Students make their way through the hallways of Patriot High School in November 2013, in Nokesville, Va. Prince William County lost more state funding during the recession than neighboring districts. (Jahi Chikwendiu/Washington Post)

Facing financial strain, Virginia cut hundreds of millions of dollars from state education funding during the recession by adjusting the formulas used to determine how much money school districts receive.

But as the state’s economy has rebounded, many of the formulas have stayed the same. The result? Researchers at the Commonwealth Institute, a Richmond-based think tank, say that Virginia schools are being shortchanged $800 million a year ­because of formulas that under­­estimate what it actually costs to educate children.

Changes to the formula amounted to “tactics used to reduce state support in a time of financial strain, and they ignore the actual costs of educating Virginia’s students,” the researchers wrote. The adjustments also had the effect of cutting state education funding for the long haul by altering how Virginia calculated what it gives to each school district.

“These were not one-time cuts that they made to the appropriation level,” said Michael Cassidy, co-author of the report. “Rather, they went in and structurally changed the education funding formulas.”

The report, released this month, comes after Gov. Terry McAuliffe (D) proposed increasing education funding, a plan that could face resistance from the Republican-controlled legislature. Because the state divvies out funds based on a district’s ability to cover its expenses, Northern Virginia districts rely less on state funding than do their counterparts in less affluent parts of the state, so it remains unclear what the increase would mean for them.

[Virginia governor proposes funding increase to hire additional teachers]

Sharon Bulova (D), head of the Fairfax County Board of Supervisors, is pressing state lawmakers for more education dollars as the state’s largest jurisdiction grapples with how to fund its school system.

The Commonwealth Institute has been a strong proponent of increasing funds for education, arguing that the state should begin restoring cuts made during the recession.

In the report, “Virginia’s Eroding Standards of Quality,” Cassidy and co-author Chris Duncombe called the recession-era changes to the funding formulas “arbitrary.” The formulas, called the standards of quality, are based on a variety of factors, including a district’s relative wealth and what the district spends to operate.

One of the most devastating changes lawmakers made, the report said, was to cap the number of support positions the state would help fund in school districts, an adjustment made in 2009 that saved the state $754 million over two years. The state stopped funding 12,900 positions, meaning local school districts had to pick up the tab or eliminate the jobs. For each school district, the cap was based on minimum staffing ratios and, according to the report, did not reflect the reality of what it took to operate schools day-to-day. Those cuts hit administrators, school finance officers, custodians and others who work in school operations.

In 2010, the state extended the school bus replacement cycle from 12 years to 15, cutting the funds that flowed to bus fleets and saving the state nearly $10 million a year. Another change meant the funding formula no longer took into account how much a district spent on some equipment and travel, a change that cut an estimated $122 million from districts across the state.

Poor districts that rely more on state funding felt the brunt of the cuts. The study said Lee County lost nearly $2,500 per student between 2009 and 2014, accounting for inflation, the most of any district in the state. Lee County is among the poorest counties in Virginia and spent approximately $12,000 per student in the 2013-2014 school year, so the losses had a sizable impact on the district’s budget.

Some of Virginia’s poor counties struggled to make up for the losses in state funds. The cut in state education funding blunted the ability of the state to act as an equalizer, Cassidy said, and was felt disproportionately by poor districts.

“When you have these structural changes . . . you see how it introduces much greater inequality in our education in the state,” he said.

[High-poverty school divisions harder hit by state funding cuts in Virginia, study says]

In Northern Virginia, Prince William County lost the most, at $630 per student, according to the report. The county, which gets about half of its funding from the state, saw class sizes skyrocket in that period and now spends the least per student of the districts in the Washington area.

Other Northern Virginia districts — including Fairfax and Loudoun counties — actually saw modest gains in state funding. Cassidy explained that some counties hit hard during the housing crisis got boosts because the state funding formula is based partially on property values.

The institute argues that the state funding formula should be readjusted so it “accurately reflects the real costs of running schools and educating our kids.”