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The announcement last month that Coursera, which offers free college classes online, had signed agreements with state universities enrolling more than a million students made it plain that such courses, virtually unheard-of two years ago, are now part of the higher education mainstream.

But along the way, a rancorous debate has emerged over whether such courses will lead to better learning, lower costs and higher graduation rates — or to the dismantling of public universities, downgraded or eliminated faculty jobs, and a second-class education for most students.