Investigating the effect of two-state approaches on students’ understanding of quantum measurement: A quasiexperimental field study
Kristóf Tóth, Sergej Faletič, Marisa Michelini, Gesche Pospiech, Andrea Betti, Marco Nicolini, Marco Parmiggiani, Joaquin Marc Veith, Philipp Bitzenbauer
With the rise of quantum computing, interest has grown in using two-state quantum systems (qubits) at the secondary level to foster students’ conceptual understanding. Quantum measurement, in particular, is central to quantum theory and its accurate conceptualization by students is crucial for grasping fundamental quantum principles. However, instructional methods typically make use of different contexts (i.e., different two-state systems), significantly affecting students’ conceptual development in quantum physics. In this paper, we report findings from a cluster-randomized field trial involving 181 students taught through three inquiry-based, two-state approaches: the which-path-encoded single-photon, the polarization, and the double-well potential approach. All three approaches supported students’ conceptual development, yet students taught using photon polarization and the double-well potential significantly outperformed those participating in a course following the which-path-encoded single-photon approach. Our findings indicate that students participating in the which-path-encoded single-photon approach often retain mixed-thinking frameworks, whereas those taught with photon polarization or the double-well potential approaches were more likely to develop toward quantum thinking. Thus, our findings underpin how influential the choice of (experimental) context is on students’ conceptual development (also) in quantum physics.
With the rise of quantum computing, interest has grown in using two-state quantum systems (qubits) at the secondary level to foster students’ conceptual understanding. Quantum measurement, in particular, is central to quantum theory and its accurate conceptualization by students is crucial for grasping fundamental quantum principles. However, instructional methods typically make use of different contexts (i.e., different two-state systems), significantly affecting students’ conceptual development in quantum physics. In this paper, we report findings from a cluster-randomized field trial involving 181 students taught through three inquiry-based, two-state approaches: the which-path-encoded single-photon, the polarization, and the double-well potential approach. All three approaches supported students’ conceptual development, yet students taught using photon polarization and the double-well potential significantly outperformed those participating in a course following the which-path-encoded single-photon approach. Our findings indicate that students participating in the which-path-encoded single-photon approach often retain mixed-thinking frameworks, whereas those taught with photon polarization or the double-well potential approaches were more likely to develop toward quantum thinking. Thus, our findings underpin how influential the choice of (experimental) context is on students’ conceptual development (also) in quantum physics.
Teaching quantum mechanics at the secondary school level remains a major educational challenge. Traditional historical approaches often present the theory as a sequence of disconnected phenomena, requiring extensive prior knowledge of classical physics before students can appreciate the conceptual structure of quantum physics. In this work, we present the design, implementation, and evaluation of a curriculum based on the two state (qubit first) approach, in which the fundamental postulates of quantum mechanics are introduced through mathematically accessible two level systems and realized with light polarization. The curriculum integrates theoretical instruction, laboratory activities, a coherent progression grounded in the interactive simulations, and inquiry based learning into a coherent pathway that progresses from quantum states and superposition to entanglement and the experimental violation of Bell's inequalities. A distinctive feature of the project is the experimental realization of the violation of Bell's inequalities obtained in a newly established quantum optics laboratory in an Italian high school, where students performed, for the first time in Italy, an authentic Bell test using polarization-entangled photons. The same educational framework was adopted for in service teacher professional development courses. Learning outcomes were evaluated through mixed methods. Preliminary analysis indicates significant improvements in conceptual understanding, confidence in using mathematical formalism, and appreciation of the relationship between theory, experimentation, and the foundations of quantum mechanics. The proposed curriculum shows that two-state formalism and supported by real laboratory experiences enables secondary-school students to engage more meaningfully with both the conceptual foundations of quantum mechanics and their experimental verification.
Despite formal instruction, secondary school students often struggle to move beyond classical interpretations when reasoning about quantum phenomena, especially concerning the statistical nature of quantum physics. This study explores how students conceptualize quantum randomness following instruction centered on two key experiments: the Michelson interferometer (MI) with single photons and the double-slit experiment. Qualitative content analysis of interviews with 25 students revealed three distinct reasoning types: (1) statistical ensemble interpretation, (2) ensemble reasoning involving hidden variables or spatial limitations, and (3) a focus on localization and spatial uncertainty. Notably, students referencing the MI context in their reasonings more often demonstrated advanced ensemble-based reasoning, distinguishing quantum probabilities from classical ones. In contrast, students who relied primarily on the DSE context were more capable of framing their reasoning in terms of spatial uncertainty. These findings highlight the pivotal role of experimental context in fostering students’ quantum thinking and point to promising directions for future research.
