The Arlington County School Board has rejected a proposal by Superintendent Charles E. Nunley to increase the pupil-teacher ratio in elementary schools.

The proposal, one of several changes in budget guidelines Nunley proposed for the 1982-83 school year, would have increased the pupil-teacher ratio to 25 to 1 in elementary schools. The current ratio is 24.5 to 1.

The plan, rejected unanimously by the board at its meeting last week, was opposed by several groups, including elementary school principals and a former school board member.

"To tamper with the pupil-teacher ratio is to strike at the heart of the instructional program," former board member Mary Margaret Whipple said in opposing the plan.

In addition, the elementary school principals unanimously voiced their opposition through a memo to Nunley that was presented to the board last week. The memo, signed by Sharon Steindam, principal of Barcroft Elementary, was prepared after a meeting of all 21 elementary principals, according to Steindam.

Although the memo did not outline specific objections to the proposal, it said the principals opposed the higher ratio because "such a proposal would only serve to decrease the quality of services now provided."

To give principals more flexibility in arranging class sizes, Nunley also had suggested that classes in grades 1-3 range from 22 to 27 pupils and classes for grades 4-6 range from 24 to 29 pupils. Nunley had estimated the new guidelines would save the school system about $110,000 in staff costs.

Although the board approved the range for grades 4-6, it decided on a lower range of 19 to 25 students for grades 1-3.

In an interview after the meeting, Nunley said he had hoped the 25-to-1 ratio would be established as the guideline for continuing use in Arlington.

"I thought that was a good, generous number in comparison with the rest of the country," the superintendent said. "I think we can use the number as our standard of quality for Arlington and not debate it every year. By using 25, there was no evidence to show that it would lower the standards in the schools."

Nunley added, however, that he would have no problems working with the board-approved ratio of 24.5 to 1.

In other business, the board delayed action on several recommendations from a board-appointed task force designed to bolster what the task force described as an ailing extracurricular program.

In particular, the task force of coaches, parents, teachers and administrators focused on what it said was a shortage of volunteer coaches and faculty sponsors for student clubs.

The task force said understaffing problems in those areas have been particularly acute since declining enrollments have forced the school system to transfer or lay off teachers. Such layoffs and transfers, the panel said, often resulted in a smaller and older faculty, even though most volunteer coaches and club sponsors are younger faculty members.

To help alleviate the problem, the task force recommended that principals be given more power to protect a small number of teachers vital to extracurricular programs from transfers because of declining enrollments; that the early retirement program be revised to include teachers 55 to 60 years of age with 30 years of service; that stipends be offered to faculty sponsors for several positions that are now unpaid; and that salaries be increased for those coaches and sponsors who are paid for those positions.

The task force was appointed last spring after a group of parents from Wakefield High School expressed concern that the school had lost its football coach for the past several years because of teacher layoffs or transfers.