Partial derivatives are among the many advanced mathematical topics used throughout physics to help describe the physical world. At Oregon State University, we are developing a learning progression for partial derivatives that spans undergraduate mathematics and physics courses over multiple years. We present a possible path for students to follow as they learn, use, and build upon the concepts associated with partial derivatives. We describe research on student interpretations of partial derivatives and on how these interpretations differ from course to course, with an emphasis on how students understand the idea of "holding a variable constant." We also describe researchbased instructional material designed to support students' progression through the concepts and representations related to partial derivatives that are common and critical in the study of physics.
