PROCEEDINGS OF THE 23RD ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2020
Boston, Massachusetts
Getting back to our cognitive roots: Calculus students’ understandings of graphical representation offunctions
Page: 942
The derivative is a cornerstone of the first-semester calculus course curriculum. The concepts of function, ratio, slope, variable, covariation, and rate of change are considered to be cognitive roots of the derivative (Larsen, Marrongelle, Bressoud, & Graham, 2017), and this report argues for explicit attention to student understandings of output of a function particularly when considering the derivative in the graphical context. I draw on the location-thinking and value-thinking constructs of David, Roh, and Sellers (2018) for describing students’ thinking about outputs of functions to connect student’s understanding of output to student’s conceptions of differences of outputs. Through a theoretical thematic analysis and a subsequent inductive thematic analysis of clinical interview data with calculus students (Braun & Clarke, 2006), I code the mathematical objects refer to when considering outputs of functions presented in graphical contexts. Codes and potential sources of variation in codes are presented.