Learning challenges in the interplay between physics and mathematics
- the case of the 1-D wave equation
PhD defence 
Doctoral candidate
Abstract
Physics equations are essential components for explaining numerous physical phenomena in the form of mathematical terms. However, the presence of mathematics in physics poses many challenges, both in differentiating their roles and in combining both fields. While numerous studies investigate students' perspectives about physics equations, few propose methods for understanding these equations. This thesis aims to fill this gap by investigating students' epistemological framing and learning difficulties when they attempt to make sense of a physics equation, in this case, the 1-D wave equation (WE), from several aspects. Two studies in this thesis employ a qualitative research method consisting of three steps: exploration, intervention, and evaluation. The first study explores students' understanding of the graphical representation of y(x,t)=f(x±vt), where students are presented with a non-periodical wave profile of y(x) and asked to find the velocity of points on the profile. This task requires them to consider the time dimension in their analysis. The results highlight the significant challenges students face and reveal the various difficulties encountered. The second study aims to explore students' epistemological framing of the WE from various aspects through a questionnaire comprising five questions. The findings indicate that students' responses lack physical meaning and their reasoning is not aligned with those of experts. The interventions are then designed to help students better understand the problems identified in these studies. While some students improve after the interventions, a few persist with their reasoning, indicating they hold robust beliefs about the subject matter. Finally, the third study seeks to uncover the complexity of the WE by highlighting conceptual subtleties that often go unnoticed in teaching the WE.
Download the thesis: Learning challenges in the interplay between physics and mathematics: the case of the 1-D wave equation (pdf).
Chair of defence
Assoc. Prof. Henriette Holmegaard (Department of Science Education, University of Copenhagen)
Assessment committee
Assoc. Prof. Jesper Bruun (Department of Science Education, University of Copenhagen)
Prof. Paula Heron (Department of Physics, University of Washington)
Prof. Mieke De Cock (Department of Physics and Astronomy, Katholieke Universiteit Leuven)
Supervisor(s)
Assoc. Prof. Ricardo Karam (Department of Science Education, University of Copenhagen)
Assoc. Prof. Christian Joas (Department of Science Education, University of Copenhagen)
Place: Universitetsparken 5, HCØ, auditorium 05, 2100 København Ø - or you can join the defence via zoom: https://ucph-ku.zoom.us/j/63579201524?pwd=WUFBWTRZNHZnT1JJNVZ5VTZiUC8rQT09