all administrative positions were eliminated while there was an approximately equal reduction (about 12 percent) in the city's teaching staff. Still, it should be noted that, although the cuts were of nearly equal size, they had vastly different impact. The 10 percent reduction in administration was, at most, a small setback to an overstaffed bureaucracy.But that same 10 percent cut crippled a modest corps of teachers that some people felt was too small to begin with. The brunt of last year's budget cuts was felt in the classroom, not downtown in school board headquarters.

If more budget cuts are approved for next year, the school board is saying, school will not open until Oct. 1, there will be no pre-kindergarten classes and the student-teacher ratio may leap to 35 to 1. The result of such threats has been the formation of groups of parents to fight any proposed budget cuts. And Mayor Barry has been put in a corner, facing angry parents and the school board, and labeled an enemy of public education.

But the mayor is no child-hater. The school board is no collection of saints (to put it mildly). Instead of offering warnings of disaster for the public schools of its budget is cut at all, the board should be figuring out how to slash its administrative costs and all marginal programs.Only then can it plausibly contend that the schools need more money.