  Undergraduate physics students are known to have difficulties with
understanding mathematical tools, and with applying their knowledge of
mathematics to physical contexts. Using survey statements based on student
interviews and written responses to open-ended questions, we investigated the
prevalence of correct and incorrect conceptions regarding the divergence and
curl of vector fields, among both mathematics and physics students. We compare
and contrast pre-instruction responses from intermediate-level E&M students at
KU Leuven and the University of St Andrews, with post-instruction responses
from St Andrews students enrolled in a vector calculus course. The differences
between these student populations were primarily in areas having to do with
physics-related concepts and graphical representations of vector fields. Our
comparison of pre- and post-instruction responses from E&M students shows that
their understanding of the divergence and curl improved significantly in most
areas, though not as much as would be desired.
