College students' misconceptions of the order of operations.

Abstract

This research examines the reasons why students struggle with manipulating mathematical expressions and equations when the order of operations process is necessary. It was hypothesized that students in a liberal arts mathematics course would have difficulty using the correct order of operations process when manipulating expressions and solving equations. It was also hypothesized that non-mathematics major college students would have equal difficulty solving for variables using the order of operations process. During this study, students completed a ten-problem assessment. The assessment was generated by polling professors of mathematics. Students were instructed to solve each problem, showing all work, without the use of a calculator. The score for each problem was recorded and compared to a survey that students answered reporting their confidence in using the order of operations process. The results of the study indicated that problems using different types of grouping symbols (not just parentheses) and problems involving fractions were incorrect most frequently. Additional results revealed that there was no difference in scores based on gender and year in college.