Middle school students' generalization process of quadrilaterals in dynamic mathematics software based environment

This research examines middle school students' generalization processes of quadrilaterals in a dynamic mathematics software-based environment. In this context, the environment where participants will question quadrilaterals and the relationships between them were supported by GeoGebra, and the processes were examined according to the generalization taxonomy. The research participants are nine students, three from each grade, studying in the 6th, 7th, and 8th grades, determined by the purposive sampling method, and with lower-intermediate, intermediate, and advanced mathematical academic achievements. The research was designed with a case study, one of the qualitative research methods. The research used GeoGebra activities and semi-structured interview forms as data collection tools. The first activity examined the realization situations of the relating stage of generalizing actions. The second activity examined the stages of searching and extending of generalizing actions, and the identification or statement, definition and influence of reflection generalizations. The data obtained from the transcripts of the audio and video recordings of each interview were analyzed descriptively. As the results of the research, in the 6th grade, the advanced participant showed all of the generalizing actions and 'descriptive' level of Van Hiele geometry thinking level; the intermediated participant showed 'visual' level and improvement at the 'descriptive' level of Van Hiele geometry thinking levels while performing the 'relating' and 'searching' stages of the generalizing actions; the lower intermediated participant showed 'visual' level and improvement at the 'descriptive' level of Van Hiele geometry thinking levels and only 'relating' stage of generalizing actions. In the 7th grade, the advanced participant showed all of the generalizing actions and the 'identification or explanation' stage of the reflection generalization, and 'descriptive' level and improvement at the 'informal deduction' level of Van Hiele geometry thinking levels; the intermediated participant showed the 'relating' and 'searching' stages of the generalizing actions, and 'descriptive' level of Van Hiele geometry thinking levels; the lower intermediated participant showed only 'relating' stage of generalizing actions and 'visual' level of Van Hiele geometry thinking levels. In the 8th grade, the advanced participant showed all of the generalizing actions and reflection generalization and 'formal logic' level of Van Hiele geometry thinking levels; the intermediated participant showed all of the generalizing actions and 'descriptive' level of Van Hiele geometry thinking levels; the lower intermediated participant showed the 'relating' and 'searching' stages of the generalizing actions and 'descriptive' level of Van Hiele geometry thinking levels. According to the research results, GeoGebra was quite effective in generalization and supported improving the Van Hiele geometry thinking levels. Suggestions were made for future research.