Investigating University Students' Argumentations and Proofs Using Dynamic Mathematics Software in Collaborative Learning, Debate, and Self-Reflection Stages

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.