PROCEEDINGS OF THE 15TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION (Vol 2)
2012
Portland, Oregon
Two-Variable Functions: Novice and Expert Shape Thinking
Page: 2-261
This study describes two first-semester calculus students’ understandings of functions of two variables in a teaching experiment that focused on thinking about function as the simultaneous variation of quantities. The students’ actions, responses, and construction of graphs revealed that one student thought about graphs as a malleable wire and another student considered graphs as the result of tracking the values of covarying quantities, which I characterize as novice and expert shape thinking. In this talk, I outline importance of understanding students’ ways of thinking about functions of more than one variable, the methodology used to collect and analyze data. I conclude by discussing the implications of thinking about graphical representation of functions using novice and expert shape thinking.