Investigation of seventh grade students' mathematical reasoning on polygons through Geogebra enhanced Acodesa method

The object of this study is to examine 7th grade secondary school students' mathematical reasoning on polygons in an environment supported by GeoGebra enhanced ACODESA method. Nine 7th grade secondary school students form the participants of this study that is conducted adopting ethnographic case study which is one of qualitative research methods. As data collection tools, mathematical tasks that are designed for 7th grade polygon concept, video and audio recordings, GeoGebra files, researcher's notes are used. Before implementation of this study, 5 weeks GeoGebra lectures were given to students and the implementation process was lasted during 6 weeks by using mathematical tasks once in a week. Mathematical tasks are implemented using ACODESA method's stages (individual work, teamwork, debate, self-reflection and institutionalization) in a learning environment supported by social interaction and dynamic mathematics software. Students mathematical reasoning are analyzed through dialogic approach and Toulmin's scheme of argumentation by transcribed video and audio recordings. As mathematical reasoning framework in data analysis, a conceptual model of mathematical reasoning for school mathematics improved by Jeannotte and Kieran is adopted. On the results obtained from this study, structural aspects of students mathematical reasoning are characterized by deductive, inductive and abductive structures. As for the process aspect of students mathematical reasoning process; comparing, classifying, generalizing and justifying processes come out. Nevertheless, in this study, which was analyzed according to the conceptual model of mathematical reasoning improved by Jeannotte and Kieran, proof and formal proof processes did not emerge. In collaborative environment, students' performance created in both individual and collaborative stages, and their claims and warrants inferred in teamwork and scientific debate contribute team's or class's collective reasoning. The learning environment supported by GeoGebra and ACODESA method reinforces coming out students' mathematical reasoning both structural and process aspects. It can be recommended to use dynamic mathematics software such as GeoGebra in learning environments for the observation and development of students' reasoning. ix Keywords: ACODESA, Dialogical approach, GeoGebra, Mathematical reasoning, Polygons, Toulmin's model