Lets start from the basics here, and full disclosure. My son (10) is a student at Sudbury Valley School - that's one of those unschools that this entire article is about. He's been there 6 years. He has never had a math course, never had a social sciences course, has never sat through a lecture on American History.
He is a talented Python programmer, plays the guitar, and reads about a dozen books a week. Why does he do these things? Because he enjoys them. He's also socially adept, polite, communicative, and inquisitive. He gets along with kids outside his age group - older and younger - because he's exposed to all ages, every day, at his school
I have to point out this boggling statement by you:
Do you know what happens when you let children run around, be inquisitive, ask questions, appreciate concepts, and open doors of wonderment in every topic? You get Arts students. Arts and Humanities students who know how to appreciate everything and know how to do absolutely nothing. People who can master the art of appearing intelligent whilst remaining shockingly ignorant. People whose ideas and tastes and practices are simply imitations of something that was actually original.
What a nauseatingly narrow minded and petty person you must be. "know how to do absolutely nothing" - such as, oh, I don't know. Paint? Do music? Dance? Act? Free an arts student from having to sit through a Biology class (required in every public school), and you know what they'll pursue? Art.
Sudbury Valley has produces scientists, teachers, politicians, and engineers. When a student finds something they're interested in, around age 11-13, they start focusing in on it, learning at their own pace, reading and studying, perhaps taking courses on their own. If they want to go onto college, they prepare in their own way.
Forcing a student to take courses they have no interest in does nothing except disillusion the student on the learning process.
(oh, by the way. My 10 year old son who never took a math course? Loves doing math problems with me. We do them when driving, because he finds them fun. My son loves going to school, and hates when he's home sick or has other obligations. How many children in the public school system absolutely CANNOT WAIT until the first day of school?)
Learn. There are more things in heaven and earth, Horatio, Than are dreamt of in your philosophy.
Saliva causes cancer, but only if swallowed in small amounts over a long period of time. -- George Carlin