## An examination of high school students' misconceptions about methods of exponential equations.

##### Subject

Exponential functions.; Logarithmic functions.; Algebra -- Study and teaching (Secondary).; Trigonometry -- Problems, exercises, etc.; Calculus -- Problems, exercises, etc.; Mathematics -- Study and teaching (Secondary).##### Abstract

This study examined the errors and misconceptions exhibited by high school students when solving exponential equations. It was hypothesized that high school students in Algebra 2/Trigonometry and Pre-Calculus classrooms would use guess-and-check strategies and linear arithmetic approaches to solve exponential equations. Few or no students would use logarithmic properties to assist them in solving an exponential equation. During this study, a ten-problem assessment was given to New York students in an Algebra 2/Trigonometry class, an Algebra 2/Trigonometry Honors class, a Pre-Calculus class, and a Pre-Calculus Honors class. The instrument was generated by using past state tests appropriate for students in Algebra 2/Trigonometry according to the state and national mathematics standards. Immediately following the assessment, students were asked to complete a nine-question survey in which they described their reaction to the assessment and their knowledge of exponential equations. The results of the assessment and surveys were collected and analyzed to determine if any correlations existed. The data collected showed that high school students primarily used logarithms to solve exponential equations. Additional results revealed that the Pre-Calculus Honors students scored the highest, the Algebra 2/Trigonometry students scored the lowest, and that students made fundamental errors while solving exponential equations.