- 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

Introducing quantum physics concepts and Dirac notation at the secondary school level: Insights into student reasoning from an acceptance survey

Fabian Hennig1, Kristóf Tóth2, Joaquin Veith3, and Philipp Bitzenbauer3

PDF

Phys. Rev. Phys. Educ. Res. 20, 020147 – Published 26 November, 2024

DOI: https://doi.org/10.1103/PhysRevPhysEducRes.20.020147

Abstract

[This paper is part of the Focused Collection in Investigating and Improving Quantum Education through Research.] Evidence from physics education research suggests that the introduction of a formalistic description of quantum phenomena can be beneficial to student learning, particularly in terms of helping students move away from naive realist views of quanta or space-time descriptions of quantum phenomena. However, the mathematical requirements for mastering quantum formalism are typically far beyond the scope of secondary school education. Therefore, in previous research, we have proposed a reduced Dirac notation tailored to the capabilities of secondary school students, which is included in a novel teaching-learning sequence. However, the cognitive processes of students when confronted with an introduction to quantum physics via a reduced Dirac notation have not been thoroughly investigated: In particular, it seems important to investigate whether this approach is actually beneficial to students’ learning and to explore the learning difficulties students are likely to encounter in such a setting. This paper contributes to this research gap by reporting the findings of an acceptance survey: N=14 learners participated in one-on-one interviews following a protocol consisting of four cyclical phases (information phase, acceptance evaluation, paraphrasing phase, and application phase). The findings of our study indicate that the instructional elements within our new teaching-learning sequence were generally well accepted by students but also revealed learning difficulties that students may encounter. Thus, on the one hand, the findings of this study pave the way for future research on students’ learning of quantum physics using Dirac notation. On the other hand, the in-depth findings reported here may guide teachers in designing learning environments that introduce Dirac notation at the upper secondary school and introductory university levels.

View figure in article

Physics Subject Headings (PhySH)

Collections

This article appears in the following collection:

Focused Collection in Investigating and Improving Quantum Education through Research

Focused Collection in Investigating and Improving Quantum Education through Research

Article Text

References (86)

