https://doi.org/10.1140/epjqt/s40507-024-00274-6
Research
Mathematical sense making of quantum phenomena using Dirac notation: its effect on secondary school students’ functional thinking about photons
1
Professur für Physikdidaktik, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstraße 7, 91058, Erlangen, Germany
2
Institute of Physics and Astronomy, ELTE Eötvös Loránd University, Pázmány Péter prom. 1A, H-1117, Budapest, Hungary
3
Czuczor Gergely Benedictine Secondary School, Széchenyi square 8-9, H-9022, Győr, Hungary
4
Institute of Physics Education, Leipzig University, Vor dem Hospitaltore 1, 04317, Leipzig, Germany
d
philipp.bitzenbauer@uni-leipzig.de
Received:
14
August
2024
Accepted:
17
September
2024
Published online:
27
September
2024
Previous research has consistently demonstrated that students often possess an inadequate understanding of fundamental quantum optics concepts, even after formal instruction. Findings from physics education research suggest that introducing a mathematical formalism to describe quantum optical phenomena may enhance students’ conceptual understanding of quantum optics. This paper investigates whether using formal descriptions of quantum optics phenomena – such as photon anticorrelation at a beamsplitter or single-photon interference in a Michelson interferometer – expressed in Dirac notation, can support secondary school students in developing functional thinking about photons. To investigate this, we conducted a clusterrandomized field study, comparing the improvement in functional thinking between 67 students in the intervention group, who were taught using both qualitative and quantitative reasoning, and 66 students in the control group, who were taught using only qualitative reasoning. The results indicate that mathematical formalism can indeed promote functional thinking about photons. However, the comparison between the intervention and control groups revealed that the control group exhibited a greater increase in functional thinking than the intervention group. In response to these findings, we conducted a follow-up study aimed at gaining a deeper understanding of the cognitive load associated with both approaches. Specifically, we compared the intrinsic and extraneous cognitive load of 71 students in the intervention group with those of 65 students in the control group. The data analysis revealed that the two groups had statistically significant differences in intrinsic cognitive load while the extraneous cognitive load did not difer statistically significant, indicating a higher mental effort associated to the quantitative reasoning.
Key words: Quantum physics / Photon / Dirac notation / Secondary school
© The Author(s) 2024
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
