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

Toward thinking quantumly: Student reasoning about the enigma of QM

Marc L. Whiting1, Lauren Barth-Cohen1,2, Adrian L. Adams1, Jordan Gerton2, and David Stroupe1

Phys. Rev. Phys. Educ. Res. 22, 020129 – Published 9 September, 2026

DOI: https://doi.org/10.1103/9ym4-5t4s

Abstract

The physics education research (PER) literature on quantum mechanics (QM) often acknowledges and minimizes what we refer to as the enigma of QM, viewing these aspects of QM as a challenge to overcome, rather than an inherent feature to be leveraged for learning. Using the overlapping theories of knowledge-in-pieces and resource theory as connected to an epistemological framing perspective, we focus on students’ descriptions of the enigma of QM and the epistemological frames that students view as relevant when approaching QM. Data comes from interviews with 10 undergraduate physics students who had learned quantum physics topics across different courses in the curriculum, ranging from sophomore-level modern physics to an advanced undergraduate-level QM course. To elicit students’ ideas on QM, the interview protocol emphasized their perspectives and empowerment when possible. Iterative rounds of qualitative analysis coded the data for how students described enigmatic aspects of QM, along with three epistemological frames students identified as their reasoning strategies: reasoning about scale, reasoning about the connections between QM and mathematics, and reasoning about the connections between QM and classical mechanics. The results document that students are aware that something about QM is unexplainable, an enigma to acknowledge. We argue that acknowledgment of the enigma of QM is a key part of what we refer to as thinking quantumly. Additionally, the epistemological frame of reasoning about scale has not been widely discussed in the QM-PER literature, which students use to distinguish QM from classical mechanics and to explain why mathematical models are needed. These results are important for amplifying students’ voices in how they approach enigmatic aspects of QM. Thus, our results begin to move the QM-PER literature beyond viewing enigmatic aspects of QM as obstacles to be corrected through refined instruction, toward an asset-based orientation as a source of meaningful insights for the learning process.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (90)

