arXiv subjects

Paul van Kampen

Publications and source records attributed to Paul van Kampen.

3 recordsLinked to original sources

arXiv2026

Students' understanding of the 2D Heat Equation: An APOS approach

In this paper, we use the APOS theoretical framework to validate a hypothetical learning trajectory of the 2D heat equation, a preliminary genetic decomposition that stresses the conceptual understanding of its mathematical formulation. We design questions to probe specific mental constructions of the preliminary genetic decomposition. We interview 8 students in the second year of the B.Sc. enrolled in either engineering, physics or twin (mathematics and physics) majors. Our findings indicate that students engage with many predicted mental constructions. In particular, coordination and encapsulation of two process conceptions of the Laplacian of the temperature improve understanding although it is challenging. Other parts of the genetic decomposition require refinements. These include mental constructions related to the temperature distribution function, heat flow, and the temperature gradient.

physics.ed-ph↗

arXiv2015

Student thinking about the divergence and curl in mathematics and physics contexts

Undergraduate physics students are known to have difficulties with understanding mathematical tools, and with applying their knowledge of mathematics to physical contexts. Using survey statements based on student interviews and written responses to open-ended questions, we investigated the prevalence of correct and incorrect conceptions regarding the divergence and curl of vector fields, among both mathematics and physics students. We compare and contrast pre-instruction responses from intermediate-level E&M students at KU Leuven and the University of St Andrews, with post-instruction responses from St Andrews students enrolled in a vector calculus course. The differences between these student populations were primarily in areas having to do with physics-related concepts and graphical representations of vector fields. Our comparison of pre- and post-instruction responses from E&M students shows that their understanding of the divergence and curl improved significantly in most areas, though not as much as would be desired.

physics.ed-ph↗

arXiv2015

Students' difficulties with vector calculus in electrodynamics

Understanding Maxwell's equations in differential form is of great importance when studying the electrodynamic phenomena discussed in advanced electromagnetism courses. It is therefore necessary that students master the use of vector calculus in physical situations. In this light we investigated the difficulties second year students at KU Leuven encounter with the divergence and curl of a vector field in mathematical and physical contexts. We have found that they are quite skilled at doing calculations, but struggle with interpreting graphical representations of vector fields and applying vector calculus to physical situations. We have found strong indications that traditional instruction is not sufficient for our students to fully understand the meaning and power of Maxwell's equations in electrodynamics.

physics.ed-ph↗