I totally relate. I have to move in order to think. If I don't move, I don't absorb information and I have trouble thinking straight. And it's not just any movement- it's repetitive mindless movement such as shaking my leg, rolling a pencil on the desk, playing with a strand of my hair, etc.

Have you tried "fidgets"? The above poster mentioned a stress ball. I find those to not be as effective as something that I can just shake or wiggle. A stress ball requires physical effort to continuously squeeze. My therapist has some of these like, twisty plastic loops. You can pull it apart and put it back together and do all sorts of weird things with it and it doesn't make any noise. Also, my school has ball chairs in some of the classrooms (like those big yoga balls). I love to roll around on those and bounce on them during class.