Arlington County public schools received a pat on the back and a punch to the profile last week as turmoil over the quality of education in the county continued.

Stephen H. Detwiler, vice chairman of the Arlington County Board, joined board chairman and fellow Republican Walter Frankland, in accusing the current, Democratic-backed school administration of "not providing the necessary leadership that the school system demands."

In a letter to The Washington Post, Detwiler endorsed Frankland's earlier suggestion that two of the five school board members, Mary Margaret Whipple and Richard Barton, resign before their terms expire in June. Detwiler went further by calling for Arlington Superintendent Larry Cuban to "consider the same advice" and leave before his contract ends in June 1981. t

Likening the struggle over school control to a boxing match, Detwiler wrote, "The final bell has already rung. The fight is clearly over."

Detwiler's letter arrived the same day that Arlington schools released the results of achievement tests taken last year, which Cuban cited as "dramatic proof" of educational improvement in schools since he became superintendent in 1974.

"In my professional judgment, this is an extraordinary achievement on the part of Arlington teachers and administrators," Cuban said of the scores of students on the Science Research Associates achievement tests. The tests are given each year in seven subject areas to grades 4, 6, 8 and 11. In each of the four grades tested, scores in mathematics and reading either improved or remained the same when compared to last year's results.

The most dramatic improvement occurred in the sixth grade where reading scores improved by seven points over last year and mathematics scores rose by 13 points. Scores in the five other subject areas rose by a total of 40 points over last year's and were higher by an average of seven points per subject when compared to scores five years ago.

Results were less encouraging in the 11th grade. While math scores rose four points over last year, reading scores remained the same and scores in the five other subject areas were an average of five points lower when compared to scores fives years ago.

"I'm willing to predict that the same kind of improvement will show up at the secondary level in the years to come," said Cuban after last week's school board meeting where congratulations for the test results were being liberally passed around.

It was partly on the basis of earlier test results, which showed a decline in students' college board scores, that Frankland criticized the schools. At his swearing-in ceremony as County Board chairman, Frankland characterized the schools as deteriorating and called for the resignations of the two school board members. Both Whipple and Barton refused.

School board Chairman Ann Broder, who was in the audience at the ceremony, called Frankland's remarks "stupid" and "self-serving." Cuban accused Frankland of making "reckless" attacks on the school system based on a "personal vendetta."

Detwiler, however, said the dispute was "not just a simple contest of differing opinions." He said the resignation suggestions were made in an effort to give the new school board members who would replace Whipple and Barton a voice in the shape of next year's budget, which will be prepared by the school board and staff next month.

At a meeting last week, the County Board voted to accelerate the nomination process for the two school board positions to be vacated by Whipple and Barton. In the past, the deadline for applications was April 1 and the actual appointments were made in May. By a vote of 3-0, with John Purdy absent and Ellen Bozman abstaining, the three Republican-backed board members -- Frankland, Detwiler and Dorothy Grotos -- moved the application deadline up one month, to March 1. While state law does not allow the appointments to be officially made until May, the resolution called for "designations" to be made April 12.

"All of this business came as a complete surprise," said Minnie Sue Ripy, president of the county Council of PTAs. "It's a disservice to the communnity because it does not give the community time for input."

The PTA council traditionally has held public meetings in March and April to question prospective school board candidates. When the PTA council learned the County Board would discuss the proposal Saturday, the council sent Shirley Pallansch, a member of the council's executive board, to the meeting.

After some discussion, the board rejected a plan by Frankland to designate new school board members in mid-March. The PTA council thought the issue was resolved.

"I left the meeting thinking it was settled, that things would remain as they were," said Pallansch.

But at the continuation of the County Board meeting three days later -- with no one from the PTA council present -- Frankland introduced a new proposal, extending the designation date to April 1. It was that proposal which was approved.

"We didn't decide anything on Saturday because we had not finished that agenda item," Detwiler said.

But Pallansch maintains that the board had moved onto other items on the list before the meeting was adjourned.

"The timing," said Pallansch, "was very, very poor."

Grotos, who voted for Frankland's resolution, expressed a willingness this week to return to the old appointment schedule if the new format caused difficulties.

"I don't see this as any big deal one way or another," said Grotos, who has not joined her Republican-backed colleagues in calling for school board resignations. "I can wait a few more months."