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Investigation into prospective middle school mathematics teachers' noticing of students' algebraic thinking within the context of pattern generalization

Özel, Zeynep.
The purpose of this study was to investigate prospective middle school mathematics teachers’ noticing skills of students’ algebraic thinking within the context of pattern generalization. In order to obtain in- depth exploration and understanding of issue, the qualitative research method, in particular, the case study design was used. Thirty-two prospective teachers who were studying at one of the public universities located in Ankara were selected via purposive sampling as participants. Data was collected in the fall semester of the 2018-2019 academic year through questionnaire and semi-structure interviews. In the data collection process, the questionnaire was applied to all the participants, and then semi-structured interviews were conducted with eight of them. The data was analyzed using the constant comparative method based on an existing theoretical framework for professional noticing of children’s mathematical thinking identified by Jacobs, Lamb and Philipp (2010). The findings of this study demonstrated that a vast majority of the prospective teachers could attend to students’ solutions regarding pattern generalization with robust evidence and emerging evidence. However, it was revealed that prospective teachers had difficulty in interpreting students’ algebraic thinking based on their solutions. Also, they had more difficulty in interpreting algebraic thinking of students with incorrect solutions than correct solutions. The findings about prospective teachers’ deciding how to respond on the basis of students’ algebraic thinking demonstrated that they could support the algebraic thinking of students with incorrect solutions asking follow-up questions. However, they could not extend the existing algebraic thinking of students who solved the problem correctly. They only provided responses by asking a drill or providing a general response.