An examination of secondary school students' mathematical reasoning about triangles in the GeoGebra supported learning environment designed with the ACODESA method

This study aims to examine the structural and process aspects of the eighth-grade students' mathematical reasoning about triangles in a technology-enhanced collaborative learning environment and to reveal how these aspects support each other. The participants of this study are 12 eighth-grade students studying at a public school. The study was designed as a teaching experiment, which is one of the qualitative research methods. Mathematical tasks developed by the researcher, students' GeoGebra files, video and audio recordings captured during the research, researchers' field notes, and task-based interviews were used as data collection tools. Students' mathematical reasoning were analysed using the Toulmin's model and dialogical approach. The data analysis showed that the structural aspect of students' mathematical reasoning about triangles includes deductive, inductive and abductive; and also justifying, comparing, conjecturing, and generalizing components of the process aspect. On the other hand, it has been seen that comparing and justifying processes support deductive reasoning, conjecturing and exemplifying processes support abductive reasoning, and generalizing and identifying a pattern process support inductive reasoning. Based on the results, the technology-enhanced collaborative learning environment created using the ACODESA method and GeoGebra software allows students to generate ideas and claims about triangles, make explanations and validations, recognize mathematical relationships and invariances, reach the correct conclusions and discover formulas; therefore, it has been concluded that these processes allow students to reasoning. In summary, it allows the students to perform reasoning. In line with these results, it is recommended to use the technology-enhanced collaborative learning environments to support the process and structural aspects of students' mathematical reasoning. Keywords: ACODESA method, Dialogical approach, GeoGebra, Mathematical reasoning, Toulmin's model, Triangles