Writing Radical Wrongs: A Study of Students' Misconceptions With Radicals and Rational Exponents

Abstract

This research serves to analyze college students’ misconceptions with regard to computations involving radicals and rational exponents. The goal of this study was to attempt to explain some misconceptions that students exhibit when simplifying radicals, working with rational exponents, and solving equations that contain radical expressions. It was hypothesized that college students in introductory mathematics courses would be able to simplify expressions containing radicals and rational exponents with little success. These students would experience greater success on problems containing radicals than rational exponents and they would use factor trees as the main approach to solve problems containing radicals. The results of this study indicate that students performed better on problems containing radicals than those containing rational exponents. These results were found to be statistically significant with a p-value of 0.000. Furthermore, factor trees were the most common method used among students who obtained accurate answers to problems containing radicals. Students revealed that radicals and rational exponents were difficult to work with and not valuable in their current, day-to-day lives.