This is the classic result of formal language theory, but there is too much slack between context free and context sensitive, which is PSPACE (larger than NP!).
By Noam Chomsky.
TODO had seen a good table on Wikipedia with an expanded hierarchy, but lost it!
This is one of the main reasons why Ciro Santilli invested in OurBigBook.com.
Ciro believes that the only thing students must be forced to learn is to speak read and write English and that a teacher's main job after that is to help students find their next big goals and also ties into the backward design philosophy.
Everything else, the student must choose.
This idea is generally known as self-directed learning.
This is most notable in University entry examinations of poor countries, where students often have to waste one extra year of their lives to go through preparation for the useless university entry exams. And then, surprise surprise, if they actually get in, they find that this is not what they really wanted to do, and they just go through to the end miserably because they understandably they don't want to risk another year of their lives.
And importantly: It must be easy to change your area of study.
Ciro saw this first hand École Polytechnique which was way freer than his university in Brazil.
Steve Jobs's university dropout stories from Steve Jobs' 2005 Stanford Commencement Address also come to mind.
Interesting projects:
- Brown University's Open Curriculum concept sounds exemplary:
- Gallatin School of Individualized Study from New York University
- Advanced Placement
Godfrey Hounsfield, 1979 Nobel Prize in Physiology and Medicine:[ref]
They tried hard to educate me but I responded only to physics and mathematics