Markov Chain Monte Carlo Methods for Dynamic Student Assessment

In this paper we explore an application of Markov Chain Monte Carlo (MCMC) methods to the field of educational assessment. The aim of our approach is to dynamically evaluate student understanding and adaptively tailor question difficulty and topic coverage in real-time. In particular, our model employs a variant of a classical algorithm to decide on question transitions, optimising the assessment process to balance exploration of the student's knowledge base and exploitation of known learning gaps. The model not only adjusts the sequence of questions based on previous responses, but also integrates student-reported confidence levels to refine the estimation of their understanding.