[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.] 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
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.
Abstract This paper describes the design of a new teaching-learning sequence on quantum physics aimed at upper secondary school students. In this teaching-learning sequence, GeoGebra simulations and interactive screen experiments are used to investigate the behaviour of a single photon at beam splitter and single photon interference in a Michelson interferometer. We propose a minimal formalism using Dirac notation, which avoids complex numbers and elaborate vector calculus, to make a quantitative description of the quantum optics experiments accessible to secondary school students. With this new educational pathway, we take into account findings from physics education research, which suggest that the introduction of a mathematical formalism tailored to students’ abilities might help them to overcome naive-realist views of quanta or space-time descriptions of quantum phenomena, while at the same time facilitating a transition to a functional understanding of quantum models.
Abstract Learning quantum mechanics (QM) is widely recognized as a challenging task, as it involves highly abstract concepts and requires a significant shift from classical physics reasoning. Developing expertise in QM requires students to represent physical concepts using multiple formalisms, such as Dirac notation and algebraic representations, and to move flexibly between them. This study investigates two main categories of student difficulties related to Dirac notation. The first concerns difficulties in expressing a generic state vector in the position and momentum representations. The second relates to challenges in writing the eigenvectors of the position and momentum operators in Dirac notation. To explore these issues, we administered questionnaires to third-year undergraduate physics students enrolled in a QM course at the Lyon 1 University. We present a detailed analysis of student responses, identify the principal difficulties encountered, and compare our findings with results reported in prior American studies. Our results show that many students struggle to establish a clear connection between Dirac notation and its functional algebraic representation. In particular, students find it easier to recognize state vectors and eigenvectors than to construct them explicitly. Additionally, common difficulties include confusion between bras (e.g. x | and p |) and the corresponding operators, as well as confusion between the Dirac delta distribution and the Kronecker delta. Finally, we propose some interpretations of our results in light of those reported in previous studies.
This paper is part of the Focused Collection on Upper Division Physics Courses.]Most introductory quantum physics instructors would agree that transitioning students from classical to quantum thinking is an important learning goal, but may disagree on whether or how this can be accomplished.Although (and perhaps because) physicists have long debated the physical interpretation of quantum theory, many instructors choose to avoid emphasizing interpretive themes; or they discuss the views of scientists in their classrooms, but do not adequately attend to student interpretations.In this synthesis and extension of prior work, we demonstrate the following: (i) instructors vary in their approaches to teaching interpretive themes; (ii) different instructional approaches have differential impacts on student thinking; and (iii) when student interpretations go unattended, they often develop their own (sometimes scientifically undesirable) views.We introduce here a new modern physics curriculum that explicitly attends to student interpretations, and provide evidence-based arguments that doing so helps them to develop more consistent interpretations of quantum phenomena, more sophisticated views of uncertainty, and greater interest in quantum physics.
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.
[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