Dana Goldstein examines the data:

Simply put--and decades of polling on class size backs this up--Americans love the idea of their children getting more one-on-one attention from teachers. Indeed, OECD data shows the U.S. has one of the world's largest gaps between average public school class size (23.6 sstudents) and average private school class size (19.4 students), suggesting that small class size is one of the main perks affluent Americans are paying for when they pull their kids out of public schools.

All that said, it's certainly true that small class size is not clearly correlated with high achievement--and neither is large class size.

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