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Die Quantenphysik bildet schon heute das Fundament zahlreicher aktueller Technologien. Zukünftige Quantentechnologien, wie Quantencomputer, werden sowohl in der Industrie als auch für die Gesellschaft an Bedeutung gewinnen.
In vielen nationalen und internationalen Schulcurricula ist die Quantenphysik als Thema für den Physikunterricht mittlerweile fest verankert. Aber trotz des enormen Bedeutungszuwachses von Quantentechnologien ist der Unterricht zur Quantenphysik an Schulen nach wie vor von semi-klassischen Modellen und quasi-historischen Zugängen geprägt, während moderne Begriffe der Quantenphysik häufig unberücksichtigt bleiben. Die Folge sind oft klassisch-mechanistisch geprägte Vorstellungen Lernender zur Quantenphysik.
Hier setzt diese Arbeit an: mit dem Erlanger Unterrichtskonzept zur Quantenoptik wird ein Konzept vorgestellt, mit dem Lernende der gymnasialen Oberstufe Quanteneffekte anhand quantenoptischer Experimente kennen lernen. Konzepte der Quantenoptik, wie die Präparation von Quantenzuständen, die Antikorrelation am Strahlteiler und die Einzelphotoneninterferenz verhelfen Lernenden zu einem modernen Bild über Quantenphysik. Im Rahmen einer summativen Evaluation im Mixed-Methods-Design mit 171 Schülerinnen und Schülern zeigte sich, dass Lernende mit dem Erlanger Unterrichtskonzept zu quantenphysikalisch dominierten Vorstellungen gelangen und verbreitete Lernschwierigkeiten vermieden werden können.

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... Currently, only a few studies with relatively small samples have been published exploring obstacles that students encounter with regards to quantum optics [33,[51][52][53][54]]. An exploratory interview study identifying N = 25 students' difficulties regarding different quantum optics content domains is reported in Ref. [55]. In [55], it was shown that (a) students are predominantly unprejudiced towards the experimental and technical foundations of quantum optics experiments, e.g., with regard to the preparation of single-photon states in experiments with heralded photons via coincident events on binary detectors, and that (b) most of the students can cope with the underlying principles [55]. ...

... An exploratory interview study identifying N = 25 students' difficulties regarding different quantum optics content domains is reported in Ref. [55]. In [55], it was shown that (a) students are predominantly unprejudiced towards the experimental and technical foundations of quantum optics experiments, e.g., with regard to the preparation of single-photon states in experiments with heralded photons via coincident events on binary detectors, and that (b) most of the students can cope with the underlying principles [55]. These indications are also supported in further studies, e.g., exploiting the technique of probing acceptance [51]. ...

... An exploratory interview study identifying N = 25 students' difficulties regarding different quantum optics content domains is reported in Ref. [55]. In [55], it was shown that (a) students are predominantly unprejudiced towards the experimental and technical foundations of quantum optics experiments, e.g., with regard to the preparation of single-photon states in experiments with heralded photons via coincident events on binary detectors, and that (b) most of the students can cope with the underlying principles [55]. These indications are also supported in further studies, e.g., exploiting the technique of probing acceptance [51]. ...

Quantum technologies have outgrown mere fundamental research in laboratories over recent years, and will facilitate more and more potentially disruptive applications in a wide range of fields in the future. In foresight, qualification opportunities need to be implemented in order to train qualified specialists, referred to as the future quantum workforce, in various fields. Universities world-wide have launched qualification programmes for engineers focusing on quantum optics and photonics. In many of these programmes, students attend courses on quantum physics contextualized via quantum optics experiments with heralded photons, because: (1) their experimental and physical foundations may be directly leveraged to teaching a number of quantum technology applications, and (2) physics education research has provided empirical evidence, according to which such quantum optics-based approaches are conducive to learning about quantum concepts. While many teachers are confident about the effectiveness of their concepts, there is little empirical evidence due to the lack of content-area-specific research tools. We present a 16-item concept inventory to assess students’ conceptual understanding of quantum optics concepts in the context of experiments with heralded photons adopted from a test instrument published in the literature. We have administered this Quantum Optics Concept Inventory as a post-test to N = 216 students after instruction on quantum optics as part of an undergraduate engineering course. We evaluated the instruments’ psychometric quality, both in terms of classical test theory, and using a Rasch scaling approach. The Quantum Optics Concept Inventory enables a reliable measure (α = 0.74), and the data gathered show a good fit to the Rasch model. The students’ scores suggest that fundamental quantum effects pose striking learning hurdles to the engineering students. In contrast, most of the students are able to cope with the experimental and technical foundations of quantum optics experiments with heralded photons and their underlying principles, such as the coincidence technique used for the preparation of single-photon states. These findings are in accordance with prior research, and hence, the Quantum Optics Concept Inventory may serve as a fruitful starting point for future empirical research with regard to the education of the future quantum workforce.

