Examining mathematics pre-service teachers? subject matter and pedagogical content knowledge by using knowledge quartet: the case of limit

The purpose of this study is to examine the reflection of secondary mathematics student teachers? subject matter knowledge and pedagogical content knowledge about the limit concept on their teaching processes using Knowledge Quartet.The study conducted by utilizing case study design that is one of the qualitative methods. The participants of the study consisted of four volunteer mathematics student teachers who were attending School Experience-II Course.The data were obtained by semi-structured interviews, observation and writing documents. The lesson plans related to limit concept that prepared by the participants were brought, then the researcher had interviews with participants related to their process of preparing lesson plans. Four mathematics lessons (16 lessons in total) about limit concept taught by each of the participants were observed and videotaped. The individual interviews were realized at the end of the participants? each lesson concerning particular episodes. When the participants? four-hours teaching process were completed general interview and one more interview about how they evaluate themselves related to indicators of the Knowledge Quartet. Seven interviews were carried out with the four participants, 28 interviews in total, and audio-taped. The data obtained from videotapes and audio-tapes were verbatim transcribed and therefore the writing forms of each participant?s lessons transcripts were constructed. These transcripts contained the expressions of the participants and their students as well as the screen captures of the participants? computer presentations and screen captures of the writings on the board. The particular episodes of the participants? lessons were examined in the context of Knowledge Quartet?s indicators. While the transcriptions of the lessons were investigating in the context of indicators? thematic coding were used and by using content analysis the frequency were determined.The data analysis showed that the planning process of the lessons and the teaching process of the participants? were affected by their beliefs according to mathematics. The participants who designed their teaching based on the Secondary Mathematics Curriculum and its attainments had problem in determining students? probably misconceptions and difficulties about the limit concept because of the lack of experiences. The participants? constructed their own teaching process of limit concept, they used four different representations and they transformed each of them. It was seen that the participants used examples in the context of teaching concepts and procedures, and the provision of exercises, and also seen that one participants generally selected examples in terms of practices and familiarization of concepts, rules and properties.While all the participants generally try to respond appropriately to students? comments, answers and questions, two of the participants took care of more than the others to effective questioning.