Physicists solve problems and communicate their work using many external representations, such as equations, words, diagrams, graphs, sketches, pictures, and more. To learn physics, then, students must learn to use external representations. In this dissertation, I present three manuscripts. Each manuscript discusses how upper-division Paradigms in Physics students use multiple representations during in-class activities specifically designed to develop deeper physics understanding and build connections between representations. In the first two manuscripts, I looked at an activity where students generate equipotential curves for two different collections of point charges. I show how the representations were used together in one group’s science practices, particularly developing and using models, using mathematics and computational thinking, constructing explanations, and engaging in argument from evidence. I conclude in my analysis of the equipotentials activity that some representations are more useful for students to represent their own understanding to each other and the instructor, preparing them to discuss representations that serve as evidence. Furthermore, having multiple representations allowed the students to make very direct comparisons and identify essential underlying elements of all the representations. In the third manuscript, I looked at a thermodynamics activity and discuss how several different groups of students selected a representation and how the students reasoned about covariation. I conclude that the students effectively chose a graph where the variable they were told to change was on an axis, but that the students tended to assume that the other axis variable must then be held constant. This dissertation builds on current ideas about the use of external representations in physics by showing how specific representations support student learning, and how students use multiple representations to learn. Relevant extensions of this work are investigations of how student-generated representations connect to student reasoning, and how students select external representations when exploring physical systems
