  Physics makes powerful use of mathematics, yet the way this use is made is
often poorly understood. Professionals closely integrate their mathematical
symbology with physical meaning, resulting in a powerful and productive
structure. But because of the way the cognitive system builds expertise through
binding, experts may have difficulty in unpacking their well established
knowledge in order to understand the difficulties novice students have in
learning their subject. This is particularly evident in subjects in which the
students are learning to use mathematics to which they have previously been
exposed in math classes in complex new ways. In this paper, we propose that
some of this unpacking can be facilitated by adopting ideas and methods
developed in the field of cognitive semantics, a sub-branch of linguistics
devoted to understanding how meaning is associated with language.
