Scaffolding Trajectories in Small-Group Mathematical Modeling Discussions: A Teacher–Student Interaction Perspective

Source abstract

Abstract Scaffolding is widely regarded as an effective approach for supporting students’ mathematical modeling. However, relatively little is known about how scaffolding trajectories unfold during modelling activities. In this study, we investigated scaffolding trajectories in mathematical modeling from a teacher–student interaction perspective. A qualitative multiple-case study was conducted in China, involving five groups of eighth-grade students from Shanghai who participated in three mathematical modelling activities. Based on a contingency, fading, and transfer of responsibility framework, we analyzed teacher–student interactions during small-group discussions across three modeling phases: (1) understanding and simplifying, (2) mathematizing and working mathematically, and (3) validating, modifying, and interpreting. The analysis showed that responsibility for modeling was continuously negotiated through teacher–student interactions rather than being transferred progressively from teachers to students. Fading and transfer of responsibility did not always develop synchronously, although teacher responsibility frequently reemerged when students faced increased modeling demands. Scaffolding trajectories also varied across modeling phases, with responsibility transfer occurring most frequently during understanding and simplifying, and stronger teacher involvement occurring during validating, modifying, and interpreting. These findings highlight the dynamic nature of scaffolding in mathematical modeling and suggest that support and responsibility are continually reconfigured in response to students’ modeling needs.