Automatic evaluation and error identification of solutions to single-variable algebraic questions

Abstract

There are two types of single-variable equation solving questions that are present in the Ordinary Level mathematics curriculum in Sri Lanka: linear equations with fractions and quadratic equations. Answers to these questions are open-ended and multi-step in nature. This thesis describes a mechanism that evaluates answers to these two types of questions and awards full/ partial credit. It is quite common that students make mistakes in their answers, which results in partial credit. They may repeat the same errors if they do not receive feedback on their mistakes. Therefore feedback in student errors is important for any subject. This thesis introduces a method to automatically identify the errors that the students make in their answers for the aforementioned two types of questions. To the best of our knowledge, this is the first work on automatically identifying student errors in complex multi-step solutions to single-variable equation solving questions. Our evaluations show that the system we have implemented is capable of awarding full/ partial credit to student answers according to a marking scheme and also to identify errors in student answers with minimal teacher intervention. These evaluations were carried out using student answers from different sources.