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  • Open Access

Gaze behavior as a key to revealing strategies for identifying indirectly proportional graphs in thermodynamic and mathematical context

Paula Fehlinger1,2,*, Sebastian Becker-Genschow3, and Bianca Watzka1

  • 1RWTH Aachen University, Institute of Physics IA, Didactics of Physics and Technology, Sommerfeldstraße 16, 52074 Aachen, Germany
  • 2Otto von Guericke University Magdeburg, Faculty of Natural Sciences, Institute of Physics, Universitätsplatz 2, 39106 Magdeburg, Germany
  • 3University of Cologne, Faculty of Mathematics and Natural Sciences, Digital Education Research, Herbert-Lewin-Straße 10, 50931 Cologne, Germany

  • *Contact author: fehlinger@physik.rwth-aachen.de
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Phys. Rev. Phys. Educ. Res. 21, 020129 – Published 23 September, 2025

DOI: https://doi.org/10.1103/4pn3-fs4y

Abstract

The ability to accurately interpret mathematical functions is crucial for understanding complex physical and mathematical concepts. Differentiating isothermal from adiabatic change of state in p−V diagrams respectively graphs of indirectly proportional functions from graphs of power functions in x−y diagrams presents a common challenge for students. This study examines the gaze behavior of 80 10th-grade students to identify the processing strategies they use when distinguishing these graphs of functions in mathematical and thermodynamic contexts. The cluster analysis of the gaze data revealed two main strategies: focusing on the value pairs, often resulting in a higher number of correct responses, and focusing on the graph itself, often resulting in misunderstandings. Interviews indicated that students who relied on graph-focused strategies often followed intuitive and less effective approaches. These findings underscore the need for adaptive support measures to address individual learning challenges and improve students’ understanding of graphs of indirectly proportional functions. Beyond the specific focus on indirectly proportional and power functions, the methodology and results of this study offer a transferable framework for identifying learning difficulties across various function types and contexts, complementing existing research on students’ understanding of linear functions.

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Phys. Rev. Phys. Educ. Res. 21, 020129– Published 23 September, 2025
  • Received 10 December 2024
  • Accepted 25 June 2025
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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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