  1. W. B. Lane, M. Michelini, and C. Singh, Editorial: Focused collection: Investigating and improving quantum education through research, Phys. Rev. Phys. Educ. Res. 21, 010002 (2025).
  2. D. H. McIntyre, Quantum Mechanics: A Paradigms Approach (Cambridge University Press, Cambridge, 2023).
  3. D. J. Griffiths and D. F. Schroeter, Introduction to Quantum Mechanics, 3rd ed. (Cambridge University Press, Cambridge, 2018).
  4. J. S. Townsend, A Modern Approach to Quantum Mechanics, 2nd ed. (University Science Books, Sausalito, CA, 2012).
  5. J. J. Sakurai and J. Napolitano, Modern Quantum Mechanics, 3rd ed. (Cambridge University Press, Cambridge, UK, 2021).
  6. R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics, Vol. III: Quantum Mechanics (Basic Books, New York, NY, 2011).
  7. E. Marshman and C. Singh, Framework for understanding the patterns of student difficulties in quantum mechanics, Phys. Rev. ST Phys. Educ. Res. 11, 020119 (2015).
  8. V. Borish and H. J. Lewandowski, Student reasoning about quantum mechanics while working with physical experiments, Phys. Rev. Phys. Educ. Res. 20, 020135 (2024).
  9. M. L. Whiting, L. A. Barth-Cohen, A. L. Adams, D. Stroupe, and J. M. Gerton, Amplifying physics students’ voices: How learners approach wonky and unknowable quantum mechanics, in Physics Education Research Conference Proceedings (PERC) 2025, PER Conference (American Association of Physics Teachers (AAPT), Washington, DC, 2025), pp. 447–453.
  10. V. Karakostas and P. Hadzidaki, Realism vs. constructivism in contemporary physics: The impact of the debate on the understanding of quantum theory and its instructional process, Sci. Educ. 14, 607 (2005).
  11. S. Pollock, G. Passante, and H. Sadaghiani, Adaptable research-based materials for teaching quantum mechanics, Am. J. Phys. 91, 40 (2023).
  12. F. Hennig, K. Tóth, J. Veith, and P. Bitzenbauer, Introducing quantum physics concepts and Dirac notation at the secondary school level: Insights into student reasoning from an acceptance survey, Phys. Rev. Phys. Educ. Res. 20, 020147 (2024).
  13. W. D. Riihiluoma, Z. Topdemir, and J. R. Thompson, Network analysis of students’ conceptual understanding of mathematical expressions for probability in upper-division quantum mechanics, Phys. Rev. Phys. Educ. Res. 20, 020102 (2024).
  14. E. M. Stump, M. Hughes, N. G. Holmes, and G. Passante, Do students think that objects have a true definite position?, Phys. Rev. Phys. Educ. Res. 20, 010154 (2024).
  15. C. Baily and N. D. Finkelstein, Refined characterization of student perspectives on quantum physics, Phys. Rev. ST Phys. Educ. Res. 6, 020113 (2010).
  16. P. J. Emigh, G. Passante, and P. S. Shaffer, Student understanding of time dependence in quantum mechanics, Phys. Rev. ST Phys. Educ. Res. 11, 020112 (2015).
  17. F. Savall-Alemany, J. L. Domènech-Blanco, J. Guisasola, and J. Martínez-Torregrosa, Identifying student and teacher difficulties in interpreting atomic spectra using a quantum model of emission and absorption of radiation, Phys. Rev. Phys. Educ. Res. 12, 010132 (2016).
  18. R. Sayer, A. Maries, and C. Singh, Quantum interactive learning tutorial on the double-slit experiment to improve student understanding of quantum mechanics, Phys. Rev. Phys. Educ. Res. 13, 010123 (2017).
  19. C. Singh, Interactive learning tutorials on quantum mechanics, Am. J. Phys. 76, 400 (2008).
  20. G. Zhu and C. Singh, Improving students’ understanding of quantum measurement. I. Investigation of difficulties, Phys. Rev. ST Phys. Educ. Res. 8, 010117 (2012).
  21. C. Keebaugh, E. Marshman, and C. Singh, Investigating and addressing student difficulties with a good basis for finding perturbative corrections in the context of degenerate perturbation theory, Eur. J. Phys. 39, 055701 (2018).
  22. C. Keebaugh, E. Marshman, and C. Singh, Improving student understanding of corrections to the energy spectrum of the hydrogen atom for the Zeeman effect, Phys. Rev. Phys. Educ. Res. 15, 010113 (2019).
  23. P. Hu, Y. Li, and C. Singh, Challenges in addressing student difficulties with quantum measurement of two-state quantum systems using a multiple-choice question sequence in online and in-person classes, Phys. Rev. Phys. Educ. Res. 19, 020130 (2023).
  24. G. Zhu and C. Singh, Improving student understanding of addition of angular momentum in quantum mechanics, Phys. Rev. ST Phys. Educ. Res. 9, 010101 (2013).
  25. E. M. Stump, M. Dew, G. Passante, and N. G. Holmes, Context affects student thinking about sources of uncertainty in classical and quantum mechanics, Phys. Rev. Phys. Educ. Res. 19, 020157 (2023).
  26. E. Marshman and C. Singh, Investigating and improving student understanding of the probability distributions for measuring physical observables in quantum mechanics, Eur. J. Phys. 38, 025705 (2017).
  27. C. Singh and E. Marshman, Review of student difficulties in upper-level quantum mechanics, Phys. Rev. ST Phys. Educ. Res. 11, 020117 (2015).
