Mathematical Question Structure Extraction and Possibilities of Automatic Question Making by Plane Graph

Abstract

This paper proposes an analysis method of mathematic question structure and considers the possibility of automatic question making of mathematics. In previous researches, method for effective usage and automatic generation on multiple choice problems had been considered. When we consider automatic generation of problems, automatic generation of calculation problems such as arithmetic operations can be easily implemented, and some have been implemented as e-learning systems. However, it is not easy to automatically generate the type of problem that derives the answer while applying some formulas. Therefore, in this research, we propose a method to extract the structure of mathematic questions by analyzing problems with induction of university entrance level using the structure of plane graph. A plane graph of mathematic question can be created by using a unit to be learned in a textbook as a vertex and constructing an edge connecting the vertices according to the procedure of inductions. By creating a plane graph in this way, clustering of mathematical problems using information other than learning items and fields, and information to be a hint of new problem creation can be obtained. It is also possible to recommend question structures that are candidates for new questions from such hints. Furthermore, it is also possible to apply it to the development of new teaching materials by giving the examinee's score information to a plane graph.