Examining the Effectiveness of Teaching Through Definitions in the Definition and Conceptualization of Number Sets by Pre-Service Mathematics Teachers

The purpose of the present study is to identify the effectiveness of the teaching process undertaken by means of definitions on the definition of the mathematical concepts included in number sets by pre-service mathematics teachers as well as their conceptualization concerning the operations performed. The study is designed as a case study, a qualitative research method, and conducted with the participation of 68 pre-service middle-school mathematics teachers selected through purposive sampling. It makes use of individual interviews, worksheets, and videos of teaching process as data collection tools. The study is conducted in two stages: The first stage involves revealing the definitions by pre-service teachers of the mathematical concepts included in number sets with individual interviews in pre-concept teaching through definitions. As for the second stage, the definitions and conceptualization proposed by the pre-service teachers were examined within the framework of worksheets and videos of teaching process during the course entitled "Fundamentals of Mathematics I" taught through definitions. This allows the researcher to identify the effectiveness of definitions through using definitions and conceptualization among pre-service teachers. The findings of the present study led to the conclusion that teaching through definitions is effectiveness in the definition and conceptualization of the concepts included in number sets by pre-service teachers. Furthermore, pre-service teachers are also seen to make definition-based explanations during proving. Definitions are found to be effectiveness in the use of mathematical language and representation by pre-service teachers.