PROCEEDINGS OF THE 21ST ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2018
San Diego, California
Peter’s Evoked Concept Images for Absolute Value Inequalities in Calculus Contexts
Page: 949
Statements involving absolute value inequalities, such as the definition of continuity at a point, abound in Advanced Calculus. In textbooks, such statements are frequently illustrated with graphical representations. Despite their abundance, how students think about absolute value inequalities and their representations in these contexts is not widely known. This study examines one undergraduate mathematics student’s evoked concept images (Tall & Vinner, 1981) for absolute value inequalities in various contexts, including those from Advanced Calculus. The student’s evoked concept image differed based on the context of the statements involving absolute value inequalities. Notably, the student’s evoked concept image did not support his understanding of the visual representation of the formal definition of continuity. The results of this study suggest that some students may not conceive of absolute value inequalities in ways that are productive for understanding the formal definitions of Advanced Calculus concepts.