Geometry question generator: Question and solution generation, validation and user evaluation

Abstract

Current massively open online courses (MOOCs) are providing several technical challenges for educators. One of these challenges is automated generation of questions, along with the solutions, in order to deal with a large number of students. Geometry is an important part of the high school curriculum. Hence, in this paper, we have focused on the high school geometry domain. We have proposed a framework that combines a combinatorial approach, pattern matching and automated deduction to generate and solve geometry problems for high school mathematics. The system would help teachers to quickly generate large numbers of questions on a geometry topic and may also support the setting of standardized tests such as PSLE, GMAT and SAT. Our novel methodology uses (i) a combinatorial approach for generating geometric figures from the user input, (ii) a pattern matching approach for generating questions, and (iii) automated deduction to generate new questions and solutions. By combining these methods, we are able to generate questions involving finding or proving relationships between geometric objects based on a specification of the geometry objects, concepts and theorems to be covered by the questions. We propose several algorithms to avoid generation of repeated questions and to avoid questions having redundant information, which increases the effectiveness of our system. We have tested our generated questions on an existing geometry question solving software JGEX, verifying the validity of the generated questions. A survey with the real users such as high school teachers and students on generated questions and solutions shows that our system is effective and useful.