Investigation of the Concept Images of Mathematics Educators and Preservice Mathematics Teachers Regarding Slope, Rate of Change, and Derivative

The aim of this study is to examine the concept images of mathematics educators and pre-service elementary mathematics teachers regarding the relationships between the concepts of slope, rate of change and derivative. Four mathematics educators working in different state universities and responsible for Analysis courses, three pre-service elementary mathematics teachers who successfully completed the Calculus 1 course at a state university, and four pre-service elementary mathematics teachers who successfully completed the Calculus 1 and Calculus 2 courses participated in the study. In order to determine the concept images of the participants about the concepts of slope, rate of change and derivative, the participants were asked semi-structured interview questions prepared by the researcher and application questions including the second stage questions. The audio recordings obtained from the interviews were transcribed and then the second stage questions were applied to the participants. The second stage questions were received in writing from the participants and analysed by the researcher through descriptive content analysis. As a result of this study, mathematics educators were able to use the concept images they had in the first stage questions in the second stage questions. On the other hand, pre-service elementary mathematics teachers were able to use the concept images they had in the first stage questions in the second stage questions.