Task design in APOS Theory

Abstract

This paper discusses the role of task design in APOS Theory. The role played by the genetic decomposition in the theory and in task design is discussed. An example of a genetic decomposition for the concepts of inverse matrix transformation and inverse matrix is given. Tasks designed using this tool as a guide are exemplified as well as a description of their relationship to the genetic decomposition. In this way we provide insights about each task and the specific detailed construction it has as its aim. The role of the tasks in the classroom is discussed since the combination of collaborative work of students in sequences of tasks and in group discussions are the foundation of APOS Theory’s potential to promote essential constructions needed for a deep learning of mathematical concepts.

Keywords

• Task design
• APOS Theory
• inverse transformation
• inverse matrix