While the District of Columbia Board of Education has been locked in a well-publicized battle with its teachers' union, 11 candidates have been campaigning quietly for an at-large seat on the board. And, despite their differences on many subjects, the candidates agree that the board should have avoided the strike by extending the union's old contract-which a judge did anyway after the walkout had lasted 23 days.

"It just wasn't worth it this year for the board to take the risk, when it did'nt have the means to win the battle," said candidate Eugene Kinlow, of 4124 Second St. SW. "The contract should be extended until 1980, when the board will have the power to negotiate pay."

Another contender in the special election May 1, Samuel R. Carson, of 226 Oneida St. NE, said the strike has overshadowed other issues. "But the strike is not the big issue-not really," Carson said. "It's timely, but there are a lot of other things that people are talking about."

In the May 1 election, the school board race will share the ballot with contests to fill two vacancies on the D.C. City Council-one at-large seat, formerly held by Mayor Marion Barry, and the Ward 4 post, held by Arrington Dixon until he was elected council chairman last fall.

The vacancy on the 11-member school board was created by a political promotion-the election last November of Betty Ann Kane to the City Council.

The winner of the school board race will serve the remaining seven months of Kane' term. Under D.C. law, there are no run-off elections. The candidate with the most votes wins, even if he or she falls far short of a majority. An election for a full term to the seat will be held next November.

Under city law, the school board is supposed to appoint someone to fill its vacancies. But the board is so badly divided usually on a 6-4 vote, that it asked the City Council to add the vacancy to the special election ballot.

The winner of the May election may cause a shift in the board's close balance of power, particularly if Victoria Street, a member of the board majority, wins her bid for the Ward 4 council post.

However, none of the candidates has declared which faction they will join, and several present themselves as peace-makers. One candidate, Vincent S. Jones, of 1619 Evarts St. NE, says his first priority will be to persuade the board to take "human relations training to develop group cohesion and leadership skills."

Nevertheless, Kinlow, who was cochairman of Barry's transition task force on education, carries a warm endorsement from Kane, who was an influential part of the board majority. Dick Brown, of 641 A St. SE, has been endorsed by Barbara Lett Simmons, a leading member of the majority that backed former Superintendent Barbara Sizemore.

Kinlow, 38, also is supported by former board presidents Virginia Morris and Thurman Evans, and is mounting the best-financed campaign in the race with a budget of about $4,000.

An administrator with the Department of Health, Education and Welfare, Kinlow stresses his record as chairman of the Anacostia Community School Board. The Anacostia board is an elected advisory group that has strongly favored imposing minimum standards through tests before promoting students from grade to grade and before graduating students from high school.

Kinlow said he wants to develop an incentvie pay plan for teachers, tied to student achievement gains that would be similiar to a proposal made in 1970 by psychologist Kenneth B. Clark.

Brown, 49, describes himself as a "longtime activist in the civil rights and peace movements . . . (and) a lieutenant of (the late) Julius Hobson Sr." He now is public relations director for the D.C. Mental Health Association and carries a strong endorsement from City Council member Jerry Moore.

In 1974 and 1975, Brown was an unsuccessful candidate for the Ward 6 school board seat.

He said his chief theme in the current campaign is "getting the school board to stop the personality clashes and deal with the issue of educating our children." He said he wants greater community involvement in schools and improved education for the mentally retarded.

The other candidates, in the order their names will appear on the ballot, are:

Hilton Cobb, 43, of 2801 15th St. NW. Cobb taught in the school system for 10 years and now works for the Veterans' Administration.

"When you go by some schools, they're like a circus," Cobb said. "The permissiveness is just ridiculous."

Cobb said his top priorities would be to "re-establish calm and discipline" and rid the school system of many innovations imposed by "wild-eyed liberals."

"We've forgotten," he said, "that what the schools should be about is a good, basic education."

David L. Wellington, 33, of 2625 Bowen Road SE. Wellington is program director of Neighborood Development Center No. 3 in Anacostia, which is sponsored by the United Planing Organization.

Wellington served as cochairman of the youth task force on Barry's transition team. He said his primary concerns would be to end the divisions on the school board and those between the board and the teachers' union.

