> I think it's unfair to place the blame squarely on the student. Even in college, the academic system emphasizes memorization and surface-level application (kn

> I think it's unfair to place the blame squarely on the student. Even in college, the academic system emphasizes memorization and surface-level application (knowing how to "use a formula") over the kind of "thinking" you're describing. You're quite right. I can't possibly give a fair, nuanced description of the issue in a couple of paragraphs, and I'm nowhere near qualified to give the definitive account of the problem. Still, you're right that I do place more blame on the learners than most. Maybe people shy away from these ideas because they're dangerously close to some rather sinister Brave New World-style educational theories. In teaching, I think we have a chicken-and-egg problem. We want students to learn both the underlying abstraction and the surface details. But the weaker students are resistant to learning the underlying abstraction, so we drop that and drill them harder on the surface details instead. I see no easy solutions to this problem. > Also, many professionals are called upon to solve problems that require this same kind of "thinking". Academics are not the only ones wrestling with difficult problems. Sure. Computer programmers are an obvious case. But a perusal of the Daily WTF's archives (http://thedailywtf.com/ http://thedailywtf.com/), or the fact that many professional programmers with long careers still can't pass the FizzBuzz test, shows you that there is still a problem.