The D.C. school board should withdraw its proposal for a longer school day and school year in this year's bitter contract dispute with the Washington Teachers' Union, according to an impartial fact-finder who has studied the negotiations.

At the same time, the teachers' union, which went on strike for 17 days in March when the board refused to extend the old teachers' contract, should accept board proposals dealing with teachers' evaluations, student grading, and requiring teachers to supervise school hallways between classes and keep attendence records.

James M. Harkless, the impartial chairman of a three-person fact-finding panel, said the report which he authored offers the union and the school a framework for resolving 14 issues that separate the two parties from agreeing on a contract before school opens Sept. 10.

Spokesmen for both sides said yesterday they have not had time to read the report and decide what portions of it they will go along with.

But in any event, neither the board nor the union has to abide by the fact-finder's report, which was requested by Superior Court Judge Gladys Kessler as part of the terms she set for ending the teachers' strike.

The possibility of another strike is real, however. Union president William Simons told reporters after Harkless released the report that, if a new contract is not signed before school opens, teachers will strike unless the old contract is extended.

"I hope the board of education will act in a responsible manner and permit schools to open on time in September," said Simons. "Teachers have made it absolutely clear: no contract, no work. All that is needed is for the board to reinstate the contract while we work on this."

But several school board members said yesterday that they do not intend to extend the old contract again.

From her home, Minnie S. Woodson, president of the school board, said she could not speak for the whole school board but she personally felt that there is no need to extend the contract again.

"Today is August 9th," Woodson said. "That gives us ample time to look at what the fact-finder has come up with and reach a new contract agreement. There is no need for the contract to be extended again."

The teachers' union has said that it is pleased with the old contract and has no objections to extending it. But school board members have said the contract gives teachers and the union too much say in board policy that determines how schools are run by the superintendent and principals.

The school board, according to Harkless' report, feels that with a new contract - one that would remove teachers and their union from policy making decisions - the school board could make teachers work harder and get better results for the school system.

But in his report Harkless noted that the board's objections to the old contract involve agree?ents that the board and union have had since the first board-union contract was signed in 1967.

"Therefore," Harkless wrote, "unless it is shown that these provisions have prevented Management from running a more effective school system or are unnecessary the Impartial Chairman judges it unwise and a probable source of continuing friction between the parties to change such provisions of the agreement merely for the sake of principle."

In the case of the board's proposal to extend the school day and the school year Harkless said the board should wait until after Jan. 1980 to seek union agreement to a longer work schedule because the board will then have the authority to negotiate salaries and fringe benefits for teachers.

On the issue of working conditions for teachers, Harkless repeatedly ruled in favor of the union, saying that teachers should not have to attend more than three parent-teachers meetings; lesson plans should not be used to evaluate teachers; and class size should be regulated by the contract and not be a matter of board policy.

But he gave the school board victories by saying the board has the right to select teachers who will serve on committees to improve educational programs; teachers on the union's negotiating committee can have only 80 hours away from their classes for negotiations and teachers must sign out when they leave the school building.

The board and union now have five days to begin meeting on Harkless' recommendations and 15 days to publicly announce if they will abide by his findings. They could decide to return the issues to additional fact-finding, enter in binding arbition, resume arbitration or do nothing.