  1. S. M.-L. Pfaendler, K. Konson, and F. Greinert, Advancements in quantum computing–viewpoint: Building adoption and competency in industry, Datenbank-Spektrum 24, 5 (2024).
  2. H. Stadermann, E. van den Berg, and M. 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).
  3. R. De Wolf, The potential impact of quantum computers on society, Ethics Inf. Technol. 19, 271 (2017).
  4. A. Merzel, P. Bitzenbauer, K. Krijtenburg-Lewerissa, K. Stadermann, E. Andreotti, D. Anttila, M. Bondani, M. L. M. Chiofalo, S. Faletič, R. Frans et al., The core of secondary level quantum education: A multi-stakeholder perspective, Eur. Phys. J. Quantum Technol. 11, 27 (2024).
  5. G. Pospiech, Teaching the EPR paradox at high school?, Phys. Educ. 34, 311 (1999).
  6. G. Pospiech, Uncertainty and complementarity: the heart of quantum physics, Phys. Educ. 35, 393 (2000).
  7. T. S. Moraga-Calderón, H. Buisman, and J. Cramer, The relevance of learning quantum physics from the perspective of the secondary school student: A case study, Eur. J. Sci. Math. Educ. 8, 32 (2020).
  8. Y. Bloom, I. Fields, A. Maslennikov, and G. G. Rozenman, Quantum cryptography—a simplified undergraduate experiment and simulation, Physics 4, 104 (2022).
  9. P. Bitzenbauer and T. Zenger, Online course on quantum physics: Reading primary sources with secondary school students, Phys. Teach. 60, 572 (2022).
  10. S. Aehle, P. Scheiger, and H. Cartarius, An approach to quantum physics teaching through analog experiments, Physics 4, 1241 (2022).
  11. M. Malgieri and P. Onorato, Recent progress on the sum over paths approach in quantum mechanics education, Physics 4, 1012 (2022).
  12. E. Y. Weissman, A. Merzel, N. Katz, and I. Galili, Phenomena and principles: Presenting quantum physics in a high school curriculum, Physics 4, 1299 (2022).
  13. K. Tóth, M. Michelini, and P. Bitzenbauer, From light polarization to quantum physics: Supporting lower secondary school students’ transition from gestalt to functional thinking, Eurasia J. Math. Sci. Technol. Educ. 20, em2449 (2024).
  14. M. Waitzmann, K.-A. Weber, S. Wessnigk, and R. Scholz, Key experiment and quantum reasoning, Physics 4, 1202 (2022).
  15. M. S. Ubben, J. M. Veith, A. Merzel, and P. Bitzenbauer, Quantum science in a nutshell: Fostering students’ functional understanding of models, Front. Educ. 8, 1192708 (2023).
  16. K. Krijtenburg-Lewerissa, H. J. Pol, A. Brinkman, and W. Van Joolingen, Insights into teaching quantum mechanics in secondary and lower undergraduate education, Phys. Rev. Phys. Educ. Res. 13, 010109 (2017).
  17. C. Singh and E. Marshman, Review of student difficulties in upper-level quantum mechanics, Phys. Rev. ST Phys. Educ. Res. 11, 020117 (2015).
  18. A. J. Woitzik and O. Passon, Fehlvorstellungen zur Superposition in der Quantenphysik, arXiv:2301.06299.
  19. M. Michelini, A. Stefanel, and K. Tóth, Implementing Dirac approach to quantum mechanics in a Hungarian secondary school, Educ. Sci. 12, 606 (2022).
  20. G. J. Posner, K. A. Strike, P. W. Hewson, and W. A. Gertzog, Toward a theory of conceptual change, Sci. Educ. 66, 211 (1982).
  21. G. Ireson, The quantum understanding of pre-university physics students, Phys. Educ. 35, 15 (2000).
  22. G. Zuccarini and M. Michelini, Promoting the transition to quantum thinking: Development of a secondary school course for addressing knowledge revision, organization, and epistemological challenges, arXiv:2301.00239.
  23. R. Scholz, S. Wessnigk, and K.-A. Weber, A classical to quantum transition via key experiments, Eur. J. Phys. 41, 055304 (2020).
  24. M. S. Ubben and P. Bitzenbauer, Two cognitive dimensions of students’ mental models in science: Fidelity of gestalt and functional fidelity, Educ. Sci. 12, 163 (2022).
  25. P. Bitzenbauer, Effect of an introductory quantum physics course using experiments with heralded photons on preuniversity students’ conceptions about quantum physics, Phys. Rev. Phys. Educ. Res. 17, 020103 (2021).
  26. R. Feynman and R. Leighton, The Feynman Lectures on Physics (Addison-Wesley, MA, 1965), Vol. 3.
  27. M. S. Ubben and S. Heusler, Gestalt and functionality as independent dimensions of mental models in science, Res. Sci. Educ. 51, 1349 (2021).
  28. M. Ubben and P. Bitzenbauer, Exploring the relationship between students’ conceptual understanding and model thinking in quantum optics, Front. Quantum Sci. Technol. 2, 1207619 (2023).
  29. C. Stefani and G. Tsaparlis, Students’ levels of explanations, models, and misconceptions in basic quantum chemistry: A phenomenographic study, J. Res. Sci. Teach. 46, 520 (2009).
