Investigation of the development of a mathematics teacher's noticing skills and mathematical discourses through learning trajectories

The aim of this study is to investigate how a mathematics teacher's noticing skills and mathematical discourse develop through learning trajectories (LTs). For this purpose, the study examined the teacher's noticing skills and mathematical discourse throughout a professional development program (PDP) based on LTs on ratio and proportion. The study was structured with a qualitative approach based on the Teacher Development Experiment (TDE) methodology and was conducted over a 16-week period during the 2020-2021 academic year with a middle school mathematics teacher working in a public school. The TDE was completed in six cycles, each with four stages: planning, teacher education, lesson observation, and noticing interviews. Data were collected through video recordings, semi-structured interviews, and researcher diary. Noticing skills were analyzed using thematic analysis of interview data based on video clips and students' written responses; while mathematical discourse was analyzed using descriptive analysis of the lesson videos. The findings indicate that LTs significantly contributed to the teacher's ability to understand and explain students' thinking and strategies, interpret their understanding, and make instructional decisions; while also transforming the teacher's mathematical discourse into a richer, more conceptual, and relational structure. The study highlights the role of LTs in PD and offers recommendations for practice and future research on noticing, mathematical discourse, and ratio-proportion.