Investigating the proof images of secondary school 8th grade students

Generally accepted as a math-specific process, a proof is an effort to prove the validity or invalidity of a judgment, argument or conclusion with sufficient evidence (Yıldırım, 2000). But proving is not limited to this. The proof also has an important role in strengthening the links between the learning of a student's learning process and the newly acquired knowledge. It is more likely that a student who has set up links between information and has undergone inquiry-based learning processes within a cause-and-effect relationship is using new learned information and transferring them to different situations. Therefore, the student's proof making process is a subject that needs to be studied and is already working. In literature, there are studies examining the process of proving. However, only a few of these studies aimed to examine this process on secondary school level. This study aims to study this topic on secondary school students. In order to achieve this, mathematical proofs' of students were investigated according to proof image of Kidron and Dreyfus (2014) with taking three levels of proofs presented by Balacheff (1988) into account. This study is descriptive and qualitative and is a qualitative case study which qualitative research methods are used. In the first step, the Proof Level Determination Forms, consisting the basic level proof questions, has been applied to 100 middle schools 8th-grade students in order to determine the proving levels of the students according to the proof levels set by Balacheff. Expert opinion and help were taken during preparing of forms. At the end of the study, three volunteered students were selected to participate in the research further. Three separate semi-structured interviews were conducted with students and three separate interview forms have been prepared. The semi-structured interviews were conducted in order to obtain the proof images of the students. According to the results deducted from the Proof Level Determination Form, it has been observed that students often find it appropriate to give an example to prove the statements given to them. Therefore, the proofs of large part of the students have done, are at the pragmatic proof level in Balacheff's In addition, analyzes were made on the cognitive and affective behaviors of the participating students in interviews. As a result, it was seen that the images of evidence that students made during the proof process had the characteristics of the cognitive and affective components of the image of evidence put forth by Kidron and Dreyfus (2014).