Nonmonotonic Inductive Student Modeling Algorithms

Student modeling is one of the most important topics of ITS research, because the behavior of an ITS largely depends on a student model which represents a snapshot of the student's knowledge. In this research, we formulate the student modeling problem as an inductive inference problem, i.e., a problem of constructing a model explaining observed data which are, in our case, student's answers to the problems given.

Tutoring is to guide students toward a better understanding of teaching material. This means that the learning process is essentially attained through the change of their minds and hence the consistency of student's answers can be easily lost. Therefore, student modeling methods should be able to automatically manage the consistency of student's answers in order to follow the student's change. Contradictions which a modeling system should cope with are classified into the following two types:

(1)contradictions which should be resolved by revising the student model, and (2)contradictions which should be captured as they are.

Generally speaking, an ITS should follow a student's nonmonotonic change. A student modeling system should realize flexible modeling behavior and construct reasonable student models from didactic viewpoints by embodying a teacher's insight, e.g., the ability to capture her student's status by asking fewer questions. In order to cope with contradictions of type (1) which inevitably appear in the student modeling process, a student modeling system is required to have the ability to cope with various kinds of nonmonotonicities by making belief revisions to keep data for inference consistent.

HSMIS

We have been attacking this issue and developing an inductive student model inference algorithm HSMIS (Hypothetical Student Model Inference System) which employs the ATMS (Assumption-based Truth Maintenance System) (deKleer, 1986) to maintain consistency of the student modeling process (Ikeda et al,1988). The architecture of HSMIS is based on a logic-based inductive inference algorithm SMIS (Ikeda et al,1989), whose model description language is also a logic-based language called SMDL (Student Model Description Language) which takes four truth values to represent a student's understanding. Thus HSMIS realizes relatively high model representation power and modeling ability.

THEMIS

The second problem, that is, to capture a student's contradictory knowledge as it is, seems more important from educational viewpoints. The Socratic method, for example, is a contradiction-based tutoring strategy which teachers use especially to help students in the first stage of learning. In order to generate sophisticated tutoring behavior like the Socratic method, student modeling methods should be able to cover a student's contradictory knowledge.

THEMIS is a new nonmonotonic and inductive model inference system which incorporates de Kleer's ATMS as a vehicle for formulating both nonmonotonicities (contradictions). Two types of contradictions are formulated. Type (1) is named "single world contradiction" which is dealt with by HSMIS and type (2) is named "multi-world contradiction" which is dealt with by the structure of a concept discrimination tree. In the newly formulated THEMIS, ATMS plays another important role of managing multiple worlds which enable the modeling of students with contradictions.

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