Arlington School Superintendent Arthur W. Gosling proposed a $96 million operating budget yesterday for the 1988-89 school year, a 5.9 percent increase that includes money for improved science programs, a seventh period for students in secondary school and support for special English-language classes.

The proposed budget includes an average 2 percent increase for teacher salaries, on top of a cost-of-living raise that will be determined by the county in February. Last year, Gosling proposed a 5.2 percent increase in teacher salaries above the cost-of-living rise.

Gosling said in a news conference yesterday that the budget "fits into the general ethos of this community," which has demanded excellence in education. He said the salary proposal keeps Arlington in a "strong competitive position" with surrounding jurisdictions.

But Marjorie McCreery, executive director of the teachers' Arlington Education Association, called the salary proposal "window dressing" and was sharply critical of the increase offered to career-level teachers. She said teachers with 16 years' experience and a master's degree would earn about $3,000 less than their counterparts in Fairfax.

"The message is, start here and go to Fairfax if you want to earn a living," said McCreery.

The School Board will hold a public hearing on the budget Feb. 18 and vote on its recommendation Feb. 25.

The County Board, which appropriates money for schools, will hold a budget hearing March 15 and vote on the proposal April 30.

The proposed spending increase, significantly lower than the 9.7 percent increase Gosling requested last year, reflects the relative stability of the Arlington student population, which increased only slightly from last year, said Gosling. Last year the budget included money for 118 new positions. This year 7.5 new positions are proposed.

There are 14,662 students in Arlington public schools, an increase of less than 1 percent from last year.

It also is an indication, said county and school officials, of the county's desire to hold spending down while it tries to persuade the public to consider its first school bond referendum in more than a decade.

The bonds would help finance a 20-year capital improvement program for school facilities estimated to cost $66 million. The county board will decide this summer whether to put the issue before the voters.

County Board Chairman John G. Milliken said the budget proposal "certainly doesn't strike me as outrageous . . . but it may not be something we can fully fund."

In addition to operating expenses, Gosling is asking the county for $4.4 million for community activities, $2.1 million for capital projects and $2.3 million for food services, which will be repaid through a 10-cent increase in the cost of school meals.

Money for schools come from four sources. This year the County Board is being asked to spend $76.2 million, an increase of 7.8 percent over last year.

Gosling said he expects the state's contribution to drop by 4.1 percent, to $11.6 million.

The legislature is debating changes in the way it allocates money to school districts. Sales tax is expected to account for $7.1 million and federal aid is expected to bring $650,000 to the budget.

Major instructional expenditures include $528,000 needed to add a seventh period for students in secondary schools.

An additional $168,000 is proposed for an enhanced science curriculum, and $117,000 is requested to test a computer-based learning program in two elementary schools.