An examination of elementary school mathematics teachers' pedagogical content knowledge on ratio and proportion

The purpose of this study is to analyze pedagogical content knowledge (PCK) of secondary school mathematics teachers on the subject of ratio and proportion through taking advantage of the theoretical framework of ''Mathematical Knowledge for Teaching'' (MKT) model developed by Ball, Thames and Phelps (2008). Mixed research method was used in the study. The study was executed with 90 volunteer middle school mathematics teachers working in the city center of Afyonkarahisar in 2017-2018 academic year and selected according to the maximum diversity sampling. In the study, a questionnaire consisting of 14 questions based on MKT model was applied to 90 teachers, then semi-structured interviews were conducted with 13 teachers, with at least one of each seniority level, who were volunteers from these teachers and determined by purposeful sampling. Then, the four-hour courses were observed in which 6 teachers, selected from these 13 teachers with purposive sampling, taught the subject of ratio and proportion. After the course process observations, unstructured interviews were conducted with the teachers. All observations and interviews were recorded with video and audio recordings and these recordings were written on computer. Content analysis methods was used in the analysis of the obtained data. According to the findings of the study; teachers' pedagogical content knowledge (PCK) on the subject of ratio and proportion has been identified as insufficient in the context of Specialized Content Knowledge (SCK) and Knowledge of Content and Teaching (KCT) which are the components of Mathematical Knowledge for Teaching (MKT). Although their Common Content Knowledge (CCK) and Knowledge of Content and Students (KCS) is sufficient, it was detected that they have some troubles on the definition of ratio. Moreover, most of them do not know the definition of ratio, and prefers to tell the students who answered incorrectly by rule based and theoretical explanations. In addition, it was found that as teachers' professional seniority level increases, their CCK, KCS and KCT decreases, however their SCK increases. Keywords: Ratio and Proportion, Pedagogical Content Knowledge, Elementary School Mathematics Teachers