Mathematics student teachers' views on the method of two column proof and the analysis of their proving process based upon this method

Mathematical proof provides a warrant for mathematical knowledge and is an essential activity in doing and understanding mathematics (Almeida, 2000: 869). Concept of proof which is thus much important for mathematics, similarly, plays an important role for the teaching of mathematics and geometry. In the teaching of geometry, different methods and approaches are used to eliminate the general problems related to proof such as understanding and constitution of the proof. Two Column Proof (TCP) is one of these alternative methods which took place in the New Geometry Curriculum started to be implicated since 2010 in Turkey, however, it is commonly used in the outside of Turkey especially in the USA (see Gfeller, 2004; Herbst, 2004; Weiss, Herbst & Chen, 2009). This study aimed to contribute this method to be known, become widespread and take the attention of research area in terms of its instructional effectiveness. TCP's limited usage in our country and students' general problems related to proving established a ground for doing this research. It is known that teachers' approaches are the most important factors for students' knowledge, attitudes and skills of proof and proving. Hence, in studies regarding TCP, it would be helpful to begin with teachers' pre-service and in-service education and development processes. This study was designed from this point of forth in order to determine future mathematics teachers' approaches/ status based on the method of TCP and their views about this method as well. This study which carried out quantitative research methodology was a case study. Participants were 12 student teachers enrolled in Secondary Mathematics Education Department in a public university in Turkey . Participant student teachers are asked to complete 5 TCP for 4 weeks with a total of 20 TCP. During the study, one semi-structured and one structured interview were carried out. One of the interviews was carried out after the implementation in order to reveal student teachers' opinion about TCPs (its structure, function, usefulness, hard-easy aspects, limitations, important points etc.) and the other one was also carried out after examining student teachers' proving situations, after the implementation, in order to determine prominent cases and successful or inadequate points and to find out their reasons. Data were handled by examining documents and interviews one by one with the consideration of paternal qualities and prominent cases with the content analyze method. For the analysis of the first set of interviews, themes and categories in respect to these themes were generated. As for the analysis of the second set of interviews, participants were examined one by one and prominent cases were determined. For the cases in which paternal qualities exist, themes and categories were generated as well to obtain an analysis result regarding the overall situation.The main result of this study is all the student teachers gave positive opinion about TCP methodology. Participants agreed on that the TCP method is useful and functional tool in geometry courses as well as in doing proofs and understanding proofs. Moreover, participants succeed in completion of the proofs correctly. During the implementation, student teachers had no problem except writing reasons.Keywords: Proof, Proving, Geometric Proof, Two Column Proof, Mathematics Student Teacher.