Rule-based Cognitive Modeling and Model Tracing in a Math Story Problem Tutor

Intelligent Tutoring Systems (ITSs) are intended to help in tutoring the students in specific domains typically by improving their problem solving skills. An important aspect of such ITSs is their ability to solve the generated problems in the same way that the student would in addition to interpreting the student actions to provide relevant feedback and help. Cognitive models that mimic the way knowledge is represented in human minds are excellent means toward achieving this goal. This paper discusses cognitive modelling in the MAth Story problem Tutor (MAST). MAST is a Web-based ITS that can generate probability story problems of different contexts, types and difficulty levels. The paper also discusses the model tracing approach of MAST to interpret the student actions in symbolizing the word problems and estimating the required probabilities to provide relevant feedback and help. A major contribution of the paper is in considering the symbolization of the probability word problems to convert them to the symbolic form and tracing the students errors in this process. As an example, the paper considers the context of rolling a die and tossing a coin. Evaluation results have shown the ability of MAST to considerably improve the probability story problem solving skills of the students.