It was nearing lunchtime on a recent Thursday, and ninth-grader Noah Schnacky of Windermere, Fla., really did not want to go to algebra. So he didn't.

Tipping back his chair, he studied a computer screen listing the lessons he was supposed to complete that week for his public high school—a high school conducted entirely online. Noah clicked on his global-studies course. A lengthy article on resource shortages popped up. He gave it a quick scan and clicked ahead to the quiz, flipping between the article and multiple-choice...