  Learning to use math in physics involves combining (blending) our everyday
experiences and the conceptual ideas of physics with symbolic mathematical
representations. Graphs are one of the best ways to learn to build the blend.
They are a mathematical representation that builds on visual recognition to
create a bridge between words and equations. But students in introductory
physics classes often see a graph as an endpoint, a task the teacher asks them
to complete, rather than as a tool to help them make sense of a physical
system. And most of the graph problems in traditional introductory physics
texts simply ask students to extract a number from a graph. But if graphs are
used appropriately, they can be a powerful tool in helping students learn to
build the blend and develop their physical intuition and ability to think with
math.
