Examining the problem-posing performance of seventh-grade students with high and low problem-solving performance

The present study aimed to investigate the similarities and differences in the problem-posing performance of seventh-grade students with high and low levels of problem-solving performance. A total of 243 students participated in the study. In line with criteria such as establishing connections to real-life and incorporating visual representations, three tasks—namely "Theater," "Road," and "Piggy Bank"—were designed on the topic of patterns. For each task, problem-solving and problem-posing tests were developed in a parallel structure. Students' problem-solving performance levels were determined based on the scores they received from the problem-solving sections of each activity, and high- and low-performance groups were subsequently formed for each task. The problems posed by these two groups were initially analyzed in terms of their mathematical nature. Problems identified as mathematical were then further examined for their contextual relevance to the associated task. Those deemed both mathematical and contextually appropriate were analyzed utilizing the "product" and "process" components proposed by Zhang et al. (2022). In the output phase, mathematically relevant problems related to the activity were analyzed in terms of their clarity and comprehensibility, the number of different types of problem structures, and solvability. In the process phase, solvable problems with different structures were analyzed according to how they were constructed, in terms of variables and their interrelationships, following Cai's (1998) analytical framework. Additionally, each component was analyzed in the context of the addition of new conditions and limitations. The findings revealed statistically significant differences in the performance of the groups regarding the posing task-related problems and the output phase components. However, in terms of the process phase components, there were more similarities than differences between the groups' performances. The results contribute not only to the development of frameworks for analyzing posed problems in the literature but also provide recommendations for integrating problem posing into mathematics classrooms and enhancing students' problem-posing performance.