Ortaokul matematik öğretmenlerinin rasyonel sayılar konusundaki pedagojik alan bilgileri ile inanışları arasındaki etkileşimi

The aim of this study was to investigate middle school mathematics teachers' PCK regarding rational numbers and their mathematics-related beliefs, and to understand the nature of the possible interaction between their PCK and beliefs. Data of the study were collected by (i) observation of six middle school mathematics teachers' lessons about fractions and/or rational numbers content, (ii) two rounds of semi structured interviews, and (iii) vignettes. Data about their PCK were analyzed qualitatively with the Teacher Education Study in Mathematics(TEDS-M) Framework whereas belief data were analyzed in light of the related literature. The analyses revealed that, participants mostly tended to teach with direct instruction method, they provided verbal explanations and rules, and they seemed to have sufficient mathematical knowledge most of the time. They connected the previous topics to the rational numbers and fractions in their teaching. They believed that this way of teaching was effective in teaching or that they had to use it because that was what suited the classroom context and the topics. Almost none of participants wanted to change their teaching even when students had better knowledge and skills, but they tried to change the level of questions they asked. Participants' beliefs and their PCK were mostly consistent in the interview and observation data. Analysis revealed that there was an interaction between their beliefs and PCK in direct and non-direct ways. Almost all of PCK dimensions of teachers interacted with their beliefs except for the Mathematical Curricular Knowledge.