Test on the effectiveness of the sum over paths approach in favoring the construction of an integrated knowledge of quantum physics in high school

In this paper we present the results of a research-based teaching-learning sequence on introductory quantum physics based on Feynman’s sum over paths approach in the Italian high school. Our study focuses on students’ understanding of two founding ideas of quantum physics, wave particle duality and the uncertainty principle. In view of recent research reporting the fragmentation of students’ mental models of quantum concepts after initial instruction, we collected and analyzed data using the assessment tools provided by knowledge integration theory. Our results on the group of $n=14$ students who performed the final test indicate that the functional explanation of wave particle duality provided by the sum over paths approach may be effective in leading students to build consistent mental models of quantum objects, and in providing them with a unified perspective on both the photon and the electron. Results on the uncertainty principle are less clear cut, as the improvements over traditional instruction appear less significant. Given the low number of students in the sample, this work should be interpreted as a case study, and we do not attempt to draw definitive conclusions. However, our study suggests that (i) the sum over paths approach may deserve more attention from researchers and educators as a possible route to introduce basic concepts of quantum physics in high school, and (ii) more research should be focused not only on the correctness of students’ mental models on individual concepts, but also on the ability of students to connect different ideas and experiments related to quantum theory in an organized whole.

Figure 1

The version of the TLS tested in high school. The central row (light orange) shows the main steps of the sequence, which is summarized in Appendix pp2. The green ovals are the most important conceptual themes and principles discussed, and the gray rectangles are the experimental evidence introduced.

Figure 2

Results for the task on the uncertainty principle (T1a “Recognize that the presentation is not consistent with the current understanding of the principle and explain”).

Figure 3

Results for task T2 (wave particle duality in the context of the Mach-Zehnder experiment with one photon at a time).

Figure 4

Results for task T3 (wave particle duality in the context of Young’s experiment with one electron at a time).

Figure 5

Results (number of answers judged as basically correct) for each item in the final assessment test ($N=17$).

Figure 6

Depiction of the uncertainty principle from the Heisenberg microscope perspective (reproduced from Ref. [53]).

Figure 7

The ordinary Mach-Zehnder experiment and its results (the two arms of the apparatus have the same length).

Figure 8

Results for the Mach-Zehnder experiment with an intermediate detector C, which can reveal the passage of the photon without destroying or perturbing it.

Figure 9

The Merli-Missiroli-Pozzi experiment 1974–76, reproduced from Ref. [49] with the permission of the American Association of Physics Teachers.

Figure 10

The Michelson interferometer.