Eighth grade students' processes of solving non-routine geometry problems

The aim of this study is to examine eighth-grade students' solving processes for non-routine geometry problems. A multiple case study, one of the qualitative research methods, was adopted in the study. The study group was formed using critical case sampling, one of the purposive sampling methods. To collect data, the Van Hiele Geometric Thinking Levels Test was administered to 8th-grade students attending three public middle schools in the Bulanık district of Muş province during the 2023-2024 academic year. Item difficulty and discrimination indices for the Van Hiele Geometric Thinking Levels Test, administered to a total of 200 students, were calculated to identify the three students with the highest and the three students with the lowest geometric thinking levels. Six students, selected according to their geometric thinking levels, were asked to solve the Geometry Problems Test, which consisted of non-routine geometry problems used in the PISA and TIMSS exams, aloud. The six students' problem solutions were video-recorded, and the dialogues were transcribed. The obtained data were analyzed using themes based on the research questions and the codes assigned to the students using descriptive analysis. According to the findings, students with high geometric thinking levels were found to use the problem-solving steps of understanding the problem, preparing a plan, and implementing the plan in non-routine geometry problems, but not the solution-checking step. Students with low geometric thinking levels were found to use the problem-solving step of understanding the problem but not the other steps. Students with high geometric thinking levels were found to use relationship search, estimation and checking, drawing figures and diagrams, and reasoning strategies in the problem-solving process. Students with low geometric thinking levels were found to not use problem-solving strategies. Students with low geometric thinking levels were observed to not produce solutions to non-routine geometry problems and to perform four random operations or suggest skipping the problem. Furthermore, the study determined that students with high geometric thinking levels used more than one strategy.