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

Abstract

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.