I've been teaching an 8-year old beginner's piano lessons since July or so; it's great to see her progress, though sometimes frustrating when I don't know whether to babysit her or try and teach her about dynamics, or if I run out of ways to describe what an octave is. I think she secretly soaks up everything I say, though, as sometimes if she plays something screwy one week, she'll play it near perfectly the very next week and I'll know she was listening.
I'm also glad to see that she wants to be creative with music, so sometimes we'll make up improvisations, or write "songs" together. Once she wrote a song all by herself (and notated it!) and it was called Fiesta. She even remembered to put in a time signature, though none of the measures had anywhere near the right number of notes (nor were barlines relatively vertical, but we're working on it).
Today we had to stop the lesson a little early as I just couldn't get her to focus on the song at hand–she was just too excited about writing a song down on some manuscript paper I copied for her. The song is to be called A Day in Life and the Times of Egypt. Her mom asked her to do something else, but she snapped back, "But I forgot to put in my staccato markings!!"
And that's when I teared up a little inside with composer's pride.