1,721,003 research outputs found
Experiments and models about the force between permanent magnets: Asymptotic analysis of a difficult problem
No full textWe propose a simple experiment, which allows students to explore quantitatively the magnetic interaction between neodymium cylindrical magnets. The experiment employs a precision digital balance, two screws with known thread pitch and two transparent tubes to measure the repulsive force between two magnets as a function of their distance. Different measurements are performed, focusing on the behavior of the interaction force at short and long distances and the role of the magnets' aspect ratio. We discuss the comparison between theoretical expectations resulting from conceptually simple approximate models and experimental results. The experiments employ inexpensive materials and address a relevant topic in the physics curriculum. Thus, they are appropriate for the undergraduate physics laboratory, for advanced high school students, and in the context of teacher education and in-service training to enhance students' knowledge of magnetism
Modeling and Representing Conceptual Change in the Learning of Successive Theories: The Case of the Classical-Quantum Transition
No full textMost educational literature on conceptual change concerns the process by which introductory students acquire scientific knowledge. However, with modern developments in science and technology, the social significance of learning successive theories is steadily increasing, thus opening new areas of interest to discipline-based education research, e.g., quantum logic, quantum information, and communication. Here, we present an initial proposal for modeling the transition from the understanding of a theory to the understanding of its successor and explore its generative potential by applying it to a concrete case—the classical-quantum transition in physics. In pursue of such task, we make coordinated use of contributions from research not only on conceptual change in education, but also on the history and philosophy of science, on the teaching and learning of quantum mechanics, and on mathematics education. By means of analytical instruments developed for characterizing conceptual trajectories at different representational levels, we review empirical literature in the search for the connections between theory change and cognitive demands. The analysis shows a rich landscape of changes and new challenges that are absent in the traditionally considered cases of conceptual change. In order to fully disclose the educational potential of the analysis, we visualize categorical changes by means of dynamic frames, identifying recognizable patterns that answer to students’ need of comparability between the older and the new paradigm. Finally, we show how the frame representation can be used to suggest pattern-dependent strategies to promote the understanding of the new content, and may work as a guide to curricular design
Teaching the heat transfer law using a stochastic toy model
No full textIn this paper we present a simple stochastic toy model playable with dice, coins and tokens, meant to represent the system composed of a conducting bar between two heat reservoirs. The toy model is meant to be used in the context of a computational approach to teaching thermal physics to undergraduates, and allows one to highlight step by step the mechanism by which deterministic differential equations for macroscopic quantities can arise from underlying microscopic processes which are inherently random. Since this mechanism crucially requires the passage to the thermodynamic limit, in order to test it on their own students are required to code and perform numerical simulations of the toy model system with an increasingly large number of elements. From the point of view of training students with programming skills, the toy model offers a suitable ground for an early activity, since the simulation of a game they can actually perform is expected to produce less cognitive load than the simulation of more abstract problems and equations, allowing students to concentrate on learning the basics of programming
Bubble: Experimenting with Feynman’s sum over paths approach in the secondary school
No full textWe discuss a teaching experiment on the introduction of elements of quantum physics already at the level of the fourth year of high school (17–18 years old students) using Feynman’s sum over paths approach. More precisely, the educational sequence is constructed on the juxtaposition of the wave and quantum theories of light, and it constitutes an attempt to anticipate the current status of the past, secular debate on the nature of light to young students, while providing them with a unifying perspective on different approaches, models and theories which are encountered in high school. The experimentation is part of the research on quantum physics education in secondary school conducted by the Physics Education group in Pavia, and it was developed by the author as a thesis work in the context of the IDIFO-6 Master coordinated by the University of Udine. The focus of the work is on the gradual introduction of innovative elements in the traditional high school didactics. Analysis of the experimentation data shows very rich and complex patterns, allowing to identify activities which may be more productive for students and to uncover weak points and student’s difficulties
GeoGebra simulations for Feynman’s sum over paths approach
Full text linkWe present a collection of interactive simulations meant to complement the educational approach to quantum physics in high school developed since 2013 by the physics education research group at the University of Pavia. The collection, organized as a “book” within the online repository GeoGebra Tube is intended primarily for being used by physics teachers wishing to deepen their understanding of Feynman’s sum over paths approach. The simulations represent several problems of physical interest, and aim at clarifying different aspects of Feynman’s model. The collection has been used as an educational tool in the context of the IDIFO-6 Master
coordinated by the University of Udine, and encouraging indications have been collected. In particular, the use of an open-source software which is very widely known and used in the community of teachers may encourage them to produce their own example simulations, or make easier for them to modify the existing ones according to their preferences and needs
Investigating the beliefs of experts on teaching quantum physics at secondary schools: key concepts, topics, and fundamentals
No full textQuantum technologies: a course for teacher professional development
No full textWe present an educational path for teacher professional development whose primary purpose is to enhance physics teachers' knowledge and awareness of topics related to quantum computation and quantum information, and of their relevance for technological advancement. Besides their objective importance, also stressed by several authors and projects, the choice of topics not traditionally covered in the final year physics curricula also arises from the concrete possibility of developing a multidisciplinary path, able to represent under a unified perspective several subjects treated in secondary school physics and mathematics. The project is realized in the context of the Italian PLS (Plan for Science Degrees) and the education section of the Quantum Flagship. Due to the limitations related to the COVID-19 pandemic it was entirely delivered in the form of synchronous distance learning and was attended by around 30 teachers. Asynchronous discussion was performed using both generally available tools (Google drive, forms etc.) and a dedicated online forum set up on the servers of the University of Pavia. We discuss the structure of the educational path and the results of the first part of the course whose purpose was describing the transition from classical to quantum computation. In general, from both the written pre-questionnaire and the mid-course interviews, strong appreciation and fascination emerge for the cultural significance of the introduced topics and connections
Three years evaluation of a teaching learning sequence on rolling motion based on a blended learning environment
No full textApproximate time–energy uncertainty relationship from the fixed-energy sum over paths approach
No full textIn this article, we show how an approximate time–energy uncertainty relationship of the form ΔEΔt ≃ ћ can be derived in the context of the fixed-energy sum over paths approach to quantum bound systems. The relationship connects the indeterminacy Δt on the travel time of the quantum object to the width ΔE of the resonance in the approximate Green function corresponding to an allowed value of energy. The mathematical origin of the relationship is to be tracked to the Fourier transform relationship between the time propagator and energy-dependent Green function; however, the core of the derivation does not use advanced mathematics, may be carried out using mostly graphical and geometrical methods, and may provide insight to students on the meaning and origin of the time–energy uncertainty relationship. Our work may contribute to close a gap by which the time–energy relationship is most often taught with insufficient explanation at elementary level
Recent Progress on the Sum over Paths Approach in Quantum Mechanics Education
No full textIn this paper, we present an overview of recent developments in the Feynman sum over paths approach for teaching introductory quantum mechanics to high school students and university undergraduates. A turning point in recent research is identified in the clarification of the distinction between the time-dependent and time-independent approaches, and it is shown how the adoption of the latter has allowed new educational reconstructions to proceed much farther beyond what had previously been achieved. It is argued that sum over paths has now reached full maturity as an educational reconstruction of quantum physics and offers several advantages with respect to other approaches in terms of leading students to develop consistent mental models of quantum phenomena, achieving better conceptual understanding and a higher degree of longitudinal integration of knowledge
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