What is the best way to distribute efforts among students: Towards quantitative approach to human cognition

In a typical class, we have students at different levels of knowledge, student with different ability to learn the material. In the ideal world, we should devote unlimited individual attention to all the students and make sure that everyone learns all the material. In real life, our resources are finite. Based on this finite amount of resources, what is the best way to distribute efforts between different students? Even when we know the exact way each student learns, the answer depends on what is the objective of teaching the class. This can be illustrated on two extreme example: if the objective is to leave no student behind, then in the optimal resource arrangement all the effort goes to weak students who are behind, while more advanced students get bored. If the effort is to increase the school´s rating by increasing the number of graduates who are accepted at top universities, then all the effort should go to the advanced students while weak students fail. An additional difficulty is that in reality, we do not have exact information about the cognitive ability of each student, there is a large amount of uncertainty. In this paper, we analyze the problem of optimal resource distribution under uncertainty. We hope that the resulting algorithms will be useful in designing teaching strategies.