Automatic model answer generation for simple linear algebra-based mathematics questions

Abstract

This research is focused on automating the process of generating answers to simple linear equation related mathematical problems. Simple linear algebra based questions are a part of most Mathematics examinations. These linear algebra questions can appear as word type problems, where the question description is given in a textual form. Addition, subtraction, multiplication, division and ratio calculation are some of the known categories for linear equation based word type problems. Addition and subtraction based problems can be further divided based on their textual information as change type (join-separate type), compare type, and whole-part type. This research focuses on linear equation questions belonging to these three categories. Mainly four approaches are followed by existing research for answer generation for linear algebra questions. These are rule/inference based, ontology based, statistical based, and hybrid based approaches. In this research, a statistical approach is selected to automatically generate answers for simple linear algebra based model questions. The implemented system shows better accuracy than the other statistical systems reported in previous research for the same types of questions. This result is achieved by using ensemble classifiers and smart feature selection. Also, a new data set is created for training and evaluation purposes.