In Colorado, school districts have lost thousands of students to virtual schools, and, in 2006, a state audit found that one school, run by a rural district, was using four licensed teachers to teach 1,500 students across the state. The legislature responded last year by establishing a new division of the Colorado Department of Education to tighten regulation of online schools.

The Wisconsin Virtual Academy has 20 certified, unionised teachers, and 800 students who communicate with one another over the Internet. The school has consistently met federal testing requirements, and many parents, including Mrs. Weldie, expressed satisfaction with the K12 curriculum, which allows her children to move through lessons at their own pace, unlike traditional schools, where teachers often pause to take account of slower students.

Isabel Weldie, 5, is in kindergarten, “But in math I’m in first grade,” she said during a break in her school day recently.

“That’s what I love most about this curriculum,” Weldie said. “There’s no reason for Isabel to practice counting if she can already add.”