Investigation of mathematical thinking processes of gifted students in different environments: GeoGebra’s potential

Abstract

Mathematical thinking is a higher-order thinking style specific to mathematics that allows the solving of problems. In this context, it is inevitable to consider mathematical thinking in determining giftedness specific to mathematics. How superior mathematical thinking should be measured and the potential of different environments to elicit this mathematical thinking are a matter of debate. In this study, it was investigated how mathematical thinking in gifted students differed between using a paper and a pencil and using dynamic geometry software. Three gifted students’ solutions for given tasks in the paper-and-pencil and GeoGebra environments were compared within the scope of sub-dimensions (specializing, generalizing, conjecturing, and proving) of mathematical thinking. As a result of this study, the work undertaken by the students in the specializing step were seen to be similar in both the P&P and GeoGebra environments. On the other hand, it can be said that GeoGebra had the potential to reveal high-level work at the generalizing step. Different environments seemed to be important in revealing the ability to make assumptions. And it was seen that higher-order thinking skills for proof can be revealed with GeoGebra.