I have thought about this lately also. I don't necessarily think my son is very advanced but his thinking is just different.
Here is an example:
We go to the dog park a lot. My four year old has gotten tired of going and only has fun when he finds another little kid there he can play with. We are unloading and he is walking around a bit while I am getting the baby in the carrier and the dog leashed. He comes up and says he wants to go home because he is the only kid there. I say you can't know there are no kids here. There are over fifty acres of forested trials and there is only a small meadow visible from the parking lot. His response - no cars here have car seats or boosters. I checked. I am the only kid here.
It is not like coming to that conclusion the way he did was necessarily advanced, it just seemed like a creative way to determine if there were kids in the forest.
Anyway, he doesn't seem all that academically advanced. He has little interest in reading by himself, writing or math. He'll sometimes read a big word or randomly do multiplication in his head but nothing with any consistency to make advanced school work necessary. Those moments seem to come out of nowhere and he won't or can't explain how he came up with it in the first place. If it weren't for his scores, I would wonder if he was gifted at all and didn't just have a big vocabulary an amazing memory and an odd way of looking at the world.
