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

Investigative analysis tool for physics textbook representations: The force diagram case study

Alessandro Pietro Ventura, Francesco Longo, Maria Peressi, and Valentina Bologna

Phys. Rev. Phys. Educ. Res. 22, 020159 – Published 6 November, 2026

DOI: https://doi.org/10.1103/ryn8-5gd7

Abstract

Recent advancements in educational research have underscored the significance of multiple representations (MR) in teaching practices, supporting student learning outcomes. Despite this progress, to our knowledge, two issues remain open: currently, there is no established tool for evaluating the quality of representations used in learning materials, and there is no comprehensive research on how such representations are integrated into teaching resources, especially in school textbooks. Our study aims to address these gaps by developing an analytical tool for categorizing representations in physics learning materials. We designed a grid for the analysis based on the theoretical underpinnings of MR, cognitive load theory, and modes of reasoning subframeworks. This grid helps identify MR features: building parameters, functionalities, and levels of optimization for learning environment usage, thus establishing the insights necessary to improve and enhance the quality of the representations. We also tested and applied this tool to force diagrams (FDs), which are commonly used in helping students learn mechanics, examining these representations across selected chapters from widely used high school physics textbooks. In this paper, we provide the results of our investigation of the current state of FDs in these textbooks as a compare-and-contrast case study. At the same time, we aim to offer insights into the effectiveness and potential areas for improvement in deploying MR for teaching-learning purposes.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (97)

  1. S. Ainsworth, The functions of multiple representations, Comput. Educ. 33, 131 (1999).
  2. R. J. Dufresne, W. J. Gerace, and W. J. Leonard, Solving physics problems with multiple representations, Phys. Teach. 35, 270 (1997).
  3. A. Van Heuvelen and X. Zou, Multiple representations of work–energy processes, Am. J. Phys. 69, 184 (2001).
  4. A. Van Heuvelen and D. P. Maloney, Playing physics jeopardy, Am. J. Phys. 67, 252 (1999).
  5. S. Ainsworth, The educational value of multiple-representations when learning complex scientific concepts, in Visualization: Theory and Practice in Science Education, edited by J. K. Gilbert, M. Reiner, and M. Nakhleh (Springer Netherlands, Dordrecht, 2008), pp. 191–208.
  6. M. Opfermann, A. Schmeck, and H. E. Fischer, Multiple representations in physics and science education–why should we use them?, in Multiple Representations in Physics Education, edited by D. F. Treagust, R. Duit, and H. E. Fischer (Springer International Publishing, Cham, 2017), pp. 1–22.
  7. D. Rosengrant, E. Etkina, and A. Van Heuvelen, An overview of recent research on multiple representations, AIP Conf. Proc. 883, 149 (2007).
  8. J. H. Larkin, The role of problem representation in physics, in Mental Models, edited by D. Gertner and A. L. S. Erlbaum (Psychology Press, Hillsdale, 2014), pp. 83–106.
  9. M. T. H. Chi, P. J. Feltovich, and R. Glaser, Categorization and representation of physics problems by experts and novices, Cogn. Sci. 5, 121 (1981).
  10. A. Van Heuvelen, Learning to think like a physicist: A review of research-based instructional strategies, Am. J. Phys. 59, 891 (1991).
  11. X. Zou, The Use of Multiple Representations and Visualizations in Student Learning of Introductory Physics: An Example from Work and Energy, Ph.D. thesis, The Ohio State University, 2000.
  12. E. Etkina, D. Rosengrant, and A. Van Heuvelen, Using multiple representations to improve student learning in mechanics, in Advanced Placement Special Focus: Multiple Representations of Knowledge: Mechanics and Energy, edited by G. D. (College Board., Cham, 2008), pp. 3–25.
  13. D. Rosengrant, A. Van Heuvelen, and E. Etkina, Do students use and understand free-body diagrams?, Phys. Rev. ST Phys. Educ. Res. 5, 010108 (2009).
