Investigation of the learning process of 7th grade secondary school students on themes of circle and circular region in a learning environment designed according to the hypothetical learning trajectory

The purpose of this research is to examine students' learning processes in the learning environment designed according to the hypothetical learning trajectory of circle and circular region topics in the seventh grade mathematics course curriculum. The research used the teaching experiment method, one of the qualitative research methods. The research began by identifying student insufficiency in preclinical interviews and was then completed over five weeks with teaching sessions and clinical interviews. The research participants were determined through criterion sampling, one of the purposive sampling methods, and was conducted with eight seventh grade students. To examine the teaching process in detail, three focal students were selected from students with low, medium, and high performance levels. Clinical interviews were conducted with the focal students after each teaching session to examine their learning processes in detail. Research data were obtained through video recordings of teaching sessions with students, clinical interviews with focal students, activity sheets, and student journals. Continuous and retrospective analyzes were performed on the data obtained during the research. In the findings resulting from the research, the deficiencies in the preliminary learning of the three focal students regarding the basic concepts of the circle were eliminated; The teaching process and clinical interviews based on the hypothetical learning trajectory contributed positively to the students. It has been observed that the study resulted in students learning meaningful formulas and rules instead of memorizing them, such as establishing a relationship between the central angle and the arc in a circle, calculating the length of a circle and a circle's segment and calculate the area of a circular region and circular regions's segment.