An investigation of the noticing skills of middle school in-service and prospective mathematics teachers in the context of using representations of fractions

The purpose of this study is to examine the noticing skills of middle school in-service and prospective mathematics teachers regarding the use of representations in fractions. In this holistic multiple-case design study, as a case study being one of the qualitative research methods, two teachers with 12 and two years of experience working in a public school in a province in the Southeastern Anatolia Region and two prospective teachers who are senior students in the Department of Elementary Mathematics Teaching in the same province were the participants. The data were obtained from individual pre- and post-interviews conducted on four videos shot on the use of representations in fractions in a real classroom environment and discussions conducted in an online discussion environment. The data obtained were subjected to content analysis based on Jacobs, Lamb, and Philipp's (2010) theoretical framework. In this context, the data were analyzed by taking into account which mathematical ideas the teachers/prospective teachers paid attention to, how they interpreted students' mathematical ideas, and how they would respond to students in the next step while analyzing the teachers/prospective teachers' responses to student thinking in the videos. The findings of the study revealed that the teachers/prospective teachers were able to reach the level of robust evidence in the attending to skill, they were mostly able to provide partial evidence in the interpretation skill, and they could not reach the level of robust evidence in the responding skill. Regarding the responding skill, it was observed that the participants mostly planned to respond to student thinking by asking simpler or more difficult questions. The findings were discussed in the light of the related literature.