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    Students' mathematical reasoning on the area of the circle: 5E-based flipped classroom approach
    (Taylor & Francis Ltd, 2023) Demir, Mehmet; Zengin, Yilmaz; Ozcan, Sule; Urhan, Selin; Aksu, Nazli
    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.
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    Teachers' Use of Rational Questioning to Support Students' Collective Argumentation Through 5E-Based Flipped Classroom Approach Using GeoGebra
    (Springer, 2024) Ozcan, Sule; Zengin, Yilmaz
    The purpose of this study was to investigate how teachers' rational questioning strategies support students' collective argumentations in the 5E-based flipped classroom approach using GeoGebra. The participants of this study were 18 seventh-grade students. Technology-enhanced tasks, audio recordings, and dynamic constructions of the participants were used as data collection tools. The analysis of the qualitative data was based on the teacher rational questioning framework and Toulmin's model. The results indicate that in the 5E-based flipped classroom approach using GeoGebra, the teacher's rational questioning regarding the area of the circle encompasses epistemic, teleological, and communicative components (by Habermas' lens). Teacher's questions including different rationality components (epistemic, teleological, and communicative) encourage students to contribute to various elements of reasoning (e.g., generalizing and justifying) and thus support collective argumentation in mathematics classrooms. In the teachers' rational questionings through the 5E-based flipped classrooms using GeoGebra, the students created productive arguments using different representations for the area of the circle in their collective argumentations.