İstatistikle İlgili Modelleme Etkinlikleri Bağlamında Öğretmen Farkındalığı: Bir Durum Çalışması

Abstract

Teacher noticing is an important aspect of teacher competence and an essential factor for effective teaching. Teacher noticing of students' mathematical thinking involves hearing what students say, seeing their actions, interpreting what they mean, and using this knowledge to identify their needs and design the instruction accordingly. Model eliciting activities, also known as thought-revealing activities, provide a good context for teachers to observe students' matematical thinking. However, we know little about what teachers notice and how they notice (state, interpret, and justify) in such contexts. This study aims to investigate one middle school teacher's noticing of her students' thoughts as they engage in model eliciting activities that involve statistics. The study was conducted in one seventh grade mathematics classroom. Case study design was employed. Data were collected through semi-structured interviews with the teacher, classrom observations, and document analysis. Students were grouped by the teacher and engaged in four model eliciting activities. Two groups were selected as focus groups and their work was video-recorded. At the end of each modeling activity, semi-structured interviews with the teacher was conducted. During these interviews, the teacher watched the video recordings of students' group work and examined students' reports (posters, letters etc.) that they produced. She was asked to talk about what she had noticed as she review the students' work. Data were analyzed in order to examine what the teacher had noticed and how she had noticed. What she noticed was analysed in terms of three aspects: (a) student thinking related to the cycles of mathematical modeling, (b) difficulties experienced by students, and (c) interactions between instructional material and the students. On the other hand, how the teacher noticed was analysed in terms of three aspects: (a) descriptions and explanations, (b) evaluations and interpretations, and (c) justifications. Findings showed that the teacher noticed several aspects of her students' thinking related to the cycles of mathematical modeling. She mostly attended to students' thinking as they decided their solution method and applied the procedures. However, she attended to students' work to a lesser extend as they tried to understand the problem situation (i.e., description phase). We also observed very few instance related to students' prediction and verification of their work. Even though the teacher also noticed that students struggled with interpreting the findings in the context of the problem, she rarely attended to such issues. It has been determined that the teacher's noticing of student difficulties mostly focuses on the difficulties of conceptual understanding. She pointed out that even though students know the procedural aspects (i.e., compute mean, median, mod, range) of statistical concepts, they had limited understanding of what these measures mean in a problem context. She also attend to students' struggle in explaining mathematical ideas to each other. The teacher pointed out issues related to students' interactions with the task (i.e., model eliciting activities.) She noticed how students' performances had changed with respect to the nature of the activities (i.e., when data set was not given). She also pointed out that modeling activities support student attention, conceptual understanding, and skills to apply mathematics in real life. The teacher mostly repeat students' statements or describe their actions as she describe her noticing. She usually over-hear what her students said and usually performed process-oriented evaluations when interpreting students' conceptual difficulties. She mostly justified her interpretations based on her knowledge and expectations related to students whereas she occasionally provide evidence from students' work.