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Physical Review Physics Education Research

Test on the effectiveness of the sum over paths approach in favoring the construction of an integrated knowledge of quantum physics in high school

Massimiliano Malgieri, Pasquale Onorato, Anna De Ambrosis

Published Jan 3, 2017• 29 citations
Publisher

Abstract

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.

DOI
10.1103/physrevphyseducres.13.010101

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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.
In 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.
We present a research-based teaching sequence in introductory quantum physics using the Feynman sum over paths approach. Our reconstruction avoids the historical pathway, and starts by reconsidering optics from the standpoint of the quantum nature of light, analysing both traditional and modern experiments. The core of our educational path lies in the treatment of conceptual and epistemological themes, peculiar of quantum theory, based on evidence from quantum optics, such as the single photon Mach–Zehnder and Zhou–Wang–Mandel experiments. The sequence is supported by a collection of interactive simulations, realized in the open source GeoGebra environment, which we used to assist students in learning the basics of the method, and help them explore the proposed experimental situations as modeled in the sum over paths perspective. We tested our approach in the context of a post-graduate training course for pre-service physics teachers; according to the data we collected, student teachers displayed a greatly improved understanding of conceptual issues, and acquired significant abilities in using the sum over path method for problem solving.
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.
Teaching quantum mechanics at the secondary school level remains a major educational challenge. Traditional historical approaches often present the theory as a sequence of disconnected phenomena, requiring extensive prior knowledge of classical physics before students can appreciate the conceptual structure of quantum physics. In this work, we present the design, implementation, and evaluation of a curriculum based on the two state (qubit first) approach, in which the fundamental postulates of quantum mechanics are introduced through mathematically accessible two level systems and realized with light polarization. The curriculum integrates theoretical instruction, laboratory activities, a coherent progression grounded in the interactive simulations, and inquiry based learning into a coherent pathway that progresses from quantum states and superposition to entanglement and the experimental violation of Bell's inequalities. A distinctive feature of the project is the experimental realization of the violation of Bell's inequalities obtained in a newly established quantum optics laboratory in an Italian high school, where students performed, for the first time in Italy, an authentic Bell test using polarization-entangled photons. The same educational framework was adopted for in service teacher professional development courses. Learning outcomes were evaluated through mixed methods. Preliminary analysis indicates significant improvements in conceptual understanding, confidence in using mathematical formalism, and appreciation of the relationship between theory, experimentation, and the foundations of quantum mechanics. The proposed curriculum shows that two-state formalism and supported by real laboratory experiences enables secondary-school students to engage more meaningfully with both the conceptual foundations of quantum mechanics and their experimental verification.
Abstract Teaching and learning quantum mechanics is one of the most demanding educational and conceptual challenges, in particular in secondary schools where students do not possess an adequate mathematical background to effectively support the description of quantum behaviour. Educational research shows that traditional approaches, generally based on historical and narrative perspectives, are only partially effective. The reason is that they do not address in depth those basic quantum concepts that radically question the fundamentals of classical physics. A research-based educational program has been proposed to two final-year classes of an Italian scientific high school. In order to build the main concepts of quantum mechanics and their formal basic representation via real and simulated experiments, the program uses the light polarization as a context. A quantum game was then integrated in the educational program, to support students’ learning. Their conceptual paths, monitored by means of tutorials and questionnaires, show significant student learning especially on the concept of state and on appropriating the formalism meaning, whereas students more frequently referred to the geometrical vector representation instead of the algebraic-analytic formula. The quantum game has emerged to support intuition and operative experience in distinguishing the foundational concepts of superposition and entanglement.
We analyse part of the implementation of a didactic sequence to teach different aspects of light in a unified non traditional framework. The goal was to propose the quantum theory of light as a universal framework to describe different phenomena observed. The laws of quantum mechanics for light using Feynman´s “Sum of all Paths” approach adapted to the mathematical level of the students was proposed as a model to explain the experiences. This particular denomination of Feynman´s approach is an intentional choice to avoid the language of "integral" because the students haven't had calculus. Graphic representations and basic operations with vectors capturing the essential aspects of the theory, were used. Simulations made with the software GeoGebra(R) and Modellus were created to help students visualize the formulation. The sequence was carried out in four courses (aged 15-16). For the data analysis, an answer categorization was formulated, considering among other aspects the quantum reformulation of experiment shown herein. This analysis seeks to understand the student´s conceptualization process about quantum interpretation. The results support the conclusion that the conceptualization is complex, and slow, due to both the concepts involved and the representation systems demanded by the situations.