Investigating student understanding of cross products in a mathematical and two electromagnetism contexts

We investigated the influence of context on students’ understanding of cross products of vectors using three isomorphic multiple-choice tests asking for the direction of a cross product in different geometrical settings. One version of the test involved the Lorentz force, the second version involved...

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Autores principales:	T. Deprez, S. E. Gijsen, J. Deprez, M. De Cock
Formato:	article
Lenguaje:	EN
Publicado:	American Physical Society 2019
Materias:	Special aspects of education LC8-6691 Physics QC1-999
Acceso en línea:	https://doaj.org/article/d4516da747d84dc680f5a8c99984a13d
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spelling	oai:doaj.org-article:d4516da747d84dc680f5a8c99984a13d2021-12-02T11:44:47ZInvestigating student understanding of cross products in a mathematical and two electromagnetism contexts10.1103/PhysRevPhysEducRes.15.0201322469-9896https://doaj.org/article/d4516da747d84dc680f5a8c99984a13d2019-09-01T00:00:00Zhttp://doi.org/10.1103/PhysRevPhysEducRes.15.020132http://doi.org/10.1103/PhysRevPhysEducRes.15.020132https://doaj.org/toc/2469-9896We investigated the influence of context on students’ understanding of cross products of vectors using three isomorphic multiple-choice tests asking for the direction of a cross product in different geometrical settings. One version of the test involved the Lorentz force, the second version involved the torque on an electric dipole, and the third version was without physics context. We administered the tests to 216 first-year pre-med students at a Belgian (Flemish) university. We found that students perform significantly better in the context of the Lorentz force. Students more often chose the incorrect alternative corresponding to the vector sum in the test versions involving an electric dipole or without physics context when the vectors are not orthogonal. For orthogonal vectors, a sign error—i.e., inverting the direction of the resulting vector—was the most common mistake in both tests with physics context, while without physics context selecting the alternative corresponding to the sum remained the most common mistake. Prior familiarity with a right-hand rule in a specific context seems to be able to explain improved scores in the test version concerning the Lorentz force. Instructors and curriculum developers can benefit from adopting an integrated approach in which the mathematical aspects of the cross product are treated together with multiple examples in physics, allowing students to transition from using specific rules to determine a cross product, to a more integrated understanding of it.T. DeprezS. E. GijsenJ. DeprezM. De CockAmerican Physical SocietyarticleSpecial aspects of educationLC8-6691PhysicsQC1-999ENPhysical Review Physics Education Research, Vol 15, Iss 2, p 020132 (2019)
institution	DOAJ
collection	DOAJ
language	EN
topic	Special aspects of education LC8-6691 Physics QC1-999
spellingShingle	Special aspects of education LC8-6691 Physics QC1-999 T. Deprez S. E. Gijsen J. Deprez M. De Cock Investigating student understanding of cross products in a mathematical and two electromagnetism contexts
description	We investigated the influence of context on students’ understanding of cross products of vectors using three isomorphic multiple-choice tests asking for the direction of a cross product in different geometrical settings. One version of the test involved the Lorentz force, the second version involved the torque on an electric dipole, and the third version was without physics context. We administered the tests to 216 first-year pre-med students at a Belgian (Flemish) university. We found that students perform significantly better in the context of the Lorentz force. Students more often chose the incorrect alternative corresponding to the vector sum in the test versions involving an electric dipole or without physics context when the vectors are not orthogonal. For orthogonal vectors, a sign error—i.e., inverting the direction of the resulting vector—was the most common mistake in both tests with physics context, while without physics context selecting the alternative corresponding to the sum remained the most common mistake. Prior familiarity with a right-hand rule in a specific context seems to be able to explain improved scores in the test version concerning the Lorentz force. Instructors and curriculum developers can benefit from adopting an integrated approach in which the mathematical aspects of the cross product are treated together with multiple examples in physics, allowing students to transition from using specific rules to determine a cross product, to a more integrated understanding of it.
format	article
author	T. Deprez S. E. Gijsen J. Deprez M. De Cock
author_facet	T. Deprez S. E. Gijsen J. Deprez M. De Cock
author_sort	T. Deprez
title	Investigating student understanding of cross products in a mathematical and two electromagnetism contexts
title_short	Investigating student understanding of cross products in a mathematical and two electromagnetism contexts
title_full	Investigating student understanding of cross products in a mathematical and two electromagnetism contexts
title_fullStr	Investigating student understanding of cross products in a mathematical and two electromagnetism contexts
title_full_unstemmed	Investigating student understanding of cross products in a mathematical and two electromagnetism contexts
title_sort	investigating student understanding of cross products in a mathematical and two electromagnetism contexts
publisher	American Physical Society
publishDate	2019
url	https://doaj.org/article/d4516da747d84dc680f5a8c99984a13d
work_keys_str_mv	AT tdeprez investigatingstudentunderstandingofcrossproductsinamathematicalandtwoelectromagnetismcontexts AT segijsen investigatingstudentunderstandingofcrossproductsinamathematicalandtwoelectromagnetismcontexts AT jdeprez investigatingstudentunderstandingofcrossproductsinamathematicalandtwoelectromagnetismcontexts AT mdecock investigatingstudentunderstandingofcrossproductsinamathematicalandtwoelectromagnetismcontexts
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Investigating student understanding of cross products in a mathematical and two electromagnetism contexts

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