PROCEEDINGS OF THE 19TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2016
Pittsburgh, Pennsylvania
Physics students’ construction and use of differential elements in an unconventional spherical coordinatesystem
Page: 397
As part of an effort to examine students’ understanding of non-Cartesian coordinate systems when using vector calculus in the physics topics of electricity and magnetism, we interviewed four pairs of students. In one task, developed to compel students to be explicit about the components of specific coordinate systems, students constructed differential length and volume elements for an unconventional spherical coordinate system. While all pairs eventually arrived at the correct elements, some unsuccessfully attempted to reason through spherical or Cartesian coordinates, but recognized the error when checking their work. Analysis of student work identified actions and aspects of students' concept images when constructing differential vector elements. Findings suggest that attention to multiple components and dimensionality were useful aspects of students’ concept image, while students had difficulty appropriately applying the idea of projection.