Extending the action, process, object, schema theory to physics education: A genetic decomposition of the two-dimensional heat equation

In this paper, we describe our extension of the action, process, object, schema (APOS) theory to capture the complex interplay of mathematics and physics. We do this in the context of the 2D heat equation. We describe a hypothetical learning trajectory of the 2D heat equation, a preliminary genetic decomposition that stresses the conceptual understanding of its mathematical formulation. In our extension of APOS to physics education, we highlight how our approach precisely captures the interplay between mathematics and physics in different mental constructions of the framework. In addition to this core focus, we consider other layers when designing the preliminary genetic decomposition: the key concepts and the necessary depth of students’ prerequisite knowledge of the chosen context, the challenges students commonly face with these concepts, and the use of multiple external representations. We conclude by giving an overview of future research to be done after the design of the preliminary genetic decomposition.