Investigating mathematics teachers' knowledge for teaching about equation concept

The aim of the study is to examine the knowledge of secondary school mathematics teachers on the subject of in the linear equations with one unknown with the Mathematics Knowledge for Teaching (MKT) model developed by Ball, Thames and Phelps (2008).The research was conducted by making use of the special case study pattern, which is one of the qualitative research methods. The participants of the research are three secondary school mathematics teachers who voluntarily participated in the study. In order to obtain information about the specialized content knowledge of secondary school mathematics teachers in the study, the Equation Knowledge Test for Teaching was applied to each teacher. The answers given to the test were clarified by interviewing the teachers immediately after the test application. After the application of the knowledge test and the completion of the interview processes, ten-hour teaching processes of teachers related to the linear equations with one unknown were observed. In addition, during these teaching processes, discussions were held with teachers about the lessons. During the interviews about the lessons, the events that occurred during the teaching process and the reasons of these events, the real thoughts of the teachers about the events in the lessons, and their self-criticism about the lessons were questioned. The data obtained from teachers' knowledge test, observation data and voice recordings were evaluated through analytical rubrics prepared according to the sub-dimensions of specialized content knowledge. The three sub-dimensions of specialized content knowledge (justification, explanation and representation) form the basis of the research. The research data were primarily evaluated for the suitability of each sub-dimension. Subsequently, the data of the teachers were examined in terms of the types of each sub-dimension and the necessary classifications were made. As a result of the research, it was determined what the behaviors that teachers are expected to have in relation to each of the sub-dimensions of their specialized content knowledge in teaching the subject of the linear equations with one unknown. It is thought that teachers' performing the teaching practices considering the aforementioned behaviors will affect the quality of the teaching positively. Another result of the research is that teachers need student knowledge and pedagogical knowledge in order to make the necessary mathematical evaluation in the teaching processes. It has been determined that teachers 'insufficient content and student knowledge negatively affect the process of obtaining information about teachers' specialized content knowledge. In the research, it was also concluded that the teachers' specialized content knowledge about the linear equations with one unknown is insufficient. While teachers did not find it difficult to answer questions about the equations, they had problems explaining the meaning of the questions to the students. In addition, while evaluating alternative solution methods, it was observed that the students mentioned the correctness of the transaction steps and made rule-oriented approaches. Another result obtained is that teachers who have insufficient specialized content knowledge, avoid using visual representation in their teaching processes. The insufficient specialized content knowledge has also been effective in material selection.