D.C. School Superintendent Vincent E. Reed has asked city school board members to let him know within the next two weeks whether they intend to reappoint him for another three years or dismiss him when his current term ends in March.

Reed, who has been popular superintendent, is generally credited with bringing some administrative order to the troubled school system since he took over in March 1976. But some school board members have indicated concern that there has been no significant improvement in the educational performance of city school pupils.

Although Reed has been spared the sharp public criticism and ridicule by board members that the string of superintendents in the 1960s and early 1970s were subjected to, he has had something less than solid support from the current, highly factionalized school board.

Among the concerns raised in interviews yesterday most of whom asked not to be quoted, with six of the 11 school board members, were: that test scores of city pupils remain among the lowest in the nation; the slowness with which Reed has implemented the Competency Based Curriculum he brought to the school system, and Reed's decision to cut arts, music and foreign language classes.

Some of the board members also criticized Reed for what they described as a condescending attitude toward the board. They said Reed has little respect for the board and sees himself as head of the school system instead of as an employe of the board.

Reed was not available for comment yesterday.

He asked for the up-or-down decision on his reappointment in a letter to board members Tuesday. In the letter, a copy of which was obtained by The Washington Post, Reed said one of the reasons he wanted a decision soon was that his staff will need time to find jobs if he is not reappointed.

"The Nov. 15 date will serve further the interests of all parties should the board choose not to renew my appointment," Reed said in his letter. "It will allow ample time for the board to select a new superintendent. . ."

In the interviews with board members yesterday, all six indicated they have reservations about offering Reed immediate reappointment.

"I've been keeping a report card on him since I've been on the board," said one member "and out of 23 grades he's only got three passing marks. Only three times out of 28 has he satisfactorily dealt with problems I've pre sented to him."

Another board member said: "He's an emotional man and he has a great sense of indignation. He thinks of the board as politicians and he is the educator. He has little regard for politicians and tremendous respect for educators so instead of seeing us [the board] as his boss and the people who have ultimate responsibility for the school system he sees us as interfering with his school system."

Frank Schaffer-Corona, an at-large member of the board, said Reed frequently gives loose interpretations of board policy so it will fit his goals for the school system. Shaffer-Corona said he would expect most good administrators to do that, however.

"He talks a good game," Shaffer-Corona added, "but he does things that are antieducational. He cuts the foreign language program, the arts and closes schools. And he did a lot of that without board approval. It's partly the board's fault."

Reed first served in the city school system in 1956 as a junior high school teacher. Later, he was a coach, a shop teacher, an assistant principal and principal of Woodrow Wilson High School before becoming assistant superintendent of schools in charge of personnel in 1969.