Pre-service Mathematics Teachers’ Modes of Thinking in Linear Algebra: The Case of Linear Transformation

The aim of this research was to determine the modes of thinking that pre-service mathematics teachers’ employ to solve problems related to the concept of linear transformation in linear algebra. A study was conducted with 22 pre-service mathematics teachers’ using the case study method - a qualitative research method. The data of the research were collected through four problems defined in the context of the “definition of linear transformation” and “matrix representation of linear transformation”. 10 codes were created upon the descriptive analysis of the data collected, and those codes were classified in the context of Sierpinska’s (2000) theoretical framework modes of thinking (analytical-structural, analytical-arithmetic, synthetic-geometric). According to the study, pre-service mathematics teachers’ had different modes of thinking in “definition” and “matrix representation” but they could not switch between modes of thinking. It was found that analytical-arithmetic thinking was more common than analytical-structural and synthetic-geometric thinking throughout the study. The concept of linear transformation could not be internalized with all its components and it was a challenging process for pre-service teachers’ to switch to the matrix representation of linear transformation.