  When students are learning to use math in physics, one of the most important
ideas they need to learn is that equations are not just calculational tools;
they represent relationships between physical variables that change together
(covary). How much a change in one variable or parameter is associated with a
change in another depends on how they appear in the equation: their functional
dependence. Understanding this sort of relationship is rarely taught in
introductory mathematics classes, and students who have not yet learned to
blend conceptual ideas with mathematical symbols may not see the relevance and
power of this idea. We need to explicitly teach functional dependence as part
of our effort to help students to learn to use math productively in science.
