Yazar "Urhan, Selin" seçeneğine göre listele

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    Investigating University Students’ argumentations and proofs using dynamic mathematics software in collaborative learning, debate, and self?reflection stages
    (Springer Nature, 2023) Urhan, Selin; Zengin, Yılmaz
    The purpose of this study is to examine the performances of university students’ using dynamic mathematics software GeoGebra in argumentations and proving processes. A task related to the limit involving sinx/x was designed and 18 university students worked on the task during the collaborative learning, scientific debate, and self-reflection stages. Students’ argumentations and proofs were analyzed based on Toulmin’s model and Habermas’ construct of rationality. The results revealed that the rationality components can be used to explain the implicit features of warrant in Toulmin’s model. It was found that the semiotic mediation opportunities offered by GeoGebra and the teamwork and debate stages in the teaching method enabled the students to create geometrically the ranking relation between the value of an angle and the sine and tangent values of this angle. They also facilitated using the various kinds of representation and enhanced the transformations within and/or between the representations. GeoGebra tools as instruments of semiotic mediation helped the students to construct productive arguments, validate them, be productive by providing backing and rebuttal to the collective arguments put forward during the teamwork stage, and reach consensus thanks to scientific debate.
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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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    Students' Proof Construction through Computer-Supported Collaborative Learning: The Perspectives of Habermas' Theory of Rationality and Duval's Theory of Registers of Semiotic Representation
    (Springer, 2024) Urhan, Selin; Zengin, Yilmaz
    This study aims to examine how students' performance in constructing and transforming representations during the proving of calculus rules unfolds in a computer-supported collaborative learning (CSCL) environment, within the context of rationality. The CSCL environment was designed by integrating the ACODESA method and dynamic mathematics software GeoGebra. The participants included 18 university students. The proofs and GeoGebra files of the participants and transcripts of arguments during the GeoGebra-integrated collaborative phases of ACODESA were analyzed based on Habermas' theory of rationality and Duval's theory of registers of semiotic representation. The students improved their proof in building a geometric representation (e.g., drawing a secant line on a constant function graph), and in the treatment within the algebraic register (e.g., during the expansion of (x+h)n)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${(x+h)}<^>{n})$$\end{document} in the context of epistemic rationality. They developed their proof in the conversion (e.g., drawing a secant line in the geometric register and hence obtaining algebraic representation of the derivative function) in the context of teleological rationality. The students provided more understandable proofs due to their improvement in the context of communicative rationality. The difficulties experienced by the students in building representations, treatment, and conversion could be analyzed with the combined application of Duval's theory of registers of semiotic representation and Habermas' theory of rationality. Based on the results of the study, it is suggested to design GeoGebra-integrated CSCL environments to support students' performance in constructing and transforming representations within the context of being rational during the teaching of proofs related to calculus concepts.