Related idea: semi-computerized instruction.

To the best of my (limited) knowledge, while there are currently various computerized exercises available, they aren't that good at offering instruction of the "I don't understand why this step works" kind, and are often pretty limited (e.g. Khan Academy has exercises which are just multiple choice questions, which isn't a very good bad format). One could try to offer a more sophisticated system - first, present experienced teachers/tutors with a collection of the problems you'll be giving to the students, and ask them to list the most common problems and misunderstandings that the students tend to have with such problems. Then attempt to build a system which will recognize the symptoms of the most common misunderstandings and attempt to provide advice on them, also offering the student the opportunity to ask it themselves using some menu system or natural language parser. (I know some existing academic work along these lines exists, I think applying Bayes nets to build up a model of the students' skills and understanding, but I couldn't find the reference in the place where I thought that I had read it.)

Of course, there will frequently be situations where your existing database fails to understand the student's need. So you combine this with the chance to ask help online, either on a forum with other students, or one-on-one with a paid tutor in an interactive chat session. As the students' problems are resolved, the maintainers follow the conversations and figure out a way for the system to recognize the new problems in the future, either automatically or via the "ask a question" menus.

In particular, the system would be built so that having e.g. forgotten some of the prerequisites in a previous course wouldn't be a problem - if that happened, the system would just automatically lead you to partially rehearse those concepts enough that you could apply them to solve the current problem. At the same time, it could be designed that all of the previous knowledge was being constantly drawn upon, thus providing a natural method for spaced repetition.

This method is naturally most suited for math-like subjects with clear right/wrong answers. But if one wanted to get really ambitious, they could eventually expand the system so as to create a single unified school course that taught everything that's usually taught in high school, abandoning the artificial limits between subjects. E.g. a lesson during which you traveled back in time to witness an important battle (history), helped calculate the cannon ball trajectories for one of the sides (physics), stopped to study a wounded soldier and the effects of the wounds on his body (human biology), and then finally helped the army band play the victory song (music)... or something along those lines. Ideally, there'd be little difference between taking a school lesson and playing a good computer game.