The D.C. school board and the Washington Teachers' Union remain for apart as court-ordered fact finding on contract issues separating the board and the union enters its last month. Both sides say it is unlikely that a new contract will be signed before the city's public schools open Sept. 4.

"Unless the fact-finding panel shows the wisdom of King Solomon, I don't see the slightest chance of setting the thing this summer . . .," said a labor expert who has been close to the negotiations and fact finding.

"It doesn't look good," said a school board member who didn't want to be quoted as predicting a strike. "But realistically, unless something changes dramatically there iis no reason to think we are going to settle it. . . The fact finding isn't binding. No one has to agree to what they come up with."

William Simons, president of the Washington Teachers' Union, agreed that little or no progress has been made. The fright over the terms of a new contract has been going on since January 1978, when the old contract expired and caused a strike that took most teachers out of District public schools for 23 days in March.

"I'm an eternal optimist," Simons said. "I always look for the sunshine and the silver lining. But there is no reason for optimism."

Although most persons close to the contract bargaining do not see an imminent settlement, there has been minor progress in the talks since the strike.

The board and union have agreed to six parts of a new contract that were still being debated during the strike.

Those include agreements that would require the board to hire a substitute is available and that would compel school administrators to take seniority into consideration when they select teachers for summer school jobs.

In addition to agreeing to some parts of a new contract, the board and the union have changed their stances on other issues and to some degree change the character of the negotiations.

Before the strike, the school board said it was trying to take back control of the school system from the teacher's union, which board members said had too strong a contract. The board said the teachers' union was making decisions about how schools should be run instead of those in authority, the principals, the superintendent and the school board.

The board refused to neogotiate with the union on several issues that board members said were "matters of board policy," Some of those issues includes how students would be graded, how students would be disciplined, how teachers are trained and curiculum decisions.

For the fact-finding sessions that began after the strike, the board has submitted proposals on some of those issues, including student discipline. The board's proposals seek to establish that there should be discipline and a system of grades without allowing the union a role in deciding how grading and discipline will be handled.

Nevertheless, the board's decision to submit proposals on those issues shifts the focus of negotiations. Now the board seems intent on a few major issues, chiefly lengthening the school day and the school year.

The union, meanwhile, has increased its demands since the strike.

For union, meanwhile, has increased its demands since the strike.

For example, the union has increased the number of jobs that teachers should not be required to do in school, such as filling out forms and gradebooks. And the union has cut the superintendent out of the procedure being proposed for setting disputes between principals and teachers.

The board's negotiators have accused the union of backtracking for fact finding by taking positions that they had previously abandoned in talks with the board.

Fact finding ends July 20. The board and the union then will have six weeks to agree on a contract before school is scheduled to start.

The fact finding began in April under a court order that reinstated the former contracts, thereby ending the teachers' strike.

In addition to the problem with completing fact finding and settling a contract before school resumes, Simons is currently battling to pay a $343,350 fine assessed against the union by Superior Court Judge Gladys Kessler for the union's refusal to abide by a court order that barred the union from striking.

The union has not paid the fine because it is waiting for the judge to decide if the fine can be paid in installments or into a scholarship fund for students. In addition, the judge must decide if the union should be fined an additional $200,000 for the two days it disobeyed a temporary retraining order prohibiting a strike before the court order against a strike was issued. CAPTION: Picture, Judge Gladys Kessler fined Washington Teachers' Union