In discussing home schooling with my wife, she asked me: why do I oppose public schooling so much? I've had to think about this a bit, but I think I have the answer.
Apart from the bullying, which I mostly ignored, I enjoyed my time in public education. Yet, even during this time, I started to develop a desire to home-school my children. I think part of the reason was that I liked the idea of being semi-nomadic, moving once every two or three years...and home-schooling is a way to stabilize education over vast shifts of geography.
Even during this time, though, I think the seeds were planted to distrust public education for a second reason: Public Schools are inflexible. They are designed to push people down into lesser education.
Allow me to give three examples of this:
Exhibit A. I was in "7X" English--the level between "Gifted and Talented" and just plain old 7th Grade English. Although I got straight A's in this class, my teacher took one look at a test score, and signed me up for regular 8th Grade English...and the first day, I was bored, and felt out of place. Thus, with my mom's encouragement, I went to the office and asked to be placed in the "8X" English class; the next year, I was invited into the "Gifted and Talented".
I came to realize that my teacher arbitrarily tried to stick me in a lower education track, based on a single test score.
Exhibit B. I had a friend who didn't do well in a certain math class (I can't remember if it were geometry or algebra). Although he spent some effort to make up for it during the summer, this effectively derailed him from the "Calculus" track in mathematics. Between this, and the realization that high school only requires two years of this precious skill (as opposed to four for English), I had the sense that something was wrong. Now that I'm older, I can explain it: rather than have a flexible system where you can pick and choose math classes, you're stuck on a track. If you get derailed, it's very difficult to get back to a higher track.
Exhibit C. Grade advancement, to the extent that it prevents students from progressing, holds back the student as a whole. If a student is bad at math, but good at reading--or vice verca--he is expected to be held back a grade. Or, alternatively, a student is often pushed forward, despite being bad at both, to avoid the stigmatism of being "held back".
In either case, this is the direct result of a rigid system, arbitrarily dividing the students up by age, rather than by ability, and arbitrarily tying math and reading together.
Now, I have never been one to believe in "elite classes". The one thing I despise about a lot of our mythmaking is the idea that there is a certain, small, group of people, who are born into greatness, and everyone else is doomed for the mass of sameness. You can see it in the likes of Star Wars and the Force; Harry Potter and magic-users (the masses, there, are called "muggles"); and even "X-Men" and other Superheros. I've always had the sense that anyone has the ability of greatness, if their potential is unlocked.
One work that decidedly is decidedly not in this camp is Tolkein's The Lord of the Rings. The main characters--arguably the most important characters--are common, everyday farmers, who pop out from nowhere and change the world for the better. Tolkein makes it clear that, while Bilbo, Frodo, Sam, Merry and Pippen are up to the task, almost any hobbit could have done what they did! And this, because hobbits like to do the right thing.
It is my feeling that anyone could learn calculus, and learn linear algebra, in high school. I'm an ordinary person, and I at least learned calculus in high school! All I did was dutifully do my homework; and when I decided to become a mathematician, I dutifully did my homework until I earned a doctorate. Of course, because I liked mathematics, I read up on mathematics whenever I could, above and beyond what I learned in school. But then, that's a side effect of passion...and it's also key to getting students to work.
But in our rigid school systems, teachers have limits of time, space, and bureaucracy, that keep them from teaching children to their greatest potential. To achieve that, students need one-on-one attention...and they aren't likely to get that, even in a class of fifteen, or twelve, students. And they certainly won't do that in a system designed to push students down, and even provides schools with monetary incentives to place as many students as possible in "Special" Education!
As I've read John Taylor Gatto's The Underground History of American Education, I've received confirmation on my suspicions, and I've learned a lot more besides. I have concluded that I am likely wrong about having my children learn Calculus and Linear Algebra, and being able to read The Lord of the Rings, by the age of eighteen: I ought to expect my children to be able to do these things by the age of twelve.
And my children will likely be able to do these things, not because they are gifted, but because they are human.