Montessori and Sudbury/Democratic schools do not work on the sit down shut up and do as you're told model and they do very well.
And if we're going to do the sit down, shut up and do as you're told model why can't we at least use the best method for it, Direct Instruction?
A highly gifted or profoundly gifted child does not need education in the traditional sense, they need emotional support. The intellectual support the average teacher is going to be able to provide will very frequently be inadequate.
It was suggested I go to a democratic school, but I declined. Such a thing would have been good for me,but what would have been better: Just let me get on with learning about the world with a group of my peers.
In school, whenever a new concept was introduced, I often found that I understood it pretty quickly, but that we'd spend days on the topic while several other students in class struggled to grasp it. During that time, I was expected to sit there and pay attention -- even though it was a waste of time. Even creative outlets, like drawing, were not allowed. If I could have used that time to learn something new on my own, through the Internet or whatever else, that would have been a lot better than just sitting there. Even just letting the students who understand the topic out to play or something until the next topic is introduced would be better and more productive than just having them sit there.
Once I got to college it got a lot better -- I was able to skip classes that I knew would be a waste of time and do more productive things, or bring a laptop to class and do something else when the professor was explaining something I already understood. But prior to college I didn't own a laptop -- not that it would have been allowed even if I did!
Where would you have found peers outside of a school environment? Given the normal school system is 0 and unschooling is 10 where would you place democratic schools?
I presume unschooling is a good approximation to your ideal.
So, I'd do other things when I didn't need to pay attention. When I was really little, I'd act out. Doctors tried to tell my parents I had ADD and prescribe drugs -- fortunately my parents knew better (my dad had the same issues when he was a kid). Later, I actually found a healthy outlet -- I brought a sketchpad to school and drew pictures when I wasn't learning anything. Still, the teachers got upset and eventually took that away.
I feel like it would've been a lot more beneficial to me if there had been some alternative. Or, at least, if I hadn't constantly got in trouble for what essentially amounts to being bored.