- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Physics Education Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Inventory of Galilean Transformation of uniform linear motion in position-time graphs

E. B. Merki1,*, S. I. Hofer2, A. Vaterlaus1, and A. Lichtenberger1

  • *Contact author: merkie@phys.ethz.ch
PDF

Phys. Rev. Phys. Educ. Res. 21, 020118 – Published 25 August, 2025

DOI: https://doi.org/10.1103/ww1x-kr12

Abstract

When describing motion in physics, the selection of a frame of reference is crucial. The graph of a moving object can look quite different based on the frame of reference. In recent years, various tests have been developed to assess the interpretation of kinematic graphs, but none of these tests have specifically addressed differences in reference frames. Moreover, existing tests that explore differences in reference frame typically focus on the equivalence principle through written answers, interviews, or simple calculations and vector addition; however, none of these tests evaluate position-time graphs. To address this gap in the research, we developed and evaluated the Inventory of Galilean Transformation of uniform linear motion in position-time graphs (IGT). The IGT consists of 15 multiple-choice items that systematically use position-time graphs of linear uniform motion to assess the understanding of 3 types of Galilean transformations: the identity transformation, the transformation between two (opposing) stationary displaced frames of reference, and the transformation from a stationary into a uniformly moving frame of reference. Herein, we presented the development and validation of the IGT. A total of 532 upper secondary school students in the advanced track participated in the multistage development process. We evaluated the psychometric properties via classical test theory and item response theory. The degree of item discrimination and reliability were within the desired range. The IGT demonstrated good internal consistency (ω=0.88), and confirmatory factor analysis supported the intended structure of the test. Rasch analysis revealed that the item difficulties were consistent with the increasing complexity of the three different transformations. The IGT also revealed several alternative student conceptions about frames of references, such as confusion between two scenarios of cars crossing versus overtaking, as well as misunderstandings regarding the changing shape of a graph when a uniformly moving object is transformed into a moving frame of reference. In its current form, the IGT serves as a new instrument for assessing students’ ability to interpret position-time graphs under the influence of the Galilean transformation, making it suitable for formative or summative assessment in advanced upper secondary education.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (58)

