The toolbox of algebraic manipulations that students traditionally learn to use in multivariable and vector calculus is not a good match for many applications in other disciplines, such as physics. Mastery of electromagnetism, for example, requires a geometric understanding of vector fields and their derivatives. Furthermore, most mathematical modeling requires a robust understanding of the relationship between discrete data and its idealization as smooth mathematical objects. These applications require students to have rich concept images of partial derivatives that go well beyond what is typically taught in second-year calculus.
This talk describes efforts at Oregon State University to help students master the use of partial derivatives in such physical and geometric contexts, in both mathematics and physics courses. Several examples will be presented where language differences between disciplines lead to student difficulties, as will some of the methods and tools that we have developed to address them, including some of the underlying education research.
(OLSUME talks are recorded, and easily available afterward.)