[thaumasiotes]

> if you give a tough math problem to 1,000,000 students, and want to have a tutor walk them through the problem, you'd need to have 1,000,000 tutors. But there are probably only 20 types of mistake one can make on a given math problem. So if you had a "choose your own adventure" solution, one math teacher could, in a month, record lessons that reach a hundred million students at a personalized level.

Not quite. There may be 20 different types of mistake you could make on the problem (I would make a lower estimate, personally), but you can make them in several different places, and the influence of a mistake will be felt in the rest of the problem.

Udacity deals with this currently by never assigning complicated problems that might see a mistake in one step show up in a later step; this isn't quite ideal as instruction, but it makes it possible to automate handling the assignments.

Some relevant cartoons:

http://spikedmath.com/240.html

http://smbc-comics.com/index.php?id=3011