Shared Resources in Student Understanding of Spherical Unit Vectors in Upper-division E&M, A Cross-Case Comparison

We are interested in better understanding ways that students collaborate to solve conceptual physics problems in the context of spherical unit vectors in upper-level E&M, especially problems that have been shown to be difficult for students to solve individually on their own, but which groups of students have been more successful at. We apply the framework of shared resources to examine cases where students collaborated effectively--first one student activated a conceptual resource and expressed it, then another student took up that idea, and finally the whole group together used that idea to move forward with the problem. In our provisou work, we reported our methodology and the results from one group interview to illustrate one shared resource we identified and the role it played in helping students collaboratively solve the conceptual problem in that context.In this talk, we compare examples from two different groups to consolidate our theory and analysis. Our goal is to construct a more complete set of typical, sharable resources in students' understanding of spherical unit vectors and suggest implications for instruction.