A study released last month by researchers at Western Michigan University found that only 27.7 percent of the full-time virtual schools run by the nation’s largest online education company, K12 Inc., met federally mandated Adequate Yearly Progress goals, compared to 52 percent of public schools.

Students at its schools scored lower in both reading and mathematics and had a graduation rate of only 49 percent, compared to a 79 percent average among comparable students at public schools in the 24 states where the virtual schools are located.

“Across a wide variety of school measures, they do very poorly, even though their demographics looked to us like suburban schools,” said the study’s lead author, Gary Miron, who is also a fellow at the National Education Policy Center. “We didn’t see high poverty or a lot of (English as a Second Language) students.”

Proponents of the schools — including Maine education commissioner Stephen Bowen — often quote a 2009 U.S. Department of Education study that found programs that blended online and face-to-face programs fared better than conventional learning. They do not mention that the report found this effect only “for undergraduate and older students, not elementary or secondary learners” and that it concluded that there was currently no “scientific evidence for the effectiveness of these emerging alternatives to face-to-face instruction.”

In Pennsylvania, where some 30,000 students are enrolled in virtual schools at an average cost of $10,000 per student, pupils scored 13 percent worse in reading and 24 percent worse in mathematics than students at ordinary public schools, according to a 2011 study by Stanford University’s Center for Research on Education Outcomes. The researchers broke out the data for separate student groups — those poor enough to qualify for free or reduced lunch, those still learning to speak English, grade repeaters, blacks and Hispanics — and compared them to their counterparts at ordinary charter schools. “In every subgroup with significant effects,” they reported, “cyber charter performance is lower than the brick-and-mortar performance.”

The Stanford study may have helped prompt The New York Times to conduct an investigation of K12 Inc.’s virtual charter schools later that year, which concluded the company “tries to squeeze profits from public school dollars by raising enrollment, increasing teacher workload and lowering standards.”

At the K12-managed Agora Cyber Charter School in Pennsylvania — which reportedly generated $72 million in revenue — the Times found 60 percent of students were behind grade level in mathematics and nearly 50 percent in reading, and a third were not graduating in time.

“Hundreds of children, from kindergartners to seniors, withdraw within months after they enroll.” The company had spent $681,000 lobbying in the state between 2007 and the end of last year.

In Idaho, K12 donated $44,000 to the re-election of the state’s top education official, Tom Luna, who pushed through requirements that students take online classes to graduate, according to an investigation by The Idaho Statesman. Another Idaho paper, The Times-News, found that while state law allowed taxpayer funds to go only to schools operated by nonprofits, the state’s largest virtual school diverted 70 percent of the $9 million it had received from the state to its contractor, K12; a smaller virtual school sent 85 percent of its $829,000 allocation to its for-profit provider, Connections Education of Baltimore, the country’s second-largest online education provider.

“K12 actually gets paid transportation costs in Idaho because they argue that since they bring the school to the children, they should be paid the same as (ordinary) schools,” said former Republican state Sen. Gary Schroeder, of Moscow, Idaho, who chaired Idaho’s education committee for 18 years and sponsored that state’s 2004 charter school law. “Virtual charter schools are organized for the most part by money, and the decision-making process in your state will be influenced heavily by education management organizations like K12.”

K12, which was co-founded by convicted junk bond trader Michael Milken in 1999, counters that the studies and investigations of their record are flawed, unfair or both.

Adequate Yearly Progress is a poor metric, as it judges how many students have achieved competency, rather than how much they’ve progressed, said Jeff Kwitowski, the company’s senior vice president for public affairs. “Most educators agree this is the key of measuring if a school is effective,” he said. “One of the benefits of online education is that you can tailor teaching to the individual student. If you can provide an individual education, you should have individualization of assessment.”

Kwitowski instead pointed to a recent study by researchers from the University of Arkansas in which individual students at the K12-managed Arkansas Virtual Academy were paired with demographically similar students at conventional schools in their hometowns. Between 2009 and 2011, the virtual students performed 5 percent better on mathematics tests and 3 percent better in reading, with students in grades four to six accounting for most of the gains.

As for political giving, Kwitowski said his company is “extraordinarily small” compared to teachers unions such as the National Education Association, which oppose much of its agenda. “We support individuals who believe in expanding education options for children,” he said.