Pre-Service Classroom Teachers' Proof Schemes in Geometry: A Case Study of Three Pre-service Teachers

Problem Statement: Recent research and evaluation reports show that students are not learning geometry efficiently. One identifier of student understanding related to geometry is teachers' knowledge structures. Understanding what a proof is and writing proofs are essential for success in mathematics. Thus, school mathematics should include proving activities. Proofs are at the heart of mathematics, and proving is complex; teachers should help their students develop these processes in the early grades. The success of this process depends on teachers' views about the essence and forms of proofs. Hence, it is necessary to investigate the classroom teachers' perceptions related to proofs. Purpose of the Study: The purpose of this study is to determine the proof scheme of pre-service teachers when proving a geometry theorem. In this sense, the study is oriented by the research question: which proof schemes do pre-service teachers use when making proofs in geometry? Method: The current case study is a detailed examination of a particular subject. Firstly, an open ended question was asked, and then semi-structured interviews were conducted. The three students investigated in this study were selected by considering their Basic Mathematics scores. Two girls having maximum and average scores and a boy having a minimum score voluntarily participated. The students were asked to proof "the sum of the interior angle measurements of a triangle is 180 degrees". After proving this, each student was interviewed about what they think about proofs and proving. Findings: The findings of the study reveal that pre-service classroom teachers have difficulties related to proving. Also, the participants' attitudes are not parallel to their achievements in the lesson. Another result of this study concerns using proofs in teaching and learning processes. When students are asked about their opinions regarding proofs, it is understood that they have the common idea that the lessons should be made with proofs. Conclusion and Recommendations: The results of this study and other studies in the field reveal that pre-service teachers are not able to prove even a simple geometry theorem. What underlies this is that pre-service teachers are thought to have insufficient knowledge about the definitions of geometric concepts as well as the misconceptions concerning the topic. Another reason can be that participants do not experience any proving processes in previous education. Hence, students should realize how valuable proving and acquiring knowledge is through the counsel of a teacher.