Preservice teachers' processes of construction of algebraic properties of real numbers

Numbers and number systems have an important role in mathematics teaching processes as they are at the foundation of mathematics. One of these number systems, the real number system, is considered to be the origin of modern mathematics. Some algebraic properties that can be constructed by utilizing the field axioms provided by the real number system and that increase the function of number systems have been constructed. It is known that these algebraic properties of real numbers are given directly to students in school mathematics and used in teaching processes starting from primary education. In this context, this study aimed to examine the knowledge construction processes of preservice mathematics teachers about the algebraic properties of real numbers within the framework of the RBC model. These algebraic properties were determined as a.0=0 and a.(-1)=(-a). The study is a case study designed with a qualitative research approach. The study group consisted of six primary mathematics teaching program students. The data of the study were obtained within the scope of teaching interviews conducted through the form of activity practice. Think-aloud approach was adopted during the teaching interviews. The data obtained were analyzed within the framework of epistemic acts of recognizing, building-with and constructing in the RBC model. As a result of the analysis of the data, one of the participants could only perform the act of recognizing in the process of constructing the two algebraic properties. Three participants were able to perform both recognizing and building-with actions. Two participants were able to construct both algebraic properties. In addition, it was observed that university students frequently used the identity element property of addition, the distributive property, and the inverse element property of addition in the knowledge construction process. It was found that the participants who could not construct knowledge may have inadequate understandings about both proof and real numbers and their algebraic properties. Finally, some recommendations were made.