Abstract
An in-depth investigation to identify cognitive resources upper division physics students use to reason about unit vectors, position vectors, and velocity vectors in polar coordinates.
Highlights
Using non-Cartesian coordinate systems continues to be difficult for undergraduate physics students [1,2,3] even in upper-division physics courses where application of these mathematical ideas plays a more significant role [4,5,6,7]
As part of a larger initiative into exploring the math-physics interface in upper-division physics courses [8,9], our current collaboration has initiated the development of a research-based curriculum for a mathematical methods course for undergraduate physics majors
On spiral question A (SQA), Mark gave accurate and complete definitions for rand θ, drawing rvectors in the same direction as the corresponding r⃗ vectors (Fig. 6) and stating the following two justifications respectively (M# are Mark’s statements): M1 “[rpoints] away from the origin” M2 “[θ] is in the direction of increasing θ where θ is like your azimuthal.”
Summary
The polar coordinate system, both planar and spherical, is commonly used in a number of upper-division physics courses, including mechanics, electrodynamics, and quantum mechanics [4,5,6,7,10]. Despite this focus, research has shown that students struggle using these coordinate systems. Paoletti et al [3] found that students spend the greatest proportion of their math training using Cartesian coordinates, and apply Cartesian coordinate system conventions to polar coordinates Their findings are consistent with findings by Montiel and various colleagues [1,2] who claim mathematical meaning is often tied to the coordinate system in which a concept is learned.
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