Abstract
This study uses Action-Process-Object-Schema theory (APOS) to examine students' understanding of optimization of two-variable functions. We propose a genetic decomposition (GD) model of Schema components and relations between components, that students may construct to understand the optimization of these functions.
The GD was tested by performing semi-structured interviews with 22 students. The results suggest that students' struggles are mainly related to the topology of domain sets and those relations which help to understand the scope and limitations of some of the theorems commonly applied to solve optimization problems.
The study also contributes to a better understanding of the APOS notions of Schema and types of relations between Schema components and their use to model students' mental constructions.