... As will be discussed in Sec. III B, each approach demonstrates gains in students' understanding, but they each use a different instrument to measure these gains [18][19][20]41,43,[48][49][50][51]. It is reasonable to expect that context and teaching methods matter when learning physics. ...

... In a mixed-methods field study [50], N ¼ 173 high school students' learning of QP was evaluated using the single-photon approach as described in Ref. [70]. Through the collection of both qualitative and quantitative data, the authors found that the study participants achieved an adequate conceptual understanding of quantum optics and built up a mostly adequate understanding of the essential features of QP while at the same time finding that students struggled to detach from classical particle conceptions of the photon [48]. ...

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

... Lastly, in this article, we understand adequate conceptual understanding to be achieved by students who scored at least 50% of the total post-test score as has been achieved in prior research (cf. [34]). In this regard, it is important to note that for the clarification of the first part of RQ1 the pretest score is not relevant. ...

... The total normalized gain at 0.40 ± 0.21 is satisfactory and comparable to similar research projects (cf. 0.35 ± 0.21 in [34] (p. 156) or 0.37 ± 0.18 in [33] (p. ...

In an earlier contribution to Education Sciences we presented a new concept inventory to assess students’ conceptual understanding of introductory group theory—the CI2GT. This concept inventory is now leveraged in a pretest-post-test design with N=143 pre-service teachers to enrich this body of work with quantitative results. On the one hand, our findings indicate three recurring learning difficulties which will be discussed in detail. On the other hand, we provide a summative evaluation of the Hildesheim Teaching Concept and discuss students’ learning gain in different sub-domains of group theory. Together, the results allow for an empirical perspective on educational aspects of group theory and thus bridge the gap between qualitative and quantitative research in this field which constitutes a desideratum to date.

... If the mean value of a acceptance level for one key idea was above the cut-off value of 0.5, it was seen as acceptable (cf. [53] (p. 72)). ...

... If the mean value of a paraphrasing level for one key idea was above the cut-off value of 0.5, it was seen as acceptable (cf. [53] (pp. 75-76)). ...

In an earlier contribution to Mathematics, we presented a new teaching concept for abstract algebra in secondary school mathematics, and we discussed findings from mathematics education research indicating that our concept could be used as a promising resource to foster students’ algebraic thinking. In accordance with the Design-Based Research framework, the developed teaching concept is now being revised in several iteration steps and optimised towards student learning. This article reports on the results of the formative assessment of our new teaching concept in the laboratory setting with N=9
individual learners leveraging a research method from science education: The acceptance survey. The results of our study indicate that the instructional elements within our new teaching concept were well accepted by the students, but potential learning difficulties were also revealed. On the one hand, we discuss how the insights gained in learners’ cognitive processes when learning about abstract algebra with our new teaching concept can help to refine our teaching–learning sequence in the sense of Design-Based Research. On the other hand, our results may serve as a fruitful starting point for more in-depth theoretical characterization of secondary school students’ learning progression in abstract algebra.

... Quantum interference may serve as an example: Students who think of photons or electrons as small balls with a defined position moving along a well-defined path tend to believe, when conducting the double-slit experiment or an interferometer experiment with single quanta, no interference pattern will appear [23,39]. Another common students' idea is that of single quanta being reflected at the space between the two slits [40], or being deflected at a slit edge and moving away on a straight path [41]. ...

... In this work, there is a particular case in this respect: Quantum optics-based approaches to quantum physics differ so fundamentally from traditional courses at schools that a comparison with other approaches is not meaningfully possible via learning gains alone. Similar arguments have also been presented in previous contributions [40,66]. Hence, in our study, we do not compare the effect of the two concepts on learning gains, but on learners' conceptions as developed by students introduced to quantum physics with the respective proposal (traditional vs. quantum optics). ...

We conducted a quasiexperimental study in order to investigate the effect of a teaching concept on quantum physics based on coincidence and correlation experiments with heralded photons on preuniversity students' conceptions of quantum physics (experimental group, N = 150). We compare the results with the traditional curriculum's effect (control group, N = 130) at German secondary schools using a questionnaire to assess students' conceptions of quantum physics adapted from the literature. The results show that students introduced to quantum physics using the quantum optics concept acquire conceptions of quantum physics that are significantly less influenced by classical mechanistic and deterministic conceptions than those of the control group. In more detail, correlation and principal component analysis results indicate that the conceptions acquired by experimental group students are more consistent than those of the control group students.