  28. J. L. Docktor and J. P. Mestre, Synthesis of discipline-based education research in physics, Phys. Rev. ST Phys. Educ. Res. 10, 020119 (2014).
  29. L. C. McDermott, Research on conceptual understanding in mechanics, Phys. Today 37, No. 7, 24 (1984).
  30. L. C. McDermott, Millikan lecture 1990: What we teach and what is learned—closing the gap, Am. J. Phys. 59, 301 (1991).
  31. G. Posner, A cognitive science conception of curriculum and instruction, J. Curric. Stud. 14, 343 (1982).
  32. H. D. Nguyen, D. N. Chari, and E. C. Sayre, Dynamics of students’ epistemological framing in group problem solving, Eur. J. Phys. 37, 065706 (2016).
  33. B. Modir, J. D. Thompson, and E. C. Sayre, Students’ epistemological framing in quantum mechanics problem solving, Phys. Rev. Phys. Educ. Res. 13, 020108 (2017).
  34. B. Modir, J. D. Thompson, and E. C. Sayre, Framing difficulties in quantum mechanics, Phys. Rev. Phys. Educ. Res. 15, 020146 (2019).
  35. C. Keebaugh, E. Marshman, and C. Singh, Challenges in sensemaking and reasoning in the context of degenerate perturbation theory in quantum mechanics, Phys. Rev. Phys. Educ. Res. 20, 020139 (2024).
  36. T. Tu, C.-F. Li, Z.-Q. Zhou, and G.-C. Guo, Students’ difficulties with partial differential equations in quantum mechanics, Phys. Rev. Phys. Educ. Res. 16, 020163 (2020).
  37. K. Krijtenburg-Lewerissa, H. J. Pol, A. Brinkman, and W. R. van Joolingen, Insights into teaching quantum mechanics in secondary and lower undergraduate education, Phys. Rev. Phys. Educ. Res. 13, 010109 (2017).
  38. T. Bouchée, L. de Putter-Smits, M. Thurlings, and B. Pepin, Towards a better understanding of conceptual difficulties in introductory quantum physics courses, Stud. Sci. Educ. 58, 183 (2022).
  39. J. R. Hoehn and N. D. Finkelstein, Students’ flexible use of ontologies and the value of tentative reasoning: Examples of conceptual understanding in three canonical topics of quantum mechanics, Phys. Rev. Phys. Educ. Res. 14, 010122 (2018).
  40. I. M. Greca and O. Freire Jr., Does an emphasis on the concept of quantum states enhance students’ understanding of quantum mechanics?, Sci. Educ. 12, 541 (2003).
  41. B. W. Dreyfus, A. Elby, A. Gupta, and E. R. Sohr, Mathematical sense-making in quantum mechanics: An initial peek, Phys. Rev. Phys. Educ. Res. 13, 020141 (2017).
  42. B. W. Dreyfus, J. R. Hoehn, A. Elby, N. D. Finkelstein, and A. Gupta, Splits in students’ beliefs about learning classical and quantum physics, Int. J. STEM Educ. 6, 31 (2019).
  43. E. R. Sohr, A. Gupta, and A. Elby, Taking an escape hatch: Managing tension in group discourse, Sci. Educ. 102, 883 (2018).
  44. H. K. E. Stadermann, E. van den Berg, and M. J. Goedhart, Analysis of secondary school quantum physics curricula of 15 different countries: Different perspectives on a challenging topic, Phys. Rev. Phys. Educ. Res. 15, 010130 (2019).
  45. G. Corsiglia, S. Pollock, and G. Passante, Intuition in quantum mechanics: Student perspectives and expectations, Phys. Rev. Phys. Educ. Res. 19, 010109 (2023).
  46. R. Gray, S. McDonald, and D. Stroupe, What you find depends on how you see: Examining asset and deficit perspectives of preservice science teachers’ knowledge and learning, Stud. Sci. Educ. 58, 49 (2022).
  47. D. Hammer, Epistemological beliefs in introductory physics, Cognit. Instr. 12, 151 (1994).
  48. 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).
  49. A. A. diSessa, A history of conceptual change research: Threads and fault lines, in The Cambridge Handbook of the Learning Sciences, edited by R. K. Sawyer (Cambridge University Press, Cambridge, England, 2014), pp. –.
  50. J. Svoboda, Processing misconceptions: dynamic systems perspectives on thinking and learning, Front. Educ. 8, 1215361 (2023).
  51. M. C. Wittmann and J. T. Morgan, Foregrounding epistemology and everyday intuitions in a quantum physics course for nonscience majors, Phys. Rev. Phys. Educ. Res. 16, 020159 (2020).
  52. O. Levrini and A. A. diSessa, How students learn from multiple contexts and definitions: Proper time as a coordination class, Phys. Rev. ST Phys. Educ. Res. 4, 010107 (2008).
  53. A. A. diSessa, Toward an epistemology of physics, Cognit. Instr. 10, 105 (1993).
  54. A. A. diSessa, Why “conceptual ecology” is a good idea, in Reconsidering Conceptual Change: Issues in Theory and Practice, edited by M. Limón and L. Mason (Springer Netherlands, Dordrecht, 2002), pp. –.
  55. D. Hammer and E. Van Zee, Seeing the Science in Children’s Thinking: Case Studies of Student Inquiry in Physical Science (Pearson Education Canada, 2006) Chap. 2, pp. 13–37.
  56. L. A. Barth-Cohen, H. Swanson, and J. Arnell, Methods of research design and analysis for identifying knowledge resources, Phys. Rev. Phys. Educ. Res. 19, 020119 (2023).
  57. D. Hammer, Student resources for learning introductory physics, Am. J. Phys. 68, S52 (2000).
  58. A. Adams, L. Barth-Cohen, and J. Gouvea, Exploring student sensemaking when engaging with anomalous data, CBE—Life Sci. Educ. 23, ar63 (2024).
