Driving past a statue of George Washington and a state house designed by Thomas Jefferson, on the way to address the oldest legislative body in the United States, Arlington School Board Chairman Ann Broder was overcome with candor.

"I feel depressed already," said Broder, provoking a laugh from her chauffeur and fellow board member Mary Margaret Whipple.

Broder and Whipple were in Richmond last week to testify before two legislative committees on bills affecting Arlington schools. Both had been there many times before, and neither was particularly awed by the pomp and circumstance of the state capital.

"It's hurry up and wait, sit there for three hours and speak for three minutes," said Whipple.

But while Broder and Whipple were not convinced their testimony would win them an elected school board or a larger budget, they were also aware that in the "push and shove" of the General Assembly, their absence could cost them more.

Arlington was among four Northern Virginia school systems with representatives in Richmond last week to testify before a joint House-Senate appropriations committee considering Gov. John N. Dalton's 1980-1982 education budget. School board members and teachers' representatives from Arlington, Fairfax, Falls Church and Alexandria all made what has become a mandatory pilgrimmage to tug at the state's purse strings.

"I think it was always important to keep in touch with the legislature, but recently we've become more aware of how much control the state has over funding," said Elizabeth Blystone, a member of the Falls Church school board and president of the Virginia School Boards Association.

Blystone, representing the 141 school boards in Virginia, urged the joint committee to reject Dalton's biennial budget in favor of one prepared by the State Board of Education. The $485 million difference, said Blystone, was worht the risk of offending the governor.

"The educational community may separate on other issues, but this is something we are 100 percent in favor of," said Doreen Williams, a part-time legislative consultant to the Arlington, Falls Church and Alexandria school boards.

One of the major differences between the two budgets is the estimate of per-pupil costs for school systems, which is one of the primary components in any educational funding formula. The State Board of Education has proposed a figure of $1,259 for 1980-81, while the governor's figure for the same period is $1,027.

A related complaint of the Northern Virginia delegation is the discrepancy between programs mandated by the state, under the collective heading "Standards of Quality," and the money provided for them.

The standards regulate such basics as ratio of pupils per teacher, staff accreditation and the existence of alternative, vocational and special education programs. They also delineate guidelines for grievance procedures and personnel evaluations.When the standards were officially enacted in 1972, the General Assembly wrote into the law the provision that they be realistically funded.

Representatives of Northern Virginia's schools, however, were unanimous last week in condemning the current funding levels for those standards.

"Failure to recognize the actual cost of education in developing cost estimates for funding the Standards of Quality . . . provides possible grounds for a judicial challenge," warned Fairfax County school board member Mary Collier.

If the governor's education budget were approved, said Collier, Fairfax County schools would lose $10.5 million in fiscal year 1981.

Claudia Waller, an Alexandria school board member, lamented that while the state pays approximately 70 percent of per-pupil costs throughout Virginia, Alexandria receives "only 7.8 percent of its costs from the state."

As an example of unrealistic funding, Waller pointed to the state figures for providing funds for handicapped students.

"Funding is based on 2 percent (of all students) being in some way handicapped or learning-disabled," said Waller. "In Alexandria, it's more like 10 percent. That's a huge gap."

Marjorie Procchaska, a school board member from Falls Church, which has the highest per-pupil cost -- $3,400 -- in the metropolitan area, said her city is currently providing 86 percent of school operating funds. Without an increase from the state, said Prochaska, Falls Church property owners face further tax increases.

The Arlington delegation split the speaking duties. Whipple testified before the joint appropriations committee, inserting a few local statistics to buttress what had been said by previous speakers. Broder made her speech to the House Privileges and Election Committee directly across the hall. Her subject was a bill introduced by Del. Mary Marshall (D-Arlington) calling for the return of an elected school board to the county.

Arlington had the first -- and, from 1946 to 1956, the only -- elected school board in Virginia. The General Assembly withdrew the county's elective privilege after Arlington announced plans to desegregate schools at the same time the rest of the state was seeking ways to avoid that action.

"It was perhaps the first casualty of massive resistance," said Del. Marshall, speaking before the committee on which she has a seat.

Other speakers included Shirley Pallansch, representing the Arlington County Council of PTAs, and Walter Frankland, the chairman of the County Board and a long-time critic of the current Arlington school board. Frankland spoke in favor of an elected board, but allowed himself a few moments of delicious reverie when asked by a committee member if he would trade an elected school board for one which "served at the pleasure of the County Board."

"I'm not prepared to switch in the middle of this," said Frankland finally.

The mood of the Arlington delegation after the hearing was less than optimistic.

"I'm afraid this has become a kind of pro forma thing," said Whipple.

Broder was equally realistic about the chances of Marshall's bill, but as she and Whipple left the General Assembly building, she said one defeat does not mean surrender.

"There are always five or six crises that develop each year," said Broder waving her hand at imaginary brush fires. "We'll be back."