Bridging early mathematics and real-life applications in elementary classrooms

The purpose of this study is to investigate the reflections that arise during the implementation of mathematical modeling activities with third-grade primary school students. To achieve this goal, a case study methodology was employed. The study consisted of 9 third-grade students (average age 8), selected through purposive sampling from a public primary school. In the 5-week preparatory phase preceding the main intervention, a distinct mathematical modeling activity was implemented each week to facilitate students' acquisition of foundational knowledge and experience on. Subsequently, a focus group consisting of three students was selected using criterion sampling. These students engaged with a mathematical modeling problem entitled 'The Healthy Money Saving Problem,' developed by the authors, under carefully structured problem-solving environments and processes. The entire process was video recorded, and the dialogues were transcribed verbatim. These transcriptions, along with the students' individual work sheets, were analyzed in alignment with the modeling cycle framework. The results indicate that students engaged in collaborative group work, where they generated and critically discussed mathematical ideas, interpreted and analyzed data, used relationships between data points, and applied mathematical concepts to real-world problems. Furthermore, they developed multiple solution strategies and were able to discard unsuitable approaches. The students also employed a range of mathematical skills such as problem solving, critical thinking, and reasoning throughout the process. Additionally, the students integrated informal knowledge (the knowledge students acquire outside of school) into the modeling process and made efforts to generalize their models to validate their applicability in real-life contexts.