As Virginia’s Board of Education begins to develop a formula for calculating letter grades for each of its public schools by fall 2014, superintendents across the state are getting nervous.

The A to F scale, which was approved by the General Assembly earlier this year, is intended to give parents an easy-to-understand summary of the varying quality of each of the state’s schools. But school leaders are worried that the measures will be more of a reflection of how many poor students they serve.

“We bend over backwards to help folks in poverty, and we don’t want to get punished for it,” said Mark Lineburg, the superintendent of schools in Bristol, a small school district in southern Virginia where two in three students are eligible for free and reduced-price lunches.

Lineburg, with help from some university researchers, analyzed an initial formula that lawmakers considered, which was based largely on how well students perform on state tests. They found that 85 percent of the schools that would score a C or below had poverty ratings over 50 percent.

The legislature did not approve the formula and instead asked the state Board of Education to develop a scale that includes test performance and other measures used for state accreditation and state and federal accountability requirements, as well as measures of student growth. Del. Thomas A. “Tag” Greason (R-Loudoun), who sponsored the House bill, said that growth measures, which show how much students learn in a given year, were included in a last-minute compromise to “level the playing field” by helping schools demonstrate success even if they serve more students who are behind.

The Board of Education is scheduled to discuss Thursday what types of growth measures it should include and to approve a list by the end of July.

Still, superintendents are concerned that it’s a steep challenge to develop a system that is sensitive enough to eliminate persistent performance gaps tied to poverty.

“We know that the achievement gap walks in the door the first day of kindergarten,” said Steven R. Staples, executive director of the Virginia Association of School Superintendents. “Some districts have to work harder to make up for [outside of school] experiences.”

Virginia’s letter grades are based on a system started in Florida more than a decade ago under Gov. Jeb Bush (R). Similar A to F scales, or scales using stars or other rating systems, have been adopted in more than 20 states.

Virtually all of them include a combination of growth metrics and standardized test results, said Matthew Di Carlo, a senior fellow at the Albert Shanker Institute who has studied the grading scales. Despite this, he has found a fairly strong correlation between high poverty and lower grades.

Di Carlo analyzed the distribution of letter grades in Florida, dividing the public schools into four groups based on their percentage of students in poverty. He found that the lowest-poverty quartile of schools contained virtually all A or B rated schools, while the highest-poverty quartile had the majority of schools rated C or lower.

“This is not plausible,” he wrote in his analysis. “There is a very big difference between being a low-performing school and being a school that happens to serve lower-performing students.”

In Bristol, a city on the border of Tennessee surrounded by coal country, the recession has brought a growth in homeless students, and the rate has doubled in the past three years to 7 percent of the student enrollment this year.

The district has worked hard to help these students, Lineburg said. It turned the basement of the school board building into a kind of relief center where families could get bedding and clothes.

But such students who are moving in and out of schools tend to struggle.Lineburg said he’s concerned that a grading system that labels schools will punish schools that serve such needy students and also exacerbate disparities in the schools by encouraging some motivated families to flee the public schools.

His concerns were echoed by superintendents of wealthy districts. Loudoun County Superintendent Edgar B. Hatrick III said he feared letter grades would be misleading.

“It’s a very simplistic measure of a complex process called education,” he said.