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Students' difficulties with vector calculus in electrodynamics

DOI:10.1103/PhysRevSTPER.11.020129
Authors:
Laurens Bollen at KU Leuven
Laurens Bollen
Paul van Kampen at Dublin City University
Paul van Kampen
Mieke De Cock at KU Leuven
Mieke De Cock
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Understanding Maxwell's equations in differential form is a prerequisite to study the electrodynamic phenomena that are discussed in advanced electromagnetism courses. It is therefore necessary that students master the use of vector calculus in physical situations. In this light we investigated the difficulties second year students at KU Leuven encounter with the divergence and curl of a vector field in mathematical and physical contexts. We have found they are quite skilled at doing calculations, but struggle with interpreting graphical representations of vector fields and applying vector calculus to physical situations. We have found strong indications that traditional instruction is not sufficient for our students to fully understand the meaning and power of Maxwell's equations in electrodynamics.
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... In contrast, research showed that students had less problems determining these aspects mathematically via equations [2,10]. Bollen et al. [10] investigated students' difficulties in understanding divergence and curl using vector fields in the context of electrodynamics and electromagnetism (see also [9]). They found that students struggled with interpreting graphical representations of vector fields, indicating a lack of conceptual understanding [9,10]. ...
... Bollen et al. [10] investigated students' difficulties in understanding divergence and curl using vector fields in the context of electrodynamics and electromagnetism (see also [9]). They found that students struggled with interpreting graphical representations of vector fields, indicating a lack of conceptual understanding [9,10]. ...
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