Dynamic generation of diagrams for supporting solving process of mathematical exercises

Abstract

We have constructed the agent that takes a role of a teacher and assists the group for deriving answer of mathematical exercises in the collaborative learning support system. In mathematical exercises, the complementary diagram is drawn for the purpose of grasping the current learning situation and deducing the derivation method for the next answering step. So, the objective of our research is to construct the advising mechanism for the agent that proposes the diagram in the next answering step. In the environment that students can freely draw a diagram, it is unsuitable to prepare the appropriate diagram for each answering step in advance. So, our system analyzes the students' diagram and generates a new diagram dynamically based on the analyzed information. In our approach, stepwise generation of the complementary diagram corresponding to each step is regarded as a forward reasoning in the production system. The situation is regarded as the learner's diagram and the prepared rules are regarded as rules for drawing diagram. So, the diagram for each answering step is generated dynamically by applying particular rules to the current diagram. Consequently, by the proposed diagram, students can arrange the current learning situation and understand the derivation method for the next answering step easily. © Springer-Verlag Berlin Heidelberg 2005.