Analysis of a simple model of problem solving times

Abstract

Our aim is to improve problem selection and recommendation in intelligent tutoring systems by modeling students problem solving times. We describe a simple model which assumes a linear relationship between latent problem solving ability and a logarithm of time to solve a problem. We show that this model is related to models from two different areas: the item response theory and collaborative filtering. Each of these areas provides inspiration for parameter estimation procedure and for possible extensions. The model is already applied in a widely used "Problem solving tutor"; using the data collected by this system we evaluate the model and analyse its parameter values. © 2012 Springer-Verlag.