Argument schemes of high school students when using GeoGebra in the context of tessellations

This paper identifies and describes the arguments presented by a group of high school students when justifying their responses to geometric situations and using GeoGebra, a dynamic geometry software. The argumentation process showed to be deficient for the group of 15-18-year-old students from the Universidad Autonoma de Queretaro (UAQ) high school. Students were given a sequence of activities involving isometric transformations, in which they manipulated applets and created semi-regular tessellations using the GeoGebra software. The research was a descriptive case study. The epistemic configurations of the theoretical framework of the Ontosemiotic Approach to Mathematical knowledge and Instruction (OSA) were used for the analysis of the students' arguments, while argumentation schemes were used for the analysis of the results. These results suggest that, in the argumentation process, students resort to empirical and factual argumentation schemes, which was evidenced by the use of informal language and little mathematical language. In addition, the visual perception favored by the GeoGebra software was essential to develop the argumentation process, although it played the role of argument rather than a support to the process.