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Math modeling is an iterative process where students use their observations and reasoning abilities to create and refine predictions or explanations about a single referent system (e.g., a lab apparatus). However, modeling may be complicated by the presence of multiple problem representations in an activity (e.g., both a word problem and a video demo), in which case students have multiple referents to consider. To study students’ modeling behavior in these situations, we conducted think-aloud interviews with pairs of students around a kinematics activity. While creating process maps of students’ modeling, we found that tracking students’ “system focus” was critical to interpreting their reasoning and decisions. The model referent is no longer seen as a static object; instead, it is a dynamic object that changes in response to both structured prompts and spontaneous events. This concept gives rise to practical insights into activity design and implementation.

Tracking the referent system to understand students' math modeling processes