It’s impossible (or at least, not practical) to grade 100,000 problem sets. MOOCs need to be as automated as possible, for the sake of the course staff and the students. The website Serious Science posted a video featuring Anant Agarwal, CEO of edX, on automatic assessment in MOOCs. He touches on grading equations, matrices, and even ideas about grading essays and labs.
If you’re interested, view the video below, and visit Serious Science to learn more.