I have really enjoyed reading Lisa VanDamme's various articles on educational methods. Along with David Harriman, she appears to have created an education program that is almost revolutionary by today's standards. By understanding at a fundamental philosophical level what knowledge is and how human beings acquire knowledge, they have built a program that actually teaches children how to think. Here is a link to a recent article which also includes many other links to her articles and programs.
Pattern Recognition vs. Real Understandingby Lisa VanDamme (December 14, 2006)
...Faced with the application of differential equations to physics, Dave discovered that he had developed a subconscious, automatized ability to look at an equation and instinctively just know what technique to use. But he had never explicitly identified what he was doing, or why that was the right approach to solving this particular problem.
What he possessed was not real knowledge, but an acquired talent of pattern recognition, which—as it always does—faded when it was no longer in use.
The goal of promoting real understanding rather than memorization or pattern-seeking—is accomplished through hierarchical, integrated, purposeful lectures, and by requiring the students to write. In every subject, students are consistently required not just to provide an answer, but to explain how they arrived at the answer, to justify why it is the answer.