The Montgomery County Board of Education unanimously approved yesterday a request for $438.9 million in operating funds designed to maintain the level of education in the face of increases in enrollment.

The budget request for the fiscal year that will start July 1 is 9 percent above current spending and $4.5 million more than was proposed last month by Superintendent Wilmer S. Cody.

The request will be reviewed by County Executive Charles W. Gilchrist, who in past years has called for budget cuts.

Then it will go to the County Council, which levies taxes for schools and must act on the budget by May 15.

Most of the money the school board added to Cody's budget is designed to address the most pressing needs in the school system by providing for 134.6 new positions and negotiated raises for administrative and supervisory personnel.

Raises of 6.5 percent for teachers and 4 percent for support staff, both guaranteed in previous labor agreements, are called for in the budget. The starting salary for a teacher with a bachelor's degree would be $16,572, up from $15,561 last fall.

Cody said the 9 percent spending increase is in response to a reversal of a student enrollment decline and illustrates "a distinct departure from the trends and philosophy that have dictated our school budgets for more than a decade."

After 10 years of shrinking enrollment and the closing of 30 schools in the past three years, September figures showed that 800 more students were enrolled in the county's public schools than had been projected, bringing the total to 91,704. School officials are estimating that enrollment will rise another 2,260 next year, mostly in the elementary grades.

Since the early 1980s the school system had tried to cut back on school budgets to battle increasing costs. During the past year, board members have said the system cut back too sharply during those years and now must respond with more teachers, instructional materials and school buildings.

Most of the recent adjustments to the budget reflect the most recent baby boom. Staff positions have been added to Head Start and to elementary art and music programs; other positions have been created to provide additional kindergarten classes and increase the teacher-student ratios in kindergarten through third grade.

Other budget items cover the beginning of seven-period days at Seneca Valley, Springbrook and Walt Whitman high schools and the establishment of a staff training center to coordinate teaching and resources.

Cody would get a raise from $80,000 to $85,500 a year, making him the highest-paid school official in the Washington area after Fairfax Superintendent William J. Burkholder, whose $75,600 salary is nearly doubled by special compensation benefits.

One item that the school board will discuss at its Feb. 25 meeting would put nearly $300,000 in reserve to hire more teachers if enrollment increases more than expected.