Mathematical thinking processes for the pythagorean theorem of the secondary school students

In this study, mathematical thinking processes on geometry of 6th, 7th and 8th grade students who have the same geometric thinking levels were examined. Two students from each grade level were selected for the study. The geometric thinking levels of the students were determined as the third level. In addition, the algebraic thinking levels of the students were discussed. The three worlds of mathematics was used in the research. The mathematical thinking processes of the students were examined in terms of the embodied world, the proceptual world and the formal world. The Pythagorean Theorem was chosen as the geometry subject. Two-stage semi-structured interviews were conducted with the students. In the first part of the interviews, the verbal expression of the Pythagorean Theorem was directed to the students. In the second part, an activity was presented for them to discover the theorem in a real-life situation. As a result, while the students had difficulty in explaining the theorem in the verbal expression, they were able to express it more easily in a real-life situation. 7th and 8th grade students were more successful than 6th grade students in demonstrating the processes of the three worlds of mathematics.