International Conference on Mathematics and Mathematics Education (ICMME-2018), Ordu, Turkey, 27 - 29 June 2018, pp.663-664
As a scientific discipline, Mathematics aims to enable people to reasonably answer to questions such as ‘why’ and ‘how’. As a result of these questions, the need for proof has arisen. Although mathematical proof is regarded as an indispensable part of mathematics, it is observed that the importance and role of proof is not adequately emphasized in teaching programs, and mathematicians perceive the term as something demonstrating sufficient proof for the validation of mathematical statements [1]. For this reason, it is becoming increasingly important in advanced-level mathematics courses to focus on the proofs to mathematical propositions belonging to mathematical concepts. The importance of proof in mathematics can be summarized as follows. ? In order to confirm the accuracy of a hypothesis, there is only one way: giving the mathematical proof. ? It is agreed that proving is a process leading to perceive and understand. Being able to prove means that the studied problem is understood and perceived. Here, however, there is more. The effort to prove a hypothesis may occasionally lead to in-depth understanding and perception of the theory within the question (problem). Even the proving fails, one can gain depth in knowledge and understanding [2]. Proof methods in mathematics are; direct proof (the method in which by assuming is true, truth of q is shown in the proposition ), proof by contradiction (the method in which the statement to be demonstrated as true is accepted as false. Then, one can prove that it is false, and reach the contradiction) counterexample (in proposition, finding a case in which p is true and q is false), induction, deduction and test. This study aims to find out secondary school mathematics teacher candidates’ competence in proof methods. The study was conducted in a university in Black Sea Region in 2017-2018 school year. In the study, a data collection tool consisting of 6 questions covering each proof method is used. The questions in the tool were written after being counselled by experts after literature review. As research pattern, being a kind of case study, one-case pattern was used. The analysis unit of the study is secondary school mathematics teacher candidates. Sub-units of this unit are consisted of a total of 75 teacher candidates; 27 of whom studying at second grade; 24 from the third grade; and 24 from the fourth grade of the department. For data analysis, being a qualitative research method, categorical analysis technique of content analysis was used. The aim of using this type of analysis is to subject the determined categories to a frequency analysis. The findings obtained from the study demonstrate that the teacher candidates are weaker at proof by contradiction method compared to other methods. The most successful class level was the third grade. A possible explanation for this success might be that they receive proof-oriented courses in that academic year. In this context, further proposals are made for later researches. Key Words: Proof methods, secondary school mathematics teacher candidates, competence
REFERENCES [1] G. Hanna, Mathematical Proof. In D. Tall (Ed.), Advanced Mathematical Thinking, Dordrecht, Netherlands: Kluwer Publication, 2002. [2] Y. Dede, Matematikte İspat: Önemi, Çeşitleri ve Tarihsel Gelişimi. In İ. Ö. Zembat, M. F. Özmantar, E. Bingölbali, H. Şandır, A. Delice (Ed.), Tanımları ve Tarihsel Gelişimleriyle Matematiksel Kavramlar, Ankara: Pegem Akademi Yayınları, 2015.