Pre-service Teachers’ Mathematical Content Knowledge and Perceptions on Justification of the Differentiation of the Exponential Function

The purpose of this paper is to examine pre-service teachers' mathematical content knowledge and perceptions regarding the justification of the differentiation of the exponential function in relation to the connection between school mathematics and university mathematics. We analyzed and categorized how pre-service teachers justified the differentiation of the exponential function through semi-structured interviews, examined whether the gaps in the learning trajectory in school mathematics were rigorously addressed, and surveyed their perceptions about these gaps. This study revealed that the justification methods of pre-service teachers could be categorized into seven types, and they had difficulty rigorously addressing the gaps. Many pre-service teachers were unaware of the gaps in the learning trajectory and agreed on the need for consistent learning trajectories between school and university mathematics. This study highlights the need to improve pre-service teacher education by examining the mathematical content knowledge required for mathematics teachers in connection to school mathematics.