MATHEMATICS TEACHERS’ KNOWLEDGE OF STUDENT THINKING AND ITS REFLECTIONS ON THEIR INSTRUCTION
Performing student centred teaching practices can be possible not only by including individual student into instructional practices but also by taking into consideration students’ thinking such as what they know, in which points they can fail, how they can learn better at the same time by enabling in-class interactions, in other words, by reflecting knowledge of students’ thinking into teaching. In this context, the aim of the study is to examine mathematics teachers’ knowledge of students’ thinking. The study was based on a case study design and the participants were three mathematics teachers. Data were compiled from interviews and two-class hour observations for each teacher. Firstly, the interviews was held to reveal the views of teachers’ on what students’ thinking is, whether they have any knowledge about students’ thinking or not and whether they reflect their knowledge about students’ thinking on their instruction or not. After the interviews, 2 hours of classes of the teachers were observed. To avoid any lack of data, a video camera was used during interviews and observations and all the recordings were verbatim transcribed. While analyzing data, the framework of An, Kulm and Wu’s (2004) which was adapted by Lee (2001) was used as conceptual structure. However, an inductive approach was taken by adding new codes related to students’ thinking which occurred in the analysis process to the conceptual structure. The interviews’ finding showed that each teachers considered the knowledge of students’ thinking as knowing students’ prior knowledge. In addition, teachers expressed that they benefited from questions to find out students’ views, they promoted students to use different solutions for solving problems, they had ideas on what kinds of mistakes their students could make and the difficulties their students could face with the help of their experience. The finding obtained from their lessons showed that the participants took into account students’ prior knowledge in parallel with their statements expressed in the interviews. On the other hand, the participants did not consider their students’ difficulties, mistakes and misconceptions unless students asked a question. The teachers did not perform any approach such as trying to guess possible ideas of students and assess students’ understanding. However, they had the limited approach to some components such as building on students’ mathematical ideas, promoting students’ thinking about mathematics, eliciting different ideas and consider them, engaging students in mathematical learning, and motivating students to learn. As a conclusion, the participated could not have the required competencies for knowledge of students’ thinking and reflecting this knowledge into their instructions. It is suggested that the possible problems are overcome by examining mathematics teachers’ knowledge of students’ thinking and its reflection on their instruction in detail.