As a discipline, physics is concerned with describing the world by constructing models, the end product of this modelling process often being an equation. As such, physics equations represent much more than a finalized, ready-to-use calculation package – to physicists they are the culmination of a whole range of actions, assump- tions, approximations and historical discoveries. Moreover, physics equations are not simply stand-alone entities, rather they are intimately bound up with other equa- tions. Together, this web of equations represents an integrated, coherent whole that signals the way the community of physicists view the world.

Clearly, such a nuanced, expert-like understanding of physics equations is not spontaneously available to undergraduate physics students when they meet an equa- tion for the first time. In this respect, research suggests that we should not expect students to display conceptually coherent understanding across settings. Rather it has been suggested that understanding is built up from context-dependent knowl- edge in pieces (diSessa 1993, 2018). In this characterization, different aspects, or ways of viewing the same phenomenon, are leveraged in different settings. Students gradually develop their understanding in two ways: by forging links between these separate ‘pieces of knowledge’ and by coming to appreciate the usefulness of a given ‘piece of knowledge’ for a given task. Educationally then, we are interested in identifying these pieces of knowledge – in our case the range of ways that students understand equations. What are students’ default positions with respect to equa- tions? Which aspects of equations do students tend to focus on and which aspects tend to go unnoticed? Once we have documented the range of ways of understand- ing, the next task concerns how to help students discern other aspects of equations than those they may initially notice. Do the tasks that students are presented with in their undergraduate education encourage them to move towards a more nuanced, coherent, holistic understanding of physics equations?