Politics rumbled and churned at the center of school administration last week and finally, after 10 ballots in two days, the school board named a president to preside over the policy-making body for Montgomery County public schools.

Carol F. Wallace won the seat over her conservative rival and one-time sponsor Marian L. Greenblatt, but not until conservative in-fighting and personal rivalries made for a gloomy atmosphere in the newly constituted board's first two meetings.

The school board has five members who call themselves educational conservatives and two who take a more moderate -- usually called liberal -- stand on education issues.

That the divisions are far more complex was apparent after last week's vote. Joseph R. Barse and Blair G. Ewing supported Wallace for president, Eleanor Zappone and Suzanne Peyser were behind Greenblatt, and Elizabeth W. Spencer tried to stay out of the fray by voting for herself.

No one budged for nine ballots until Spencer announced that in the 10th ballot she would not vote for herself.

"The school system will continue to educate the children of Montgomery County regardless of the individual actions of the members of this board," she said. "However, in the best interest of our students and staff it is incumbent upon all of us to come to some agreement and elect new officers for 1981. Therefore . . . on this ballot I shall not vote for myself."

Spencer cast her vote for Wallace, and then Spencer was elected vice president.

Wallace, 44, of Silver Spring, was born and grew up on Staten Island in New York City, took law courses at Brooklyn College, got a B.S. degree in education from Wagner College on Staten Island, and taught special education for nine years.

A Montgomery County resident since 1964, she has two sons, one a sophomore at Springbrook High School and the other in the eighth grade at White Oak Junior High School.

She ran unsuccessfully for the school board in 1976 and was elected on a slate with Barse and Zappone in 1978, the year the conservatives took a majority of the board's seven seats.

"My educational philosophy was given to me by a principal who used to tell us what when working with children, build a corral big enough for them to roam but not enough to get lost," she said.

"There's such a thing as in loco parentis and I believe in that. When parents send youngsters off to school, they think the youngster's in school."

She said she expects the new board to continue monitoring the policies that are in place and to make cuts in administrative overhead, a move the board took at its first meeting by voting to reduce the school system's administrative areas from five to three and to cut staffing from 205 to 168.

She said that because the schools face the scrutiny of the non-parents who outnumber the parents in the county, one of the jobs of the board is to promote the importance of public education. "They want to know what they are paying for and they want to see it going for something concrete," she said.

As president, with the responsibility of setting the agenda for meetings and acting as board spokesman, she said she would like to see the board take a look at all the school policies now on the books. "It will be tedious but it is long overdue. I think we will find many things board members themselves are not aware of."

Wallace is not one to sit quietly in school board meetings, and she said that presented something of a dilemma in serving as president. The board president, she said, should preside more and speak less.

"I used to be very opinionated but I've tried to change," she said. "Being on the board has softened me, although I still say what I think."

The school board's first big task is the processing of the system's operating budget of more than $300 million. The board has until mid-February to approve a budget that will include a cost-of-living increase in teachers' salaries an increase of about 9 percent in costs other than salaries.

North Bethesda Junior High School and North Lake Elementary School will close at the end of this academic year, and the board will begin to consider other closures to keep up with dropping enrollment.

State and local school planners are working on a 15-year master facilities plan that will analyze population and housing trends and recommend school closures or reorganizations. The reorganizations will combine enrollments and correct the racial imbalance in schools such as Rosemary Hills Elementary where more than half the students are from minority groups.

A mid-January completion date for the plan has now been changed to a target date of March 1. School board members are anxious to have the report early so that its recommendations can be included in the budget. The plan will not call for any closures before the fall of 1982, but some school board members said they would like to move sooner.

"The budget decision is difficult but we have an obligation to make the best long-term decision possible," said George Fisher, head of the planning department.

He said that every community affected by the plan will have the opportunity to react to it before a final decision is made.