About 2,500 striking Washington teachers -- taking advantage of warm, sunny weather, a stalemate in negotiations and lingering, unresolved court proceedings -- staged a pep rally in front of the city school headquarters yesterday, as their strike entered its fourth day and public education continued to hobble along.

"We're in a struggle and our numbers here today will show them that we're willing to keep on struggling," union leader Harold Fisher told teachers who rallied at school headquarters at 12th Street and Pennsylvania Avenue NW.

In the city's 200 public schools, attendance continued to drop even though school administrators maintained makeshift classes. Despite the growing reluctance of many parents to send their children to school, school officials expressed optimism because more teachers apparently were coming to work.

"We're losing kids by the day. We had 45 percent of our kids in school today," said school system spokes-woman Gloria T. Adams. "But we're definitely up with teachers. We have 45 percent. That's encouraging."

The continuing impasse at the bargaining table and in the courtroom indirectly offered Mayor Marion Barry more encouragement to become involved in mediating the controversy, as the mayor's aides say he is anxious to do.

Barry and his aides have persistently tried to forge a role for him in the controversy.But school board leaders, jealously guarding their political independence and wary of Barry's ties to the teachers union -- which endorsed his campaign for mayor -- flatly dismissed involvement by the mayor.

"The mayor's intervention would be to the detriment of the board, the children, and improving the quality of education in Washington, D.C.," said board President Minnie S. Woodson. "It [to have Barry intervene] is without a doubt a strategy of the union.

"They may not want to negotiate with the school board, but they are going to have to," Woodson said. "Just because they can strike, doesn't mean they are going to get their way."

Much of the hope for decisive action in the conflict yesterday was focused on D.C. Superior Court. There, Judge Gladys Kessler listened to testimony on how the walkout has affected city pupils. The school board has asked Judge Kessler to cite striking teachers for contempt of court for violating an order issued Monday evening forbidding the walkout. But testimony by board witnesses could not be completed before the end of the court day, and Kessler recessed the proceedings until 9 a.m. today.

"I'm hopeful," the judge said, "that both parties can use the evening for constructive and useful acts related to this dispute."

At some city schools, there were fewer pickets in line yesterday, apparently because many teachers chose to attend the rally at the downtown school board headquarters and another rally that followed at Greater New Hope Baptist Church at Eighth and I streets NW.

Some pickets, saying they had been warned by union leaders not to talk to reporters, remained tight-lipped, or agreed to talk only if their names were not used. They maintained that they could absorb the financial hardships of a continuing strike -- something that school board officials hope they will not be able to do.

"Most teachers can afford 40 to 60 days at most," said a man picketing at Wilson High School at Nebraska Avenue and Chesapeake Street NW. "They can miss two payments of monthly bills... But the school system can't stand 60 days without teachers."

School officials reported no incidents of violence and said the "educational program ran well" with the improvised classroom, curriculum and teaching plans.

Still, some parents said they refused to send their children to school, either for fear of the children's safety of because they saw no value in what was taking place in the makeshift classes.

Cleo Williams kept her 6-year-old daughter, Tangela, out of classes at Wilkinson Elementary School, at Pomeroy and Erie streets SE, because, she said, she did not want her first-grade daughter attending classes with kindergarteners.

"The teacher was always spanking people and I didn't want her to be spanking me," Tangela said. "They spent the day counting to 100 and saying the ABCs. I wanted to do something else."

Bernice King said she kept her two children away from classes because she felt they would not receive proper supervision in the understaffed school. Dorothy Anderson said she decided to keep her daughter, Donna, away from sixth-grade classes after the girl reported that "kids were running up an down the halls and fighting."

The continuing state of uncertainty in the negotiations and doubtful conditions in the schools prompted a formal letter of "grave concern" yesterday from an ad hoc coalition of church and community groups to school board President Woodson.

The Washington Urban League, Operation PUSH, the NAACP, the Council of Churches of Greater Washington and the Baptist Convention of Washington, D.C. and Vicinity urged a resumption of negotiations. There were no talks scheduled yesterday.

"The effects of the strike will be reflected in the quality of our young people's lives," the letter said. "Many of them are behind in achievements. We are concerned that a prolonged strike will result in permanent damage to their future."

While immediate resolution of the surface issues remained unlikely, the continuing undercurrent of political maneuvering between Mayor Barry, the school board and the teachers union became more pronounced.

Knowledgeable sources said that Barry, who by law has no authority to enter the conflict, has been asking school board President Woodson to convene a special meeting of the board members so that they could consider empowering him to intervene, perhaps as a face-to-face negotiator with the teachers union.

The mayor and some of his advisers believe, the sources said, that Barry has enough political influence to win the six board votes necessary to give him a role once such a board meeting is called.

But, one board member said, "If the board capitulates or lets Marion Barry set school board policy for dealing with the union just because there is a strike, then there is no need for a school board."