The Montgomery County Council yesterday approved a $370 million budget for the public schools for next year. The appropriation is $17 million more than this year's but contains relatively little money for new programs and services.

The council gave the schools about $3 million more than County Executive Charles W. Gilchrist had recommended but $4 million less than the school board had sought.

The appropriation will allow the school board to fully fund negotiated raises for the county's 6,220 public school teachers.

The biggest cut from the board's request came out of administration--$1 million, including money for 20 positions.

School Superintendent Edward Andrews said later that those 20 administrative slots can be eliminated without layoffs. "We'd always like to have more," said Andrews, who is leaving the schools at the end of this school year. "I think they gave us every shot at defending (our) budget."

The council also approved funds for seven-period days at two more high schools rather than eight high schools as school officials wanted. The county's 14 other high schools already have seven-period days.

Other cuts will come from the transportation budget; the school's special education program, which pays the salaries of school psychologists; and another special account that places public school children in special schools with facilities not available in public schools.

The council-backed budget will allow the school board to keep open Takoma Park Junior High School at a cost of $543,640 and will provide $205,000 for the "magnet" program in accelerated math and science at three Chevy Chase schools, including Rosemary Hills Elementary, that feed into Bethesda-Chevy Chase High School.

The approved budget also restores 56 teacher aides, the cornerstone of the board's new philosophy that modern schools have a responsiblity to assist students in more than classroom instruction.

This years' school budget battle had been more bitter and acrimonious than in the past.

During the months of debate, school officials warned that children would suffer and teachers would be laid off under the budget Gilchrist recommended.

Gilchrist and his aides, for their part, accused school officials of engaging in scare tactics and being unwilling to tighten their belts like every other county department. The budgets proposed by Gilchrist and the school board contained higher percentage increases than any other county department.

After yesterday's meeting, school officials, council members and even Gilchrist's budget director, Jacqueline H. Rogers, said they were satisfied. "The council's cuts were serious cuts," Rogers said.

She added, however, "The council's going to have a little bit of a funding problem come tax rate time."

Council member Esther P. Gelman, the vice president, said, "I think we can defend this budget to our citizens."