On using markov chain to evidence the learning structures and difficulty levels of one digit multiplication

Abstract

Understanding the behavior of learners within learning applications and analyzing the factors that may influence the learning process play a key role in designing and optimizing learning applications. In this work we focus on a specific application named "1x1 trainer" that has been designed for primary school children to learn one digit multiplications. We investigate the database of learners' answers to the asked questions (N > 440000) by applying the Markov chains. We want to understand whether the learners' answers to the already asked questions can affect the way they will answer the subsequent asked questions and if so, to what extent. Through our analysis we first identify the most difficult and easiest multiplications for the target learners by observing the probabilities of the different answer types. Next we try to identify influential structures in the history of learners' answers considering the Markov chain of different orders. The results are used to identify pupils who have difficulties with multiplications very soon (after couple of steps) and to optimize the way questions are asked for each pupil individually.