>I was talking about 3rd graders playing Beethoven. That is in the casual sense?
There are prodigies, of course. Math prodigies too. I thought you were talking about the typical piano student who gets a very simplified version of some Beethoven melody to play. Of course, the child can appreciate the melody, and learns to play some harmony to it. But he doesn't have the full appreciation of everything that's there in a typical Beethoven sonata.
I sat through a group recital in my neighborhood, where a 9 year old friend was playing. There was not a single performance that actually sounded like music, even though the senior performer played an entire Beethoven sonata. The main problem is in fact rhythm. Too much emphasis on correct notes, and the music, in fact, slips away.
I think there is some connection with that syndrome to the recog/recall dichotomy Kirby has brought up here.