  Mathematics is an essential element of physics problem solving, but experts
often fail to appreciate exactly how they use it. Math may be the language of
science, but math-in-physics is a distinct dialect of that language. Physicists
tend to blend conceptual physics with mathematical symbolism in a way that
profoundly affects the way equations are used and interpreted. Research with
university physics students in classes from algebra-based introductory physics
indicates that the gap between what students think they are supposed to be
doing and what their instructors expect them to do can cause severe problems.
