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 mathematical symbology in a different way than mathematicians do. In this talk we analyse how developing the competency of mathematical modelling 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.

This paper is part of a select compilation of exemplary proceedings, titled Key Competences in Physics Teaching and Learning. All articles in this compilation were presented at the GIREP-EPEC 2015 conference, organized by the International Research Group on Physics Teaching (GIREP); European Physical Society – Physics Education Division. See Related Materials for a link to purchase the full book, available in both digital and nondigital formats.