No abstract

In upper division physics courses students are required to work with various coordinate systems. This skill becomes particularly important when learning Electricity and Magnetism, where the most appropriate coordinate system will often depend on the geometry and symmetry of a problem. This study aims to identify and describe "resources" used by students when answering physics questions regarding unit vectors in non-Cartesian coordinate systems, specifically polar coordinates [1]. Data were collected in the form of written responses and interviews in upper division physics courses at two universities. After deeper analysis we identified several resources that students use in ways that can be productive and unproductive.

The Classroom Observation Protocol for Undergraduate STEM (COPUS) instructional styles reliably distinguish between frequency patterns of classroom behaviors, but do not readily discern differences in formative assessment and feedback. Given the positive relationship between formative assessment and student learning, this study highlights the limitations of the COPUS in documenting the results of STEM reform.

An essential skill for success in upper-division physics curricula is the ability to work with and apply mathematical and physical concepts through Cartesian and non-Cartesian coordinate systems. These skills are most notably necessary in electricity and magnetism, wherein students must build and solve integrals and perform vector derivatives in Cartesian, spherical, and cylindrical coordinate systems. While limited in scope, early investigations into students understanding of coordinate systems has shown that students have considerable difficulty. Through the analysis of four one-on-one semistructured interviews, students were observed to activate numerous productive resources, despite frequently incorrect answers. This paper will revisit our previously identified student resource clusters for unit vectors. We also identify additional resources that cast additional light on students' thinking about position vectors, and velocity vectors in non-Cartesian coordinate systems. Through detailed analysis of a single student, we identify several groupings of resources that will serve as a baseline for future analysis of additional students and provide initial insight into potential curriculum development.