*45%*:**Representation issues: Using mathematics in upper-division physics***41%*:**Student difficulties with quantum states while translating state vectors in Dirac notation to wave functions in position and momentum representations***40%*:**Research-Based Course Materials and Assessments for Upper-Division Electrodynamics (E&M II)***40%*:**Tapping into Juniorsâ€™ Understanding of E&M: The Colorado Upper-Division Electrostatics (CUE) Diagnostic***40%*:**Student Objections to and Understanding of Non-Cartesian Unit Vector Notation in Upper-Level E&M***39%*:**Student Ideas around Vector Decomposition in the Upper Division***37%*:**Standing fast: Translation among durable representations using evanescent representations in upper-division problem solving***34%*:**E&M Tutorial III: Distinguishing between the electric field & electric flux***34%*:**Nesting in graphical representations in physics***34%*:**Student understanding of unit vectors and coordinate systems beyond cartesian coordinates in upper division physics courses***33%*:**Student difficulties in translating between mathematical and graphical representations in introductory physics***32%*:**Assessing students' ability to solve introductory physics problems using integrals in symbolic and graphical representations***32%*:**Algebra-Based Students and Vector Representations: Arrow vs. ijk***31%*:**Paradigms in Physics E&M: Acting Out Charge Densities***31%*:**Paradigms in Physics E&M: Total Charge***31%*:**Investigating graphical representations of slope and derivative without a physics context***31%*:**Improving Student Understanding of Vector Fields in Junior-Level E&M***31%*:**A Comparison of Visual Representations of E&M Plane Waves***30%*:**E&M Tutorial IV: Exploiting Gauss's Law to Find the Magnitude of the Electric Field**