How to make sure that students spend enough time studying: Fuzzy-motivated optimization approach to selecting a grading policy

Students do not always spend enough time studying. How can we encourage them to study more? In this paper, we show that a lot depends on the grading policy. At first glance, the problem of grading may seem straightforward: since our objective is that the students gain the largest amount of knowledge and skills at the end of the class, the grade should describe this amount. We show, however, that it is exactly this seemingly straightforward grading policy that often leads to an unfortunate learning behavior. To improve the students' learning, it is therefore necessary to use a grading policy which goes beyond the straightforward approach. In this paper, we use fuzzy-motivated intuition to formulate selection of a grading policy as a precise optimization problem, and, in the first approximation, provide a solution to this optimization problem. This solution is in line with what experienced instructors are actually doing when grading the class.