Automatic assessment and error identification of multi-step answers for matrix questions

Abstract

This paper presents an automatic assessment and error identification system for student answers with matrix expressions, and which may have multiple steps. Teacher’s intervention is needed only during the question set-up stage, to provide the marking rubric. The system currently supports four types of matrix questions: multiplying a matrix by a constant number, matrix addition and subtraction, finding unknown elements within a matrix, and finding the unknown matrix from an equation. A CAS (Computer Algebra System) is used to evaluate each step of the student’s answer. The system is capable of giving full/partial marks according to a marking rubric. Errors commonly made by students were identified and categorized by analyzing sample student answers. Using this categorization, the system is capable of identifying the exact error(s) made by a student.