Stochastic learning paths in a knowledge structure

Abstract This paper presents a stochastic process describing the progress of subjects (for example, students learning a particular field) over a period of time. Typical data involve a fixed sample of subjects tested repeatedly. At the core of the model is a knowledge structure, that is, a possibly large collection Q of items, together with a family of its subsets representing the possible knowledge states. The basic prediction concerns the joint probabilities P ( R t1 = R 1 , …, R ta = R n ) of observing sets of correct responses R 1 , …, R n at times t 1 t n (Thus, R t 1 , …, R t n are jointly distributed random variables taking their values in 2 Q , for any choice of the times t 1