The schools, many managed by for-profit companies, are great at driving up enrollment with catchy advertising. They excel at lobbying. They have a knack for making generous campaign donations.

But as new state report cards coming out now make clear, there’s one thing they’re not so good at: educating kids.

( Also on POLITICO: Do American public schools really stink? Maybe not)

In state after state, online school after online school posts dismal scores on math, writing and science tests and mediocre scores on reading. Administrators have long explained their poor results by saying students often come to their schools far behind and make excellent progress online, even if they fall short of passing state tests.

But lately, more states have begun measuring how much students actually learn during the school year — and a POLITICO review of the data shows many cyber schools are flunking that test.

Ohio’s six biggest cyber schools all got Fs on their state progress reports, meaning students learned nowhere near a year’s worth of material in a year of studying online. In Colorado, students at five of the six biggest cyber schools failed to make as much annual growth in math as peers around the state — often by yawning margins. In South Carolina, all four cyber charter high schools had academic growth ratings of ‘below average’ or ‘at risk,’ as did two of the three elementary schools.

Of the eight virtual schools with growth data in Pennsylvania, only one made adequate gains with students in both reading and math. And kids at Tennessee Virtual Academy made less academic progress this past year than students at every other school in the state.

The scores are so bad, especially at the largest and most high-profile cyber schools, that even fervent advocates of online learning have begun to worry.

( See also: POLITICO’s Morning Education)

“Unless we address these quality issues that have emerged quite profoundly,” the poor performance of cyber schools will “put the entire industry of education innovation at risk,” said Susan Patrick, president of the International Association for K-12 Online Learning, an industry trade group. “We need to have an honest discussion about this.”

Fans of online schools, which serve about 275,000 full-time students nationwide, say they offer a flexibility and freedom that traditional schools can never match because students move through the curriculum at their own pace. Advocates say they’re ideal for aspiring athletes and actors with heavy travel schedules; children with serious medical problems; and kids who never felt they fit in at a traditional school.

( Also on POLITICO: Online courses don’t live up to hype)

Yet those strengths are also weaknesses. Students can email or call teachers for help or log in to online lectures, but there’s little personal interaction. Many assignments meant to check for understanding are multiple choice; there’s no way to stop kids from looking up the answers online. And the cyber schools, which get additional funds for each student enrolled, have incentives to keep families happy, which some teachers say leads to pressure to award passing grades regardless of effort.

K12 Inc., the largest cyber school management company, explicitly encourages teachers to forgive strings of zeros on homework and quizzes if the student can later show he’s learned the concepts. Otherwise, kids who fail to do any work for weeks might get discouraged and drop out, said Allison Cleveland, an executive vice president at K12. “We shouldn’t create an environment for students that they can’t overcome,” she said.

Such policies have fed growth at K12. Last month, the company reported its operating income jumped 58 percent in fiscal year 2013, with total revenue soaring to $848 million, much of that from state and federal education funds.

K12 executives have long rejected as invalid poor state reports on their students’ progress. They have urged parents and investors to focus instead on an internal metric they use to measure progress, a series of multiple-choice tests known as Scantron, which students take at home without a proctor.

The company boasts that Scantron results show its students outpace the national norm for yearly growth in reading and match it in math. When the Securities and Exchange Commission questioned K12 about its academic results earlier this year, K12 again pointed to the Scantron data as proof of its success.

Yet those data are “not as accurate as they could be,” K12 Executive Chairman Nathaniel Davis acknowledged in an interview.

The Scantron tests are optional for K12 students, and about 30 percent decline to take them. That means the company has been comparing a self-selected group of K12 students to the national norm, which isn’t appropriate, Davis said.

The company, he said, needs to find “a more honest assessment” of student progress.

Davis said he pushed teachers to prod more students to take the Scantron last spring in hopes of getting a more valid sample. The company has not released data from those exams.

But the results may not much matter to the bottom line. After K12’s stellar earnings report last month, analysts on a call with top executives didn’t ask a single question about academic performance. And despite its notably poor results in schools across the country, K12 won approval to open new schools in states including Florida, Kansas, Michigan, South Carolina and Ohio this fall.

To be sure, there are a few bright spots in online education, a diverse field that includes both charter schools and schools overseen by states and local districts. Smaller cyber schools tend to do better. So do those that spend more on instruction to keep the student-teacher ratio low, state regulators say. Among big networks, schools run by Connections Education, a division of the publishing giant Pearson, tend to post better results.

Yet when researchers from the National Education Policy Center at the University of Colorado Boulder evaluated academic achievement at every one of the more than 300 online schools in the U.S., they found “serious and systemic” problems throughout the industry. There has been little effort by legislators to rein them in, said Gary Miron, a co-author of the report. The NEPC receives funding from unions that generally oppose online schools, but even strong proponents of digital learning say there’s been a disturbing lack of movement to close failing cyber schools.

