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It reminds me of a text that Feynman wrote about when he gave classes in Brazil, the students knew all the theory and the math behind it, but they could not recognize the phenomenon when it happened in the real world.

So I guess that is not only in math, but in the entire corpus of knowledge, our system makes us prepared for grading tests, not for applying the knowledge.

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Is this what you're talking about? http://v.cx/2010/04/feynman-brazil-education

He told a room full of students that a French curve (that extremely curvy shape used in technical drawing) has the remarkable property that the tangent of the lowest point is always horizontal.. and they all believed him.

Well it's true, isn't it? I think that point was that they were astounded that the curve had that feature because they didn't understand why it was always horizontal. They thought it was magic.

Uh the point seemed that they knew the theory (of differentiation, tangents, trig etc) but were absolutely helpless in practically applying it. Couldn't relate the theory they had learnt to what they knew of the world, at all. Didn't think 'But the lowest point of ANY curve is horizontal!'

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