# Solving Absolute Value Equations and Inequalities on a Number Line

9-2016

Thesis

## Degree Name

Master of Arts in Teaching, Mathematics

Mathematics

Wallace, Laura

## Abstract

Absolute value has often been taught procedurally. Many students struggle with solving absolute value equations and inequalities because they do not have an understanding of the underlying concepts. This study was designed to determine to what extent solving absolute value equations and inequalities by using the concept of distance on a number line is an effective method. The claim is that if students use the distance concept on a number line, they will develop the necessary conceptual understanding in addition to just a procedural knowledge that will lead to the success with and flexibility in the use of strategies for more challenging problems. The following questions were addressed in this study: How and to what extent can using a number line develop a conceptual understanding of absolute value equations and inequalities? What solution strategies do students tend to use to solve absolute value equations and inequalities? Does the strategy depend on the complexity of the problem? To what extent do they exhibit flexibility in their use of strategies? What extensions are students able to make? What misconceptions do they have? In this study, lessons and assessments were implemented based on the “best practice” of using multiple representations with a focus on conceptual understanding of absolute value. The lessons were consistent with current content standards. Students completed a pre and post assessment, and some students were selected to participate in a 15 minute interview based on their responses from their assessments. The results were analyzed qualitatively and show that students struggled with remembering the procedure for solving absolute value equations and inequalities. The results also show that students were more successful when using the distance concept on a number line.

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