Avraham Merzel

Editorial: The physics-mathematics nexus: Connecting formalism, meaning, and classroom practice.

This paper presents a set of accessible, quantitative calorimetric experiments designed to support the teaching of energy change as a crosscutting concept across scientific domains. Building on an operational definition of energy change based on temperature variation of a standard body, the proposed approach treats calorimetry as an empirical unifying framework for studying diverse processes, including mechanical, electrical, radiative, and chemical processes. In contrast to traditional instruction that often rests on a predefined abstract concept (work), these experiments engage learners in constructing quantitative relationships empirically by identifying proportional dependencies between temperature change and relevant variables that characterize different processes. The experiments are intentionally simple to implement in classroom settings and adaptable across educational levels. Through this approach, students can develop a coherent understanding of energy change as a measurable quantity associated with a range of processes, rather than categorizing distinct forms of energy. We illustrate how this framework supports interdisciplinary connections, promotes inquiry-based learning, and provides a foundation for linking macroscopic observations with later microscopic explanations. Implications for teaching, including the role of experimental design, variable control, and the transition from temperature change to energy change, are discussed.

The interplay of mathematics within physics—termed here as —presents unique cognitive challenges for students, requiring coordination between mathematical reasoning and physical sensemaking. While previous studies have documented common physmatic difficulties, capturing these challenges as they emerge in classroom instruction is rare. This study analyzed 273 teacher–student interactions from 23 video-recorded physics lessons taught across a diverse range of classrooms, aiming to identify and categorize physmatic difficulties as they naturally arose during instruction. Twenty-four codes of difficulties were identified through content analysis and grouped into five overarching clusters: (i) , (ii) , (iii) , (iv) , and (v) . A key finding of this study was the identification of systematic associations between the modeling skills teachers aimed to develop (i.e., mathematization, manipulation, interpretation, and validation) and the corresponding student difficulties. These findings underscore the centrality of modeling as a pedagogical framework for physics instruction and suggest that teachers who are aware of the links between skills and difficulties may be better prepared to anticipate student struggles, respond to them in real time, and even leverage them as part of their instructional practice.

As quantum technologies increasingly impact society and the workforce, there is a growing need to integrate quantum physics (QP) education into all levels of the curriculum, including secondary education. However, despite increasing interest, there is little consensus on which topics should be covered and to what depth. This study addresses this issue by exploring experts’ perspectives on the future of QP education at the secondary school level. Using an adapted Delphi method, we conducted three rounds of surveys with a diverse panel of quantum physics and physics education experts. The study aimed to identify the most appropriate QP concepts for inclusion in secondary school curricula and the instructional level at which they should be taught. The findings show strong expert support for including foundational QP topics, such as quantum interference, superposition, and quantum measurement, taught at a conceptual rather than a mathematical level. More advanced topics related to quantum technologies were widely deemed unsuitable for the secondary school. These results are consistent with existing national curricula and provide valuable insights into current perspectives on QP education, reinforcing the importance of core quantum physics concepts in secondary education. These insights lay the groundwork for further research into the future direction of quantum education and support the integration of quantum technologies into secondary school curricula.

This study examines how the characteristics of a disciplinary professional learning community (DPLC) of middle school science and technology teachers function as resources for pedagogical design. Qualitative data were collected through in-depth interviews with teachers and community leaders, alongside passive observations of community meetings. The thematic analysis revealed the interconnectedness of five key DPLC dimensions—structural, content, social–affective, common-production, and meta-community—with two established categories of teacher resources: personal and curricular. Participants explicitly linked these resource types, leading to the development of a new model for understanding pedagogical design resources. This model offers guidance for DPLC leaders and teacher educators in intentionally leveraging DPLC dimensions to enhance teaching practice.

Students often face significant challenges related to the interplay between physics and mathematics, referred to as “physmatics.” This invited diagnosing the possible sources of students’ difficulties in this respect. The current study aims to identify and interpret students’ difficulties in three specific physmatic areas required for physics learning: arithmetic operations, overgeneralization of the mathematical zero-product property, and the region of applicability of a formula, distinguishing these from independent difficulties in mathematics or physics. The research is designed to investigate whether these difficulties originate from pure mathematics limited skills, from applying mathematical thinking to real-world problems, or from applying it specifically to problems in physics. A questionnaire was administered to 199 high school students to examine the influence of the context–purely mathematical, physics, and economic–on their responses. Findings indicate that limited mathematical skills do not explain students’ difficulties in solving real-world problems. We infer that the students harness three different content dependent mathematical thinking approaches when addressing the challenges posed to them: context-oriented thinking, mathematical thinking, and unripe-mathematical thinking. Each of these approaches is characterized by varying attentiveness to context. Understanding these thinking approaches can help educators develop instructional strategies that address students’ cognitive challenges, potentially improving physics education outcomes.

While teachers’ professional learning communities (PLCs) have been extensively studied, discipline-specific PLCs (DPLCs) have received less attention, particularly regarding the subject matter’s role and its connection to other community dimensions. To explore this, we conducted two independent studies on DPLCs. Study 1 examined physics teacher DPLCs, using participant observations and literature-based analysis. Study 2 investigated science and technology teacher DPLCs through interviews and passive observation, which was analyzed through content analysis. Both studies yielded remarkably similar findings, leading to a synthesized model encompassing five dimensions: the structural dimension, reflecting the community’s tangible and logical organization; the content dimension, emphasizing the discipline-specific focus of the DPLC; the common production dimension, showcasing joint enterprise activities and products of the DPLC; the social-affective dimension, addressing social, emotional, and value-based aspects that establish a sense of community; and the meta-community dimension, exploring the DPLC’s relationships with its broader environment. These dimensions operate bidirectionally: inward—the effect of the community on the individual, and outward—the effect of the individual teacher on the community. We discuss how interactions between these dimensions shape DPLCs and influence teacher development. Additionally, we highlight the significance of this unified model for DPLC leaders, researchers, and policymakers in teacher development.

[This paper is part of the Focused Collection in Investigating and Improving Quantum Education through Research.] Teaching quantum physics (QP) to high school (HS) students is gaining momentum, necessitating the exploration of various effective methods. Specifically, the research on quantitative teaching methods is still in its early stages. Understanding the power of Dirac notation (DN) in teaching is crucial for grasping the complexities of QP, as it provides a concise and powerful symbolic framework that facilitates both conceptual and computational understanding. This study investigates the proficiency of HS students in interpreting, producing, and manipulating DN within QP. Utilizing qualitative content analysis of student responses to various tasks, quizzes, and final tests, the study aims to uncover the sensemaking opportunities DN provides and the difficulties students encounter. The findings indicate that DN facilitates both conceptual understanding and quantitative problem solving in QP by enabling students to interpret and produce representations of quantum states. The results highlight the importance of extensive practice and well-structured teaching sequences in developing DN proficiency, reinforcing the role of DN as an effective tool for teaching QP at the HS level. The study contributes to the ongoing discourse on integrating mathematical modeling in physics education, emphasizing the potential of DN in enhancing students’ grasp of QP concepts and their application in problem solving. Published by the American Physical Society 2024