Abstract

Exponents are at the heart of our understanding of certain mathematics-dependent concepts such as population growth, compound interest, and radioactive decay. However, exponents remain challenging to learn. As a result, students make errors when working with problems involving simplifying exponents. This article describes students’ thinking about the errors they and their peers make when simplifying exponential expressions. Understanding students’ thinking behind their errors is essential for teachers to provide constructive feedback. A purposive sample of forty-two first-year engineering students was selected from one of South Africa’s public universities located in the Gauteng Province. Qualitative data were generated using a mathematics test compiled by researchers, students’ written answers to the mathematics test, students’ performance marks, and students’ responses to group interviews. The findings of this study indicated that students’ explanations of their thinking about the errors they make can be divided into four categories: mixing of exponential rules with algebra rules, misapplication of exponential rules, distribution error, and factorization error.