In an earlier contribution to Education Sciences we presented a new concept inventory to assess students’ conceptual understanding of introductory group theory—the CI${}^2$GT. 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.

Prior research has shown how incorporating group theory into upper secondary school or undergraduate mathematics education may positively impact learners’ conceptual understanding of mathematics in general and algebraic concepts in particular. Despite a recently increasing number of empirical research into student learning of introductory group theory, the development of a concept inventory that allows for the valid assessment of a respective conceptual understanding constitutes a desideratum to date. In this article, we contribute to closing this gap: We present the development and evaluation of the Concept Inventory of Introductory Group Theory—the CI²GT. Its development is based on a modern mathematics education research perspective regarding students‘ conceptual mathematics understanding. For the evaluation of the CI²GT, we follow a contemporary conception of validity: We report on results from two consecutive studies to empirically justify that our concept inventory allows for a valid test score interpretation. On the one hand, we present $N=9$ experts‘ opinions on various aspects of our concept inventory. On the other hand, we administered the CI²GT to $N=143$ pre-service primary school teachers as a post-test after a two weeks course into introductory group theory. The data allow for a psychometric characterization of the instrument, both from classical and probabilistic test theory perspectives. It is shown that the CI²GT has good to excellent psychometric properties, and the data show a good fit to the Rasch model. This establishes a valuable new concept inventory for assessing students’ conceptual understanding of introductory group theory and, thus, may serve as a fruitful starting point for future research into student learning of abstract algebra.

Physics education research on explanatory videos has experienced a boost in recent years. Due to the vast number of explanatory videos available online, e.g. on YouTube, finding videos of high explaining quality is a challenging task for learners, teachers, and lecturers alike. Prior research on the explaining quality of explanatory videos on classical mechanics topics has uncovered that the surface features provided by YouTube (e.g. number of views or likes) do not seem to be suitable indicators of the videos’ explaining quality. Instead, the number of content-related comments was found to be statistically significantly correlated with the explaining quality. To date, these findings have only been observed in the context of explanatory videos on classical mechanics topics. The question arises whether similar correlations between the explaining quality and YouTube surface features can be found for videos on topics that are difficult to access visually and verbally, for example from quantum physics. Therefore, we conducted an exploratory study analyzing the explaining quality of N = 60 YouTube videos on quantum entanglement and tunnelling. To this end, we made use of a category-based measure of explanatory videos’ explaining quality from the literature. We report correlations between the videos’ explaining quality and the surface features provided by YouTube. On the one hand, our results substantiate earlier findings for mechanics topics. On other hand, partial correlations shed new light on the relationship between YouTube’s surface features and explaining quality of explanatory videos.

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 ($\alpha =0.74$), 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.

[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

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.