"The (few) students who make an effort to discover and think through something on their own are criticized for wandering from the beaten path, even on the occasions when they're actually right."

I remember I just -couldn't- accept that we can't take square roots of negative numbers. I mean, sure, two negatives multiplied together is a positive, but...there HAS to be a way! Numbers, to my 6th grade mind, weren't arbitrarily going to deny your ability to manipulate them.

Fortunately for me, I happened to be reading a book on Mandlebrot and in the course of discussing his work the author introduces the concept of imaginary numbers. So the next day in class I asked: "Are you suuuure?"

"Yes, I'm sure."

"Well, I was reading in this book and so-and-so says you can take the square root of negative numbers, you get 'i' for the root of -1 and..."

"Why don't you go wait outside."

Where I got told that although I move to the beat of a different drummer, when I'm in her class, I really just need to be quiet. That's when public education and I had a falling out from which our relationship has never recovered.

All of that to say: I think part of the 'problem' is that kids who do try to think on their own are often in a situation where they're challenging accepted rules without the social grace to do so constructively. But rather than being taught the social skills, they're just shut down. Very sad, actually. They could be taught how to 'wander well'.