In their study of physics beyond the first year of University?termed upper-division in the US, many
of students? primary learning opportunities come from working long, complex back-of-the-book style
problems, and from trying to develop an understanding of the underlying physics through solving such
problems. Some of the research at the upper-division focuses on how students use mathematics in
these problems, and what challenges students encounter along the way. There are a number of
different and diverse research studies on students? use of mathematics in the upper-division. These
typically utilize one of two broad approaches, with some researchers primarily seeking out and
addressing challenges students face, and others working chiefly to unpack students? in-the-moment
reasoning. In this paper, we present and discuss both approaches, and then review research efforts
that strive to connect these two approaches in order to make sense of students? use of mathematics
as well …