Sunday’s newspaper featured a story about full-time public virtual schools, a new model of education that’s growing fast even though critics say there’s scant evidence that it is an effective way to teach kids.

The story focused on Herndon-based K12 Inc., the nation’s largest operator of virtual schools. Its schools (which educate about 95,000 students in 29 states and the District) tend to have lower state test scores and graduation rates than brick and mortar schools.

Many struggling students are drawn to virtual schooling as a last resort, K12 officials say. Others — like 10-year-old Dumfries student Gennifer Hirata, pictured here with her mother — are high-achievers who appreciate the flexibility of online schooling. (Dayna Smith/For The Washington Post)

They have a point — it’s difficult for any school to ensure that a child lagging far behind his peers in September can pass a state test in May. By the same token, a high school junior who comes to K12 having already failed a bunch of classes will have trouble graduating on time no matter what K12 does.

But of course those are the same challenges faced by thousands of traditional schools around the country — and under the federal No Child Left Behind law, all of them are judged according to state test scores and graduation rates.

K12’s performance numbers vary by school. Here are some examples from Sunday’s story:

At the Colorado Virtual Academy, which is managed by K12 and has more than 5,000 students, the on-time graduation rate was 12 percent in 2010, compared with 72 percent statewide.

That same year, K12’s Ohio Virtual Academy — whose enrollment tops 9,000 — had a 30 percent on-time graduation rate, compared with a state average of 78 percent.

Last year, about one-third of K12-managed schools met the achievement goals required under the federal No Child Left Behind law, according to Gary Miron, a Western Michigan University professor who called that performance “poor.”

Here’s how K12 chief executive Ron Packard explained the low performance figures in an interview earlier this month:

“As we grow, we’re getting more and more kids who are coming to us behind grade level. We’re talking two, three years behind grade level. ...

“Now, if you’ve got a kid who’s in 6th grade, who’s three years behind grade level, that means his rate of learning is a half-year per year. If we are able to double that so that he’s progressing one year each year, we’ve doubled his learning rate. That’s phenomenal progress. But guess what? He’s still behind. And that kid will never catch up.”

K12 has tried to counter the poor state test scores by administering internal tests at the beginning and end of each school year. Company officials say the results of those tests — called the Scantron Performance Series — show that even if many K12 students can’t pass state tests, their achievement is growing quickly. Faster than the national norm, in fact.

But that claim is not always backed up by state data. Pennsylvania, for example, has its own measure of student growth. And in that state, the K12-managed Agora Cyber Charter School showed “significant evidence” that Agora did not meet growth standards last year.

The Scantron Performance Series is used by school districts around the country to assess students’ strengths and weaknesses.

Professor Daniel Koretz, a school-testing expert at Harvard, said he was unfamiliar with the Scantron test and couldn’t comment on its validity as a measure of growth over time. But “gains on any test, even a very good one, are suspect if they don’t generalize to other tests,” Koretz wrote in an e-mail.

“If kids are really learning more math,” he wrote, “that improvement ought to show up on other tests, although not necessarily to the same degree.”

The key thing a parent might want to know is how a child would fare in a full-time virtual school versus a face-to-face classroom. Would his achievement gains be greater when he learns by computer? Smaller? Indistinguishable?

And that’s a question researchers haven’t yet answered.