Currently focused on university physics majors (though the project could easily expand into K-12), this research focuses not on the content of the mathematics that students bring to bear in physics, but rather, on the ways they approach problem solving using math. We find that physics majors have developed multiple "modes" of using math in physics, ranging from math rule/procedure quoting, in which a mathematical algorithm is trusted as a black box for producing an answer, to mapping math to physics, in which the student tries to read off the physical meaning corresponding to a given mathematical equation or operation. A key result here is that students don't have a fixed "learning style" for using math in physics; we observe each individual student shifting among the various modes based on contextual factors that we are now studying.
How do students use mathematics in physics problem solving?