  A primary goal of physics is to create mathematical models that allow both
predictions and explanations of physical phenomena. We weave maths extensively
into our physics instruction beginning in high school, and the level and
complexity of the maths we draw on grows as our students progress through a
physics curriculum. Despite much research on the learning of both physics and
math, the problem of how to successfully teach most of our students to use
maths in physics effectively remains unsolved. A fundamental issue is that in
physics, we don't just use maths, we think about the physical world with it. As
a result, we make meaning with math-ematical symbology in a different way than
mathematicians do. In this talk we analyze how developing the competency of
mathematical modeling is more than just "learning to do math" but requires
learning to blend physical meaning into mathematical representations and use
that physical meaning in solving problems. Examples are drawn from across the
curriculum.

Physics Education