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Student difficulties regarding symbolic and graphical representations of vector fields

Bollen, Laurens; van Kampen, Paul; Baily, Charles; Kelly, Mossy; De Cock, Mieke


Laurens Bollen

Paul van Kampen

Charles Baily

Mossy Kelly

Mieke De Cock


The ability to switch between various representations is an invaluable problem-solving skill in physics. In addition, research has shown that using multiple representations can greatly enhance a person’s understanding of mathematical and physical concepts. This paper describes a study of student difficulties regarding interpreting, constructing, and switching between representations of vector fields, using both qualitative and quantitative methods. We first identified to what extent students are fluent with the use of field vector plots, field line diagrams, and symbolic expressions of vector fields by conducting individual student interviews and analyzing in-class student activities. Based on those findings, we designed the Vector Field Representations test, a free response assessment tool that has been given to 196 second- and third-year physics, mathematics, and engineering students from four different universities. From the obtained results we gained a comprehensive overview of typical errors that students make when switching between vector field representations. In addition, the study allowed us to determine the relative prevalence of the observed difficulties. Although the results varied greatly between institutions, a general trend revealed that many students struggle with vector addition, fail to recognize the field line density as an indication of the magnitude of the field, confuse characteristics of field lines and equipotential lines, and do not choose the appropriate coordinate system when writing out mathematical expressions of vector fields.


Bollen, L., van Kampen, P., Baily, C., Kelly, M., & De Cock, M. (2017). Student difficulties regarding symbolic and graphical representations of vector fields. Physical Review Physics Education Research, 13(2), Article 020109.

Journal Article Type Article
Acceptance Date Apr 5, 2017
Online Publication Date Aug 16, 2017
Publication Date Aug 16, 2017
Deposit Date Jun 28, 2018
Publicly Available Date Oct 27, 2022
Journal Physical Review Physics Education Research
Print ISSN 2469-9896
Electronic ISSN 2469-9896
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 13
Issue 2
Article Number 020109
Public URL
Publisher URL


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Copyright Statement
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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