Automated generation of geometry questions for high school mathematics

Abstract

We describe a framework that combines a combinatorial approach, pattern matching and automated deduction to generate and solve geometry problems for high school mathematics. Such a system would help teachers to quickly generate large numbers of questions on a geometry topic. Students can explore and revise specific topics covered in classes and textbooks based on generated questions. The system can act as a personalized instructor - it can generate problems that meet users specific weaknesses. This system may also help standardize tests such as GMAT and SAT. Our novel methodology uses (i) a combinatorial approach for generating geometric figures (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. Experimental results show that a large number of questions can be generated in a short time. We have tested our generated questions on an existing geometry question solving software JGEX, verifying the validity of the generated questions.