Unpacking the process of mathematical modeling in collaborative problem-solving

We designed a layered modeling approach to engage students in collaborative problem-solving of open, ill-structured, physics problems, implemented in a course for preservice physics teachers. We present an analysis of the unfolding work of a group of three students (~2 hours). The data included video and student-generated artifacts. We developed a twofold coding scheme for the students' discourse, grounded in the data and informed by established conceptualizations of mathematical modeling. Guided by research on collaborative learning, we also coded the coherence of consecutive turns. The discourse progression across modeling phases, the complexity of the physical model employed, and the temporal coherence of students' discourse were quantitatively plotted as a function of time. The coarse-grained picture reveals a progression of reasoning that aligns with linear conceptualizations of the modeling cycle. However, the fine-grained picture exhibits frequent fluctuations between modeling phases. Findings also show how instructors' moves affect discourse coherence (focusing or scattering). The study clarifies how modeling unfolds in practice and offers analytical tools for examining collaborative mathematical modeling alongside practical guidelines for instructors.