Grading Math Exams
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.