• Open Access

Student difficulties regarding symbolic and graphical representations of vector fields

Laurens Bollen, Paul van Kampen, Charles Baily, Mossy Kelly, and Mieke De Cock
Phys. Rev. Phys. Educ. Res. 13, 020109 – Published 16 August 2017

Abstract

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.

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  • Received 5 April 2017

DOI:https://doi.org/10.1103/PhysRevPhysEducRes.13.020109

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.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Physics Education Research

Authors & Affiliations

Laurens Bollen1,*, Paul van Kampen2,†, Charles Baily3,‡, Mossy Kelly4,§, and Mieke De Cock1,∥

  • 1KU Leuven, Department of Physics and Astronomy & LESEC, Celestijnenlaan 200c, 3001 Leuven, Belgium
  • 2Centre for the Advancement of STEM Teaching and Learning & School of Physical Sciences, Dublin City University, Glasnevin, Dublin 9, Ireland
  • 3School of Physics & Astronomy, University of St Andrews, St Andrews, KY16 9SS, United Kingdom
  • 4Department of Physics and Mathematics, University of Hull, Kingston-upon-Hull, HU6 7RX, United Kingdom

  • *Laurens.Bollen@kuleuven.be
  • Paul.van.Kampen@dcu.ie
  • crb6@st-andrews.ac.uk
  • §Mossy.Kelly@hull.ac.uk
  • Mieke.DeCock@kuleuven.be

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Issue

Vol. 13, Iss. 2 — July - December 2017

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