RUME 27
2025
Alexandria, Virginia
Using Schemas to Model in APOS: The Case of the Differential Calculus of Two-Variable Functions
Page: 18
In this report, we use the Schema portion of Action-Process-Object-Schema (APOS) theory to frame a study of student understanding of the differential calculus of two-variable functions. The use of Schemas allows us to obtain a more holistic perspective of students’ understanding. Data was obtained from semi-structured interviews with eleven students. We argue that the APO portion of the theory can give detailed information about specific Schema components but that it does not inform about the interrelations between the different components. However, the notion of Schema and its instrumentalization via the notions of genetic decomposition, types of relations between components, and the triad stages of Schema development can provide a more comprehensive picture encompassing the different components of the differential calculus Schema. The notions of the scope of an instrument and the graph of a Schema are introduced to afford a visual representation of a student’s Schema.