Knowledge Based Mechanisms for Tutoring Systems in Science and Engineering

In science and engineering courses, students are often presented a situation for which they are asked to identify the relevant principles and to instantiate them as a set of equations. For an ITS to determine the correctness and rel- evance of the student's answer and generate effective feed- back, it must map the student variables and equations onto the physical properties and concepts that are relevant to the situation. The space of possible mappings of variables and equations is extremely large. Domain independent tech- niques by themselves are unable to overcome the complexity hurdles. This paper describes how an ITS can use constraint propagation and algebraic techniques combined with do- main and problem-specific knowledge to solve the mapping problem with systems of algebraic equations. The tech- niques described in this paper have been implemented in the PHYSICS TUTOR tutoring system and evaluated on three data sets that contain submissions from students in several introductory Physics courses.