Another point about pedagogy that is obscured by institutionalization: children get smarter every year. Unless a child is living under some sort of frank abuse, that child is going to get smarter every year NO MATTER WHAT. That's just how humans roll, developmentally. And it has absolutely nothing to do with any specific kind of schooling.

Ya know the tragedy of forcing kids to read too early, how some obsessed competitive enthusiastic parents make this mistake? Forcing math on kids too early is equally stupid. Imagine trying to understand 1 plus 1 when you are 1. Now imagine trying to understand it when you are 15. Obviously, you can labor over the wrong information at the wrong time, or you can wait for the right time when the information is developmentally appropriate. We can work hard or we can work smart, its a choice. Its pretty dang tricky to judge developmental readiness for anyone else--enthusiasm or willingness would be the best bet, I think. 

Notice that the only time its socially acceptable to force extended challenge on someone else is in school. No where in the adult world, does this happen. With the exception of prison and illness, adults are always free to weigh their own reasons and the payoff before embarking on challenge. The argument that challenging young children, for 13 years in an institution, is good for them intellectually (or emotionally) has zero science to back it up. Life is insanely challenging, already. Adding to that willfully is akin to bullying. Coddling is equally absurd, don't get me wrong. But don't try to tell me institutionalized kids are made smarter through the process. That's bullshit unproven.

Anyhow, a bunch of teenagers ended up over here last night, hanging out. Eventually they drifted over to the puzzle we've got going on. They knocked out a bunch of the difficult pieces. Thanks y'all!