Data calibration for statistical-based assessment in constraint-based tutors

Item Response Theory models for constraint-based intelligent tutoring systems.Data-driven assessment of problem solving tasks.Data filtering criteria for Item Response Theory parameters estimation.Best model fit selection criteria. Intelligent Tutoring Systems (ITSs) are one of a wide range of learning environments, where the main activity is problem solving. One of the most successful approaches for implementing ITSs is Constraint-Based Modeling (CBM). Constraint-based tutors have been successfully used as drill-and-practice environments for learning. More recently CBM tutors have been complemented with a model derived from the field of Psychometrics. The goal of this synergy is to provide CBM tutors with a data-driven and sound mechanism of assessment, which mainly consists in applying the principles of Item Response Theory (IRT). The result of this synergy is, therefore, a formal approach that allows carrying out assessments of performance on problem solving tasks. Several previous studies were conducted proving the validity and utility of this combined approach with small groups of students, in short periods of time and using systems designed specifically for assessment purposes. In this paper, the approach has been extended and adapted to deal with a large set of students who used an ITS over a long period of time. The main research questions addressed in this paper are: (1) Which IRT models are more suitable to be used in a constrained-based tutor? (2) Can data collected from the ITS be used as a source for calibrating the constraints characteristic curves? (3) Which is the best strategy to assemble data for calibration? To answer these questions, we have analyzed three years of data from SQL-Tutor.