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Instruction-based clinical eye-tracking study on the visual interpretation of divergence: How do students look at vector field plots?

P. Klein1,*, J. Viiri2, S. Mozaffari3, A. Dengel3,4, and J. Kuhn1

  • 1Department of Physics, Physics Education Research Group, University of Kaiserslautern, Erwin-Schrödinger-Strasse 46, 67663 Kaiserslautern, Germany
  • 2Department of Teacher Education, University of Jyväskylä, 40014 Jyväskylä, Finland
  • 3Smart Data & Knowledge Services, German Research Center for Artificial Intelligence, Trippstadter Strasse, 122, 67663 Kaiserslautern, Germany
  • 4Computer Science Department, University of Kaiserslautern, Erwin-Schrödinger-Strasse 46, 67663 Kaiserslautern, Germany

  • *pklein@physik.uni-kl.de
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Phys. Rev. Phys. Educ. Res. 14, 010116 – Published 28 March, 2018

DOI: https://doi.org/10.1103/PhysRevPhysEducRes.14.010116

Abstract

Relating mathematical concepts to graphical representations is a challenging task for students. In this paper, we introduce two visual strategies to qualitatively interpret the divergence of graphical vector field representations. One strategy is based on the graphical interpretation of partial derivatives, while the other is based on the flux concept. We test the effectiveness of both strategies in an instruction-based eye-tracking study with N=41 physics majors. We found that students’ performance improved when both strategies were introduced (74% correct) instead of only one strategy (64% correct), and students performed best when they were free to choose between the two strategies (88% correct). This finding supports the idea of introducing multiple representations of a physical concept to foster student understanding. Relevant eye-tracking measures demonstrate that both strategies imply different visual processing of the vector field plots, therefore reflecting conceptual differences between the strategies. Advanced analysis methods further reveal significant differences in eye movements between the best and worst performing students. For instance, the best students performed predominantly horizontal and vertical saccades, indicating correct interpretation of partial derivatives. They also focused on smaller regions when they balanced positive and negative flux. This mixed-method research leads to new insights into student visual processing of vector field representations, highlights the advantages and limitations of eye-tracking methodologies in this context, and discusses implications for teaching and for future research. The introduction of saccadic direction analysis expands traditional methods, and shows the potential to discover new insights into student understanding and learning difficulties.

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Phys. Rev. Phys. Educ. Res. 14, 010116– Published 28 March, 2018
  • Received 13 November 2017
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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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