Determining how students arrange their mathematical knowledge about the concept of proof in the frame of the main components of the secondary mathematics curriculum with the discourse analysis

The purpose of this study is to determine how secondary school students arrange their mathematical knowledge about the concept of proof on the basis of communication in the classroom. Therefore, the discourse employed by the students in the processes of communication in the classroom has been taken into consideration. The study, which can be described as a specific case study based on the qualitative research paradigm, has a sample of 15 people consisting of 13 eleventh-year students from a private science high school and their mathematics and geometry teachers. The data include the three-month video recordings of both mathematics and geometry classes, and the researcher?s field notes. The number of the recorded lessons in this period is 53. The spoken discourse between the teachers and the students has been especially focused on, and the analysis has been realised on the transcription obtained from these video recordings. A detailed analysis has been done by means of a coding system chosen from the relevant literature. It is a qualitative discourse analysis study in terms of its design, questions, style of data collection and analysis. The theoretical frame of the study is based on the socio-cultural learning approach and pragmatics. The coding system is Halliday and Hasan?s triadic model developed in the Systemic Functional Grammar and includes the field of discourse, the tenor of discourse and the mode of discourse. The findings have indicated that the classroom discourse has an important effect on the students? learning and constructing knowledge in relation to proof. Using teacher and student talk it has been observed that there are some shortcomings and restrictions about the definition of proof, the meanings of basic terms and concepts of proof, and the perception of the mechanism of proving.