[This paper is part of the Focused Collection in Investigating and Improving Quantum Education through Research.] Quantum information science and engineering (QISE) is a rapidly developing field that leverages the skills of experts from many disciplines to utilize the potential of quantum systems in a variety of applications. It requires talent from a wide variety of traditional fields, including physics, engineering, chemistry, and computer science, to name a few. To prepare students for such opportunities, it is important to give them a strong foundation in the basics of QISE, in which quantum computing plays a central role. In this study, we discuss the development, validation, and evaluation of a Quantum Interactive Learning Tutorial, on the basics and applications of quantum computing. These include an overview of key quantum mechanical concepts relevant to quantum computation (including ways a quantum computer is different from a classical computer), properties of single- and multiqubit systems, and the basics of single-qubit quantum gates. The tutorial uses guided inquiry-based teaching-learning sequences. Its development and validation involved conducting cognitive task analysis from both expert and student perspectives and using common student difficulties as a guide. For example, before engaging with the tutorial, after traditional lecture-based instruction, one reasoning primitive that was common in student responses is that a major difference between an N -bit classical and N -qubit quantum computer is that various things associated with a number N for a classical computer should be replaced with the number 2 N for a quantum computer (e.g., 2 N qubits must be initialized and 2 N bits of information are obtained as the output of the computation on the quantum computer). This type of reasoning primitive also led many students to incorrectly think that there are only N distinctly different states available when computation takes place on a classical computer. Research suggests that this type of reasoning primitive has its origins in students learning that quantum computers can provide exponential advantage for certain problems, e.g., Shor’s algorithm for factoring products of large prime numbers, and that the quantum state during the computation can be in a superposition of 2 N linearly independent states. The inquiry-based learning sequences in the tutorial provide scaffolding support to help students develop a functional understanding. The final version of the validated tutorial was implemented in two distinct courses offered by the physics department with slightly different student populations and broader course goals. Students’ understanding was evaluated after traditional lecture-based instruction on the requisite concepts and again after engaging with the tutorial. We analyze and discuss their improvement in performance on concepts covered in the tutorial. Published by the American Physical Society 2024
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.
For more details about the files, please open "readme.docx". Abstract This article reports an empirical study involving N = 82 secondary school students, exploring their conceptions of quantum entanglement. The study utilizes a teaching-learning sequence based on photon polarization, covering both single-photon and photon-pair entanglement. Adopting a mixed-methods approach, we analyzed student responses to a questionnaire using quantitative methods and qualitative content analysis. The findings reveal a fragmented knowledge structure among learners. Students demonstrated functional reasoning and competency with mathematical formalism, often anchoring their explanations in specific experimental contexts. However, they frequently reverted to classical, causal, or hidden-variable narratives when interpreting the nature of correlations. While students aligned with quantum perspectives regarding holism and non-separability, they exhibited persistent classical thinking regarding causal influence and interaction. We also observed that students often engaged in overgeneralization of cases of perfect correlation. We conclude that competence in formalism does not necessarily imply a coherent, quantum-consistent understanding. Consequently, we propose specific refinements to the educational material through a design-based methodology — such as the inclusion of partially entangled states and explicit contrasts between classical causation and quantum correlations — to better address deeply rooted classical intuitions and foster a coherent understanding of entanglement.
Quantum mechanics (QM) has taken on a paradigmatic role in how physics describes and builds new knowledge about the world. It also has a growing role in our society thanks to recent and rapid developments in the field of new quantum technologies. These are becoming increasingly important in our society, in the world of work and which will also decisively influence future socio-economic choices. Also for this reason QM has an increasing role in the education of young people and has been introduced in many different ways also in secondary school in all continents. The change in the theoretical and cultural frame has profound implications that are often not intuitive, which involve the appropriation of a specific way of thinking. Neither macroscopic phenomenology, nor intuition help, because there is no simple evidence of how quantum objects must be thought to interpret that unobservable microscopic world and for which we must enter another interpretative paradigm even if we want to limit ourselves to describe it. PER has carried out several studies on the learning of key concepts, on the learning nodes, the ways of reasoning, the difficulties of the students, their spontaneous ideas, according to two main strands: above all at university level, conceptual difficulties and misunderstandings often linked to a formal approach, which, moreover, underpins the very nature of the entities involved; at secondary school level in relation to how students acquire a quantum view of phenomena on the basis of specific approaches adopted to address QM. In particular, a vast literature, which has increased considerably and especially in relatively recent times, has studied how university students deal with certain concepts such as that of state, superposition, measurement in quantum mechanics rather than how quantum quantities evolve over time. These studies are based on the use of questionnaires that allow to explore different levels: the verbal, formal and representative one, with different representations (eg. wave function, Dirac notation), rather than different representative modes (eg. Graphs of probability amplitudes, or probability distributions). At the secondary school level, the most important studies on student learning were instead conducted evaluating the educational impact and outlining the learning paths of students who had followed formative activities based on differentiated innovative research-based educational paths. In particular, the learning outcomes were compared to those activated by proposals based on the historical reconstruction approach of quantum physics. This approach is privileged in traditional curricula and school texts and consequently in the ways of teachers approaching the topic. It was developed in schools with a narrative or descriptive dimension of solutions based on old physics of quanta for the interpretation of phenomena not explained by classical physics. The innovative approaches instead make use of contexts whose formal treatment is simple (quantum properties described in a two-state space such as polarization or spin) with the aid of simulations that compensate for the problem of students” limited mathematical-formal skills, avoiding any historical reference. In particular, there is a significant difference between the survey tools and the survey contexts in the high school environment compared to surveys conducted with university students. This paper presents a review of the research literature, focusing in particular on the learning processes of secondary school students and outlining how research perspectives have evolved.