Kriston,
I'm not saying kids never make leaps and bounds. Rather, that higher level studies - high school and beyond - typically require some effort and concentrated study. For students who are smart and have good solid skills (reading, math, critical thinking, etc.) it is within grasp to make substantial progress in less time than would be required in traditional schooling. (clearly I don't question that as our child entered college quite young).

I don't however accept the contention that like walking and talking students will naturally learn calculus. It is a very different process requiring very different skills. Some of the skills most required for academic success are really only acquired through some practice. I'm thinking of skills such as working through frustration, not letting the perfect get in the way of good, etc. Having homeschooled a child all the way through I see that while yes, some skills from baking or archery or whatever the kid likes may apply to academics, there are some separate skills required for more upper level work that really are difficult to develop in another context.

What I've seen very often in the unschooling community is this complicated and somewhat contradictory relationship with academic acheivement. It is on the one hand rejected as "schooled" thinking and rejected as being irrelevant to a happy life. At the same time, the stories of the unschooled kid who had a great academic accomplishment (entered college early, went to Harvard, won the big science fair) are repeated as a validation of the entire movement. I've heard these sorts of references about my child as though his particular accomplishments are a validation of someone else's child led learning rather than probably revealing a couple of things. 1. he's freaky smart. 2. his kind of smarts works very well with academics.