David Brooks wrote an op-ed criticizing Amy Chua's hypercritical, education-status oriented child-rearing strategy (see her WSJ piece here). Chua clearly presents an unsympathetic portrait: no play dates, 3 hour mandated violin practice, etc. I think if kids want to practice for 3 hours, great. If, like me, you hated practicing instruments, it just teaches you to hate it even more. By clearly going too far on an otherwise good idea, it makes fun fodder for commenters.
Brooks' main point is that preventing kids from sleep-overs and other childhood games deprived them of essential, nay, dominant skills in managing status rivalries, negotiating group dynamics, understanding social norms, navigating the distinction between self and group. These are the really important skills learned in childhood.
Clearly, these are essential skills, but the problem with prioritizing this kind of competence is you can't really monitor them, and what you can't monitor, you can't instruct, drill, or correct, other than simple things like teaching your kids to say please and thank you, and to see 'getting mad' as basically an internal failure. So, while letting your kid play with other kids is essential, I don't see it as a more important parenting strategy because kids will naturally work these skills without prompting. Math, reading, and writing, are not natural activities, and there's a brief window in childhood where one can put these concepts into their brain efficiently. As they were discovered a mere 5 millenia ago, our monkey brains need external stimuli from outsiders old enough to know they are actually important to force us to focus on these skills. On the other hand, our brains were made to master speech and social networks, so that doesn't need so much guidance.
As the Serenity prayer notes, the issue of what is important yet unmanageable, and what is important and manageable, is a very important distinction. It is far more important your kids have common sense than know calculus, but while you do you best every day in teaching common sense, it isn't really something to address directly. You can and should, however, make them learn their math tables.