2021 Research in Undergraduate Mathematics Education Reports
2021
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Conceptualizing and Representing Distance on Graphs in Calculus: The Case of Todd
Page: 214
Numerous calculus concepts rely on the ability to conceive of and represent distances in the Cartesian plane. Yet, research has found that undergraduate students, even those who have studied calculus, may not readily do so (Parr, 2020). This study reports on findings from the development of a hypothetical learning trajectory aimed at supporting students in representing distance in the Cartesian plane. We hypothesized that this skill would require (a) the ability to represent a distance on a number line as a difference and (b) drawing on the Cartesian connection to represent a horizontal or vertical distance in terms of x and in terms of y. We analyze the types of reasoning used by a Calculus I student while working on these tasks, as well as obstacles she faced relative to these two target understandings.