Grading

The human brain is excellent at learning and this is abundantly apparent grading math tests. Students are extremely adept at recognizing and reproducing patterns. Often times this stands in for an understanding of the underlying concepts. The result is that a student will try to solve a problem using an approach that is completely inappropriate, but similar in some regard to the correct approach. Here is an analogy by Feynman (intended for slightly different purposes) that captures what I'm talking about perfectly:

In the South Seas there is a cargo cult of people. During the war they saw airplanes land with lots of good materials, and they want the same thing to happen now. So they've arranged to imitate things like runways, to put fires along the sides of the runways, to make a wooden hut for a man to sit in, with two wooden pieces on his head like headphones and bars of bamboo sticking out like antennas--he's the controller--and they wait for the airplanes to land. They're doing everything right. The form is perfect. It looks exactly the way it looked before. But it doesn't work. No airplanes land.

The full text can be found here.