The Webster unabridged 1966 dictionary defines doodle as: an aimless more or less automatic scribble, outline, design, or improvised sketch traced while one is mentally occupied with something else (collected his random doodles from his wastebasket, inked over the penciled lines, submitted the pictures to the art editor – Russell Maloney)
So does doodling help you pay attention or does it take your mind away from what you should be listening to. Does it help you stay more focused? Maybe it depends on how much we are concentrating on what we are doodling. A lot a daydreaming can be going on when we should be concentrating. When I’m doing art work I can listen and draw and chew gum at the same time but if I’m trying to work on a book dummy or some writing then I can’t chew gum. It takes full concentration. So is that student in your classroom listening while he is doodling away at his paper. Maybe the doodling is helping him concentrate and remember more about what is going on around him. Maybe it is waking up both sides of the brain or maybe his mind is a million miles away.