Examining the process of creating Pythagorean relationships of 8th grade students according to the RBC+C model

Purpose: In this study, it was aimed to examine the processes of creating Pythagorean Theorem knowledge of 8th grade students, who have subjects that require abstract thinking, by using the RBC + C abstraction model. Method: The case study approach, one of the qualitative research methods, was used in the study. The study group was selected from 8th grade students in a secondary school in the central district of Çanakkale. According to the results of the preliminary knowledge level determination test, the research was conducted with six students in three groups with upper-middle, middle-middle and low-low levels. Before starting to work with these students, a pilot study was conducted with two students with high and inter-mediate levels of prior knowledge. The data in the research consists of data obtained through activities with student answers, observation, researcher diaries and video recordings. The students' knowledge creation processes were tabulated by examining their answers to the activities. In the observation part of the research, the implementation process of the activities was recorded by the researcher and student comments and behaviors were recorded. The-se activities were created by the researcher to help students reveal their knowledge of the Pythagorean relation. The questions in the activity were examined by 3 experts in the field and the necessary corrections were made and presented to the students. A level determina-tion test was applied before the application to measure readiness levels. Research data were collected through five activities related to the subject specified in the problem statement, at a time appropriate to the research calendar, in a sufficiently large study room within the school, with students working in groups of two. In the study, an intertwined single case design, one of the qualitative research designs, and content analysis, one of the qualitative data analyses, were used. Results: When the epistemic actions of students with a high-medium prior knowledge level in the activities were compared with other students, it was seen that stu-dents with a low prior knowledge level performed more creation and reinforcement acti-ons. The difficulties experienced by students in using materials in general caused the dura-tion of the activity to be extended. In teaching the Pythagorean Theorem, it took time for students with lack of prior knowledge to give the expected answers to the activities. There were differences in the levels of students at the same prior knowledge level in reaching the RBC+C steps. Conclusion and Suggestions: In order for 8th grade students to be able to create the Pythagorean Relation with the activities in the study, they must have acquired knowledge on subjects such as square root expressions, algebraic expressions, triangle and area of the square. When students' abstraction processes were examined in the activi-ties, it was seen that a subject that had not been learned before could be discovered by students if their prior knowledge was sufficient. In order to eliminate the difficulties experienced in operations with geometric sha-pes, it may be suggested that the achievements in this field should be given as a separate course at earlier stages and the use of materials in mathematics courses should be increa-sed. Keywords: Pythagorean Theorem, RBC+C Model, Abstraction