Mathematical sense making of quantum phenomena using Dirac notation: its effect on secondary school students’ functional thinking about photons

Abstract

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.