Minnie S. Woodson, a retired District of Columbia elementary school teacher and member of a faction on the city school board that generally believes in back-to-basics instruction, was elected board president yesterday.

Woodson, 56, the board's representative from Ward 7 in the far Northeast area of the city, defeated John Warren, Ward 6 school board member, by a 7-to-4 vote.

Conrad Smith (Ward 1), board president last year, announced he would not seek reelection. Smith said he intends to run for the at-large City Council seat being vacated by Mayor-elect Marion Barry.

Yesterday's vote revealed again the ideological divisions on the board.

The three board members who supported Warren's candidacy usually vote with him. They generally favor bringing new educational ideas and strong community input into the school system. In addition to Warren those board members are Barbara Lett Simmons, Frank Shaffer-Corona (at large) and Bettie Benjamin (Ward 5).

Most of the six board members who voted for Woodson also usually vote together. Generally they are back-to-basic advocates who have a voting pattern that argues that the city public schools have had enough of revolutionary educational theories.

That group has supported hard work and longer hours for teachers as well as students as the cure for low test scores and poor performance of city schools.

That six-person majority includes former board president Smith; Carol Schwartz, Ward 3 representative who was reelected board vice president yesterday; Betty Ann Kane, an at-large member of the board who has resigned to take the at-large City Council seat she won in November; Alaire Rieffel (Ward 2); Victoria Street (Ward 4), and Woodson.

Board member R. Calvin Lockridge, Ward 8 representative and one of Woodson's supporters yesterday, describes himself as a "swingman," with a foothold in both factions.

After her election yesterday, Woodson, who was born in the Deanwood section of Northeast Washington and has lived in the Northeast area of the city all her life, said she plans to continue the "deliberate" work that she said the board has been doing under Smith.

"There are some important (things)," Woodson told the 11-member board after she took the president's seat, "that the board has not accomplished in the last year which will be the focus of this board in the upcoming year. Nothing will be my focus, it will be the focus of this board."

Woodson listed three items for the board's attention: community relations, refining the procedure for reviewing the superintendent's work and evaluating his performance and redefining how the community can properly participate in the school system.

Woodson, like Smith, is a supporter of Superintendent Reed.

Woodson has a long history of involvement in city schools. She was a teacher in the system for 27 years, first as an elementary school teacher and then as a reading specialist.

Howard D. Woodson, her father-in-law and a civil engineer, is the man for whom Woodson Senior High School, was named and one of her brothers-in-law Granville Woodson, was an assistant superintendent of the city schools in charge of buildings and grounds.

Woodson's priorities are in keeping with the ideas she brought to the board when she was appointed in January 1977. At that time, she defended the quality of the city public schools in an interview, saying, "Many people say the schools are failing. But I can't see that the schools are failing. It might be that the home is failing, that the churches are failing, that no one is taking the child to a library, that no one cares whether or not he is in school . . ."

Woodson has also said that she believes city schools are improving and are in an "embryonic state and . . . need to be nurtured."

He ideas are in opposition to the thinking of the minority group on the board.

In the words of Shaffer-Corona, a member of the minority faction, the city school system is the heart of a "regressive and racist monster" that cripples the city's mostly black children for life by giving them a bad education. Shaffer-Corona and other members of the minority faction on the board feel the school system could stand to be restructured.

As a result of the split between the two groups the board has experienced a slight resurgence of the controversy and personality conflicts that were the hallmark of city school board meetings in the early 1970s.

At a board meeting Wednesday night, for example, resigning board member Kane said, "I will miss all of my colleagues on the board."

"All of us?" asked Warren, a member of the opposition group.

And at the November board meeting Barbara Lett Simmons castigated then-board president Smith, a member of the majority group, as "incompetent" for not allowing her to read a report. She went on to read the report even though Smith ruled her out of order.

The majority of the board, the back-to-basics advocates, have generally favored closing schools because of declining enrollment and limited budget. But the board minority argued heatedly that school closings hurt neighborhoods, foster a purge of poor blacks from the city as wealthier whites move in and could mean that some children would have to cross busy streets to get to school.

Woodson was considered a "compromise" candidate for the presidency.

Woodson, who has said, "I don't know how to campaign for an office," became a candidate after the back-to-basics faction began to splinter because of personality conflicts with board president Smith, according to several board members.

Smith has also had trouble in his professional life. In November the D.C. Bar's Disciplinary Committee recommended that Smith's license to practice law be suspended for 18 months. The bar said Smith was guilty of "perpetrating a fraud" on a client and two charges of neglecting a client. Smith is appealing the bar's findings in court.