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Graphs of real-valued functions figure prominently in the study of calculus as a means of illustrating key definitions, theorems, and results. While the use of graphs in instruction has shown promise for supporting students’ understanding of calculus, previous research has also shown that students may interpret graphs in ways that differ from an instructor’s intention. In this talk, I will share results from a study investigating how students interpret expressions from calculus statements on graphs of functions. I conducted 150-minute clinical interviews with 13 undergraduate mathematics students who had completed at least one calculus course. In the interviews, students evaluated six calculus statements for various real-valued functions depicted in graphs in the Cartesian coordinate system. In analyzing students’ responses to these tasks, variations in students’ graphical interpretations emerged. I describe the characteristics of four distinct interpretations of expressions from these statements on graphs that students used in this study, which I refer to as (1) nominal, (2) ordinal, (3) cardinal, and (4) magnitude. In some contexts, some of these interpretations supported students in correctly evaluating the given statements, while other interpretations created obstacles for students. I will also discuss some implications of these findings for teaching and directions for future research.
Bio: Dr. Erika David Parr is a Visiting Assistant Professor at Rhodes College where she teaches calculus courses. Erika earned her PhD in Mathematics Education and MA in Mathematics at Arizona State University in 2019 where she taught mathematics and mathematics education courses. Her research focuses on how students understand the representations of mathematical ideas, including undergraduate students' interpretations of graphs.