It's late June, nine months into the first year at Khan Lab School, Khan's educational R&D lab in Mountain View. At most schools, the students would be counting down the minutes until their summer vacation. But the Lab School eschews most of the traditional trappings of US education, including summer break. So the kids here don't seem particularly fidgety. Or at least not any more fidgety than your standard group of 9- to 12-year-olds sitting in a warm room analyzing the decline of the Weimar Republic.

Khan himself is the famed creator of Khan Academy, the online juggernaut that provides thousands of hours of free video tutorials and exercises to anyone with an Internet connection. Plenty of big-brained tech types—including the likes of Bill Gates, Ann and John Doerr, and Walter Isaacson—have hailed Khan Academy as a breakthrough: world-class teaching unencumbered by space and time, an agile system that lets students learn at their own pace, the most compelling case yet for how technology might revolutionize education around the globe.