Statistical Techniques to Explore the Quality of Constraints in Constraint-Based Modeling Environments

Abstract

One of the most popular student modeling approaches is Constraint-Based Modeling (CBM). It is an efficient approach that can be easily applied inside an Intelligent Tutoring System (ITS). Even with these characteristics, building new ITSs requires carefully designing the domain model to be taught because different sources of errors could affect the efficiency of the system. In this paper a novel mechanism for studying the quality of the elements in the domain model of CBM systems is presented. This mechanism combines CBM with the Item Response Theory (IRT), a data-driven technique for automatic assessment. The goal is to improve the quality of the elements that are used in problem solving environments for assessment or instruction. In this paper we propose a set of statistical techniques, i.e., the analysis of the point-biserial correlation, the Cronbach’s alpha and the information function, to explore the quality of constraints. Two different tools have been used to test this approach: a problem solving environment designed to assess students in project investment analysis; and an independent component that performs assessments using CBM and IRT. Results suggest that the three methods produce consistent diagnosis and may be complementary in some cases. In the experiments we have carried out they were able to detect faulty, bad and good quality constraints.