Student attendance dropped markedly yesterday on the second day of a strike by most of the 6,000 District of Columbia teachers, amid the first signs of new efforts to settle the dispute that has crippled the city's public school system.

Negotiations between school officials and the striking Washington Teachers Union, which have been halted since Monday night, are scheduled to be resumed at 3:30 p.m. today, a spokesman for the Federal Mediation and Conciliation Service announced. Both sides greeted the prospective return to bargaining with guarded optimism.

Despite the severe impact the strike has had on the city's approximately 200 schools, Superintendent Vincent E. Reed maintained his efforts to keep the school system open, relying on an often-haphazard staff of nonstriking teachers, administrators, substitutes and parents who volunteered to help.

"We don't want to close the schools. Even if things get worse, it's better than having the kids out on the streets where they wouldn't get nay education at all," Reed said yesterday.

School officials said that attendance, out of a total of 113,000 public school students in the city, had decreased from about 73,000 to 79,000 Tuesday to about 50,000 to 56,000 yesterday.

"It's a hopeful sign that we're getting back together, but it has no effect on the stricke," said union President William Simons. "I feel very good about it," said school board Vice President Carol Schwartz, expressing hope that the talks might persuade the union to call off its walkout.

In a related development, D.C. Superior Court Judge Gladys Kessler set a hearing for 9 a.m. today on a request by school officials that the union be held in contempt of court for violating a court order prohibiting the walkout. The school officials charged that the union had "willfully and wantonly violated" Kessler's previous temporary restraining order and contended that the strike has caused "irreparable harm" to pupils, especially handicapped youngsters who need special education.

Of the more than 6,000 city teachers, about 5,200 are Washington Teachers Union members. The union and the school administration continued to issue conflicting estimates yesterday of the number of teachers taking part in the walkout. Ther are also varying estimates of the total number of teachers in the system -- ranging from about 6,100 through about 6,600.

Union President Simons told a WTU rally yesterday that the number of striking teachers had risen from 85 percent of the system's total teaching staff on Tuesday to 89 percent yesterday. School Superintendent Reed contended that the percentage of teachers reporting for work yesterday had climbed to 40 percent, slightly more than his estimate of 35 to 40 percent Tuesday. Neither side provided additional statistics to support its assertions. The number of strikers picketing varied widely from school to school.

Meanwhile, D.C. Mayor Marion Barry went on what he described as a "fact-finding visit" to five public schools. "I think the mayor has to be awfully concerned about this -- and I am," Barry said during his 2 1/2-hour tour. "I don't think this can go on this way forever." Barry is a former president of the school board.

Barry's press secretary, Florence L. Tate, said later that the mayor was studying possible recommendations that he will soon make to school officials and the union on procedures to help resolve their disputes and minimize school disruption. She declined to disclose the nature of the recommendations.

"He doesn't want to be seen as invading the school board's prerogatives," Tate said, nothing that the school system operates largely independently of the city government. "He wants to be in a neutral posture."

The teachers' union's strike -- its first since 1972 -- stemmed from long-standing disputes between the union and the Board of Education over a numer of largely noneconomic issues.

These include proposals by the school board to lengthen the school day and the school year, the board's refusal to extend for a fourth time a contract with the union that initially expired in January 1978, efforts by the board to reduce teachers' influence over school policy and a demand by the union for an "agency shop," in which nonunion teachers would be required to pay a union fee equivalent to union dues.

At a school board meeting in ward 5 last night, there were indications that the 10-member board is sharply divided over the negotiations with the teachers' union.

Board members Barbara Lett Simmons, John Warren, Frank Shaffer-Corona and Bettie Benjamin criticized various actions of the six-member "back to basics" majority, drawing applause from more than 330 teachers who turned up at the meeting. The same four members had refused to sign board petitions asking for issuance of the temporary restraining order and contempt citations against the union.

Warren complained that board members, who under curret board regulations cannot participate in negotiations, should at least be able to sit in on talks with the union. He attempted to pass an emergency resolution to allow board members to participate in negotiations, but failed because a quorum of six was not present.

Visits by Washington Post reporters to a number of schools yesterday appeared to bear out official reports of a substantial drop in student attendance, although there were considerable variations from school to school.

At McKinley High School in Northeast Washington, for example, about 2,000 of the school's 2,400 students were reported to have attended school Tuesday. Yesterday, only slightly more than 1,000 students were said to have shown up in the morning, and by midday all but 100 had left. Those who remained sat in a cafeteria, eating, talking and playing cards. Most of the school's corridors were closed off with metal grates and makeshift barricades in an effort ot prevent possible vandalism.

At Eastern High School on East Capitol Street, a substitute teacher said, "I'm baby-sitting today. You can't teach in an atmosphere like this. The most you can do is keep control."

School officials said the decline in attendance was to be expected after the discovery by parents and students on Tuesday of the crippling effect the strike had had on the schools. Officials and visits to some schools by Washington Post reporters both indicated that more instruction took place in small elementary and junior high schools than in large senior high schools, where teaching frequently had come to a halt.

Also contributing to this story were Washington Post staff writers LaBarbara Bowman, Jean S. Fugett Jr., Alfred E. Lewis and Joseph D. Whitaker .