• Eliminate the substitution or substitute the elimination?

      Hammond, Ricardo S. (2013-01-25)
      This research examines the different methods used for solving systems of equations, how those methods are taught, and how they can be applied to real world situations. More specifically, this research examines which of these methods student tend to favor, as well as whether or not students can properly apply the concept of systems of equations to real world situations. “It is hypothesized that high school algebra students will use substitution over elimination when solving systems of equations, and that students who have not been previously introduced to any method will naturally use “guess-and-check.” Furthermore, it is hypothesized that students’ general approach to solving systems of equations is “procedural,” causing them to score higher on algebraic-type problems than on word problems". It was determined that students who had already been instructed on solving systems of equations were likely to favor substitution over other methods. It was also concluded that students who had not yet been instructed on solving systems of equations had a tendency to favor guess-and-check over other methods. Furthermore, students performed better on the algebraic problems than the word problems. Many students approached the word problems differently than how they approached the algebraic problems. Regardless of the methods used in the algebraic problems, many students abandoned those methods when attempting the word problems.--
    • An examination of high school students' misconceptions about methods of exponential equations.

      Hewson, Ashley E. (2013-10-21)
      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.