  1. M. Caprile, R. Palmen, P. Sanz, and G. Dente, Encouraging STEM studies: labour market situation and comparison of practices targeted at young people in different Member States European Union, 2015, p. 38, http://www.europarl.europa.eu/RegData/etudes/STUD/2015/542199/IPOL_STU(2015)542199_EN.pdf.
  2. B. Cowie and B. Cooper, Exploring the challenge of developing student teacher data literacy, Assess. Educ. 24, 147 (2017).
  3. M. Planinic, L. Ivanjek, A. Susac, and Z. Milin-Sipus, Comparison of university students’ understanding of graphs in different contexts, Phys. Rev. ST Phys. Educ. Res. 9, 020103 (2013).
  4. P. Klein, A. Lichtenberger, S. Küchemann, S. Becker, M. Kekule, J. Viiri, C. Baadte, A. Vaterlaus, and J. Kuhn, Visual attention while solving the test of understanding graphs in kinematics: An eye-tracking analysis, Eur. J. Phys. 41, 025701 (2020).
  5. P. Alstein, K. Krijtenburg-Lewerissa, and W. R. van Joolingen, Teaching and learning special relativity theory in secondary and lower undergraduate education: A literature review, Phys. Rev. Phys. Educ. Res. 17, 023101 (2021).
  6. S. Panse, J. Ramadas, and A. Kumar, Alternative conceptions in Galilean relativity: Frames of reference, Int. J. Sci. Educ. 16, 63 (1994).
  7. R. J. Beichner, Testing student interpretation of kinematics graphs, Am. J. Phys. 62, 750 (1994).
  8. A. Lichtenberger, C. Wagner, S. I. Hofer, E. Stern, and A. Vaterlaus, Validation and structural analysis of the kinematics concept test, Phys. Rev. Phys. Educ. Res. 13, 010115 (2017).
  9. P. Barniol and G. Zavala, Test of understanding of vectors: A reliable multiple-choice vector concept test, Phys. Rev. ST Phys. Educ. Res. 10, 010121 (2014).
  10. D. Hestenes, M. Wells, and G. Swackhamer, Force concept inventory, Phys. Teach. 30, 141 (1992).
  11. S. I. Hofer, R. Schumacher, and H. Rubin, The test of basic Mechanics Conceptual Understanding (bMCU): Using Rasch analysis to develop and evaluate an efficient multiple choice test on Newton’s mechanics, Int. J. STEM Educ. 4, 18 (2017).
  12. S. Flegr, S. Becker, S. Kuechemann, K. Scheiter, and J. Kuhn, Development and validation of the ray optics in converging lenses concept inventory, Phys. Rev. Phys. Educ. Res. 18, 020131 (2022).
  13. P. Barniol and G. Zavala, Mechanical waves conceptual survey: Its modification and conversion to a standard multiple-choice test, Phys. Rev. Phys. Educ. Res. 12, 010107 (2016).
  14. J. S. Aslanides and C. M. Savage, Relativity concept inventory: Development, analysis, and results, Phys. Rev. ST Phys. Educ. Res. 9, 010118 (2013).
  15. E. Saltiel and J. L. Malgrange, “Spontaneous” ways of reasoning in elementary kinematics, Eur. J. Phys. 1, 73 (1980).
  16. Z. Tanel, Student difficulties in solving problems concerning special relativity and possible reasons for these difficulties, J. Balt. Sci. Educ. 13, 573 (2014).
  17. P. Klein, S. Gröber, J. Kuhn, A. Fleischhauer, and A. Müller, The right frame of reference makes it simple: An example of introductory mechanics supported by video analysis of motion, Eur. J. Phys. 36, 015004 (2015).
  18. M. Kozhevnikov, J. Gurlitt, and M. Kozhevnikov, Learning relative motion concepts in immersive and non-immersive virtual environments, J. Sci. Educ. Technol. 22, 952 (2013).
  19. J. Ramadas, S. Barve, and A. Kumar, Alternative conceptions in Galilean relativity: Inertial and non-inertial observers, Int. J. Sci. Educ. 18, 615 (1996).
  20. J. Larkin, J. McDermott, D. Simon, and H. Simon, Expert and novice performance in solving physics problems, Science 208, 1335 (1980).
  21. S. Brand-Gruwel, I. Wopereis, and Y. Vermetten, Information problem solving by experts and novices: Analysis of a complex cognitive skill, Comput. Hum. Behav. 21, 487 (2005).
  22. S. Klinaku, Galilean transformation in polar coordinates and Doppler effect, Results Phys. 31, 104885 (2021).
  23. L. Ding and R. Beichner, Approaches to data analysis of multiple-choice questions, Phys. Rev. ST Phys. Educ. Res. 5, 020103 (2009).
  24. D. G. Janelle, M. Hegarty, and N. S. Newcombe, Spatial thinking across the college curriculum: A report on a specialist meeting, Spat. Cognit. Comput. 14, 124 (2014).
  25. M. Kozhevnikov, M. A. Motes, and M. Hegarty, Spatial visualization in physics problem solving, Cognit. Sci. 31, 549 (2007).
  26. J. Ramadas, S. Barve, and A. Kumar, Alternative conceptions in Galilean relativity: Distance, time, energy and laws, Int. J. Sci. Educ. 18, 463 (1996).
  27. R. E. Scherr, P. S. Shaffer, and S. Vokos, Student understanding of time in special relativity: Simultaneity and reference frames, Am. J. Phys. 69, S24 (2001).
  28. L. C. McDermott, M. L. Rosenquist, and E. H. van Zee, Student difficulties in connecting graphs and physics: Examples from kinematics, Am. J. Phys. 55, 503 (1987).
  29. S. Wineburg, J. Breakstone, S. McGrew, M. D. Smith, and T. Ortega, Lateral reading on the open Internet: A district-wide field study in high school government classes, J. Educ. Psychol. 114, 893 (2022).
