The Analysis of Pre-service Math Teachers’ Level of Understanding the Derivative Concept within the Context of APOS Theory

¹ Hacettepe University, Department of Mathematics and Science Education, Ankara, Türkiye
² Hacettepe University, Department of Mathematics and Science Education, Ankara, Türkiye

^* Corresponding author: selin.urhan@hacettepe.edu.tr

Abstract

APOS (Action-Process-Object-Schema) learning theory is the result of the studies of a mathematics education research group named Research in Undergraduate Mathematics Education Community (RUMEC), whose aim is to examine students’ level of comprehending university mathematics subjects. This study aimed to investigate how secondary mathematics education pre-service teachers in a public university structured the geometric dimension of the concept of derivative in their minds in the context of the components of the APOS theory. As data collection tools, questions developed by Çekmez [1] based on the genetic decomposition of Asiala, Dubinsky, Cottrill and Schwingendorf [2] for the geometric dimension of derivatives were used. The study revealed that secondary mathematics education pre-service teachers did not have the mental structures related to this topic and could not learn it at the desired level.