PROCEEDINGS OF THE 17TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2014
Denver, Colorado
Students’ Use of Parameters and Variables to Reason about Multivariable Functions
Page: 1128
The purpose of this paper is to characterize students’ ways of thinking about parameters and variables to reason about the behavior of multivariable functions. I focus on two single variable calculus students, Lisa and Carl, as they participated in a sequence of semi-structured exploratory teaching interviews intended to gain insight into 1) their approaches to reasoning about the behavior of single variable functions, and 2) what role those approaches played in their initial thinking about the behavior of functions of two, three and four variables. The interviews suggest that the students’ ability to move flexibly between thinking about a function’s variables as parameters allowed them to generalize their reasoning patterns about functions of n variables and extend that to functions of n+1 variables. I argue that their ability to parameterize functions allowed them to reason about functions for which they could not initially visualize representations.