... In contrast to the analysis of conference papers, we can provide more details on the design products, because of the more detailed descriptions in theses. Seven authors present a concept for practice that is curricular in nature, such as a teaching-learning environment (Tobias, 2010), a learning environment (Küpper, 2021), a teaching-learning arrangement (Haagen-Schützenhöfer, 2016), a concept for instruction (Bitzenbauer, 2020;Burde, 2018), or a learning unit (Wiener, 2017). All of these authors provide teaching and learning materials as well as a content structure, except for Wiener (2017), who primarily suggests typographical illustrations and how to implement them. ...

Researchers often develop teaching-learning solutions to improve the quality of instruction. Some of these solutions are developed in the paradigm of design-based research (DBR). The output of DBR projects goes beyond design products for practice and includes contributions to local theories about teaching-learning in specific subject areas and contexts as well as knowledge about how to design and implement these processes. Design knowledge and contributions to local theories are intended to construct a cumulative, content-specific body of knowledge about teaching and learning that is transferable to related subject areas or contexts. To make this process work, dimensions of DBR need to be systematically reported. However, DBR projects are sometimes criticized for focusing more on practical output than on reports about research output and the form of cooperation with practitioners. To empirically investigate these presumed voids, we examined DBR projects conducted by the German-speaking physics education research community during the past 20 years.

... These key items are also part of the international core curriculum on quantum physics which was extracted by the analysis of curricula from 15 nations [2]. Empirical research on the students' learning processes can provide arguments for or against the use of a respective teaching proposal [11][12][13][14]. Establishing a proposal as a valid school curriculum requires the support of physicists on school boards, in professional associations, and in academic teaching. ...

No consensus has been reached so far concerning the key topics on quantum physics suitable for secondary school teaching, despite comprehensive research. We identified the variety of associations with quantum physics among professionals as a potential cause. From an explorative mind map study with N = 29 physics researchers, we derive six subject-specific focal points in the associations that researchers have with quantum physics.

Recent research has boosted the inclusion of introductory group theory into secondary and undergraduate mathematics education due to manifold potentials, e.g., with regards to the promotion of students’ abstract thinking. However, in addition to research on cognitive processes, learners’ affective characteristics have largely remained unexplored in the context of teaching and learning group theory to date. In this paper, we contribute to closing this gap: We report on an empirical study investigating n=143 students’ affective characteristics within a two-weeks course program–the Hildesheim teaching concept. In our study, this concept was used to introduce pre-service primary teachers into group theory. A multiple linear regression analysis reveals that neither mathematics-specific ability self-concept nor subject interest are significant predictors of the achieved conceptual understanding of group theory after the intervention indicating that group theory is not reserved for only the mathematically interested students or students with a high mathematics-specific self-concept.

Background: Quantum physics is both a highly topical and challenging topic of physics education. Learning quantum physics is inherently difficult because it is unimaginative, counterintuitive and fundamentally different from what learners know from their everyday life and classical physics. The results of recent studies underline that students are often not aware of the relevance of quantum physics and its technologies for their own lives, which makes studying quantum physics even more difficult. This is the starting point of this article: With the Erlanger teaching concept, we present an introductory teaching concept for quantum physics at secondary schools with the aim, among others, to raise students’ awareness of the importance of modern quantum technologies today and in the future.
Purpose: In order to evaluate which conceptions about the quantum world arise among students who are introduced to quantum physics with the Erlanger concept, we conducted an interview study.
Sample/Setting: A random sample of N = 25 students was interviewed after the intervention (15 male, 10 female) in order to answer the questions mentioned above. The interviews had a duration of 25 – 40 minutes. Prior to the intervention, none of the students had any classroom instruction in quantum physics.
Design and Methods: The students’ answers were transcribed and then evaluated on the basis of deductive and inductive categories using qualitative content analysis. The coding was done by independent coders (𝜅=0.84,95%−𝐶𝐼 [0.68;1.00]). Additionally, a cluster analysis was performed and a three-cluster solution was extracted. The three clusters could be interpreted in terms of content and thus facilitate the characterization of occurring types of students’ conceptions after the intervention.
Results: After the intervention with our concept, we found elaborated conceptions about the quantum world with the majority of respondents. 11 of the 25 students (cluster 1, labelled Primarily elaborate conception) are aware of the striking differences between quantum and classical physics, as all students in this cluster characterize the quantum world via effects or aspects that do not exist in classical physics. The importance of quantum physics for future technologies was named by the students combined in the cluster 2, labelled Quantum world as the world of technology. 10 of the students interviewed (cluster 3, labelled Quantum world as a classical world on a small scale) seem to stick to their pre-conceptions dominated by classical ways of thinking.
Conclusions: Our article provides implications for both classroom practice and future research. For classroom practice, the Erlanger teaching concept serves as a proposal to bridge the gap between quantum physics and the everyday life of the learners. In addition, the results of the interview study presented in this paper make a contribution to the empirical research on students’ conceptions about quantum physics. We not only find individual, independent conceptions of learners, but we also show that there are dependencies between them, allowing us to extract types of conceptions. The extraction of such types of student conceptions for various further concepts of quantum physics will be part of future research and could contribute to our understanding of learning processes in quantum physics.

