Determining the geometric thinking habits of middle school mathematics teachers and investigating their reflections of geometric thinking habits on skill-based problems

The aim of this study is to investigate teachers' geometric thinking habits and how these habits are reflected during teaching and in skill-based problems. The study is qualitative, with data collected and analyzed using a case study method. Several data collection tools were employed during the data collection procedure. Data obtained from teachers' responses to the geometric thinking habits test (GDAT) and the MEB skill-based problems test (BTPT), as well as student documents and teachers' evaluations of these documents, researcher observation notes, interviews, and video recordings of interviews were analyzed with descriptive analysis, and content analysis. The GDAT and BTPT were first administered to the teachers, who then administered the tests to the students and solved the problems in a classroom setting. Five teachers of mathematics employed by MEB-affiliated schools in Mersin were questioned during the second semester of the academic year 2022-2023. According to the findings, the teachers did not engage in enough geometric thinking habits of mind. Teachers' most common habits are associating, exploring and reflecting, searching for constants, considering exceptional instances, and generalizing. When instructors' habits in skill-based problems were analyzed, it was discovered that all teachers used the same solutions to each other. Except for one problem, teachers only benefited from the association habit in skill-based problems. Because the teachers did not employ other habits and used the same solutions in their classroom environment, we concluded that skill-based issues do not support the usage of geometric thinking habits. Teachers' responses to both tests, as well as their expressions in the classroom, were investigated using the framework of geometric thinking habits, and variations in teachers were discovered. According to the findings, the participants were divided into three categories: developing teachers, changing teachers, and repeating teachers. As a result, it could be argued that mathematics teachers should be trained in geometric thinking habits, and that their teaching should be enhanced in this context.