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When asked for evidence of the schools’ effectiveness, the Association of Waldorf Schools of North America points to research by an affiliated group showing that 94 percent of students graduating from Waldorf high schools in the United States between 1994 and 2004 attended college, with many heading to prestigious institutions like Oberlin, Berkeley and Vassar.

Stanford University on artificial intelligence, to be taught this fall by two leading experts from Silicon Valley, has attracted more than 58,000 students around the globe — a class nearly four times the size of Stanford’s entire student body.

For example, the Khan Academy, which focuses on high school and middle school, intentionally turns the relationship of the classroom and homework upside down. Students watch lectures at home, then work on problem sets in class, where the teacher can assist them one on one.

Dr. Widom said that having Stanford courses freely available could both assist and compete with other colleges and universities.

Online education is booming, but not at elite universities—at least not when it comes to courses for credit.

But UC's ambitions face a series of obstacles. The system has been slow to adopt online instruction despite its deep connections to Silicon Valley. Professors hold unusually tight control over the curriculum, and many consider online education a poor substitute for direct classroom contact. As a result, courses could take years to gain approval.

The goal is to determine whether online courses can be delivered at selective-research-university standards.