PROCEEDINGS OF THE 20TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2017
San Diego, California
Physics students’ use of symbolic forms when constructing differential elements in multivariable coordinatesystems
Page: 895
Analysis of properties of physical quantities represented by vector fields often involves symmetries and spatial relationships that are best expressed in three dimensional non-Cartesian coordinate systems. Many important quantities, both scalar and vector in nature, are determined by paths, areas, or volume integrals of multivariable functions. The differential quantities in these systems are not trivial for students to understand and implement correctly. As part of an effort to investigate physics students’ understanding of the structure of non-Cartesian coordinate systems and the associated differential elements when using vector calculus in Electricity and Magnetism (E&M), we interviewed four pairs of students in the junior-level E&M course. In one particular task, students were asked to construct differential length elements for an unconventional spherical coordinate system. A symbolic forms analysis (Sherin, 2001) of student reasoning revealed both known and novel forms, and found that student difficulties with vector differential quantities were primarily conceptual rather than symbolic.