Automatic generation of answers using solution network for mathematical exercises

Abstract

The objective in this paper is to construct a mechanism for generating the answers for mathematical exercises automatically. A mathematical exercise is decomposed into several small exercises that are called sub-exercises. An answer of an exercise is a collection of answers of its sub-exercises. If the inclusive relations among exercises are managed, answers for exercises can be generated easily. In our approach, the inclusive relations of exercises are represented as a solution network. The solution network is structured as a tree. In the solution network, nodes correspond to the exercises and links indicate inclusive relations of exercises. By traversing the solution network from the node corresponds to the target exercise and detecting its sub-exercises, the answer of the target exercise is able to be generated automatically. © Springer-Verlag Berlin Heidelberg 2005.