  30. J. E. Fan, Drawing to learn: How producing graphical representations enhances scientific thinking, Transl. Issues Psychol. Sci. 1, 170 (2015).
  31. E. B. Merki, S. I. Hofer, A. Vaterlaus, and A. Lichtenberger, Evaluating an interactive 360-degree learning environment for Galilean transformation of uniform motion in graphs developed on the basis of analyzed peer discussions, Doctoral thesis, ETH Zürch, 2025, 10.3929/ethz-b-000738033.
  32. See Supplemental Material at http://link.aps.org/supplemental/10.1103/ww1x-kr12 for the English version IGT in PDF format.
  33. R Core Team, R: A Language and Environment for Statistical Computing (R Foundation for Statistical Computing, Vienna, Austria, 2024), https://www.R-project.org/.
  34. A. Oosterhof, Classroom Application of Educational Measurement (Prentice Hall, Englewood Cliffs, NJ, 2001).
  35. P. Potthoff, Measurement theory for the behavioral sciences: Edwin E. Ghiselli, J. P. Campbell, and S. Zedeck, San Francisco: W. H. Freeman and Company, 1981, pp. 491, $27.95, Math. Soc. Sci. 4, 319 (1983).
  36. H. W. Marsh, K.-T. Hau, J. R. Balla, and D. Grayson, Is more ever too much? The number of indicators per factor in confirmatory factor analysis, Multivar. Behav. Res. 33, 181 (1998).
  37. Y. Rosseel, lavaan: An R package for structural equation modeling, J. Stat. Software 48, 1 (2012).
  38. P. M. Bentler and D. G. Bonett, Significance tests and goodness of fit in the analysis of covariance structures, Psychol. Bull. 88, 588 (1980).
  39. L. t. Hu and P. M. Bentler, Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives, Struct. Equation Model. 6, 1 (1999).
  40. R. E. Schumacker and R. G. Lomax, A Beginner’s Guide to Structural Equation Modeling, 4th ed. (Routledge, New York, 2015), 10.4324/9781315749105.
  41. J. H. Steiger, Structural model evaluation and modification: An interval estimation approach, Multivar. Behav. Res. 25, 173 (1990).
  42. S. Epskamp, semplot: Unified visualizations of structural equation models, Struct. Equation Model. 22, 474 (2015).
  43. F. B. Baker, The Basics of Item Response Theory, 2nd ed. (ERIC Clearinghouse on Assessment and Evaluation, College Park, MD, 2001), https://eric.ed.gov/?id=ED458219.
  44. G. Rasch, Studies in Mathematical Psychology: I. Probabilistic Models for Some Intelligence and Attainment Tests (Nielsen & Lydiche, Oxford, England, 1960).
  45. B. Wright and M. M. C. Mok, An overview of the family of Rasch measurement models, in Introduction to Rasch Measurement: Theory, Models and Applications, edited by E. V. Smith, Jr., and R. M. Smith (JAM Press, Maple Grove, MN, 2004), pp. 1–24, https://api.semanticscholar.org/CorpusID:17169559.
  46. J. Linacre, Sample size and item calibration stability, Rasch Meas. Trans. 7, 328 (1994), https://www.researchgate.net/publication/235361463.
  47. J. Linacre, Data variance: Explained, modeled and empirical, Rasch Meas. Trans. 17, 942 (2003), https://www.rasch.org/rmt/rmt173g.htm.
  48. R. F. Waugh and E. S. Chapman, An analysis of dimensionality using factor analysis (true-score theory) and Rasch measurement: What is the difference? Which method is better?, J. Appl. Meas. 6, 80 (2005), https://pubmed.ncbi.nlm.nih.gov/15701946/.
  49. A. Robitzsch, T. Kiefer, and M. Wu, TAM: Test analysis modules, R package version 4.2-21, https://CRAN.R-project.org/package=TAM (2024).
  50. P. Mair and R. Hatzinger, Extended Rasch modeling: The erm package for the application of IRT models in R, J. Stat. Software 20, 1 (2007).
  51. R. William, psych: Procedures for psychological, psychometric, and personality research, version 2.4.6, https://CRAN.R-project.org/package=psych (2024).
  52. H. Wickham, ggplot2: Elegant Graphics for Data Analysis (Springer-Verlag New York, 2016).
  53. R. L. Doran, Basic measurement and evaluation of science instruction. National Science Teachers Association, 1742 Connecticut Ave., N.W., Washington, DC 20009 (Stock No. 471-14764; no price quoted), htps://files.eric.ed.gov/fulltext/ED196733.pdf.
  54. S. B. Green and Y. Yang, Reliability of summed item scores using structural equation modeling: An alternative to coefficient alpha, Psychometrika 74, 155 (2009).
  55. R. J. Adams, Reliability as a measurement design effect, Stud. Educ. Eval. 31, 162 (2005).
  56. B. D. Wright, Comparing Rasch measurement and factor analysis, Struct. Equation Model. 3, 3 (1996).
  57. A. Marzari, M. Di Mauro, T. Rosi, P. Onorato, and M. Malgieri, Investigating the principle of relativity and the principle of equivalence in classical mechanics: Design and evaluation of a teaching–learning sequence based on experiments and simulations, Educ. Sci. 13, 712 (2023).
  58. E. B. Merki, A. Lichtenberger, and S. I. Hofer, IGT Data (V3.0), OSF, 10.17605/OSF.IO/2WH4P.

Outline

Information

Phys. Rev. Phys. Educ. Res. 21, 020118– Published 25 August, 2025
  • Received 28 December 2024
  • Accepted 26 June 2025
Crossmark - Check for updates button
Creative Commons Logo

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

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation