Investigating noticing levels of teachers regarding to students' mathematical reasoning and proving skills

This study aimed to investigate the levels of students' mathematical reasoning and proving skills and how teachers notice students' reasoning and proving skills. To achieve this goal, a qualitative research method, specifically a case study design, was employed. Firstly, to determine the levels of student reasoning and proof, a proof test consisting of five questions was administered to 96 eighth-grade middle school students. The responses of ten students selected from the results of the proof test, analyzed according to students' reasoning and proof levels, were presented to four mathematics teachers working in the same school through individual teacher interview protocols. The responses provided by the teachers were descriptively analyzed regarding teachers' attention to students' mathematical reasoning and proof skills, interpretation of students' mathematical proof and skills, and decision-making regarding students' mathematical reasoning and proof skills. As a result of the proof test administered to the students, it was observed that the students' levels of mathematical reasoning and proof consisted mostly of Level 1 (experimental level) responses. The least encountered proof level was Level 3 (analytical level) responses. Based on the findings obtained from the teacher individual interview protocols, it was observed that responses at the insufficient evidence level were most prevalent in all skills, including attention to students' strategies, interpretation of their understandings, and decision-making on how to respond based on their understandings. Responses at the robust evidence level were the least encountered. The proportion of insufficient evidence level was highest in interpretation skills and lowest in attention skills.