PROCEEDINGS OF THE 15TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION (Vol 2)
2012
Portland, Oregon
Raising Students’ Calculus Understandings to the Surface in Multivariable Calculus
Page: 2-590
This presentation will share initial observations and data collected from a pilot classroom study in which groups of multivariable calculus students made physical measurements and drew actual curves on real, tangible surfaces to construct geometric mathematical objects fundamental to the course and discover their properties. Students completed short group activities focusing on relationships between functions and level curves, properties of gradient vectors and directional derivatives, and solutions to optimization problems before other symbolic representations or procedures were discussed in lecture. Initial self-reported data suggests working with the surfaces helped students visualize functions. It also appears the activities helped students develop strong connections between the geometric, symbolic, and verbal representations of multivariable calculus concepts. Collected data suggests the surfaces helped uncover students’ single variable misconceptions which hindered their new understandings. The goal of this presentation is to receive feedback for the design of a rigorous phase two study of this project.