Student difficulties with boundary conditions in the context of electromagnetic waves

Abstract

Identifying and understanding student difficulties with physics content in a wide variety of topical areas is an active research area within the physics education research community. Of particular value are investigations of physics topics that appear multiple times in different contexts across the undergraduate physics curriculum. As these common topics reappear, students' difficulties can perpetuate from one context to the next, or new difficulties can emerge as students encounter new physical contexts. One example of such a topic is boundary conditions, which is broadly considered to be an important topic that advanced physics undergraduates are expected to understand and apply in multiple topical areas including classical mechanics, quantum mechanics, and throughout electricity and magnetism. We report findings from an investigation of student difficulties using boundary conditions while focusing on the context of electromagnetic waves. Our data sources include student responses to traditional exam questions, conceptual survey questions, and thinkaloud interviews. The analysis was guided by an analytical framework that characterizes how students activate, construct, execute, and reflect on boundary conditions during physics problem solving. Commonly observed student difficulties include activating boundary conditions in appropriate contexts, constructing a complex expression for the electromagnetic waves, mathematically simplifying and manipulating complex exponentials, and checking if the reflection and transmission coefficients are physical. We also present potential pedagogical implications based on our observations.

Reworking exam problems to incentivize improved performance in upper-division electrodynamics

“…The presented research represents a portion of a planned analytical framework to further understand students within upper-division electromagnetism [11]. First, qualitative data from interviews using think-aloud protocol of students who have finished the EM 1 course sections will identify expert-like vs. novice-like approaches to learning problem solving within the presented course structure, as has been previously done with quantum mechanics [1,9], and seeking evidence of issues noted in recent literature for this course [12].…”

Undergraduate students' difficulties with boundary conditions for the diffusion equation

“…However, a growing body of research suggests that intermediate and upper-division students continue to struggle with reasoning and problem solving even in the advanced physics courses (e.g. Caballero et al, 2015;Ryan et al, 2018). Student difficulties in upper-division problem solving originate, in part, from the more complicated math and more sophisticated physics characteristic of upper-division content.…”

“…However, difficulties in the upper-division might also relate to the cyclic nature of the physics curriculum, in which some physics topics appear several times in different contexts across the undergraduate curriculum (Manogue et al, 2001;Zwolak & Manogue, 2015). Ryan et al (2018) state that for these recurring topics, difficulties that are not addressed in early courses can persist, and become worse, when the topic appears again in a more advanced course.…”

“…Specifically, we focus on the mathematical description of boundary conditions (hereafter BCs) for phenomena described by the diffusion equation. Generally, BCs appear several times throughout the physics and mathematics undergraduate curriculum (Ryan et al, 2018), which make them interesting for investigating difficulties as these can persist in other contexts later on in the curriculum. BCs define the conditions physical quantities must satisfy at the boundary between two regions.…”

“…There is not a lot of research on student reasoning or difficulties in the context of PDEs in general, and, as far as we know, none in the context of the diffusion equation. Ryan et al (2018) recently investigated student difficulties with BCs in the context of electromagnetic waves . Their data sources were student responses to traditional exam questions, conceptual survey questions, and think-aloud interviews.…”