Abstract:

Along with proof is one of the sub-dimensions of mathematical thinking; it is the main component of making mathematics. In parallel, proving is also the focus of studies in mathematics education. Despite this importance, the findings of many studies reveal that students and preservice teachers have difficulties related to proving. The most important task falls to teachers in developing students' proving skill. Thus, the proving process of teachers, preservice teachers’ and academicians’ who guided the preservice teachers is important. Therefore, the aim of this study is to examine and to make comparisons with proving skills of preservice mathematics teachers, mathematics teachers and academician. The participants of the study consist of 5 people; whom of 2 preservice teachers in the last year of secondary mathematics education, 2 mathematics teachers in Anatolian high school and an academician (research assistant) in the field of mathematics at Faculty of Education. This study is used case study from qualitative research approaches. The data were collected through interviews. The participants were asked to prove that?8 is irrational and the sum of the numbers from 1 to n. All data were transferred to the computer environment; their behaviour and thinking processes were compared. Findings show that teachers and academician who receive postgraduate education are providing in short time in the proof of the first statement and aware of how they can make proving. It has seen that other participants could not prove since they did not like or memorize. Similarly, in the proof of the second statement, while academician and teachers who received postgraduate education have proved by induction; the other participants have made similar proof.

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