Republican Walter L. Frankland assumed chairmanship of the Arlington County Board yestereday, issuing a stern lecture about deterioration of the country's schools and calling for the immediate resignation of two school board members.

"I think those two old members should give serious consideration to resigning now," Frankland said in as highly partisan inaugural speech that attacked school board policies.

"We spend $3,000 per student per year in Arlington and there is still not enough emphasis on academic achievement," Frankland said, "Leadership from the school administration is not evident."

Yesterday was the day that Frankland had long awaited -- when a Republican-endorsed majority, consisting of outgoing chairman Dorothy Grotos, Stephen H. Detwiler and himself would be in firm command of the five-member County Board.

It is this freshly mandated Republican majority that will fill the seats of school board members Richard A. Barton and Mary Margaret Whipple when their terms expire in June. Whippie ran on a Democratic-endorsed ticket against Frankland and Grotos in November and was soundly trounced in the process.

Frankland, resplendent in a silvery-gray suit, used much of his short inaugural speech yesterday to condemn the state of Arlington education. He deplored both the lack of classroom discipline and what he termed the poor performance of Arlington students on standardized tests.

Frankland, who was first elected to the board in 1975, has attacked the school administration previously but his remarks yesterday seemed to indicate that he intends to make changing the school board's direction a major issue during his year as board chairman.

School board member Whipple said later she had "no intention of resigning" and school board president Ann Broder called Frankland's statement a "self-serving political move and, in the long run, stupid."

Even Grotos, Frankland's running mate, sought to disassociate herself from his remarks. Grotos said she would not support a move to oust Whipple and Barton before their terms expire.

Whipple said that under Virginia law school board members, once they have been appointed, are considered to be state officials -- not appointees subject to political pressures. "It would not at all be appropriate for me to resign," she said.

"We're in the middle of the school year and any new member (of the board) would be hard pressed to get control over what is going on," she said.

Broder, in the audience of 75 who heard Frankland's speech said he painted a "totally inaccurate description of the school system."

"Schools are an easy shot," Broder said. "In fact, we do parent surveys and 80 percent approve of what we are doing in the schools."

"It's just not good for Arlington leaders to be denigrating the Arlington school system. In the long run, it will scare people off from living in Arlington," she said.

"I didn't think of (his speech) was controversal or rough on anybody," Frankland said in an interview that followed the county board's installation at the courthouse.

"It's just that the Arlington school system needs to be changed from the school board on down," he said, hinting that School Superintendent Larry Cuban's position might be altered if he faces a strongly conservative school board.

"There's no question but that Mr. Frankland has been very critical of Mr. Cuban," Whipple said, "But its not clear that he would want to stay beyond the point where his contract expires (in July 1981 anyway," she added.

Frankland also used his speech to pronounce Arlington in excellent financial health. "We have a bond rating that other counties envy," he said.

He said that this year's board would attempt to further reduce property taxes, grapple with Arlington's declining population, develop the new Orange Line Metro corridor, and protect residential neighborhoods from over-development -- all themes of GOP's November campaign.