R Hansen says: >I agree, but if the student has kept up with *all that* and can prove it then we are probably saying the same thing. They are thinking. At least enough to take it to the next level.
I think a better way of putting it is that those students "are in the game". There's lots of other games to play, including one called "getting by". If you haven't ever met a kid who played "getting by" in math class while thinking quite seriously about other topics, you haven't been paying attention.