Proof schemes used by prerservice mathematics teachers and their ideas about proof

Proofs obtain whether a mathematical process is true or false. Proof schemas used at the proof process is important to see student?s thinking and reactions during the mathematical situations. For this reason, the aim of this study is to determine what kind of proof schemes preservice mathematics teachers use about the functions subject; to reveal how different proof schemes differentiate between different grade levels; to determine preservice teachers? views regarding on mathematical proof and present how these views changed based on different grade levels; ascertain if there is a relations between preservice teachers? views on mathematical proofs and proof schemes that they used at functions topic. For this aim, preservice mathematics teacher?s opinions on proof schemes they used and their ideas about making mathematical proof were investigated in the study.To expose the proof schemes used by preservice teachers, written exams and clinical interviews were utilized. Also, to determine the views of preservice mathematics teachers about proofs, a questionnaire developed under the named as ?Questionnaire for Constructing Mathematical Proof? was used. In the study conducted by developmental research method, the questionnaire was applied to 187 elementary mathematics preservice teachers, the written exam was applied to 158 preservice mathematics teachers and clinical interviews were conducted with 16 preservice mathematics teachers at various grade levels.The results of the study has demonstrated that preservice teachers have positive views about proof and the usage of the analytic proof schemes accepted as the highest level among the proof schemes were increased by grade level. In addition, it is determined that the proof schemes were differentiated with different class levels and there was a parallelism between the some factors in the questionnaire-scale and the proof schemes. Based on the results of the study, some suggestions have been offered to the program developers and the researchers to improve preservice teachers mathematical thinking and proof construction abilities.