Exploring Rates of Change in Calculus and Upper-Level Physics Courses

Physics is the study of change. In many cases, this change involves more than one independent and one dependent physical quantity. In these cases the partial derivative is an important tool, including the geometric combinations of partial derivatives in E & M (e.g. gradient) and the measurable combinations in thermodynamics (e.g. heat capacity). These applications required students to have rich concept images of partial derivatives which go well beyond what is typically taught in a multivariable calculus course, particularly concepts which deal with data and experimental representations. Using a mixed workshop/talk format, participants will explore examples of instructional materials designed to foster improved learning of partial derivatives concepts and experience innovative hands-on tools, such as the partial derivative machine and two dimensional dry erasable plastic surfaces. We also describe key aspects of our research to understand how students interact with these materials. This work was supported in part by NSF grant DUE-1323800.