Verständnisprozesse sind zentraler Teil des Lernens und der Bildung. Beim Erlernen von Quantenphysik sind diese Prozesse jedoch oft durch klassische Vorstellungen blockiert. Zur genaueren Erörterung dieser Problematik wird eine Studie vorgestellt, die klassische und quantenphysikalische mentale Modelle von Lernenden erhebt und zu dem allgemeinen Modellverständnis in Beziehung setzt.
Die Datenerhebung erfolgte per Onlinefragebogen und deckt eine breite Probandengruppe ab, zu der neben Lernenden verschiedener Schul- und Hochschulformen auch Lehrerinnen und Lehrer sowie viele andere Berufsgruppen gehören. Die empirischen Daten weisen darauf hin, dass die jeweilige Gestalt und Funktionalität der mentalen Modelle unabhängig voneinander in Bezug auf ihre Realitätstreue interpretiert werden. Aus dieser Beschreibung werden vier Verständnistypen mentaler Modelle abgeleitet und in die derzeitige
naturwissenschaftsdidaktische Erkenntnislage eingeordnet.
Keywords: mental model, conceptual development, understanding, physics education, chemistry education, biology education, educational science, neurology

Mit dem Erlanger Unterrichtskonzept zur Quantenoptik wird das Ziel verfolgt, eine moderne Sichtweise auf die Quantenphysik zu vermitteln. Lernende sollen anschlussfähiges Wissen bis hin zu den Wesenszügen der Quantenphysik aufbauen. Im Rahmen einer summativen Evaluation mit Schülerinnen und Schülern der gymnasialen Oberstufe wird das Konzept evaluiert. Ein mixed-methods-Ansatz wurde gewählt, um verschiedene Perspektiven auf die Lernprozesse nachzeichnen zu können. Erste Ergebnisse aus einem Fragebogen zum deklarativen Wissen in Quantenoptik im Prä-Post-Follow-Up-Testdesign sowie einem Vorstellungsfragebogen zur Quantenphysik werden vorgestellt. Es zeigt sich: Lernende gelangen zu einem angemessenen Begriffsverständnis zur Quantenoptik und bauen ein überwiegend adäquates Verständnis der Wesenszüge auf, aber eine Teilchenvorstellung von Photonen scheint stabil zu sein.

In this article, an approach to integrate contemporary quantum physics into secondary school teaching is presented. The Erlanger concept on quantum optics provides an experimental-based guideway to aspects of modern quantum physics. We avoid the traditional historical approach in order to overcome the lack of modern concepts of quantum physics. In an acceptance survey, initial empirical evidence for the acceptance of the developed explanatory approaches was evaluated.

This paper presents an educational concept for promoting quantum teaching and learning via an educational structured quantum optical experiment. The experiment is designed to demonstrate the striking differences between classical physics and quantum physics, for example quantum interference of unbreakable photons (the ability of probabilities to interfere due to a phase sensitive superposition of states) and quantum nonlocality (there is no way to locate photonic states without a fundamental loss of information about the characteristics and a complete change of the state). For this proposal, we developed an experimental setup straightforward enough to be used in advanced physics courses even in secondary school student labs. To explain, or in a more quantum-semantic way, to interpret the experimental results quantitatively, we provide an appropriately rigorous quantum optical theory. Our model combines Laplace statistics (to access the statistical behaviour of photon counting) and basic vector calculus to calculate probabilities from the phase sensitivity of probability amplitudes. This article aims to contribute to further discussion and empirical research into novel teaching strategies for a more deeply conceptual approach to quantum theory.