Wellington said he wants to increase parental involvement in school affairs and to improve the national test scores of D.C. students.

"But if there is a divided (school) system." he warned, "you cannot even address those concerns."

Rohulamin Quander, 35, of 1703 Lawrence St. NE. Quander is a lawyer specializing in juvenile cases.

He is editor of Howard University's alumni newspaper and active in Catholic groups. Quander said his family first came to the Washington area in 1684 and includes many teachers.

He makes strong appeals to teachers in his campaign brochure, which starts with the promise that Quander "recognizes and will seriously consider teachers' concerns for their own welfare."He said he will work for school programs that are "innovative and practical."

"It's absolutely essential that we get back to some of the basics" Quander said, "but I'm a little bit leery that the creativity of teachers will be suppressed."

Joseph Webb, 29, of 5 Danbury St. SW. Webb is assistant director of the school system's Franklin Adult Education Center, former director of the Harrison Community School and interim president of the University of the District of Columbia Alumni Association.

"I don't think there is any intellectual problem in the D.C. school system," Webb said. "It is a matter of feelings. People have forgotten how to feel about children . . . The discipline problems start in the third and fourth grades when the feeling stops."

When he was at Harrison School, Webb complained publicly about lost equipment and lazy employes. Last June he organized a parents' protest about possible cuts in a summer lunch program. He includes poetry in his campaign literature and signs himself as "God's Poet."

Under current law , Webb would have to resign his school system job if he is elected to the school board. He said he will challenge the law in court after the election.

Samuel R. Carson, 35, a doctoral candidate in anthropology at American University, who supports himself as a salesman for Metropolitan Life Insurance.

Carson strongly advocates the use of tests for hiring new teachers and making sure students have mastered important skills before they can graduate from high school. He said he taught for a year at Federal City College, where most of his students were graduates of high schools here.

"In many cases, I wasn't sure they could really read the assignments or understand much of what they read," Carson said.

Some students came up to him, Carson said, and pleaded, "Look, you're black, and I'm black. Why don't you go easy on me?"

He said he told them: "I'm not going to do you that sort of 'favor.'"

Carson said the standards enforced by the Washington school system should be tied to national norms.

Vincent S. Jones, 33, a human relations consultant with a master's degree in counseling psychology.

Jones said he worked four years in the school system's career development program and has been a substitute teacher. Last year, he said, he spent nine months as Marion Barry's driver and "on-site assistant" during Barry's campaign for mayor.

Besides getting board members to take human relations training, which is similar to encounter-group sessions, Jones said he wants to cut the average class size to 20 students. He said he would like to involve parents in education on an "on-going basis" by making it mandatory for parents and teachers to communicate-either face-to-face or by telephone-at least once a month.

John H. Wallace, 52, of 2939 Van Ness St. NW. Wallace is an educational consultant who came to Washington five years ago after 20 years as a high school teacher and college dean in Illinois.

"I believe someone from the outside might be able to bring a new dimension to that school board," Wallace said. "I think it's important that the board regain the status it once had."

Wallace described himself as "fairly conservative" on education issues and said he would make a stong effort to "take the rowdies out of the classroom and give them special guidance."

Wallace is the only candidate who lives in Ward 3, the predominantly white section of the city West of Rock Creek Park. Ward 3 usually has a heavy turnout in elections. Wallace is black, like all the other school board candidates.

Charlott R. Holmes, 52, of 1321 E St. NE. Holmes is a budget analyst for the Small Business Administration and chairman of Advisory Neighborhood Commission 6A. She was an independent candidate for the Ward 6 Council seat last fall.

"I believe if we had better leadership on the school board, we would be able to progress better," Holmes said. She added that she would "work closely with community leaders" and hoped to get more textbooks for students and cut administrative costs.

"There's too much negativeness," she said. "We need to go in a positive vein."

The 11th candidate is James E. Nutall, 45, of 1312 You St. SE. Nutall, a member of the Democratic State Committee, said he has decided to drop out of the race, even though his name will remain on the ballot.He said he supports Wellington. CAPTION: Illustration, no caption.