With a bullish Mayor Marion Barry leading the way, the District government began poking holes last night in the school system's $482 million budget request for next year.

At a public hearing in the D.C. Council chambers, Barry, who showed up 80 minutes into the session, presented a bright portrait of the school system, one that contrasted sharply with that presented by many parents and others in the audience.

"I heard someone say our schools are falling down," said the mayor, who is to present his budget to the council Feb. 8. "I don't agree with that."

He cited renovations at various city schools and concluded that the D.C. schools "are far ahead of some other school systems." He noted that Detroit, for example, has so much school violence that metal detectors have been placed at entrances to some schools.

Members of the mayor's budget staff peppered school administrators with questions, wondering why the city should support the requested 12 percent spending increase when the schools have not spent all the money they were allotted last year for hiring new teachers.

The director of the mayor's education office, Roland Sidwell, challenged the need for additional teachers when the school system's own statistics show that, compared with the 50 states, D.C. has the third lowest pupil-teacher ratio in the nation. And Finance Director Richard Siegel wanted to know why his son, a student at Deal Junior High, has a textbook from 1961 even after the city has given the schools $7 million to buy new books.

Associate Superintendent Patsy Blackshear fielded the questions, allowing that the book problem will take several years to solve and arguing that the system has used substitutes and retired teachers to fill teaching positions that have remained vacant.

The hearing was the first to be held as a result of the overwhelming victory last fall of the D.C. school initiative. An outgrowth of bitter budget battles in recent years, the initiative, which won 77 percent of the vote in November, was designed to prove to politicians that residents consider education "to be of the highest priority."

The initiative requires the mayor to hold public hearings on school financing, joining the D.C. Council and the school board, which already hold such sessions.

Barry, who stayed to hear only five of more than 70 speakers, did hear members of Parents United, the activist group, call for improvements in teacher salaries, class size and building conditions.