Tacit Knowledge and Embodied Insight in Mathematical Modeling

ABSTRACT Mathematical modeling is a challenging and creative process. If one considers only interim or final solutions to modeling problems or interviews modelers afterward, often only their explicit models are accessible – those expressed in work products or evinced in verbal and written reflections. The inner world of tacit knowledge and its impacts on mathematical modeling remain largely inaccessible to such approaches. To understand when and how tacit knowledge can emerge onto the explicit plane as insight during modeling, we present an exploratory and instrumental single-case study. We analyze the embodied interactions of a pair of ninth grade (age 14–15) students as they collaboratively solved a modeling problem. We introduce the phenomenon of embodied insight as a pattern of interaction, in which tacit knowledge becomes explicit and shapes modeling work, and we analyze three such episodes from this pair’s modeling. This work contributes to the field by illustrating the potential in studying embodied social discourse in collaboration to reveal the operation of tacit knowledge in mathematical modeling and its expression on the explicit plane.