İnvestigation of teachers' noticing mathematically significant pedagogical opportunities in teaching algebra

The purpose of this study is to examine the noticing skills of teachers and pre-service teachers regarding students' mathematical thinking, as well as their responses to Mathematical Instructional Opportunities (MIOs) embedded in those thoughts. The research was conducted using a qualitative case study design. The participants consisted of 4 pre-service teachers and 8 in-service teachers with varying levels of experience (4 middle school and 4 high school teachers). Data were collected through two different scenarios, and the participants' responses to student thinking were analyzed using the noticing framework developed by Jacobs et al. (2010) and the Mathematical Instructional Opportunities (MIO) framework originally proposed by Leatham et al. (2015) and adapted into Turkish by Doğan and Kılıç (2021). The findings revealed a diversity in participants' levels of noticing student thinking. While some participants demonstrated in-depth approaches in identifying conceptual cues within student responses and interpreting them pedagogically, in many cases limited strategies such as superficial explanations, direct correction of conceptual errors, and guiding students solely toward the correct answer were predominant. Additionally, participants' noticing behaviors and the depth of their responses varied depending on the nature of the mathematical content presented in the scenarios. The results of the study indicate that the development of noticing skills is shaped not only by years of teaching experience, but also by contextual knowledge related to the grade level taught and teachers' pedagogical sensitivity toward student thinking. In this context, it was concluded that teachers need structured teaching experiences, professional observation opportunities, and reflective practices in order to meaningfully interpret and respond to students' mathematical ideas. It is recommended that teacher education programs place greater emphasis on practice-based activities aimed at developing pre-service teachers' skills in analyzing and interpreting student thinking. Moreover, the inclusion of dedicated modules on professional noticing in in-service teacher training programs may contribute to improving the overall quality of mathematics instruction. June 2025, 125 pages. Keywords: Teacher Noticing, Mathematically Significant Pedagogical Opportunities, Teaching Algebra, Teacher Education, Qualitative Research