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.

[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 article provides a review of empirical research into nanoscience and -technology (NST) education at the secondary school level with regards to (a) teaching strategies or laboratory experiments implemented and evaluated for their impact on student learning about nanotechnology aspects, (b) concept inventories and methods used to assess students’ conceptual understanding, as well as (c) students’ conceptions and learning difficulties. A database search was used to identify corresponding studies published over the last decade (2012-2021) of which eleven were included in the synthesis for further analyses after screening for eligibility. The analysis revealed that learning difficulties regarding NST topics such as the differentiation between size and scale, the surface area to volume ratio or size dependent properties are widely prevalent among learners according to the current state of the literature. While our analysis identified emerging perspectives for future research with regards to the development of psychometrically characterized concept inventories in particular and empirical investigations into students’ learning progressions on nanoscience concepts in more general, a huge effort has already been put into the development of teaching concepts or laboratory experiments suitable for secondary school classrooms.

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 study examines pre-service teachers’ perceptions and knowledge regarding the visual-genetic interpretation of inverse trigonometric functions (ITF). The visual-genetic approach provides opportunities for exploring the origin, modification, and graphical and geometrical interpretations of mathematical concepts. Using a convenience sampling technique, a sample of 65 third- and fourth-year prospective mathematics teachers (23 males and 42 females) was selected from the faculty of education in Fergana, Uzbekistan. To collect data on prospective teachers’ perceptions and conceptual knowledge related to the visual-genetic interpretation of ITF, a perception questionnaire and an achievement test were employed. The collected data were coded and analyzed using descriptive statistics. The results indicated that prospective teachers perceive the ITF as boring, abstract, and difficult to learn, and that they possess limited conceptual knowledge of the fundamental concepts. As a result, over 50% of the participants were unable to build and recreate the proper mental structures required for gaining a meaningful understanding that would allow them to answer crucial basic inverse trigonometry challenges. To provide high-quality mathematics education for pre-service teachers who would shape our future in the age of artificial Intelligence, teacher educators needed to reconsider their instructional techniques and ensure that perception was well grounded and that understanding and conceptualization were firmly and securely established.

This article analyzes the methodological potential of a multiple-representation approach based on visual and illustrative modeling in teaching the fundamental concepts of trigonometry. During the learning process, students frequently experience difficulties in understanding the intrinsic relationships among the unit circle, right triangles, and the graphs of trigonometric functions. To address these challenges, the study proposes an alternative model for constructing the trigonometric circle. The proposed model aims to reveal the logical origins of trigonometric concepts, support their spatial and intuitive perception, and establish a holistic connection among the unit circle, graphical representations, and geometric models. The article examines the solution of trigonometric inequalities as an instructional example by employing various visual and analytical methods and provides a rationale for their didactic effectiveness. The impact of this approach on the efficiency of learning trigonometry was evaluated with 94 final-year high school students from two selected public schools in Uzbekistan (45 in the control group and 49 in the experimental group). A mixed-methods research design was adopted, integrating quantitative data obtained from student assessments with qualitative data collected through interviews. The findings indicate that students’ abilities to analyze problems, justify solutions, and make generalizations were significantly improved.