This might take a bit of chatting with the teacher about, but doodling has been shown to keep a mind just available for collecting the important new bits of a lecture, and that people pick up more, not less, if they are allowed to doodle.
too bad I can't go back in time and tell this to some of my high school teachers!!!
I was going to suggest a notebook for doodling or writing too. Since the teacher is aware of the boredom, can she not give him other things to do to keep him challenged? What about having him research something in an encyclopedia or book or something about a lesson they are working on?
