Abstract Wave-particle duality is included in many secondary school and university physics curricula as a concept central to quantum physics. The very term wave-particle duality suggests that a firm grasp of the individual classical concepts of wave and particle is crucial to studying quantum mechanics successfully. This raises the question whether students’ mental models of these concepts are sufficiently addressed and developed prior to the teaching of wave-particle duality. We explored Dutch upper secondary school students’ mental models of waves and particles using a short questionnaire. It was administered to a total of 147 students from two different groups. One group consisted of secondary school students prior to receiving formal education in introductory quantum mechanics while students from the other group had recently completed the Dutch national curriculum for pre-university education, which includes wave-particle duality. Our findings support the notion that students model classical particles and waves as mutually exclusive phenomena. Mental models of wave-particle duality, which require mixing the two classical models, appear to be only superficially developed. Our findings open avenues for future research on students’ mental models of waves and particles as basis for wave-particle duality.
Abstract Wave-particle duality is included in many secondary school and university physics curricula as a concept central to quantum physics. The very term wave-particle duality suggests that a firm grasp of the individual classical concepts of wave and particle is crucial to studying quantum mechanics successfully. This raises the question whether students’ mental models of these concepts are sufficiently addressed and developed prior to the teaching of wave-particle duality. We explored Dutch upper secondary school students’ mental models of waves and particles using a short questionnaire. It was administered to a total of 147 students from two different groups. One group consisted of secondary school students prior to receiving formal education in introductory quantum mechanics while students from the other group had recently completed the Dutch national curriculum for pre-university education, which includes wave-particle duality. Our findings support the notion that students model classical particles and waves as mutually exclusive phenomena. Mental models of wave-particle duality, which require mixing the two classical models, appear to be only superficially developed. Our findings open avenues for future research on students’ mental models of waves and particles as basis for wave-particle duality.
Fundamental notions of quantum physics are included in introductory university curricula, in physics teacher training, and even in secondary education, both in Argentina and in various other countries worldwide. Among these fundamental concepts is wave-particle duality (WPD), a key concept and a gateway to the quantum world. This paper presents a critical review of the literature on WPD in specialized journals on physics education and science education at the local, regional, and international context, aiming to gather the most relevant findings regarding its teaching and learning. Preliminary results indicate that these findings can be categorized based on their primary purpose into four categories: Teaching WPD, Learning WPD, Historical and Epistemological Reflections on WPD and Reviews on the Teaching and Learning of Quantum Physics (including WPD).
A lesson series on quantum physics was taught to grade 12 students in 5 different secondary schools. Among others, the series contained a special demonstration experiment for particle-wave duality (double-slit single-photon interference) which was supplemented by the PhET applet quantum wave interference. Preconceptions on particles and waves were assessed in a pretest. Interviews were conducted with 24 students in 4 schools after the demonstration. A posttest was administered to 112 students in 3 schools. Some lessons were observed by an outside observer and/or videotaped, followed by interviews. Results indicate that learning objectives of quantum physics are well within reach of the 12th grade students. This shows especially in student discussions of the PhET applet. However, understanding of wave-particle duality is hindered by insufficient understanding of the prerequisite wave concept that waves are spread out in space. Most students associated a wave with an oscillation and somehow forgot about the spatial aspects. As a consequence, the “strangeness” of wave-particle duality was underappreciated. Also, the link with the de Broglie wavelength discussed early in the lesson series was not made. As in the 5th school quantum physics started several weeks later, we were able to try an improved lesson design for the demonstration successfully. Interviews are very helpful in catching misinterpretations of demonstrations and generating suggestions for improvement. Students do appreciate the confusing wonders of quantum physics but in the post-interviews seem unaware of the many quantum-based devices around them and the many everyday phenomena (like color) which need quantum physics for explanation. Perhaps as teachers and curriculum developers, we are too eager to overemphasize the exotic and strange aspects of quantum theory and underemphasize utility in everyday applications.
In this study, we investigated students’ mental models of wave–particle duality. We interviewed six engineering and premedical students enrolled in a calculus-based physics course. We conducted a qualitative examination of student interviews and found that students displayed four different mental models: quantum model (QM), semi-quantum model (SQM), wave model (WM), and in-between model (IM). We also found that 2/3 of the students had difficulty discriminating between classical and quantum ideas and held mental models that were inconsistent and context-specific. This work provides a much-needed detailed exploration of students’ conceptions of quantum theory, which will help instructors understand conceptual barriers frequently encountered by introductory students.
In this paper we present the results of a research-based teaching-learning sequence on introductory quantum physics based on Feynman's sum over paths approach in the Italian high school.Our study focuses on students' understanding of two founding ideas of quantum physics, wave particle duality and the uncertainty principle.In view of recent research reporting the fragmentation of students' mental models of quantum concepts after initial instruction, we collected and analyzed data using the assessment tools provided by knowledge integration theory.Our results on the group of n ¼ 14 students who performed the final test indicate that the functional explanation of wave particle duality provided by the sum over paths approach may be effective in leading students to build consistent mental models of quantum objects, and in providing them with a unified perspective on both the photon and the electron.Results on the uncertainty principle are less clear cut, as the improvements over traditional instruction appear less significant.Given the low number of students in the sample, this work should be interpreted as a case study, and we do not attempt to draw definitive conclusions.However, our study suggests that (i) the sum over paths approach may deserve more attention from researchers and educators as a possible route to introduce basic concepts of quantum physics in high school, and (ii) more research should be focused not only on the correctness of students' mental models on individual concepts, but also on the ability of students to connect different ideas and experiments related to quantum theory in an organized whole.
Abstract Teaching and learning of quantum physics at secondary level is an active field of research. One important challenge is finding ways to promote understanding of quantum concepts without the mathematical formalism that is embedded in quantum mechanics but unavailable on the secondary level. We investigated Norwegian secondary students’ (N = 291) descriptions of the wave nature of quantum particles and the uncertainty principle, as expressed during work with learning resources using a sociocultural approach emphasizing history, philosophy, and nature of science aspects. Responses from university students (N = 40) given after a formalism-based course in quantum physics were included for comparison. Themes were identified using thematic analysis and analyzed from the perspective of pedagogical link-making, seeing different themes as representing different levels of explanations of the concepts (phenomenological, qualitative, mathematical). The most dominant theme in descriptions of particle wave nature was that particles exhibit wave behavior in experiments, while referring to the mathematical description of particles by wave functions was a less prominent theme, even among university students. Two uncertainty principle themes were found: uncertainty as inability to measure pairs of variables precisely, and uncertainty as innate blurriness in nature. Largely missing from descriptions of both concepts were meaningful links between different levels of explanations. Based on the results, we discuss ways forward for teaching particle wave nature and uncertainty in secondary education.
In this paper we present a proposal for teaching basic aspects of quantum mechanics in high school. Our proposal is based on a wave approach that makes use of the analogies between wave phenomena at macroscopic scales and phenomena at atomic or subatomic scales. Although the classical and the quantum model are completely different, there is a common underlying wave mathematical layer. This allows to address, via analogies, quantum aspects that are not accessible to direct experience. The quantization of energy levels, the quantum interference and the uncertainty relations are examples of quantum aspects having an analog concept in classical physics wave phenomena. In our approach we break the wave-particle “duality”, which is totally counterintuitive. Instead we enhance the underlying wave mathematical structure as a path to reach and explain emerging features of particles and quantum systems in general.