So it's no surprise that when Vi Hart decided to ignore her math teacher and doodle, it all makes so much sense:
Doodling isn’t the distraction it’s commonly thought to be, researchers say–in fact, it aids concentration, and memory. A new study suggests that doodling takes up just enough attention to keep the brain from wandering further afield, explains lead researcher Jackie Andrade.
"If someone is doing a boring task, like listening to a dull telephone conversation, they may start to daydream. Daydreaming distracts them from the task, resulting in poor performance. A simple task, like doodling, may be sufficient to stop daydreaming without affecting performance on the main task"
Vi Hart's "Mathematical Doodling" is a series of hilarious and informative narrated videos explaining doodle-games that you can play to explain mathematical concepts in a way that's much more intuitive than the traditional math-class methodologies. Above is binary trees, but be sure and click through to "Snakes + Graphs" -- a wonderful, captivating potted graph theory explanation.