PROCEEDINGS OF THE 23RD ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2020
Boston, Massachusetts
Students’ interpretations of expressions from calculus statements in the graphical register
Page: 466
Graphs of real-valued functions figure prominently in the study of calculus. While the use of graphs in instruction has shown promise for supporting student thinking, previous research has also shown that students may interpret graphs in ways that differ from an instructor’s intention. This study aimed to investigate how students interpret expressions from calculus statements in the graphical register. To this end, I conducted 150-minute clinical interviews with 13 undergraduate mathematics students who had completed a calculus course. In the interviews, students evaluated six calculus statements for various real-valued functions depicted in graphs in the Cartesian coordinate system. I describe the characteristics of four distinct interpretations of expressions from these statements in the graphical register that students used in this study, which I refer to as (1) nominal, (2) ordinal, (3) cardinal, and (4) magnitude. I discuss some implications of these findings for teaching and directions for future research.