Proof schemes used by 7 th grade students on geometry subjects in an a-didactic environment

The purpose of this study is to examine the proofs that middle school 7th grade students have revealed against the problem situations they encounter in the context of middle school mathematics lessons determined in an a-didactic classroom environment designed in accordance with the didactic situations theory according to Harel and Sowder's proof schemes. In our study, the processes of proving the problem situations of the groups and their experiences in these processes were examined according to the stages of the didactic states theory and the proofs they put forward have been tried to be placed in the proof schemes. In this study case-study approach ,one of the qualitative research techniques, was used. The data obtained with the case study approach were analyzed with the descriptive analysis technique. The research was carried out in the 2018-2019 academic year in a middle school in the center of Boyabat county of Sinop. Sixteen people, 7th grade student, attended in the research. The research was continued for four weeks and each group was recorded seperately. At the end of each week's doing practice students' worksheets were collected as data collection tools. After the activities, activity papers were examined and semi-structured interviews were conducted with some students in order to understand more detail about what students think how about their problem situations. As a result of the study, it was seen that the nature of the didactic environment provided contribution positively to the proof-making processes. Looking at the resulting proof schemes, a total of seventeen proof schemes belonging to four problem situations were put forward by the students. Of these seventeen evidence schemes, % 41 are authoritarian proof schemes, %24 are perceptual proof schemes, %24 are convertible proof schemes and %11 are habitual proof schemes. The symbolic proof scheme, sample-based proof scheme, and axiomatic proof scheme didn't appear when proving problem situations. In their proofs, the groups failed in % 53 of the proof schemes used, succeeded in % 30 and partially succeeded in %17. KEYWORDS: Theory of didactical situations, proof schemes, learning environments