Investigation of the concept images of mathematics educators and preservice mathematics teachers about slope, rate of change and derivative

This research study aims to examine the concept images of mathematics educators and pre-service primary school mathematics teachers about the concepts of slope, rate of change and derivative, and their concept images regarding the relations between these concepts. The research employed the holistic multiple case study design. Four mathematics educators who work in different state universities teaching Calculus (1,2,3) courses, and three pre-service teachers who successfully completed the Calculus1 course in the first year of a state university, and four pre-service primary school mathematics teachers who successfully completed the Calculus1 and Calculus 2 courses in the second year participated in the study. The participants were selected through the purposive sampling method. To determine the participants' concept images about the slope, rate of change and derivative concepts, the participants were asked semi-structured interview questions, which were the first-stage questions prepared by the researcher, and practice questions including the second-stage questions. After the participants' recorded responses to first-stage questions were transcribed, the second stage questions were applied to the participants. The participants responded to the second stage questions in written form and the researcher analyzed the data through descriptive content analysis. In each case, the data were analyzed using the analysis framework determined by the researcher based on the literature, and codes for the study were created. A different expert also coded the data, and the percentage of agreement was determined as .82. The study revealed that mathematics educators were able to use the concept images they had in the first stage questions also in the second stage questions. On the other hand, pre-service primary school mathematics teachers were able to use the concept images they had in the first stage questions also in the second stage questions, but it was concluded that they used more concept images in the latter stage. Since the questions in the practice questions were answered in written form, it was seen that they used different forms of representation, and it was valid for both participant groups. The formal definition of the concepts in the first stage questions did not overlap with the concept image cells, but this situation differed in the practice questions.