Create a sister site for education and teaching
I wrote a long, detailed article about how this all would work here: http://www.whattheycallgames.com/2016/05/teachtv-hypothetical-education-based.html
But the tl;dr version is a that I believe a live streaming site for teaching, tutorials, and lessons on different topics and subjects based on Twitch's model would be highly successful. This could be simply an "Education" category in the same way as "Creative", but in order to have unique features suited for education (e.g. the ability to ask questions separately from the chat, upload related files, and review teachers) and to maintain Twitch's game-centric image, a sister site to Twitch may be more ideal.
Nils T. Devine commented
Nice idea. I'm looking for something similar. Have you tried Google Classroom? I've heard good things about it. You need a .edu domain, so it won't work for me, but maybe it would for you.