The long, bitter struggle between Mayor Marion Barry and the D.C. Board of Education over public school funding has erupted again in skirmishes on several fronts, giving the schools a small budget increase but strengthening the mayor's political position against his foes on the school board.

At a congressional hearing on the city's 1982 budget yesterday, Barry renewed his charge that the board has "failed to face reality" in its demands for more money and failed to provide enough information to justify its budget request.

"All of us personally support public education," the mayor said. "We want young people to be able to read, to write, to articulate, to survive. But I think the numbers are exaggerated."

That was a reference to the board's insistence that the planned 1982 spending level of about $250 million is $22 million short of what is needed to keep class sizes and school programs at their current level.

Sen. Alfonse D'Amato (R-N.Y.), chairman of the Senate D.C. Appropriations subcommittee, showed no inclination to override the mayor's budget request -- despite pleas yesterday and at earlier hearings from school officials and parents' groups who want more funds spent on the schools.

D'Amato said his first priority was a balanced city budget, and he urged the parents who also testified yesterday to "work with the City Council and my staff to help the schools develop a policy of fiscal restraint in such a way that it would not be counterproductive."

Noting that the mayor and the school board still disagree over how much money the schools need and how education funds are actually spent. D'Amato strongly suggested that the General Accounting Office, which he considered a neutral party, be asked to prepare an analysis.

But Barry told the senator that he already has appointed his own task force to examine the school system's spending and resolve the dispute.

That task force consists mostly of former public school officials who now work for the mayor, and its existence has only augmented the school board's unhappiness over Barry's approach to the budget issue.

The members, besides budget director Gladys W. mAck and city paymaster Raymond Saulino, are former deputy superintendent Edward Winner, former school finance director James R. Boyle, and former school board executive secretaries Patricia Miner and Dwight S. Cropp -- all of whom now hold high positions in the Barry administration. Barry served as school board president from 1971-1974.

R. Calvin Lockridge,head of the school board's finance committee, noted sarcastically that during the years for which Barry has questioned the school system's spending figures, "If Mr. Winner wasn't in charge, then Mr. Boyle was. Maybe they can come up with better figures now that they are working for the mayor."

The tax force is expected to report its findings early next week. Budget director Mack said the mayor's appointment of the task force "was a defensive move. The executive branch has been widely criticized on its actions and recommendations, and much of that was based on incorrect information."

Barry, who has not ducked the political implications of this fight, is scheduled to address a parent-teacher breakfast tomorrow at Gordon Junior High School. He is expected to take credit for a trade Wednesday that put an additional $2.4 million into the 1982 school budget by authorizing the city's Department of Human Services to rent vacant school space instead of commercial offices.

Earlier this week, Rep. Stewart McKinney (R-Conn.), ranking minority member of the House District Committee, introduced a bill to give the mayor item-by-item control over school spending. Barry declined to comment on the measure, but he observed that "I don't like to have responsibility without authority."