The Montgomery County Board of Education approved a $372.4 million budget request last night that protects teacher cost-of-living raises but is certain to set off a battle with the County Council, which had asked for a much smaller spending proposal.

The budget for the next school year, which now goes to the council for its approval or modification, represents an increase of $18.3 million or 5.2 percent over this year's budget. It is $8.4 million more than proposed by County Executive Charles W. Gilchrist, who earlier this year asked the school system to limit its increase to 2.8 percent more than current spending.

The approved budget contains few major program improvements or changes but reflects a substantial shift from the previous board's educational philosophy, which focused on reducing class size by adding more teachers.

During its deliberations, the newly elected board members turned down proposals by members of the once-powerful conservative coalition to further reduce class size and instead moved frequently to restore a number of school aides, such as library media assitants. The numbers of those aides, whose services fall primarily outside the classroom, frequently were reduced by the previous board.

The board also added eight counselors at the elementary level, a move opposed by the conservatives but backed heavily for the last two years by principals.

When it became clear that Suzanne Peyser and Marian Greenblatt were going to continue to oppose adding more aides, Robert Shoenberg said the schools must take on more of the traditional family roles as more and more students have two working parents.

Before the budget was approved, Superintendent Edward Andrews warned that a stiff fight with the executive and County Council lies ahead. Yet without the 5.2 percent increase, Andrews, said, the board could be faced with laying off as many as 200 teachers and not honoring the teachers' contract, which calls for 5 percent cost-of-living raises. The raises represent nearly 80 percent of the budget increase.

Gilchrist has said he would like the school system to honor its contract, but Council Chairman David Scull has said the board should consider renegotiating the contract.

Board member Greenblatt, the only one to vote against the final budget request, said the increase is "fiscally irresponsible" and that she expects that the council will return the document to the board in May for further action.