  30. G. Pospiech, B. Eylon, E. Bagno, Y. Lehavi, and M.-A. Geyer, The role of mathematics for physics teaching and understanding, Il Nuovo Cimento C 38, 1 (2015).
  31. F. Hennig, K. Tóth, M. Förster, and P. Bitzenbauer, A new teaching-learning sequence to promote secondary school students’ learning of quantum physics using Dirac notation, Phys. Educ. 59, 045007 (2024).
  32. J. A. Greene and R. Azevedo, A macro-level analysis of SRL processes and their relations to the acquisition of a sophisticated mental model of a complex system, Contemp. Educ. Psychol. 34, 18 (2009).
  33. G. Rickheit and L. Sichelschmidt, Mental models: Some answers, some questions, some suggestions, Adv. Psychol. 128, 9 (1999).
  34. R. J. Shavelson, Some methods for examining content structure, and cognitive structure in instruction, Educ. Psychol. 11, 110 (1974).
  35. D. Gentner and A. L. Stevens, Mental Models (Psychology Press, Hove, 2014).
  36. K. Tóth and T. Tél, Quantum uncertainty: What to teach?, Phys. Educ. 58, 025019 (2023).
  37. K. Tóth, Integrating Dirac approach to quantum mechanics into physics teacher education, AIP Conf. Proc. 2843, 050011 (2023).
  38. L. Lovisetti, G. Organtini, M. Giliberti et al., Inducing the construction of formal axioms of quantum mechanics and fostering their comprehension by high school students: The effectiveness of a conceptual approach, Il Nuovo Cimento C 46, 1 (2023).
  39. J. J. Sakurai and J. Napolitano, Modern Quantum Mechanics (Cambridge University Press, Cambridge, England, 2020).
  40. E. Gire and E. Price, Structural features of algebraic quantum notations, Phys. Rev. ST Phys. Educ. Res. 11, 020109 (2015).
  41. G. Pospiech, A. Merzel, G. Zuccarini, E. Weissman, N. Katz, I. Galili, L. Santi, and M. Michelini, The role of mathematics in teaching quantum physics at high school, in Teaching-Learning Contemporary Physics: From Research to Practice, edited by B. Jarosievitz and C. Sükösd (Springer, Cham, 2021), p. 47.
  42. P. Bronner, A. Strunz, C. Silberhorn, and J.-P. Meyn, Interactive screen experiments with single photons, Eur. J. Phys. 30, 345 (2009).
  43. V. Degiorgio, Phase shift between the transmitted, and the reflected optical fields of a semireflecting lossless mirror is π/2, Am. J. Phys. 48, 81 (1980).
  44. P. Grangier, G. Roger, and A. Aspect, Experimental evidence for a photon anticorrelation effect on a beam splitter: A new light on single-photon interferences, Europhys. Lett. 1, 173 (1986).
  45. R. Müller and O. Mishina, Milq—quantum physics in secondary school, in Teaching-Learning Contemporary Physics: From Research to Practice, edited by B. Jarosievitz and C. Sükösd (Springer International Publishing, Cham, 2021), pp. 33–45.
  46. P. Bitzenbauer, S. Navarrete, F. Hennig, M. S. Ubben, and J. M. Veith, Cross-age study on secondary school students’ views of stars, Phys. Rev. Phys. Educ. Res. 19, 020165 (2023).
  47. J. P. Smith, A. A. diSessa, and J. Roschelle, Misconceptions reconceived: A constructivist analysis of knowledge in transition, J. Learn. Sci. 3, 115 (1994).
  48. A. C. Maskiewicz and J. E. Lineback, Misconceptions “are so yesterday!”, Life Sci. Educ. 12, 352 (2017).
  49. J. K. Gilbert and D. M. Watts, Concepts, misconceptions and alternative conceptions: Changing perspectives in science education, Stud. Sci. Educ. 10, 61 (1983).
  50. R. E. Scherr, Modeling student thinking: An example from special relativity, Am. J. Phys. 75, 272 (2007).
  51. L. P. Steffe, P. W. Thompson, and E. von Glasersfeld, Teaching experiment methodology underlying principles and essential elements, in Handbook of Research Design in Mathematics and Science Education (Routledge, London, 2012), pp. 267–306.
  52. G. J. Wiener, S. M. Schmeling, and M. Hopf, The technique of probing acceptance as a tool for teachers’ professional development: A PCK study, J. Res. Sci. Teach. 55, 849 (2018).
  53. J. M. Veith, P. Bitzenbauer, and B. Girnat, Towards describing student learning of abstract algebra: Insights into learners’ cognitive processes from an acceptance survey, Mathematics 10, 1138 (2022).
  54. P. Bitzenbauer and J.-P. Meyn, A new teaching concept on quantum physics in secondary schools, Phys. Educ. 55, 055031 (2020).
  55. J.-P. Burde, Konzeption und Evaluation eines Unterrichtskonzepts zu einfachen Stromkreisen auf Basis des Elektronengasmodells (Logos Verlag Berlin, 2018).
  56. J.-N. Cleve, Die Wesenszüge der Quantenphysik qualitativ und quantitativ—Entwicklung eines Lehrgangs zu Experimenten mit dem Quantenkoffer, Master thesis, Ruhr-Universitat Bochum, Fakultat fur Physik und Astronomie, 2023.
  57. C. Albert and G. Pospiech, Quantenphysik in Klasse 9: Ergebnisse einer Akzeptanzbefragung für ein Spin-first-Unterrichtskonzept, PhyDid B (2023).
