DD9's teachers are pretty laid back about the doodling. They just call out "Earth to DD!!" when she is not focused on them. Amazingly she seems to be able to still answer their questions!!
As a sometime-doodler myself, I can't say that I'm amazed. I do it in meetings, where I find it helps me keep from mentally checking out completely. Rather than daydreaming, I'm focusing on something in the here-and-now. That makes it easier stay alert through empty business-babble, endless complainers, talk of issues I have no involvement in, etc., and still notice when a topic of substance and usefulness to me shows up.
So in other words, your DD has found a good coping mechanism for boredom, and the only problem here is she takes it too far at times.
