Student reasoning about superposition in quantum mechanics

Kristóf Tóth, Marisa Michelini, Philipp Bitzenbauer

In this paper, we present a new minimal mathematical conceptual approach to quantum mechanics using light polarization for lower secondary school students with the aim of bringing students closer to the so-called quantum mechanical way of thinking. We investigated how students think about some of the basic concepts and fundamental laws and we found that certain concepts are quite well-understandable in younger grades too. We studied the introduction of the so-called state circle, which can faithfully represent quantum mechanical formalism without involving students in abstract algebraic calculations. We then categorized and analyzed students’ thoughts on the superposition principle and the lack of trajectory, finding that the concept of measurement and the lack of trajectory were problematic. We explored that younger students tend to hold gestalt-like mental models of quantum concepts, while at the same time being able to use visualizations correctly for reasoning in the quantum realm. Overall, this paper provides evidence in favor of introducing basic features of quantum mechanics as early as in lower secondary school.

Jack Cohn

Antonio Zecca A

Marc L. Whiting, Lauren A. Barth-Cohen, Adrian L. Adams +2 more

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.

Horst R. Beyer

Sergej Faletič

Abstract In my active learning course on quantum mechanics, students build their knowledge by following the scientific process as outlined by the Investigative Science Learning Environment. In this course, open-ended questions on the effect of measurement (collapse) failed to elicit meaningful responses from students. Meaningful responses are crucial for the next steps of testing students’ ideas using hypothetico-deductive reasoning. I wanted to help the students in this process with a pictorial representation. To arrive at a pictorial representation that would have meaning for students, I first asked them to provide their analogies for a superposition state. A common suggestion was the mixture of colours, but other, more inventive analogies were also suggested. I developed a pictorial representation based on the colour analogy. I reformulated the questions on collapse using this representation and a more concretized formulation. The ability of students to meaningfully answer the questions increased to the point where it was possible to complete also the testing part of the process. In the article, I discuss the analogies that students suggested and what underlying ideas known from literature they could represent. I provide the derived representation, the reformulated questions and evidence of how this helped students articulate their answers and helped identify students’ productive ideas that they could not clearly articulate in words. This enabled students to arrive at conclusions about the effect of measurement following the scientific process. This study contributes to the literature by providing student-generated analogies, using a pictorial representation derived from student-generated analogies, and showing an example of an efficiently formulated question on a difficult topic that is able to elicit meaningful responses.