“There has not been the political will to do so,” said John Bailey, executive director of Digital Learning Now!, an advocacy group.

Critics say it’s no mystery why the political will to close virtual schools is weak. Parents whose kids do thrive in the schools stage rallies and email blitzes when they perceive a threat. The online industry also works very effectively to secure political support.

K12, for instance, last year contracted with 45 lobbyists in state capitols across the country and donated $625,000 to politicians of both parties, ballot initiatives and political associations such as the Republican Governors Association, according to records compiled by the National Institute on Money in State Politics and the Center for Responsive Politics.

K12 spokesman Jeff Kwitowski calls the donation levels “extremely small” compared with the huge sums spent by other advocacy groups, such as teachers unions. Last year alone, the National Education Association and its affiliates spent tens of millions on political campaigns.

Among individual donors backing cyber schools, few have been as generous as William Lager, who founded Ohio’s largest virtual school, ECOT — and who runs both the company that manages the school and the company that sells the school its online curriculum.

Lager has contributed $387,000 to Republican politicians and political organizing committees just in the past year and a half, a period in which the state began to calculate academic growth for all students in cyber schools — and found ECOT sorely lacking. On the most recent state report card, ECOT got an F on every measure except one, for which it earned a D.

It was hardly alone. Seventh graders in two of Ohio’s big virtual schools learned enough in a year to keep pace with their peers in traditional schools, state data show. But in every other tested grade in every one of Ohio’s six largest online schools, students fell woefully behind. The state counts a progress score of -2 as a complete failure for the school. The cyber schools racked up scores as low as -12, -18 and -27.

Republican Gov. John Kasich has made clear that low scores and poor growth rates are unacceptable in Ohio’s traditional school districts. He has even proposed stripping funding from urban public schools and turning them over to private groups that promise better results.

But he and other leading lawmakers have shied away from criticizing ECOT, which serves about 14,000 students and received $88 million in public funds last year. Nor have they taken on other low-performing cyber schools in Ohio, including one run by a management firm owned by another major Republican donor, David Brennan.

Indeed, Ohio’s existing cyber schools are in line to get more money per student in the coming school year; the Legislature even voted to permit them to tap, for the first time, into funding reserved for vocational and technical education. A state legislative analysis puts the boost at an estimated $4.5 million extra for ECOT alone if it maintains its enrollment.

A spokesman for Gov. Kasich, Rob Nichols, said the bounty of donations from Lager and Brennan has not influenced treatment of their schools.

“Obviously not,” he said.

Nichols pointed to the governor’s effort last year to pass standards for cyber schools; the draft didn’t require schools to hit specific academic benchmarks but did urge them “to provide a high quality education.” The draft did not pass the Legislature.

ECOT Vice President Nick Wilson, meanwhile, said the school rejects as invalid all the F’s on its state report card. The school does its own assessments, he said, and is confident its students are learning. “Is it leaps and bounds above where they were? Not necessarily,” he said. “But it is progress.”

Wilson said he expected “many sympathetic ears” from policymakers as ECOT lobbies to change Ohio’s grading formula. Yet he said the anticipated support had nothing to do with Lager’s donations. “I don’t see that,” he said.

Ohio isn’t alone in protecting online schools despite poor results.

In Colorado, regulators are prohibited by law from considering an online education company’s track record if it applies to manage a new cyber school. So regulators said they had had little choice this spring but to approve a new school to be run by K12, though K12’s other two schools in Colorado have done quite poorly.

In Texas, a virtual school that was at risk of being shut down for low performance two years ago was allowed to wipe the slate clean by finding a new sponsor and declaring itself a new school, without any substantive changes.

Change did seem on the way in Pennsylvania last year, after student proficiency dropped — from already-low benchmarks — at nine out of the 10 cyber charters where the data were tracked. On top of that, then-Auditor General Jack Wagner announced that taxpayers overpay the state’s cyber charters by $100 million a year.

In January, Pennsylvania rejected eight proposals to launch new cyber schools. The House Republican caucus introduced a bill to cut funding to online schools.

Then cyber boosters began lobbying. The bill did not advance. There has been little momentum since, even after the recent federal indictment of Nicholas Trombetta, founder of the largest online school in Pennsylvania, on charges of stealing nearly $1 million in public funds.

In last month’s conference call with investors, K12 CEO Ron Packard said he expects many states to boost, not cut, funding for online schools. “[We] remain sanguine,” he said, “that fiscal 2014 is shaping up to be an excellent year.”

Coming Friday on POLITICO.com: A close look at growth strategies of the nation’s largest cyber school management company, K12 Inc.