  14. C. L. Wong and H.-E. Chu, The conceptual elements of multiple representations: a study of textbooks’ representations of electric current, in Multiple Representations in Physics Education, edited by D. F. Treagust, R. Duit, and H. E. Fischer (Springer International Publishing, Cham, 2017), pp. 183–206.
  15. P. Kohl, D. Rosengrant, and N. Finkelstein, Comparing explicit and implicit teaching of multiple representation use in physics problem solving, AIP Conf. Proc. 883, 145 (2007).
  16. N. Munfaridah, L. Avraamidou, and M. Goedhart, The use of multiple representations in undergraduate physics education: what Do we know and where Do we Go from here?, Eurasia J. Math. Sci. Technol. Educ. 17, em1934 (2021).
  17. V. Bologna and S. P. Leban, The puzzle of problems: Multiple representations tools to support teachers’ instructional practice, Giornale di Fisica 63, 99 (2022).
  18. J. Lemke, Talking Science: Language, Learning, and Values, Language and Classroom Processes (Ablex Publishing Corporation, New York City, NY, USA, 1990), p. 261.
  19. D. Kuhn and W. Udell, The development of argument skills, Child Dev. 74, 1245 (2003).
  20. D. Kuhn and A. Crowell, Dialogic argumentation as a vehicle for developing young adolescents’ thinking, Psychol. Sci. 22, 545 (2011).
  21. R. J. Dufresne and W. J. Gerace, Assessing-to-learn: Formative assessment in physics instruction, Phys. Teach. 42, 428 (2004).
  22. N. D. Finkelstein, W. K. Adams, C. J. Keller, P. B. Kohl, K. K. Perkins, N. S. Podolefsky, S. Reid, and R. LeMaster, When learning about the real world is better done virtually: A study of substituting computer simulations for laboratory equipment, Phys. Rev. ST Phys. Educ. Res. 1, 010103 (2005).
  23. D. E. Meltzer, Relation between students’ problem-solving performance and representational format, Am. J. Phys. 73, 463 (2005).
  24. D. T. Brookes, E. Ektina, and G. Planinsic, Implementing an epistemologically authentic approach to student-centered inquiry learning, Phys. Rev. Phys. Educ. Res. 16, 020148 (2020).
  25. G. Pospiech, B.-S. Eylon, E. Bagno, and Y. Lehavi, Role of teachers as facilitators of the interplay physics and mathematics, in Mathematics in Physics Education (Springer, New York, 2019), pp. 269–291.
  26. E. Redish and E. Kuo, Language of physics, language of math: Disciplinary culture and dynamic epistemology, Sci. Educ. 24, 561 (2014).
  27. E. F. Redish, Using math in physics: Overview, Phys. Teach. 59, 314 (2021).
  28. J. Yeo and J. K. Gilbert, The role of representations in students’ explanations of four phenomena in physics: Dynamics, thermal physics, electromagnetic induction and superposition, in Multiple Representations in Physics Education, edited by D. F. Treagust, R. Duit, and H. E. Fischer (Springer International Publishing, Cham, 2017), pp. 255–287.
  29. N. S. Podolefsky and N. D. Finkelstein, Use of analogy in learning physics: The role of representations, Phys. Rev. ST Phys. Educ. Res. 2, 020101 (2006).
  30. D. McPadden and E. Brewe, Impact of the second semester university modeling instruction course on students’ representation choices, Phys. Rev. Phys. Educ. Res. 13, 020129 (2017).
  31. B. Ibrahim and N. S. Rebello, Role of mental representations in problem solving: Students’ approaches to nondirected tasks, Phys. Rev. ST Phys. Educ. Res. 9, 020106 (2013).
  32. P. B. Kohl and N. Finkelstein, Understanding and promoting effective use of representations in physics learning, in Multiple Representations in Physics Education, edited by D. F. Treagust, R. Duit, and H. E. Fischer (Springer International Publishing, Cham, 2017), pp. 231–254.
  33. R. Tytler, P. Hubber, V. Prain, and B. Waldrip, A representation construction approach, in Constructing Representations to Learn in Science, edited by R. Tytler, V. Prain, P. Hubber, and B. Waldrip (SensePublishers, Rotterdam, 2013), pp. 31–50.
