Four new members of the Montgomery County Board of Education took office last night, forming a new majority and promising to try to mend relations with a community that has become increasingly polarized over school issues.

James Cronin, Marilyn Praisner, Odessa Shannon and Robert Shoenberg ran as a slate in last month's nonpartisan election with the stated purpose of ousting contoversial incumbents who have dominated the board for the past four years.

"The people have prevailed," Cronin said to a cheering crowd of about 200 supporters who had gathered for the inauguration ceremony in the Walter Johnson High School auditorium. The new board, Cronin said, "will truly represent all our children" and will be "dedicated to fair play and equal access for all children."

The victors' campaign attracted support from a number of community activists and minority groups, and they pledged that they would be more sensitive to racial integration questions and less rigid in style than their predecessors.

While last night's ceremony marked the beginning of one era, it signaled the end of another: one dominated by the old majority's philosophical leader, Marian Greenblatt.

Greenblatt began six years ago to build a powerful right-of-center coalition engendered with her own election in 1976 and solidified with the election of new conservative allies forming a board majority two years later.

After four years of aggressive and controversial leadership, Greenblatt last night was relegated to the role in which she started -- that of minority member on a board dominated by ideological adversaries.

Greenblatt's majority of six on the seven-member board was reduced to a minority of two--herself and Suzanne Peyser. Two of her longtime supporters, Carol F. Wallace and Joseph Barse, lost their bids for reelection. Her two other allies, outgoing board President Eleanor D. Zappone and Richard Claypoole, decided to give up their seats.

The new five-member majority consists of the four who were elected in November plus incumbent Blair Ewing, whose seat was not at stake.

Greenblatt and her allies claimed success in reviving traditional education in Montgomery County and bringing a reasoned approach to budgetary problems in the 92,000-pupil school system.

But they were dogged by stormy controversies, including furors over school-closing decisions, some of which were reversed by the State Board of Education; abolishing a minority relations monitoring committee, and replacing a semester-long mandatory black culture course for teachers with a two-day ethnic culture course.

Greenblatt stayed on the board (her second term expires in two years) while running for the GOP congressional nomination. Her opponent turned out to be another board member, Elizabeth Spencer, who resigned to run against Greenblatt and won the nomination, but then lost to incumbent Democrat Michael Barnes in November.

Last night, efforts by the new members to play down old antagonisms hit a snag when they allowed John Diggs, who had been a member of the minority relations monitoring committee abolished by the board, to make a special presentation honoring Spencer and former student board member John Lipson.

Peyser said the inclusion of the presentation in a program honoring outgoing board members was "rude" and that it indicated that the new board majority's sensitivity and compassion was "selective." Peyser voted no and Greenblatt abstained as the four new board members plus Ewing voted yes and got another standing ovation.

Also last night, Greenblatt listed accomplishments of the board under her leadership. Noting her new position she said: "There are seven oars in that rowboat. . . and I'd like to help pull one of those oars and I hope we can do it together.