Abstract:

Identification, which is one of the most basic mathematical activities along with proofing and problem solving, is one of the main components of field knowledge. Definitions also influence teachers’ didactic decisions, such as teaching methods, the order of subjects, which theories and evidence will be dealt with. The correct perception of the number sets, which are one of the most basic concepts of mathematical education, also opens the way for the understanding and use of mathematics. The first circle of natural numbers, the number sets, from natural numbers to real numbers, are dependent on each other by the preconditional relationship. It is important that teachers and teachers candidates know these sets correctly and are able to define them rigorously so that students can build the number system correctly. This research is part of a broader thesis that is done to determine the field and pedagogical field knowledge of the teacher candidates. 160 primary mathematics teachers candidates, including 40 from each class level, have been applied an open-end scale containing the definitions of 14 concepts (natural numbers, original numbers, absolute value, etc.) related to the field of learning of numbers and processes. In this study, the responses to the definition of "natural numbers" are included. The definitions have been studied in the context of various criteria created by Zazkis and Leikin (2008). The research results showed that teachers candidates were able to make definitions without the necessary or sufficient conditions when defining the natural number. Some appropriate definitions have not been found to be rigorous for reasons such as the unconsciousness of the mathematical language and the lack of minimality. When all the results are evaluated, it can be said that it is extremely important to focus on the structure, the role and the expression of equivalent definitions in teachers' education and to give opportunities to consider concepts first of all.