  34. V. Prain and R. Tytler, Representing and learning in science, in Constructing Representations to Learn in Science, edited by R. Tytler, V. Prain, P. Hubber, and B. Waldrip (SensePublishers, Rotterdam, 2013), pp. 1–14.
  35. R. Tytler, V. Prain, M. Kirk, J. Mulligan, C. Nielsen, C. Speldewinde, P. White, and L. Xu, Characterising a representation construction pedagogy for integrating science and mathematics in the primary school, Int. J. Sci. Math. Educ. 1 (2022).
  36. P. Hubber and R. Tytler, Enacting a representation construction approach to teaching and learning astronomy, in Multiple Representations in Physics Education, edited by D. F. Treagust, R. Duit, and H. E. Fischer (Springer International Publishing, Cham, 2017), pp. 139–161.
  37. D. Treagust, G. Chittleborough, and T. Mamiala, The role of submicroscopic and symbolic representations in chemical explanations, Int. J. Sci. Educ. 25, 1353 (2003).
  38. A. K. Jitendra, B. Dougherty, V. Sanchez, and L. Suchilt, Using multiple representations to foster multiplicative reasoning in students with mathematics learning disabilities, Teach. Exceptional Child. 57, 116 (2024).
  39. T.-F. Wu, M.-C. Chen, and H.-S. Lo, Utilizing multiple representation system to improve reading comprehension for students with learning disabilities, in International Conference on Computers Helping People with Special Needs (Springer, New York, 2018), pp. 527–530.
  40. C. Triantafillou, V. Spiliotopoulou-Papantoniou, and D. Potari, Visual and Argumentative Aspects in Greek School Textbooks and in Teachers’ Practices: Glances at the Concept of Periodicity, Chap. 7 (AIP Publishing LLC, Melville, NY, USA, 2023),10.1063/9780735425712_007.
  41. G.-L. Chiou and O. R. Anderson, A study of undergraduate physics students’ understanding of heat conduction based on mental model theory and an ontology–process analysis, Sci. Educ. 94, 825 (2010).
  42. T. Fredlund, J. Airey, and C. Linder, Exploring the role of physics representations: An illustrative example from students sharing knowledge about refraction, Eur. J. Phys. 33, 657 (2012).
  43. J. Schreffler, E. Vasquez III, J. Chini, and W. James, Universal design for learning in postsecondary stem education for students with disabilities: a systematic literature review, Int. J. STEM Educ. 6, 8 (2019).
  44. E. F. Redish and P. J. Cooney, Investigative science learning environment–a science process approach to learning physics, Res.-Based Reform Univ. Phys. 1, 1 (2007).
  45. R. P. Loui, J. Norman, J. Olson, and A. Merrill, A design for reasoning with policies, precedents, and rationales, in Proceedings of the 4th international conference on artificial intelligence and law (Washington University, St. Louis, MO, USA, 1993), p. 202.
  46. A. Van Heuvelen, Millikan lecture 1999: The workplace, student minds, and physics learning systems, Am. J. Phys. 69, 1139 (2001).
  47. A. R. Warren, Impact of teaching students to use evaluation strategies, Phys. Rev. ST Phys. Educ. Res. 6, 020103 (2010).
  48. M. T. Chi, N. De Leeuw, M.-H. Chiu, and C. LaVancher, Eliciting self-explanations improves understanding, Cogn. Sci. 18, 439 (1994).
  49. M. Evagorou, S. Erduran, and T. Mäntylä, The role of visual representations in scientific practices: from conceptual understanding and knowledge generation to ‘seeing’how science works, Int. J. Stem Educ. 2, 1 (2015).
  50. E. Etkina, A. Van Heuvelen, S. White-Brahmia, D. T. Brookes, M. Gentile, S. Murthy, D. Rosengrant, and A. Warren, Scientific abilities and their assessment, Phys. Rev. ST Phys. Educ. Res. 2, 020103 (2006).
