The Role of Reasoning with Quantities in Undergraduates’ Modeling Activities

Source abstract

Abstract Mathematical modeling is challenging for learners across all grade bands. Given its crucial role in STEM education, it is essential for the field to design learning environments that foster the optimal learning of modeling. One promising strategy is to support the learning of modeling as conceiving a situation consisting of quantities and quantitative relationships. However, before promoting the learning of modeling in this way, the field first needs accounts of how quantitative reasoning is present in students’ mathematical modeling activities. Drawing data from individual teaching experiments with three undergraduate STEM majors, we analyzed the ways in which reasoning with quantities manifest as they mathematically modeled dynamic situations. Through our analysis, we illustrate eight types of manifestations, making explicit connections between the modeling activities and participants' reasonings with quantities during each manifestation. Our findings indicate that learners’ modeling activities are afforded through their reasonings with quantities and suggest that students’ quantitative reasoning can be leveraged to support the learning of mathematical modeling.