  Expanding our knowledge of student difficulties in advanced undergraduate
electromagnetism is essential if we are to develop effective instructional
interventions. Drawing on an analysis of course materials, in-class
observations and responses to conceptual questions, we document specific
resources employed by students when reasoning about the divergence of a vector
field. One common student error, which persisted in our course despite explicit
instruction, is to misinterpret any "spreading out" of field lines in a diagram
as representing a place of non-zero divergence. Some of these student
difficulties can likely be attributed to having first learned about the
divergence in a mathematical context, where there was little emphasis on
graphical representations of vector fields and connections to physical
situations.
