Investigation of secondary school students' concept images and proof schemes about perimeter and area

The aim of this research is to investigate how the concept images and proof schemes of secondary school (5th, 6th, 7th and 8th grade) students about perimeter and area change with the applied teaching episodes. In order to determine the participants of the research, a written assessment tool was applied to 170 students studying in a secondary school. After examining the answers of the students, a total of eight students, two from each grade level, were determined as participants. The data of the research consists of the answers given to the written assessment tool, the clinical interviews with the students before and after the application, audio and video recordings of the individual teaching episodes, the written works of the students within the scope of the individual teaching episodes, the field notes and diaries taken by the researcher. Before the application, it was determined that the concept images of the participants about the perimeter and the area were quite far from the formal definitions and were limited. In addition, it was observed that the participants used external and experimental evidence schemes, while the analytical proof scheme was not used. It has been determined that the concept images and proof schemes of the participants have changed with the activities conducted during the individual teaching sessions on the concept of perimeter and area and the researcher guiding them to defend the correctness of their thoughts. After the application, it was determined that the concept images of the participants about perimeter and area became suitable for the formal definitions, and the limitations in the concept images were largely eliminated. Proof schemes used by the participants in defending the correctness of their thoughts have also differed. It was observed that the use of the external proof schemes of the participants decreased considerably, while the use of experimental and analytical proof schemes increased. Keywords: Concept Image, Proof Scheme, Teaching Experiment, Perimeter, Area