Mathematical knowledge for teaching of the math teachers: Analysis of the basic concepts in the sets

In this study, mathematics teachers' mathematical knowledge for teaching basic concepts in sets was examined in the context of four subcomponents of the Mathematical Knowledge for Teaching (MKT) model. The research was carried out with case study from qualitative research methods. The working group of the study is composed of 18 mathematics teachers and 210 students. Data collection tools were Set Knowledge Test for Teaching, Student Achievement Test, Classroom Observation Form, student's lecture notes and audio-video records. 18 mathematics teachers were administered Set Knowledge Test for Teaching in the study. Among these 18 teachers, the lessons of the three teachers determined according to the purposeful sampling method were recorded as video and audio. The Classroom Observation Form was used by the researcher during the course. The Student Achievement Test was applied on a total of 210 students in the classrooms in which the courses were recorded and where three teachers were enrolled, and six students were selected from the video recording classes and their lecture notes were taken. Descriptive analysis, content analysis and continuous comparison techniques were used in the analysis of the qualitative data obtained. Percentage and frequency techniques were used in the analysis of quantitative data. The findings of the research show that there is a lack of knowledge on the subject field and pedagogical content according to the levels of the MKT model of the teachers related to "Basic Concepts in the Sets." These are centered upon the "Specialized Content Knowledge" and "Knowledge of Content and Teaching" components of the MKT model. It is seen that this lack of knowledge in teachers' mathematical knowledge for teaching negatively affected the student achievement. By enriching their subject matter knowledge and pedagogical content knowledge, they should be provided to be able to approach the concepts in mathematics with different perspectives, use different notations and explain the concepts with different representations. Key Words: Mathematical knowledge for teaching, subject matter knowledge, pedagogical content knowledge, basic concepts in sets.