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

  • 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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Metadaten
Author:Pascal Klein, Jouni Viiri, Saleh Mozaffari, Andreas Dengel, Jochen Kuhn
URN (permanent link):urn:nbn:de:hbz:386-kluedo-55789
DOI:https://doi.org/10.1103/PhysRevPhysEducRes.14.010116
Document Type:Article
Language of publication:English
Publication Date:2018/03/28
Year of Publication:2018
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2019/04/08
Tag:Assessment; Concepts & Principles; Physics Education Research; Research Methodology; Undergraduate Students
GND-Keyword:Kognitives Lernen; Lernen; Physikdidaktik; Wissensrepräsentation
Number of page:17
Source:Physical review physics education research 14, 010116 (2018)
Faculties / Organisational entities:Fachbereich Physik
CCS-Classification (computer science):A. General Literature / A.m MISCELLANEOUS
DDC-Cassification:3 Sozialwissenschaften / 370 Erziehung, Schul- und Bildungswesen
5 Naturwissenschaften und Mathematik / 530 Physik
MSC-Classification (mathematics):00-XX GENERAL / 00Axx General and miscellaneous specific topics / 00A79 Physics (use more specific entries from Sections 70 through 86 when possible)
PACS-Classification (physics):00.00.00 GENERAL / 01.00.00 Communication, education, history, and philosophy / 01.40.-d Education / 01.40.Fk Research in physics education
Licence (German):Zweitveröffentlichung