Introduction

The mathematics education programme, developed and implemented in 2005 in Turkey, demands major changes in students’ and teachers’ roles (MEB, 2005). This reform movement impacts criteria for elementary mathematics teacher competence. In particular, teachers are expected to understand and attend to students’ mathematical thinking and use this information to design and implement their instruction (MEB, 2008).

Several research projects in mathematics education (e.g., Cognitively Guided Instruction, Purdue Problem-Centered Mathematics Project) have provided support that teachers could select worth-while mathematical tasks and design more student-centered instructions when they attend to student thinking. Findings also show the potential for the improvement in student conceptual understanding and attitudes towards mathematics (Cobb, Wood & Yackel, 1990; Cobb et al., 1991; Fennema, Carpenter, Franke, Levi, Jacobs & Empson, 1996; Franke & Kazemi, 2001).

Researchers, however, have documented that teachers have difficulties in understanding students’ thinking in mathematics (Kazemi & Franke, 2004; Wallack & Even, 2005). Wallack and Even (2005) explored one teacher’s descriptions and explanations of two students’ talk and action as they solve a mathematical problem. Then they identified different characteristics of the teacher’s interpretations, such as over-hearing (i.e., hearing things that were not said by the students), and under-hearing (i.e., ignoring some aspects of what students said and did). Their analysis showed the discrepancy between what students’ said and did and what the teacher heard and interpreted.

Mason (2002) argues that understanding what students’ say and do requires practicing to notice several aspects of student work. In recent years, researchers design several projects to help in-service and pre-service teachers develop skills to understand students’ mathematical thinking. As an example, Crespo (2000) examined how a mathematics letter exchange with grade 4 students provides a context for pre-service teachers to think about student thinking. The analysis of the letters and reflective writings by the pre-service teachers showed that their interpretations of students’ solutions have changed from “correctness to meaning” and from “quick and conclusive” to “thoughtful and tentative.”

Problem Statement and the Purpose of the Study

Prior research briefly described above shows that teachers and pre-service teachers need to develop knowledge, skills, and beliefs to be able to attend to their students’ mathematical thinking and design their instruction accordingly. We, however, know little about the ways pre-service teachers could develop these skills in Turkey. One way to help pre-service teachers improve their skills to notice students’ mathematical thinking is through the pedagogical courses they take during their teacher education programme. In this study, we aimed to explore pre-service teachers’ interpretations of elementary school students’ work after their interactions through interviews. The following research questions were addressed:

1) What kind of mathematical tasks did pre-service teachers select and design in order to explore student thinking?

2) How did pre-service teachers interact with the student in order to reveal his/her thinking during the interview?

3) How did pre-service teachers interpret student’s work?

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