Student Modeling Based on Problem Solving Times

Student modeling in intelligent tutoring systems is mostly concerned with modeling correctness of students’ answers. As interactive problem solving activities become increasingly common in educational systems, it is useful to focus also on timing information associated with problem solving. We argue that the focus on timing is natural for certain types of educational problems and we describe a simple model of problem solving times which assumes a linear relationship between a latent problem solving skill and a logarithm of a time to solve a problem. The model is closely related to models from two different areas: the item response theory and collaborative filtering. We describe two parameter estimation techniques for the model and several extensions – models with multidimensional skill, learning, or variability of performance. We describe an application of the proposed models in a widely used computerized practice system. Using both simulated data and real data from the system we evaluate the model, analyse its parameter values, and discuss the insight into problem difficulty which the model brings.