  58. W. Jung, Probing acceptance, a technique for investigating learning difficulties, Research in Physics Learning: Theoretical Issues and Empirical Studies (IPN, Kiel) (1992), p. 278.
  59. R. Blumör, Schülerverständnisse und Lernprozesse in der elementaren Optik, (Westarp Wissenschaften, Magdeburg, Essen, 1993).
  60. W. Jung, Erhebungen zu Schülervorstellungen in der Optik (Sekundarstufe I), Phys. Didact. 8, 137 (1981).
  61. C. Haagen-Schützenhöfer, Lehr-und Lernprozesse im Anfangsoptikunterricht der Sekundarstufe I, Universität Wien: Habilitationsschrift, Austria, 2016.
  62. P. Migdał, K. Jankiewicz, P. Grabarz, C. Decaroli, and P. Cochin, Visualizing quantum mechanics in an interactive simulation–virtual lab by quantum flytrap, Opt. Eng. 61, 081808 (2022).
  63. F. Budimaier and M. Hopf, Development of a new teaching-learning sequence on the particulate nature of matter using crystal structures, Phys. Rev. Phys. Educ. Res. 19, 020169 (2023).
  64. A. M. Colman, A Dictionary of Psychology (Oxford University Press, New York, 2015).
  65. B. S. Ambrose, P. S. Shaffer, R. N. Steinberg, and L. C. McDermott, An investigation of student understanding of single-slit diffraction and double-slit interference, Am. J. Phys. 67, 146 (1999).
  66. K. Wosilait, H. Wosilait, R. L. Paula, P. S. Shaffer, and L. C. McDermott, Addressing student difficulties in applying a wave model to the interference and diffraction of light, Am. J. Phys. 67, S5 (1999).
  67. S. K. şengören, How do Turkish high school graduates use the wave theory of light to explain optics phenomena?, Phys. Educ. 45, 253 (2010).
  68. V. Mešić, E. Hajder, K. Neumann, and N. Erceg, Comparing different approaches to visualizing light waves: An experimental study on teaching wave optics, Phys. Rev. Phys. Educ. Res. 12, 010135 (2016).
  69. G. Pospiech, Acceptance of Dirac-notation by high school students, WCPE-3 Abstracts (2021).
  70. S. E. Economou, T. Rudolph, and E. Barnes, Teaching quantum information science to high-school and early undergraduate students, arXiv:2005.07874.
  71. C. Singh and E. Marshman, Investigating student difficulties with Dirac notation, arXiv:1510.01296.
  72. E. Marshman and C. Singh, Student difficulties with quantum states while translating state vectors in Dirac notation to wave functions in position and momentum representations, arXiv:1509.04084.
  73. E. Marshman and C. Singh, Investigating and improving student understanding of quantum mechanics in the context of single photon interference, Phys. Rev. Phys. Educ. Res. 13, 010117 (2017).
  74. Özgür Özcan, What are the students’ mental models about the “spin” and “photon” concepts in modern physics?, Procedia 15, 1372 (2011).
  75. A. Richards, D. C. Jones, and E. Etkina, How students combine resources to make conceptual breakthroughs, Res. Sci. Educ. 50, 1119 (2020).
  76. P. Hubber, Year 12 students’ mental models of the nature of light, Res. Sci. Educ. 36, 419 (2006).
  77. M. Ayene, J. Kriek, and B. Damtie, Wave-particle duality and uncertainty principle: Phenomenographic categories of description of tertiary physics students’ depictions, Phys. Rev. ST Phys. Educ. Res. 7, 020113 (2011).
  78. M. Michelini, R. Ragazzon, L. Santi, and A. Stefanel, Proposal for quantum physics in secondary school, Phys. Educ. 35, 406 (2000).
  79. S. Montagnani, A. Stefanel, M. L. M. Chiofalo, L. Santi, and M. Michelini, An experiential program on the foundations of quantum mechanics for final-year high-school students, Phys. Educ. 58, 035003 (2023).
  80. C. Singh and E. Marshman, Developing an interactive tutorial on a Mach-Zehnder interferometer with single photons (2015).
  81. T. K. Stürmer-Steinmann, Implementationsprozesse begleiten (2023).
  82. G. Pospiech, Quantum cryptography as an approach for teaching quantum physics, in Teaching-Learning Contemporary Physics. Challenges in Physics Education, edited by B. Jarosievitz and C. Sükösd (Springer, Cham, 2021), pp. 19–31.
  83. C. M. Mills and F. C. Keil, Knowing the limits of one’s understanding: The development of an awareness of an illusion of explanatory depth, J. Exp. Child Psychol. 87, 1 (2004).
  84. L. Rozenblit and F. C. Keil, The misunderstood limits of folk science: An illusion of explanatory depth, Cogn. Sci. 26, 521 (2002).
  85. P. K. Ylikoski, The Illusion of Depth of Understanding in Science (University of Pittsburgh Press, Cham, 2009), pp. 100–119.
  86. www.gedeonrichter.com

Outline

Information

Phys. Rev. Phys. Educ. Res. 20, 020147– Published 26 November, 2024
  • Received 26 June 2024
  • Accepted 23 October 2024
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