Investigation into Physics Students' Interpretations of Equations and Equal Signs

The ability to meaningfully interpret equations as both representative of physical relationships and descriptive of physical phenomena is a crucial skill for students to develop throughout an undergraduate physics education. During an undergraduate degree in physics, students come across a multitude of mathematical expressions that encode physical relationships. Beyond learning how to work with these equations to successfully solve problems in homework sets and exams, it is an expectation that students develop an expert-like ability to "read" these equations in terms of the causal relationships and interactions they express between the physical quantities contained within them. To investigate the development of this skill throughout an undergraduate curriculum, an investigation was conducted on students enrolled in multiple courses at multiple institutions. Surveys were administered which asked students to interpret multiple "canonical" physical equations. These responses were analyzed to ascertain how the students viewed both the equations as a whole and the role of the equal sign. Discussion of these interpretations, as well as next steps, will be discussed.