An investigation of middle school students' real-world connection skills in problem-posing processes

The aim of this study is to examine the real-life connection skills demonstrated by eighth-grade middle school students during problem-posing processes related to the topic of linear equations. The study was conducted using a teaching experiment methodology. The participants consisted of twelve eighth-grade students enrolled in a public middle school. Data were collected through problem-posing-based activities, audio recordings, and teacher observation notes. The instructional process was structured around the five-stage problem-posing-based learning model developed by Chen and Cai (2020), and additionally benefited from Walkington and Bernacki's (2015) personalized learning approach. During the eight-week implementation period, students were first administered a pre-test and then supported with problem-posing-based learning activities designed to address their identified learning needs. In this process, students initially participated in motivational activities aimed at raising awareness, developed stories grounded in their own experiences, and subsequently posed problems based on those contexts. They then analyzed the problems they had created and explored the associated mathematical concepts. Following this, students engaged in conceptual discovery and reached generalizations during the lesson extension phase. Finally, they summarized and evaluated the entire learning process. A post-test was administered at the end of the process. The problems posed by students were evaluated using a four-criteria framework (contextuality, solvability, information/data, and language use) based on relevant literature. The problems that met these criteria were further analyzed according to the eight components defined in Palm's (2006) framework, and their scoring levels were assessed using Wernet's (2017) rubric. The findings revealed that prior to instruction, students' problem-posing performance and their ability to relate mathematics to real life were limited, and the problems they posed were mostly abstract and lacked contextual grounding. However, after the intervention, students showed significant improvement in areas such as establishing context, integrating problems with solutions, using data meaningfully, and making conceptual generalizations. In conclusion, this study demonstrated that problem-posing-based learning not only enhances students' problem-solving abilities but also improves their capacity to connect mathematics with real-life situations. The study recommends the integration of problem-posing activities as supportive strategies for conceptual learning in classroom environments. Furthermore, it suggests that incorporating problem-posing processes in the teaching of mathematical concepts in real-life contexts contributes to students' meaningful and lasting learning experiences.