Investigating the pre-service primary school mathematics teachers' definitions regarding number theory concepts

We can say that we use definitions frequently when learning and teaching mathematics. Definition activities are one of the most basic mathematical activities, along with proving and problem solving (Leikin ve Zazkis, 2010). It can be thought that in the correct perception of number sets, which are one of the most basic concepts of primary mathematics education it is important to what extent the definitions within the scope of Number Theory are known and how much importance is given by the prospective teachers. In this study, it is aimed to examine the definitions made by the prospective primary mathematics teachers about the concepts in the Theory of Numbers course and to reveal the prospective teachers' thoughts about definitions and the role of definitions in the education process. The study is a qualitative research. In this study, it will be examined in detail how prospective primary mathematics teachers define the concepts of number theory. Therefore, the research is a case study of qualitative research methods. The sample of the study consists of 50 senior prospective teachers in the Department of Primary Mathematics Teaching in a Faculty of Education. Number Theory Definitions Form (SKTF) was applied to prospective teachers. After the applied form, semi-structured interviews were conducted with some prospective teachers. Zazkis and Leikin (2008) put forward four categories as "accessibility, richness, accuracy and generality (concreteness)" in order to analyze the definition examples made by teachers. In the study, the data collected with SKTF were examined in terms of accuracy and richness criteria set by Zazkis and Leikin (2008). While examining the definitions in terms of accuracy criteria, it was seen that most of the definitions made were evaluated as 'Inappropriate Definition'. The most common defect while making the definitions was determined as not specifying the set of numbers to which the variables used in the definitions belong. When examined in terms of the richness criteria, rich definitions were found for only 5 concepts. These concepts are "Basic Division (dividing the number a by b), Rational Number, İrrational Number, Even Integer and Odd Integer" concepts. Appropriate definitions for other concepts are generally similar.