Elementary mathematics teachers' pedagogical content knowledge of students' proportional reasoning

النوع : Mémoire

Pedagogical content knowledge (PCK) is comprised of teachers’ knowledge of both content and teaching that content to students. Teachers need to be aware of their students’ misconceptions and use teaching strategies that will help their students reorganize their thinking. While most people agree that a good teacher needs to know his or her subject matter at a deep level, and needs to have good teaching skills, there is also another type of knowledge and related skills that have been defined: knowledge of content and students (KCS). This type of knowledge is more specific, as it involves knowledge of a particular content area, and the way students think about this content. For mathematics teachers, this is knowledge about ways to effectively teach important mathematical ideas and skills, ways to help students use mathematical tools, and ways to help prevent or overcome typical misunderstandings and misconnections about mathematical concepts. There were three purposes to this research study. The first purpose was to examine elementary teachers’ knowledge about students’ errors in proportional reasoning. And the second purpose was to check whether teachers are able to suggest ways for their students to overcome difficulties when solving proportional reasoning tasks, and finally, to study the relationship between teachers’ knowledge of proportional reasoning errors and teachers’ knowledge of dealing with those errors. This study is a qualitative case study. Eleven fourth and fifth grade teachers from two international schools in Jeddah participated in this study. The primary methods of data collection were interviews. Participants were provided with four proportional reasoning tasks with students’ potential responses. Then they were required to identify the error, students’ thinking about proportional reasoning, and remedial strategies for students’ errors. Results revealed that most teachers’ KCS for the proportional reasoning topic was low. A few teachers were also found to make some of the proportional reasoning errors. The results are discussed in relation to existing literature on KCS and proportional reasoning. Implications of the findings for elementary mathematics teachers are also discussed.