The development of a linear algebra schema: learning as result of the use of a cognitive theory and models

Learning is a complex phenomenon. Analyzing its development can provide knowledge about regularities and differences in students’ progress, which is needed to better understand learning. The aim of this study is to examine the development of students’ Linear Algebra Schema through an introductory one semester course. For that purpose, Action Process Object Schema (APOS) theory’s notions of Schema and Schema development were used to analyze students’ constructions at three different times throughout the course. Results show how students’ Schema are progressively constructed. They illustrate differences and commonalities in different students’ Schema development. Some concepts and factors were found to play an important role in promoting Schema development.