What does it mean to understand a physics equation?: A study of undergraduate answers in three countries

In this paper we are interested in how undergraduate students in the US, Australia and Sweden experience the physics equations they meet in their education. We asked over 350 students the same simple question: How do you know when you understand a physics equation? Students wrote free-text answers to this question and these were transcribed and coded. The analysis resulted in eight themes (significance, origin, describe, predict, parts, relationships, calculate and explain). Each of these themes represents a different disciplinary aspect of student understanding of physics equations. We argue that together the different aspects we find represent a more holistic view of physics equations that we would like all our students to experience. Based on this work we wondered how best to highlight this more holistic view of equations. This prompted us to write a set of questions that reflect the original data with respect to the eight themes. We suggest that when students are working with problem solving they may ask themselves these questions in order to check their holistic understanding of what the physics equations they are using represent. In continuing work we are asking the same question to a cohort of physics lecturers. We are also trialling the themes and related questions that we generated in teaching situations. Here we are interested in whether students perceive the questions as helpful in their learning.