No, they don't, but how many average kids left to their own devices will shout, "I'm gonna study differential equations!" They are most likely going to hang out and TM each other or play on Facebook or sell drugs. School at least gives children some structure, especially those from socio-economically disadvantaged backgrounds. I graduated from college, but I needed the structure that attending a university gave me - there was no way I would have learned organic chemistry or calculus on my own.