A study of college students' misconceptions of radical expressions.

Abstract

This study examined the common misconceptions exhibited by college students regarding the topic of radical expressions. It was hypothesized that the majority of students in the study would lack a geometric understanding of radical expressions. A total of 49 students from two undergraduate non-mathematics major courses participated in this study. Each class was given an identical ten-problem assessment and a short survey which were both completed in one class period. Results from the assessment confirm that the majority of students participating in the study were unable to solve problems which required a geometric understanding of radicals. Only one of the students in the study was able to construct an exact length of √5 using the Pythagorean Theorem. A pedagogical implication of this study is to allow students to discover geometric interpretations and algebraic properties of radicals through student-centered, guided exploration activities. This pedagogical implication is demonstrated in the five-day unit for teaching radicals which is included in the study. This unit is aligned to the Common Core State Standards in Mathematics and was created based on the results obtained from the study.