  Mathematics is the language of science. Fluent and productive use of
mathematics requires one to understand the meaning embodied in mathematical
symbols, operators, syntax, etc., which can be a difficult task. For instance,
in algebraic symbolization, the negative and positive signs carry multiple
meanings depending on contexts. In the context of electromagnetism, we use
conceptual blending theory to demonstrate that different physical meanings,
such as directionality and location, could associate to the positive and
negative signs. With these blends, we analyze the struggles of upper-division
students as they work with an introductory level problem where the students
must employ multiple signs with different meanings in one mathematical
expression. We attribute their struggles to the complexity of choosing blends
with an appropriate meaning for each sign, which gives us insight into
students' algebraic thinking and reasoning.
