Abstract
We use Action-Process-Object-Schema theory (APOS) to study the development of the differential calculus Schema for two-variable functions. This allows us to obtain information about students' constructions and also gives us information about the notion of Schema.
We performed semi-structured interviews with a group of eleven students that had completed an introductory multivariable calculus course. We use data from two students to exemplify the types of constructions observed.
To analyze the data, we use the Schema development triad and the notions of correspondence, transformation, and equivalence relations between Schema components. Our study contributes to a better understanding of these notions, how students relate differential calculus concepts, and how to support their learning and Schema development.