Examining of mathematics teachers' noticing skills of student thinking about patterns generalization

The aim of this study is to investigate mathematics teachers' noticing students' mathematical thinking about pattern generalization at the seventh-grade level. In this study, case study design, one of the qualitative research methods, was used. The research was conducted in the spring semester of the 2021-2022 academic year. The research was carried out with 5 mathematics teachers working in different public schools in Karaman. In addition, 19 students studying at a public school were included in the study for student solutions and student solution videos related to pattern questions. Shape pattern questions were used to obtain student solutions and video images of the solutions. The data sources of the research were student solution papers, student solutions' videos and semi-structured one-to-one interviews with teachers. In order to obtain student solutions, the students were asked a question involving two shape patterns. One-to-one semi-structured interviews were conducted with 5 teachers using the student solutions obtained from the students and the video of the solutions. Mathematics teachers' noticing of students' thinking was examined in terms of three dimensions of Jacobs, Lamb and Philipp's (2010) noticing framework: Attending students' thinking, interpreting student thinking and deciding how do respond student thinking. The findings of the study revealed that mathematics teachers generally provided limited evidence in attending in students' mathematical thinking, and they were also insufficient in presenting evidence in interpreting students' thinking. Mathematics teachers generally said how the student solved the question in the part of participating in the student's thinking, they did not explain students' thinking or explained what they saw on the paper one by one. In the part of interpreting the student's thinking, they talked about whether the solutions were right or wrong, or about a different subject than the student's mathematical thinking (such as poor four-operation skills, understood or did not understand the subject). Furthermore, while teachers were responding students' thinking, it was observed that mathematics teachers generally tended to ask questions or explain the subject to the students to bring the wrong answers to the right answer. Most of the mathematics teachers stated that they would congratulate the student with the correct answer. Keywords: Noticing skill, Mathematics teachers, Pattern, Student thinking