Problem Response Theory and its Application for Tutoring.

Problem solving is an important component of education. To make problem solving activities attractive, it is important to confront students with problems of suitable difficulty -- neither too easy, nor too difficult. Since students vary in their skills, it is also crucial to make problem recommendations individually adaptive. We present a novel problem response theory, which predicts how much time will a student need to solve a given problem. Our theory is an analogy of the item response theory, but instead of probability of a correct answer we model problem solving time. We introduce a problem solving tutor, which uses the theory to make adaptive predictions and to recommend students problems of suitable difficulty.