Investigation of middle school students' visual reasoning skills in geometry problems

It was aimed to investigate middle school students' visual reasoning skills in geometry problems in this research. Since it was aimed to examine the students' visual reasoning skills existing within the scope of their available knowledge and experience, an embedded multiple-case study design was preferred in the research. The participants of the research were 32 students who were selected using a maximum variation sampling. Because each class level was considered a different case in the research, it was studied with 8 students from each class level. Eight students in each case vary in terms of their school of study and levels of success. As data collection tools, the Geometry Problem Solving Test developed by the researcher, clinical interview records, and observation notes were used. Clinical interviews were conducted and observation notes were taken to specify the visual representations that the students in this research used while solving geometry problems and to reveal the actions they performed with the visual representations and the reasoning processes in detail. An integrated approach was pursued in the analysis of these data collected synchronously. In data analysis, content analysis and cross-case analysis techniques were used. The data were analysed in accordance with the conceptual framework proposed by Geçici and Türnüklü (2021). In the research, it was seen that the participants generally preferred drawing, tables, or model visual representations. Drawing is the primary visual representation used. Moreover, it was revealed that the students who used a model instead of drawing were generally more successful in exhibiting mathematical thinking components. It was detected that the students who used various representation types together exhibited mathematical thinking components more comfortably. It was concluded that using visual representation alone was not enough for mathematical thinking during the visual reasoning process and that it was also essential to make visualization on the visual representation used. As opposed to this situation, it was found that the participants who made visualization without using visual representation also had difficulty solving the problem. Therefore, it can be stated that it is a key ability to make visualization through different visual representations in problem-solving.