Discovering Prerequisite Structure of Skills through Probabilistic Association Rules Mining

Estimating the prerequisite structure of skills is a crucial issue in domain modeling. Students usually learn skills in sequence since the preliminary skills need to be learned prior to the complex skills. The prerequisite relations between skills underlie the design of learning sequence and adaptation strategies for tutoring systems. The prerequisite structures of skills are usually studied by human experts, but they are seldom tested empirically. Due to plenty of educational data available, in this paper, we intend to discover the prerequisite structure of skills from student performance data. However, it is a challenging task since skills are latent variables. Uncertainty exists in inferring student knowledge of skills from performance data. Probabilistic Association Rules Mining proposed by Sun et al. (2010) is a novel technique to discover association rules from uncertain data. In this paper, we preprocess student performance data by an evidence model. Then the probabilistic knowledge states of students estimated by the evidence model are used by the probabilistic association rules mining to discover the prerequisite structure of skills. We adapt our method to the testing data and the log data with different evidence models. One simulated data set and two real data sets are used to validate our method. The discovered prerequisite structures can be provided to assist human experts in domain modeling or to validate the prerequisite structures of skills from human expertise.