Investigation of strategies and approaches used by 8th grade middle school students with different achievement levels in pictural pattern generalization tasks

In this study, it was aimed to examine the strategies, approaches and algebraic generalization levels of students at different achievement levels in pattern generalization tasks. In accordance with this purpose, the case study method, one of the qualitative research methods, was preferred. 30 students, 6 students from each of five different secondary schools in Sorgun district of Yozgat province (2 high achievers, 2 medium achievers, 2 low achievers), were studied. The data collection tool measures skills in near generalization tasks and distant generalization tasks with 3 shape pattern questions and the options below. The data of the study was collected in the fall semester of the 2022-2023 academic year. MAXQDA program was used to analyze the data. Descriptive analysis method was used. Students generally resorted to an iterative strategy in close generalization tasks. The strategies used by students in distant generalization tasks differed. It was also observed that some students achieved results by using rules. It was found that while students used the visual approach in near generalization tasks, they used the numerical approach in both near generalization tasks and distant generalization tasks. A few have also used both approaches together in distant generalization tasks. When students' algebraic generalization levels in distant generalization tasks were examined, it was found that high-achieving and medium-achieving students gave similar algebraic level answers. The answers given by low-achieving students were accepted at the pre-algebra level.