  51. L. Groarke, Informal logic, in The Stanford Encyclopedia of Philosophy, edited by E. N. Zalta and U. Nodelman, Spring 2024 ed. (Metaphysics Research Lab, Stanford University, Stanford, CA, USA, 2024).
  52. L. Leivas Pozzer and W.-M. Roth, Prevalence, function, and structure of photographs in high school biology textbooks, J. Res. Sci. Teach. 40, 1089 (2003).
  53. R. Barthes, Rhetoric of the image, Visual Cult.:Reader 33 (1999).
  54. M. A. K. Halliday and C. M. Matthiessen, Halliday’s Introduction to Functional Grammar (Routledge, Abingdon, Oxfordshire, England, 2013).
  55. G. Kress and T. Van Leeuwen, The Grammar of Visual Design (Routledge, London and New York, 1996).
  56. F. Stylianidou, Analysis of science textbook pictures about energy and pupils’ readings of them, Int. J. Sci. Educ. 24, 257 (2002).
  57. C. Triantafillou, V. Spiliotopoulou, and D. Potari, The nature of argumentation in school mathematics and physics texts: The case of periodicity, Int. J. Sci. Math. Educ. 14, 681 (2016).
  58. R. E. Mayer, Introduction to multimedia learning, in The Cambridge Handbook of Multimedia Learning, edited by R. E. Mayer (Cambridge University Press, Cambridge, England, 2014), pp. 1–24.
  59. R. E. Mayer, J. Heiser, and S. Lonn, Cognitive constraints on multimedia learning: When presenting more material results in less understanding., J. Educ. Psychol. 93, 187 (2001).
  60. A. D. Baddeley and G. J. Hitch, Developments in the concept of working memory, Neuropsychology 8, 485 (1994).
  61. G. A. Miller, The magical number seven, plus or minus two: Some limits on our capacity for processing information, Psychol. Rev. 63, 81 (1956).
  62. J. Sweller, Cognitive load theory, learning difficulty, and instructional design, Learn. Instr. 4, 295 (1994).
  63. A. Paivio, Dual coding theory, word abstractness, and emotion: a critical review of Kousta et al. (2011), J. Exp. Psychol. Gen., 142, 282 (2013).
  64. J. Sweller, Cognitive load during problem solving: Effects on learning, Cogn. Sci. 12, 257 (1988).
  65. S. Kalyuga, Managing Cognitive Load in Adaptive Multimedia Learning (IGI Global, Hershey, PA, USA, 2008).
  66. J. Sweller, Cognitive load theory, Psychol. Learn. Motiv. 55, 37 (2011).
  67. R. Bruning, G. Schraw, and M. Norby, Cognitive Psychology and Instruction,(79-89) (Allyn & Bacon/Pearson, Boston, MA, 2011).
  68. R. E. Mayer and R. Moreno, A cognitive theory of multimedia learning: Implications for design principles, J. Educ. Psychol. 91, 358 (1998).
  69. A. Nurjanah and E. Retnowati, Analyzing the extraneous cognitive load of a 7th grader mathematics textbook, J. Phys. Conf. Ser. 1097, 012131 (2018).
  70. E. Etkina, D. T. Brookes, and G. Planinsic, Investigative Science Learning Environment: When learning physics mirrors doing physics (Morgan and Claypool Publishers, San Rafael, CA, USA, 2019), pp. 2053–2571.
  71. I. A. Halloun and D. Hestenes, The initial knowledge state of college physics students, Am. J. Phys. 53, 1043 (1985).
  72. I. A. Halloun and D. Hestenes, Common sense concepts about motion, Am. J. Phys. 53, 1056 (1985).
  73. M. S. Steinberg, D. E. Brown, and J. Clement, Genius is not immune to persistent misconceptions: Conceptual difficulties impeding Isaac newton and contemporary physics students, Int. J. Sci. Educ. 12, 265 (1990).
  74. D. Hammer and A. Elby, Tapping epistemological resources for learning physics, J. Learn. Sci. 12, 53 (2003).
  75. I. Kuczmann, The structure of knowledge and students’ misconceptions in physics, AIP Conf. Proc. 1916, 050001 (2017).
