Understanding student understanding in upper-division courses

Upper-division physics courses require students not only to engage with complex physics concepts but also to utilize sophisticated mathematical tools. As such, understanding students' struggles and the barriers they encounter in upper-division courses often requires making sense of a complex problem-solving process. Here, I will discuss several approaches to analyzing student learning in upper-division courses which target different aspects of the problem-solving process. I will also discuss lessons learned and implications for the teaching of these courses.