What Does It Mean to Understand a Physics Equation? A Study of Undergraduate Answers in Three Countries

In this chapter we are interested in how undergraduate physics students in three countries experience the equations they meet in their education. We asked over 350 students in the USA, Australia and Sweden 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 similarity of the answers we received across the three countries surprised us and led to us treating all the answers as a single ‘pool of meaning’. Qualitative analysis resulted in eight distinct themes: significance, origin, description, prediction, parts, relationships, calculation and explanation. Drawing on diSessa’s theory of knowledge in pieces, we argue that each theme represents a different disciplinary aspect of student understanding of physics equations. Educationally, we wondered how best to highlight the more holistic view of equations that analysis of the combined data sets revealed. 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 meet a new physics equation, they may ask themselves these questions in order to check their holistic understanding of what the equation represents. In continuing work we are asking our same original question to a cohort of physics lecturers in order to consolidate the themes we have already identified and to look for further themes. 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.