INTERNATIONAL JOURNAL OF MATHEMATICAL EDUCATION IN SCIENCE AND TECHNOLOGY, vol.54, no.1, pp.99-123, 2023 (ESCI)
The purpose of this study is to examine secondary school students' mathematical reasoning about the area of the circle. Mathematical tasks designed using GeoGebra were performed within the context of the 5E-based flipped classroom approach. The participants of the study are 13 secondary school students. The tasks, video and audio recordings captured during implementations, students' GeoGebra files, and researchers' field notes were used as data collection tools. The structural aspect of students' mathematical reasoning was analyzed with Toulmin's model, and the process aspect of mathematical reasoning was analyzed with the dialogical approach. The data analysis revealed that students' mathematical reasoning involved three types of reasoning (deductive, inductive, and abductive) in terms of the structural aspect. As for the process aspect, the mathematical reasoning of the students involved the processes of generalizing, justifying, comparing, and exemplifying.