Seminar: Ben Schermerhorn [Cal Poly Pomona]
Student construction of a differential length vector in an unconventional spherical coordinate system
Sep 27, 2018 11:00 AM to Sep 27, 2018 12:00 PM at Building 8 - Room 241
Vector calculus and multivariable coordinate systems play a large role in the understanding and calculation of much of the physics in upper-division electricity and magnetism (E&M). One key mathematical piece of students' use of vector calculus is the representation of differential vector elements. In an effort to examine student understanding of non-Cartesian differential length elements, students in junior-level E&M were interviewed in pairs and asked to construct a differential length vector for an unconventional spherical coordinate system. Analysis focused on students’ understanding of the mathematical structures of the expression by identifying symbolic forms [Sherin, 2001], and highlighted several common ideas in students' concept images [Tall & Vinner, 1981] of a non-Cartesian differential length vector as they determined their expressions. As no interview initially resulted in the construction of an appropriate differential, analysis addressed the role of the evoked concept images and symbolic forms on students' performance throughout the task.