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.
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.
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.
In this work, I propose a way to help high school students and the general population understand quantum concepts by adopting a new inherently dual representation. Major difficulties in explaining to people the basic concepts of quantum mechanics reside in the apparent impossibility of representing quantum superposition with examples taken from everyday life. In this context, I propose a new pictorial paradigm that illustrates a number of quantum concepts by means of optical illusions, potentially without raising misconceptions. The method is based on "bistable reversible figures", which induce in the viewer a multistable perception, conveying a direct understanding of superposition, random collapse, and observer effect via a sensorial experience. I present the advantages and discuss the limitations of this analogy, and show how it extends to the concepts of complementarity and quantum entanglement, also helping to avoiding misconceptions in quantum teleportation. Finally, I also address quantum spin and quantum measurement by using different types of optical illusions.
Quantum mechanics (QM) was prominently featured in the Dutch national physics examination for upper secondary school level in 2016 for the first time. It appears that many students have struggled to learn this new subject and had problems answering the associated examination questions. From the literature it is known that QM is difficult to understand, and to visualize in everyday settings. This is likely to hinder students' development of a conceptual understanding of QM. In this proposal we apply the perspective of Conceptual Field Theory to the learning of QM, to develop a deeper understanding of problems that arise in its learning processes. Conceptual Field Theory is a theory that emphasizes action to develop students' concepts, and the action is set in task-based situations presented to students. We argue that the main problem associated with learning QM is that it is difficult for students to come to meaningful representations appropriate for learning QM. Without meaningful representations it is hard to formulate correct propositions that help to handle and analyze presented task-based situations. In this proposal we describe why it is difficult to come to meaningful representations in QM and we suggest how research into learning and teaching QM could proceed.
We describe an investigation focusing on advanced students' and faculty members' reasoning about two questions related to the double-slit experiment with single particles.One question posed was a standard double slit question while the other question was more speculative.First, students in advanced quantum mechanics courses were asked the questions in written form and individual interviews were conducted with six students in which they were asked follow up questions to make their thought processes explicit.We also interviewed five faculty members who had taught modern physics, quantum mechanics and/or solid state physics to understand their reasoning and thought processes.The faculty members' responses shed light on what it means to think like a physicist.Student responses varied greatly in their correctness and sophistication of reasoning, suggesting that even advanced students need scaffolding support in order to learn to think like a physicist.
Not only is Quantum Mechanics (QM) conceptually rich, it is also a theory that physics students have found abstract and technically formidable. Nevertheless, compared to other classical topics of physics, university students’ understanding of QM has received minimal attention in the physics education literature. The principal purpose of this study was to characterize the variation in the ways that undergraduate physics students depict the basic concepts of QM and to extrapolate the results to scaffold possible changes to instructional practices at the university that provided the context for the study. In so doing, an adaptation of a developmental phenomenographic perspective was chosen. Empirically, the study was approached through in-depth interviews with 35 physics students from two Ethiopian governmental universities after they had been exposed to the traditional QM course for one-third of a semester. Interview responses were analyzed using phenomenographic approach where a picture of students’ depictions was established for each quantum concept by expounding the given responses. For each basic quantum concept addressed, the structure of the description categories was separately constructed, and overall, it was found that naive, quasi-classical ontology and/or variants of classical ways of visualization are dominant in students’ responses. For example, it was found that students’ depictions of the photon concept could be described with three distinct categories of description, which are (a) classical intuitive description, (b) mixed model description and (c) quasi-quantum model description. Similarly, the findings revealed that it is possible to establish three qualitatively different categories of description to picture students’ depictions of matter waves, namely, (a) classical and trajectory-based description, (b) an intricate blend of classical and quantum description and (c) incipient quantum model description. Likewise, it was found that students’ depictions of uncertainty principle can be described as: (a) uncertainty as classical ignorance, (b) uncertainty as measurement disturbance and (c) uncertainty as a quasi-quantum principle. \nWith regard to learning QM, the categories of description made clear several issues: most students did not have enough knowledge to depict the basic concepts of QM properly; they were influenced by the perspective of classical physics and their perceptions in making explanations about QM; and they also applied mixed ideas, one based on their classical model and the other from newly introduced QM. These results are also supported by the findings of previous studies in similar domains. Findings from the study were used to guide the design of multiple representations-based instructions and interactive learning tutorials on the conceptual aspects of QM that has been shown to address specific difficulties identified in the study. Theoretical and practical implications of the study, as well as potential future considerations are drawn.
This paper is part of the Focused Collection on Upper Division Physics Courses.]Energy measurements play a fundamental role in the theory of quantum mechanics, yet there is evidence that the underlying concepts are difficult for many students, even after all undergraduate instruction.We present results from an investigation into student ability to determine the possible energies that can be measured for a given wave function and Hamiltonian, to determine the probabilities of each energy measurement and how they depend on time, and to recognize how a measurement of energy affects the state.By analyzing student responses to open-ended questions, we identify five broad, interrelated sets of conceptual and reasoning difficulties related to energy measurements.Data are drawn from sophomore-, junior-, and graduate-level quantum mechanics courses.Particular attention is paid to incorrect ideas that persist across all levels.