Anne Arundel County School Superintendent Robert C. Rice has requested $238.4 million to operate the county's 115 schools. The amount sought for the next school year is a 20 percent increase over current spending.

In his first budget since taking over the school system July 1, Rice is seeking the largest fund increase in recent memory, officials said. The greatest share of that increase would pay for additional teachers to eliminate combined classes in elementary schools and to initiate what would eventually be a countywide preschool program for 4 year olds. Also, he is seeking an expanded school maintenance program.

Those two categories add up to $10.5 million, or one-quarter of the increase Rice is requesting over the 1984-85 school year's $198.7 million operating budget.

In total, 251 new teaching positions, including 38 to accommodate expected growth in the county's elementary school enrollment, are being requested at a cost of $6.5 million, and $4 million is being sought to expand school maintenance and have outside contractors repair aging buildings.

An additional $15 million is required to cover increases in existing teacher and staff salaries, school bus contracts, utilities and Social Security taxes, said Jack White, school budget officer.

"The superintendent surveyed the school system and these are a statement of needs," White said.

The budget will be reviewed during two public hearings on Feb. 6 and 13; the County Board of Education will vote on it by March 1 and then submit it to County Executive James Lighthizer and, ultimately, the County Council for final approval.

County officials said they expect the budget will be cut significantly. The county school budget grew by only 9 percent this year.

The schools' capital budget, which determines funding of construction projects, will be submitted separately to the board Feb. 6.

Despite the size of the operating budget, it differs little in priorities from the current budget. Only the preschool program, for which Rice is requesting 39 new teachers this year, is new.

The bulk of new teaching positions would be in the elementary schools where, in addition to the preschool slots, Rice is trying to eliminate combining different grade levels in the same classroom and to meet the expected surge of elementary school pupils born to members of the so-called "baby boom" generation.

Although the school system's total number of students is expected to decrease by 50 next fall to 63,750, the number of elementary school students is expected to increase by 1,000 to 30,000, White said.