A framework of generating explanation for conceptual understanding based on "semantics of constraints"

In science education, conventional problem practice hardly helps students reach "conceptual understanding" with which they can solve various problems by making appropriate models of target systems. Students often superficially read the solution of a problem and apply it wrongly to others without understanding the model. It is difficult to teach how to make appropriate models because model-making expertise includes a lot of implicit knowledge. In this paper, we propose a general framework for systematically describing such knowledge, which makes it possible not only to explain various models and the difference between them but also to design/sequence a set of problems appropriate for promoting conceptual understanding. Our framework was proved useful through a preliminary experiment in which the explanations generated based on our framework promoted subjects' (15 graduates and undergraduates) conceptual understanding in mechanics. The framework can be the basis for designing intelligent tutoring systems which explicitly help students reach conceptual understanding.