  76. D. Hestenes, M. Wells, and G. Swackhamer, Force concept inventory, Phys. Teach. 30, 141 (1992).
  77. D. Hammer, More than misconceptions: Multiple perspectives on student knowledge and reasoning, and an appropriate role for education research, Am. J. Phys. 64, 1316 (1996).
  78. D. Hammer, Misconceptions or p-prims: How may alternative perspectives of cognitive structure influence instructional perceptions and intentions, J. Learn. Sci. 5, 97 (1996).
  79. J. P. Smith III, A. A. diSessa, and J. Roschelle, Misconceptions reconceived: A constructivist analysis of knowledge in transition, J. Learn. Sci. 3, 115 (1994).
  80. D. T. Brookes and E. Etkina, “Force,” ontology, and language, Phys. Rev. ST Phys. Educ. Res. 5, 010110 (2009).
  81. V. Bologna, An EARLY PHYSICS Approach to Improve Students’ Scientific Attitudes. The Role of Teachers’ Habits, Phd thesis, Università degli studi di Trieste, Dipartimento di Fisica, XXXV Ciclo di Dottorato in Fisica, 2022.
  82. D. Rosengrant, Free-body diagrams: Necessary or sufficient?, AIP Conf. Proc. 790, 177 (2005).
  83. E. Etkina, G. Planinsic, and A. Van Heuvelen, College Physics—Explore and Apply, 2nd ed. (Pearson, London, England, 2021).
  84. J. Cutnell, K. Johnson, D. Young, and S. Stadler, La Fisica Di Cutnell e Johnson, edited by C. Betroni and E. Targa (Zanichelli, Bologna, Italy, 2019).
  85. R. E. Mayer, The past, present, and future of the cognitive theory of multimedia learning, Educ. Psychol. Rev. 36, 8 (2024).
  86. X. Liu and Y. Cui, Eye tracking technology for examining cognitive processes in education: A systematic review, Comput. Educ. 229, 105263 (2025).
  87. J. W. Creswell and V. L. P. Clark, Designing and Conducting Mixed Methods Research (Sage publications, Thousand Oaks CA, USA, 2017).
  88. V. Otero and D. Harlow, Getting started in qualitative physics education research, in Getting Started in PER, edited by C. Henderson and K. Harper, 1st ed. (American Association of Physics Teachers, College Park, 2009), Vol. 2.
  89. E. Etkina, D. T. Brookes, and G. Planinsic, The investigative science learning environment (ISLE) approach to learning physics, J. Phys. Conf. Ser. 1882, 012001 (2021).
  90. Etikna, Brookes, Planinsic, and V. Heuvelen, Instructor’s Guide for College Physics: Explore and Apply, 2nd ed. (Pearson, London, England, 2019).
  91. J. D. Cutnell, K. W. Johnson, D. Young, and S. Stadler, Physics (John Wiley & Sons, New York, 2021).
  92. U. Amaldi, Il Nuovo Amaldi per i Licei scientifici.blu, 3rd ed. (Zanichelli, Bologna, Italy, 2020).
  93. J. S. Walker, Il Walker—Corso Di Fisica (Pearson-Sanoma, Torino, Italy, 2020). secondo biennio e quinto anno.
  94. D. Halliday, R. Resnick, and J. Walker, Fundamentals of Physics (John Wiley & Sons, New York, 2013).
  95. J. M. Fraser, A. L. Timan, K. Miller, J. E. Dowd, L. Tucker, and E. Mazur, Teaching and physics education research: Bridging the gap, Rep. Prog. Phys. 77, 032401 (2014).
  96. L. C. McDermott, Bridging the gap between teaching and learning: The role of physics education research in the preparation of teachers and majors, Investigações Em Ensino De Ciências 5, 157 (2000).
  97. A. P. Ventura and V. Bologna, Investigative analysis tool for physics textbook representations: The force diagram case study—dataset (2026), 10.5281/zenodo.22673390.

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation