The relationship between multiple representations and thinking structures: example of the integral concept

In this study, the effect of teaching the concept of integral with multiple representations on the concept definitions of teacher candidates was examined. And also, the effect of teacher candidates ‘ thinking structures on their use of multiple representations was investigated. In this study, algebraic, graphical and numerical representations were used together in teaching the concept of integral at university level. Since the course content was designed by supporting multiple representations, a quasi-experimental research-experimental research design was used in the research. In this study, quasi-experimental research experimental research design was used because the course content was designed by supporting multiple representations. In this study, the study group consisted of secondary school mathematics teacher candidates. Within the scope of the research, Mathematical Process and Integral Concept Test were used. These scales were analyzed by quantitative and qualitative methods. Regardless of the thinking structures of the pre-service teachers, it has been determined that concept definitions include different representations depending on the teaching style supported by multiple representations in the course. It has been observed that the thinking structures of the pre-service teachers affect their representation preferences slightly, if not too much, while defining the concept. However, it has been determined that there are no sharp boundaries in the types of representation used by participants with different thinking structures. Even though the pre-service teachers had different thinking structures, they used multiple representations in their concept recognition. It can be concluded that this situation has a connection with the use of multiple representations in the lesson in addition to the thinking structures of the participants. It can be concluded that this situation has a connection with the use of multiple representations in the lesson in addition to the thinking structures of the participants. According to this result, the use of more than one representation in teaching a concept enables students to learn the concept in a versatile way. For this reason, it can be said that the use of multiple representations in teaching the concept of integral provides a higher level and deeper learning. This situation can be generalized to other concepts as well.