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This work is part of a broader project to investigate student understanding of mathematical ideas used in upper-division physics. This study in particular probes students’ understanding of the divergence and curl operators as applied to vector field diagrams. We examined how students reason with partial derivatives that constitute divergence and curl of the vector field diagrams. Students’ written responses to a task on derivatives, divergence, and curl of a 2D vector field were collected and coded. Students were generally successful in determining the sign of some of the constituent derivatives of div and curl, but struggled in one case in which components were negative. Analysis of written explanations showed confusion between the sign, direction, and change in the magnitude of vector field components.
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How students reason with derivatives of vector field diagrams
Physics students are introduced to vector fields in introductory courses, typically in the contexts of electric and magnetic fields. Vector calculus provides several ways to describe how vector fields vary in space including the gradient, divergence, and curl. Physics majors use vector calculus extensively in a junior-level electricity and magnetism (E&M) course. Our focus here is exploring student reasoning with the partial derivatives that constitute divergence and curl in vector field representations, adding to the current understanding of how students reason with derivatives.
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- Award ID(s):
- 1912087
- PAR ID:
- 10535983
- Editor(s):
- Dreyfus, T; González-Martín, A S; Nardi, E; Monaghan, J; Thompson, P W
- Publisher / Repository:
- The Learning and Teaching of Calculus Across Disciplines – Proceedings of the Second Calculus Conference
- Date Published:
- Page Range / eLocation ID:
- 173-176
- Format(s):
- Medium: X
- Location:
- Bergen, Norway
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Conference Proceeding:
- The DOI is not currently available.
