Students’ use of symbolic forms when constructing equations of boundary conditions

Abstract

In an effort to examine students’ understanding about the structure of boundary conditions in upper-division courses, think-aloud interviews were conducted in the context of both quantum mechanics and electricity and magnetism. In the quantum mechanics task, students were presented with a standard potential step scenario. In the electricity and magnetism task, students were given a classical question about electromagnetic waves at the boundary of two media. The analysis of the interviews was guided by the use of a symbolic forms perspective. In this paper, we report the symbolic forms identified in students’ work and provide examples of students’ reasoning. Generally speaking, students were able to generate the correct symbolic templates while having difficulties with the underlying conceptual ideas. We also discuss instructional implications from this study.