I think too that unschooling is defined differently by different people.
I think it'd be extraordinarily rare for a child to have equal interests in all areas, such that they tend to turn out well-rounded by nature; I also think that project-based learning (which is essentially what unschooling often tends to turn into, except with less structure) doesn't necessarily lay a strong foundation for something like math, where concepts tend to be based on prior ones in multiple threads. For this reason I would never consider radically unschooling anyone (i.e. taking a completely hands-off approach).
ETA: I think that aside from the fact that students' interests tend not to be well-balanced, and I think that one job of education is to make a person reasonably well-rounded, another big weakness of radical unschooling lies in lack of theoretical focus.
For example, a child may decide that it would be fun to build a certain type of project (say, a robot) and to do so, may need to learn about a certain type of math function. From reading, he may figure out how to plug numbers into the function, but without understanding it and without building the conceptual foundation to construct a similar function. Or, a student may use a calculator or program to do all the math that he doesn't know how to do himself, getting the result he wants so he can turn to other interests without having to do the hard work of learning the math himself.
Many people discuss IQ and achievement testing and scores here. How many of us know how to do more than calculate a GAI? We talk about scatter because we want to add to the conversation, and some of this seems to be based on remembering prior conversations of others, but many of us don't have an actual background in psychology to give a truly informed opinion. We've learned enough to do what we need to do-- discuss these things and help rank newbies a tiny bit-- but without developing any deep understanding, or the understanding of what a GAI really is, besides a substitute on a DYS application. This is the sort of thing I'm talking about-- imagine that knowledge of these testing constructs was one facet of math knowledge, and we were learning just the surface info in order to get through our self-selected project, never to return to the topic again. We'd be unlikely to return to the topic and deepen our understanding because it doesn't work that way-- you don't work backwards from an end result of a complicated learning process to the beginning, and lay a strong foundation in retrospect; and you don't even want to try, because it seems so frigging complicated.
Once in a while a highly interested person may decide to start at the beginning, by seeking out the knowledge at the beginning and following it through, such as a radically unschooled person winding up in college and finding that it behooves her to take remedial classes. However, that sort of thing may be highly unlikely unless forced by circumstances-- the radically unschooled person would be trained by that time to think of learning as a back-to-front and/or just-in-time, bare-minimum-necessary sort of activity. And if we accept that something like math should be known well by any student heading off to college, we really do a child a disservice by leaving it to them to self-teach math.
I do think that child-led learning is incredibly powerful, for reasons including helping to hone inner drive in the right sort of student. And drive or "spark" is in my opinion the single most important attribute of any student to nurture.
I just wouldn't be the type of "unschooler" that never provided any sort of direction. (And it goes without saying that unschoolers who let their kids play video games and drink soda all day are neglectful. Well, I've said it.)
