Washington School Board president Minnie S. Woodson, a cautious ex-teacher who became the center of bitter controversy during a 23-day teachers' strike last March, has decided to leave the school board when her term expires at the end of the year.

"It's not a new decision," Woodson said yesterday. "But [being board president] has been more than I anticipated . . . It's a political office . . . There's a certain amount you can take and hold on to your integrity, but after that you have trouble keeping your head above water."

Meanwhile, all five other board members whose terms expire this year have taken out nominating petitions for the Nov. 6 election. About 30 other potential candidates also have picked up petitions, amid indications that Mayor Marion Barry and his political associates are trying to assemble a slate to run in all six school board races. The petitions are due to be submitted by next Thursday. Only one incumbent, at-large member Eugene Kinlow, reportedly is on the list of candidates that Barry might support.

During the teachers' strike Barry and the board clashed repeatedly. Board members charged that the mayor intervened to help the teachers' union and the mayor accused the board of being "stubborn."

Conflicts have continued over the summer, with the board refusing to spend any school funds for the mayor's summer job program and the mayor seeking sharp cut-backs in school spending next year.

Privately, aids to the mayor have criticized the quality of the school system.

"Now we've agreed that the best way to improve the school system is to improve the school board," one aide to the mayor said yesterday. "We felt we had to encourage certain candidates throughout the city."

One special assistant to the mayor, Matthew F. Shannon, is running against incumbent Bettie G. Benjamin in Ward 5 (Northeast Washington).

Linda Cropp, a teacher who is the wife of Barry's executive secretary, Dwight Cropp, has picked up nominating petitions in Ward 4 (upper Northeast and Northwest east of Rock Creek Park). The incumbent there is Victoria Street.

In Ward 7 (Northeast and Southeast, east of the Anacostia River), the seat Woodson is quitting, Barry's local political organization reportedly is supporting attorney Nathanial Bush.

So far, sources said, the mayor has not decided whom to back in the other two races. But they said that incumbents Conrad Smith (ward one) and John Warren (ward six), "don't have a chance" of getting the mayor's support.

The D.C. School Board has 11 members who are elected on a staggered basis to four-year terms. Barry himself ran on a slate when he was elected to the board in 1971 before moving to the City Council three years later. Former mayor Walter Washington stayed away from school board politics.

By law, school board elections are nonpartisan and yesterday Woodson strongly denounced any involvement by the mayor.

"If [candidates] are supported by the mayor," she said, "it might turn the school board into a partisan political operation and people would lose the objectivity that education needs . . . But once they're elected, I think people won't be able to be as loyal to the mayor if they're really going to serve education."

Woodson 58, was elected to the board in 1977 after being appointed the previous year to fill a vacancy. She was a reluctant, compromise candidate for board president last December, but soon was thrust to the center of the board's bitter dispute with the teachers' union.

Some critics accused Woodson of being a weak leader, but Woodson explained: "I'm not a person who tells people what they have to do. I've tried to let the board act and not act upon them."