Grading Math Exams
This summer my son and daughter have been taking calculus, and are not entirely happy with the instructor. One of their complaints is that he grades them down on exams when they get the right answer but don't show the step by step procedure for getting it that they have been taught.
Thinking about the question, it seems to me that the instructor's policy is backwards. The ability to solve a problem by following a recipe, a step by step procedure that one has been taught for that kind of problem, is only weak evidence that the student understands what he is doing. Inventing a way of solving the problem that one has not been taught—and getting the right answer—is considerably better evidence.
I am now imagining that instructor as the schoolteacher who tried to keep a class of children—among them the young Gauss—quiet by having them add up the numbers from one to a hundred.
Opinions?