Kristóf Tóth

Evidence from physics education research suggests that the introduction of mathematical formalism in quantum physics instruction can support the development of students’ conceptual understanding, particularly by promoting functional ways of reasoning about quantum phenomena. However, empirical findings on the effectiveness of such approaches at the secondary school level remain inconclusive, and little is known about the extent to which learning outcomes are shaped by instructional design as opposed to learners’ affective and cognitive characteristics. This study addresses this gap by investigating the relative influence of instructional approach on students’ understanding of single-photon states, while controlling for prior knowledge, cognitive load, situational interest, and physics self-concept. A quasiexperimental pre-post design was implemented with N = 172 upper secondary students, comparing a qualitative instructional condition with an approach supplemented by a reduced Dirac formalism. Learning outcomes were assessed using the framework of Functional Fidelity and Fidelity of Gestalt. A multivariate analysis of covariance, followed by univariate analyses of covariance, was conducted to examine the contributions of instructional and learner-related variables. The findings indicate that affective variables emerge as strong predictors of functional understanding and suggest that learning in quantum physics is driven less by instructional format than by learners’ affective and cognitive prerequisites. In particular, fostering interest appears to be a key mechanism for supporting the development of functional understanding. The results highlight the importance of integrating affective dimensions into instructional design and provide a basis for future research on the interaction between instructional approaches and learner characteristics in quantum physics education.

Evidence from physics education research highlights the importance of affective learning characteristics, such as interest, curiosity, and enjoyment, for students’ engagement with complex and abstract topics like quantum physics. Students who show a greater interest in the subject tend to achieve better academic results, are more persistent, and are more likely to choose a university related to that subject. In recent years, one-day workshops and outreach formats have increasingly been used to introduce and promote quantum technologies at the secondary-school level. The goal of these programs is to widely disseminate new scientific findings, spark interest, and address the needs of academia and industry to fill labor shortages. However, the extent to which such short-term interventions influence students’ affective outcomes remains insufficiently understood. There are only a few studies analyzing a workshop on quantum physics and quantum technology from the perspective of student interest, curiosity, and enjoyment, specifically at the upper-secondary school level. This paper addresses this gap by reporting findings from a pre-post study investigating the impact of a one-day, hands-on quantum technology workshop on upper secondary school students. Using established instruments to assess four facets of interest and descriptive measures of curiosity and enjoyment (N = 45), the study examines changes in students’ affective learning characteristics. The results indicate no statistically significant changes in any interest dimension, while enjoyment and curiosity were reported at comparatively high levels. These findings suggest that single workshop events, such as the one described in this article, can foster positive learning experiences and situational engagement but are unlikely to support sustained interest development. Implications for the design and development of a secondary school level out-of-school quantum workshop are discussed.

This paper presents a minimalist teaching-learning sequence for quantum computation in secondary education (5 × 60 minutes) grounded in the photon polarization approach. The framework has been tailored to the secondary school level education omitting complex numbers, matrices, and programming while relying on physics concepts with which students are already familiar from photon polarization. Employing a design-based research methodology, we identified the minimal set of concepts necessary for conceptual understanding: Dirac notation, the X and H quantum gates, and the quantum advantage demonstrated using the penny flip game as an example, which was tested on a real quantum computer. Students also explore the B92 cryptographic protocol and quantum entanglement in this course.

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.

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.

Erratum for the article: Dandl, K., Tóth, K., & Bitzenbauer, P. (2024). From simulation to experiment: Using KiCad to design electric circuits in the physics classroom. Eurasia Journal of Mathematics, Science and Technology Education, 20(10), em2510. https://doi.org/10.29333/ejmste/15176

[This paper is part of the Focused Collection in Investigating and Improving Quantum Education through Research.] Evidence from physics education research suggests that the introduction of a formalistic description of quantum phenomena can be beneficial to student learning, particularly in terms of helping students move away from naive realist views of quanta or space-time descriptions of quantum phenomena. However, the mathematical requirements for mastering quantum formalism are typically far beyond the scope of secondary school education. Therefore, in previous research, we have proposed a reduced Dirac notation tailored to the capabilities of secondary school students, which is included in a novel teaching-learning sequence. However, the cognitive processes of students when confronted with an introduction to quantum physics via a reduced Dirac notation have not been thoroughly investigated: In particular, it seems important to investigate whether this approach is actually beneficial to students’ learning and to explore the learning difficulties students are likely to encounter in such a setting. This paper contributes to this research gap by reporting the findings of an acceptance survey: N = 14 learners participated in one-on-one interviews following a protocol consisting of four cyclical phases (information phase, acceptance evaluation, paraphrasing phase, and application phase). The findings of our study indicate that the instructional elements within our new teaching-learning sequence were generally well accepted by students but also revealed learning difficulties that students may encounter. Thus, on the one hand, the findings of this study pave the way for future research on students’ learning of quantum physics using Dirac notation. On the other hand, the in-depth findings reported here may guide teachers in designing learning environments that introduce Dirac notation at the upper secondary school and introductory university levels. Published by the American Physical Society 2024

[This paper is part of the Focused Collection in Investigating and Improving Quantum Education through Research.] The teaching and learning of quantum physics has recently become a topic of increasing interest in physics education research. In particular, the study of two-state systems is gaining importance as a means of teaching quantum physics at various educational levels. Meanwhile, a number of approaches have been developed that are also suitable for high school students. It can be assumed that the different approaches have different degrees of effectiveness in teaching central quantum concepts. However, suitable evaluation instruments to test this are still lacking. Therefore, as a first step, a short questionnaire on quantum measurement, suitable for both research and classroom use, was developed in several steps. First, a questionnaire with open and closed items was created and piloted with a total of N = 120 learners. The responses were evaluated qualitatively using a comprehensive coding manual, which provided insights into learners’ conceptions. These results led to the development of an eight-item questionnaire that could be adapted to different teaching approaches. This questionnaire was subjected to expert review and, finally, successfully tested for its psychometric properties with a sample of N = 201 learners. Overall, our results provide initial empirical evidence that context (i.e., which two-state approach is used) does matter for student learning, but in general, two-state approaches appear to be particularly conducive to learning quantum concepts (specified in this article for quantum measurement) compared to traditional instruction. Published by the American Physical Society 2024

Secondary school students encounter a wide range of electronic devices in their everyday lives that are not usually covered in physics classes. Examples include mobile phone power adapters that convert high-voltage alternating current to low-voltage direct current. However, such examples are often not used sufficiently in the classroom to provide students with insights into (a) the specific applications of the electronic components used and (b) the underlying electronic design process. To fill this gap, we have designed a new context-based, easy-to-implement teaching-learning sequence that guides students to how to use the electronic design and simulation program KiCad which is being widely used by professionals in the field, (2) build their own analog experimental setup of a mobile phone power supply, and thus (3) understand how a mobile phone power supply works. The presented part of the teaching-learning sequence focuses on the use of KiCad and is designed to allow students to work individually and in groups to learn according to the think-pair-share principle based on a set of tasks we created. This paper examines the pedagogical potential of KiCad and provides a detailed description of the teaching-learning sequence and reports on initial classroom experiences: A total of N = 28 students aged 16 to 17 years participated in the unit as part of an extracurricular course and completed a questionnaire based on the Technology Acceptance Model to investigate the perceived ease of use and usability of the KiCad software. We found that despite the fact that the students had not used KiCad before, they were quite positive about the educational material as a whole and the KiCad software in particular.

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.