Washington's three new school board members, elected in what some thought was a wave of anti-incumbent sentiment, say they will be taking office with a mandate to help form a quieter, more cooperative board.

"I heard from every voter that they wanted an end to the noise and the bickering and all that," said R. David Hall, the founder of an alternative school for dropouts who defeated incumbent Alaire B. Rieffel in Ward 2. The current board was blamed for driving a popular school superintendent, Vincent E. Reed, from office last year and concentrating more on infighting than on educational issues.

But the two incumbents who easily won reelection, R. Calvin Lockridge (Ward 8) and Barbara Lett Simmons (At-large), were among the group that Reed felt was the most disruptive. They both said they see their easy reelection victories as a mandate to continue the same leadership style on the board, a style that has often led to fractiousness and personality clashes among board members.

"I don't think Vince Reed was all perfect, nor do I think the board was all bad," Simmons said yesterday, adding that she has no plans to alter her often confrontational approach to board matters. "My election is the people's victory. It is a vindication of the community."

A holdover board member, John E. Warren of Ward 6, echoed Simmons, saying, "I don't necessarily associate quietness or tranquility with professionalism. Frankly, I have resented people making judgments about the board based on its decibel level."

In Tuesday's election, David H. Eaton, senior minister of All Souls Church, was elected to an at-large seat to replace the maverick Frank Shaffer-Corona, while Wanda Washburn, a parent activist in the school system, won in Ward 3 where incumbent Carol Schwartz did not seek reelection.

The new board is the first on which a majority of the members -- seven of them -- were not in office during the 23-day teachers' strike in l979 that left bitter divisions in the 11-member group.

The Rev. Raymond B. Kemp, a former board member, said he believes the election will result in a new 7-to-4 split, with Bettie Benjamin (Ward 5), Lockridge, Simmons and Warren forming the minority faction.

Kemp said he believes new Superintendent Floretta D. McKenzie will be able to draw on-going support from the other seven members, including the three newcomers elected Tuesday plus Frank Smith Jr. (Ward 1), Linda Cropp (Ward 4), Nathaniel Bush (Ward 7) and Eugene Kinlow (At-large), who were elected in November l979.

"I think Floretta is going to be able to get her way," Kemp said. "I think the schools are going to be different, not because of the board, but because of the superintendent."

"I think the board is going to be much more professional," said Bush. "I think the change started a year ago with the transition from Lockridge to Kinlow as president . . . .The more professional approach of Kinlow did do more for the image of the board."

The defeat of Shaffer-Corona, though he held relatively little power, should bring about the greatest change, Bush added. "You don't have to have power to be sufficiently disruptive to keep the board in an uproar," he said, referring to Shaffer-Corona.

Bush noted that Shaffer-Corona's defeat might serve to neutralize Simmons since Shaffer-Corona was one of her most consistent allies on the board.

Although there is no clear philosophical majority on the current board, its 11 members were nevertheless unanimous in their support of Reed's back-to-basics approach to education. But some board members, including Simmons and Warren, say Reed's strong personality and leadership led to the board's conflicts with him.

Reed, now the assistant secretary for elementary and secondary education in the U.S. Department of Education, disagreed with that view.

"Time will tell," he said, if the election of three new members creates any significant change on the board. "I just hope the new board will be able to use all of its energy for the good of the children."

The prospect of a new coalition appeared to have little effect on Lockridge, who declared after his election, "The grass roots people like me. It's fair to say there's no in between: people either like me or hate me."

Hall said that the more contentious board members would do well to interpret the election as a signal to take a quieter approach. "Other people on the board know the tone that was set," he said. "They are worried about their own elections coming up. The voters sent a message that people want performance, positive performance, and they're going to demand it."

Though the school system survived what could have been a crucial blow to its financial base with the resounding defeat of the proposed $1,200 educational tax credit, the debate over the credit did focus attention on the public school students' low scores on standardized tests. And that problem lingers.

Eaton said the tax credit's defeat should be interpreted as a healthy omen for the schools since it showed "the community came together and defeated a very divisive issue . . . Protestants, Catholics, rich, poor, east of the park, west of the park -- we gave it a resounding no."

Washburn said the fact that Tuesday's election resulted in an unusually high voter turnout for an off-year election 81,000 shows that public attention is focused on city schools and the performance of the board.

Final but still unofficial returns showed that in the at-large race, Simmons retained her seat by doing well in the mostly black, middle-class, high-voting neighborhoods of upper Northwest and Northeast, even though she did poorly in mostly white Ward 3 west of Rock Creek Park.

Simmons lagged far behind Eaton and two other challengers, Manuel B. Lopez and Phyllis E. Young, in Ward 3, whose residents cast about a fifth of the total votes Tuesday. But she more than made up for her poor showing there by finishing second to Eaton in Ward 4 upper Northwest , first in Ward 5 most of near Northeast and first in Ward 7 the far corner of the city east of the Anacostia River. Those three wards together cast nearly half the citywide vote.

Eaton was strong throughout the city, while Shaffer-Corona was trounced in all eight wards.

In the Ward 2 contest, Hall won with a strong showing in Southwest and in Shaw, overshadowing Rieffel's greater strength in the neighborhoods near Dupont Circle.

Washburn handily defeated Mary Ann Keeffe, a Democratic party activist, in Ward 3, losing only one precinct: the part of Georgetown east of Wisconsin Avenue NW, a precinct whose residents include City Council member Polly Shackleton and former New York Gov. Averell Harriman, two of Keeffe's most prominent backers. Washburn won the upper reaches of the ward by more than a 2-to-1 margin.

Lockridge also won comfortably in Ward 8, losing one precinct to Linda H. Moody, who finished third. Lockridge bettered his nearest rival, Phinis Jones, in every precinct.