Each student is different. So why not provide a web service that personalizes a topic to each student so as to maximize learning in the shortest time possible?
I'd like to see a version of Wikipedia with prerequisites. Each article would list the articles you'd have to know and understand in order to understand the current article. It would also store which articles you'd already knew, and show for which articles you'd be ready, much like the knowledge tree in Civilization (the game). This would work best for the exact sciences, since most articles don't have prerequisites.
For instance, given the article about the Heine-Borel theorem (http://en.wikipedia.org/wiki/Heine-Borel_theorem) I'd love to know which articles I'd have to read before it will start to make sense.
About personalized education: I think it's going to be huge, (good human teachers will always be better, but who can afford private sessions with good teachers?). I'm working on it as well.
But you need a lot of knowledge about the domain you're teaching, apart from all the usual technical bagage. Finding co-founders or employees with both these skills is awfully hard.
With regards to Wikipedia prerequisites: while they aren't explicit, usually they are linked in the article. For the Heine-Borel theorem, I think if you understood the Wikipedia articles subset, Euclidean Space, closed space, bounded set, open cover, compact space, metric space, complete space, and totally bounded you'd be pretty much set. Of course, these articles have their own prerequisites, like set notaiton.
My experience in school indicates that the quality of the teacher makes quality of the lesson. Also different teachers with different styles have different effects on different students. What I would like to see is series of video lessons by various teachers on a given topic in a neatly organized environment. For example, I would love a site that had links for History, Math , Science, etc. Under Math there would be links for Algebra, Geometry, Calculus, etc. Under Calculus there would be links like
Differential Calculus in 38 lessons by Dr. Math Guy.
Calculus in 3 lessons by Dr. Talks To Fast
Calculus in 7362 lessons for slow people
etc.
I recall (from my overpriced and underutilized psychology degree) that there is some pretty good tests to determnine how people learn... Some people absorb better when listening, some by reading, some people are haptic (hands-on), etc. I think that the challenge is understanding each user enough to be able to personalize the presentation/learning style.
Telling me I need to take 10 minutes of tests for a site to be able to provide value isn't going to be an easy sell.
One element would be the ability to browse topics freely, just like browsing the web.
And it would probably be helpful for the "student" to set goals for the tasks. Maybe choose from a set of goals.
Naively I'd say you can't do it without a mind-reader. Someone may not know what they don't know; thus an intelligent agent probes to determine. This is where tutoring/mentoring comes in, but it's never exact, as the instruction from any given person is probably hardly ever the most effective way to get the concept across to someone else's brain.
Just present all the material and they can skip ahead as warranted. But books tend to be better at reinforcement than introduction; e.g. go out in the field with a paleontology dig and you'll probably remember stuff you learn much better because of the associations with all your senses at once.
I often note important but subtle points in material when re-reading on a subject after personal experience, which I missed when reading the same thing previously. In the repeat case I now have references, and the written word causes those experiences to spring forth from whichever compartment of my mind contained them, whereupon I can hold up the new piece of information to see how it fits, compare it to what's already there, add it in, and then pack the whole thing back up.
The best way to teach someone is to get them as engaged as possible through as many avenues into their brain as possible. You can read about elephants all you want but there's no substitute for meeting one in person.
For instance, given the article about the Heine-Borel theorem (http://en.wikipedia.org/wiki/Heine-Borel_theorem) I'd love to know which articles I'd have to read before it will start to make sense.
About personalized education: I think it's going to be huge, (good human teachers will always be better, but who can afford private sessions with good teachers?). I'm working on it as well.
But you need a lot of knowledge about the domain you're teaching, apart from all the usual technical bagage. Finding co-founders or employees with both these skills is awfully hard.