  59. S. Kapon and A. A. diSessa*, Reasoning through instructional analogies, Cognit. Instr. 30, 261 (2012).
  60. D. Hammer and A. Elby, Tapping epistemological resources for learning physics, J. Learn. Sci. 12, 53 (2003).
  61. E. F. Redish, A theoretical framework for physics education research: Modeling student thinking, arXiv:physics/0411149.
  62. J. Tuminaro, A Cognitive framework for analyzing and describing introductory students’ use and understanding of mathematics in physics, Ph. D. thesis, University of Maryland, 2004.
  63. A. Elby and D. Hammer, Epistemological resources and framing: A cognitive framework for helping teachers interpret and respond to their students’ epistemologies, in Personal Epistemology in the Classroom: Theory, Research, and Implications for Practice, edited by L. D. Bendixen and F. C. Feucht (Cambridge University Press, Cambridge, England, 2010), pp. –.
  64. E. Goffman, Frame Analysis: An Essay on the Organization of Experience (Harvard University Press, Cambridge, MA, 1974).
  65. D. Tannen, Framing in Discourse, Framing in Discourse (Oxford University Press, New York, NY, 1993).
  66. P. W. Irving, M. S. Martinuk, and E. C. Sayre, Transitions in students’ epistemic framing along two axes, Phys. Rev. ST Phys. Educ. Res. 9, 010111 (2013).
  67. D. Hu and N. S. Rebello, Shifting college students’ epistemological framing using hypothetical debate problems, Phys. Rev. ST Phys. Educ. Res. 10, 010117 (2014).
  68. V. Dini and D. Hammer, Case study of a successful learner’s epistemological framings of quantum mechanics, Phys. Rev. Phys. Educ. Res. 13, 010124 (2017).
  69. T. O. B. Odden and R. S. Russ, Defining sensemaking: Bringing clarity to a fragmented theoretical construct, Sci. Educ. 103, 187 (2019).
  70. K. T. Hahn and E. Gire, Waving arms around to teach quantum mechanics, Am. J. Phys. 90, 778 (2022).
  71. L. A. Barth-Cohen and M. C. Wittmann, Aligning coordination class theory with a new context: Applying a theory of individual learning to group learning, Sci. Educ. 101, 333 (2017).
  72. A. Fontana and A. H. Prokos, The Interview: From Formal to Postmodern, 1st ed. (Left Coast Press, Walnut Creek, CA, 2007).
  73. K. Bhattacharya, Fundamentals of Qualitative Research: A Practical Guide, 1st ed. (Routledge, New York, NY, 2017).
  74. I. Seidman, Interviewing as Qualitative Research: A Guide for Researchers in Education and the Social Sciences, 5th ed. (Teachers College Press, New York, NY, 2019).
  75. S. Vossoughi and M. Escudé, What does the camera communicate? An inquiry into the politics and possibilities of video research on learning: Politics and possibilities of video research, Anthropol. Educ. Quarterly 47, 42 (2016).
  76. O. Parnafes and A. A. diSessa, Microgenetic learning analysis: A methodology for studying knowledge in transition, Hum. Dev. 56, 5 (2013).
  77. A. A. diSessa, How to observe knowledge, in Proceedings of the 8th International Conference of the Learning Sciences (International Society of the Learning Sciences, Utrecht, 2008).
  78. AssemblyAI, AssemblyAI Speech Recognition API (2023), accessed May 2024.
  79. C. Goodwin, Action and embodiment within situated human interaction, J. Pragmatics 32, 1489 (2000).
  80. J. Saldaña, Thinking Qualitatively: Methods of Mind (SAGE Publications, Inc., Thousand Oaks, CA, 2015).
  81. M. B. Miles, A. M. Huberman, and J. Saldaña, Qualitative Data Analysis: A Methods Sourcebook, 4th ed. (SAGE Publications, Inc., Los Angeles, CA, 2019) Chap. 4.
  82. R. E. Scherr, Video analysis for insight and coding: Examples from tutorials in introductory physics, Phys. Rev. ST Phys. Educ. Res. 5, 020106 (2009).
  83. S. J. Derry, R. D. Pea, B. Barron, R. A. Engle, F. Erickson, R. Goldman, R. Hall, T. Koschmann, J. L. Lemke, M. G. Sherin, and B. L. Sherin, Conducting video research in the learning sciences: Guidance on selection, analysis, technology, and ethics, J. Learn. Sci. 19, 3 (2010).
  84. J. Cohen, A coefficient of agreement for nominal scales, Educ. Psychol. Meas. 20, 37 (1960).
  85. J. Saldaña, The Coding Manual for Qualitative Researchers, 4th ed. (SAGE Publications Ltd, Los Angeles, CA, 2021).
  86. D. T. Brookes and E. Etkina, Using conceptual metaphor and functional grammar to explore how language used in physics affects student learning, Phys. Rev. ST Phys. Educ. Res. 3, 010105 (2007).
  87. C. Singh, Student understanding of quantum mechanics, Am. J. Phys. 69, 885 (2001).
  88. A. Gupta, A. Elby, and B. A. Danielak, Exploring the entanglement of personal epistemologies and emotions in students’ thinking, Phys. Rev. Phys. Educ. Res. 14, 010129 (2018).
  89. E. Ronayne Sohr, A. Gupta, B. J. Johnson, and G. M. Quan, Examining the dynamics of decision making when designing curriculum in partnership with students: How should we proceed?, Phys. Rev. Phys. Educ. Res. 16, 020157 (2020).
  90. U. Eriksson, C. Linder, J. Airey, and A. Redfors, Who needs 3d when the universe is flat?, Sci. Educ. 98, 412 (2014).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation