Continuity: The relation between concept image and procedural understanding

The current study aims to examine the relation between concept images and procedural understanding of prospective Mathematics teachers (PMTs) related to 'continuity' in Math. The participants (n=9) study Mathematics Education at a state university during spring 2018; they are third, fourth and fifth grade students. The data come from interviews and open-ended tests developed by the researchers. More specifically, the data of concept images were collected through interviews and the data of procedural understanding were gathered via open-ended tests. The methodological approach used in the current study is descriptive analysis. The results of the study revealed that in addition to the presence of the PMTs whose understanding of concept images and procedural understanding are in accordance with each other, there are those whose understanding of these two concepts are not compatible with each other. Moreover, it has been observed that while PMTs who hold a concordant understanding between concept image and procedural understanding tend to express the concept of 'continuity' as rooted in their images, PMTs who have an incompatible understanding between these two concepts tend to provide formal definitions for the notion of 'continuity', as different from their own images.