Sayre Wittmann on resource plasticity and coordinate systems

Eleanor C. Sayre, Michael C. Wittmann

Plasticity of intermediate mechanics students’ coordinate system choice
Phys. Rev. ST Phys. Educ. Res. 4, 020105 (2008)

We investigate the interplay between mathematics and physics resources in intermediate mechanics students. In the mechanics course, the selection and application of coordinate systems is a consistent thread. At the University of Maine, students often start the course with a strong preference to use Cartesian coordinates, in accordance with their prior physics and mathematics classes. In small-group interviews and in homework help sessions, we ask students to define a coordinate system and set up the equations of motion for a simple pendulum for which polar coordinates are more appropriate. We analyze video data from several encounters using a combination of Process/Object theory and Resource Theory. We find that students sometimes persist in using an inappropriate Cartesian system. Furthermore, students often derive (rather than recall) the details of the polar coordinate system, indicating that their knowledge is far from solid. To describe our work more precisely, we define a scale of plasticity and several heuristics for defining resources and their plasticity.