It’s Not “Just” an Equation: How Students Dynamically Coordinate Mechanistic and Mathematical Schemas with Complex Equations

Abstract

Complex scientific equations often appear opaque to students—not just because of symbolic formatting, but also due to how learners activate and coordinate different varieties of mechanistic and mathematical schemas. We present a multimodal analysis of advanced undergraduates’ reasoning across three interview tasks involving concepts modeled by the Nernst equation—an equation that models electrochemical equilibrium. Drawing on the Knowledge in Pieces framework, particularly the symbolic-forms framework, we show that students interpret the equation by coordinating the same mathematical structures with different mechanistic schemas—principally equilibrium- and balance-based reasoning. One student, Oscar, highlights dynamic shifts between these reasoning modes compared to his peers who were relatively more stable in their either equilibrium- or balance-based reasoning. We illustrate how an equation’s format can sometimes shift students away from productive mathematical schemata coupled to mechanistic schemata that align with a natural system’s structure. We argue that instructors should attend not only to students’ formal manipulations of equations but also to how task design and equation format jointly co-activate different knowledge resources and modes of reasoning. Implications for instructional design include deliberately cueing conceptual framings that develop mechanistic reasoning in addition to calculation.