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Physics Education

Prior knowledge of potential energy and the understanding of quantum mechanics

Kim Krijtenburg-Lewerissa, Hendrik Jan Pol, Alexander Brinkman, Wouter van Joolingen

Published Dec 29, 2021• 8 citations
Publisher

Abstract

Abstract Quantum mechanics (QM) has become part of many secondary school curricula. These curricula often do not include the mathematical tools for a formal, mathematical introduction of QM. QM therefore needs to be taught at a more conceptual level, but making secondary school students understand counterintuitive QM concepts without introducing mathematical formalism is a challenge. In order to accept QM, students not only have to see the need of it, but also have to see that QM is understandable and logical. Dutch secondary school students are familiar with potential energy (PE) in the context of gravitational and elastic energy. Therefore, the introduction of QM by using the potential wells and tunneling with emphasis on students’ prior knowledge of PE could be a way to make QM more understandable and logical. To explore this, we investigated the relation between the understanding of energy diagrams and the understanding of the potential well and tunneling. A module was created to promote students’ understanding of PE in classical context. Then, a quasi-experimental intervention was used, in which the experimental group received additional lessons using the module on classical energy diagrams before being taught QM. Two tests were developed in order to determine students’ understanding of PE and QM. The results of the tests showed that the experimental group not only had better understanding of PE diagrams, but also of QM even before they were being taught QM. Analysis of the tests also showed that there was a significant correlation between the understanding of PE diagrams and the understanding of QM. Therefore, the results of this study indicate that emphasis on PE can be used to reduce the gap between students’ prior knowledge and QM.

DOI
10.1088/1361-6552/ac3d3a

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Abstract Quantum mechanics (QM) has become part of many secondary school curricula. These curricula often do not include the mathematical tools for a formal, mathematical introduction of QM. QM therefore needs to be taught at a more conceptual level, but making secondary school students understand counterintuitive QM concepts without introducing mathematical formalism is a challenge. In order to accept QM, students not only have to see the need of it, but also have to see that QM is understandable and logical. Dutch secondary school students are familiar with potential energy (PE) in the context of gravitational and elastic energy. Therefore, the introduction of QM by using the potential wells and tunneling with emphasis on students’ prior knowledge of PE could be a way to make QM more understandable and logical. To explore this, we investigated the relation between the understanding of energy diagrams and the understanding of the potential well and tunneling. A module was created to promote students’ understanding of PE in classical context. Then, a quasi-experimental intervention was used, in which the experimental group received additional lessons using the module on classical energy diagrams before being taught QM. Two tests were developed in order to determine students’ understanding of PE and QM. The results of the tests showed that the experimental group not only had better understanding of PE diagrams, but also of QM even before they were being taught QM. Analysis of the tests also showed that there was a significant correlation between the understanding of PE diagrams and the understanding of QM. Therefore, the results of this study indicate that emphasis on PE can be used to reduce the gap between students’ prior knowledge and QM.
Quantum mechanics (QM) has taken on a paradigmatic role in how physics describes and builds new knowledge about the world. It also has a growing role in our society thanks to recent and rapid developments in the field of new quantum technologies. These are becoming increasingly important in our society, in the world of work and which will also decisively influence future socio-economic choices. Also for this reason QM has an increasing role in the education of young people and has been introduced in many different ways also in secondary school in all continents. The change in the theoretical and cultural frame has profound implications that are often not intuitive, which involve the appropriation of a specific way of thinking. Neither macroscopic phenomenology, nor intuition help, because there is no simple evidence of how quantum objects must be thought to interpret that unobservable microscopic world and for which we must enter another interpretative paradigm even if we want to limit ourselves to describe it. PER has carried out several studies on the learning of key concepts, on the learning nodes, the ways of reasoning, the difficulties of the students, their spontaneous ideas, according to two main strands: above all at university level, conceptual difficulties and misunderstandings often linked to a formal approach, which, moreover, underpins the very nature of the entities involved; at secondary school level in relation to how students acquire a quantum view of phenomena on the basis of specific approaches adopted to address QM. In particular, a vast literature, which has increased considerably and especially in relatively recent times, has studied how university students deal with certain concepts such as that of state, superposition, measurement in quantum mechanics rather than how quantum quantities evolve over time. These studies are based on the use of questionnaires that allow to explore different levels: the verbal, formal and representative one, with different representations (eg. wave function, Dirac notation), rather than different representative modes (eg. Graphs of probability amplitudes, or probability distributions). At the secondary school level, the most important studies on student learning were instead conducted evaluating the educational impact and outlining the learning paths of students who had followed formative activities based on differentiated innovative research-based educational paths. In particular, the learning outcomes were compared to those activated by proposals based on the historical reconstruction approach of quantum physics. This approach is privileged in traditional curricula and school texts and consequently in the ways of teachers approaching the topic. It was developed in schools with a narrative or descriptive dimension of solutions based on old physics of quanta for the interpretation of phenomena not explained by classical physics. The innovative approaches instead make use of contexts whose formal treatment is simple (quantum properties described in a two-state space such as polarization or spin) with the aid of simulations that compensate for the problem of students” limited mathematical-formal skills, avoiding any historical reference. In particular, there is a significant difference between the survey tools and the survey contexts in the high school environment compared to surveys conducted with university students. This paper presents a review of the research literature, focusing in particular on the learning processes of secondary school students and outlining how research perspectives have evolved.
We present a study of student understanding of energy in quantum mechanical tunneling and barrier penetration. This paper will focus on student responses to two questions that were part of a test given in class to two modern physics classes and in individual interviews with 17 students. The test, which we refer to as the Quantum Mechanics Conceptual Survey (QMCS), is being developed to measure student understanding of basic concepts in quantum mechanics. In this paper we explore and clarify the previously reported misconception that reflection from a barrier is due to particles having a range of energies rather than wave properties. We also confirm previous studies reporting the student misconception that energy is lost in tunneling, and report a misconception not previously reported, that potential energy diagrams shown in tunneling problems do not represent the potential energy of the particle itself. The present work is part of a much larger study of student understanding of quantum mechanics.
We present a study of student understanding of energy in quantum mechanical tunneling and barrier penetration. This paper will focus on student responses to two questions that were part of a test given in class to two modern physics classes and in individual interviews with 17 students. The test, which we refer to as the Quantum Mechanics Conceptual Survey (QMCS), is being developed to measure student understanding of basic concepts in quantum mechanics. In this paper we explore and clarify the previously reported misconception that reflection from a barrier is due to particles having a range of energies rather than wave properties. We also confirm previous studies reporting the student misconception that energy is lost in tunneling, and report a misconception not previously reported, that potential energy diagrams shown in tunneling problems do not represent the potential energy of the particle itself. The present work is part of a much larger study of student understanding of quantum mechanics.
We describe the development of a course of quantum mechanics for secondary school designed to address the challenges related to the revision of classical knowledge, to the building of a well-organized knowledge structure on the discipline, and to the development of a plausible picture of the quantum world. The course is based on a systemic approach to conceptual change, which relies on its analysis in the transition from classical to quantum mechanics, and coordinates cognitive and epistemological aspects. We show how our approach drives the derivation of design principles, how these principles guide the development of the instructional sequence and of its strategies, how their implementation requires the blending of different research perspectives and learning systems. The first challenge is addressed through a path of revision of classical concepts and constructs which leverages prior knowledge according to the dynamics of each notion in theory change. The second by adopting a framework that promotes the construction of a unifying picture of quantum measurement across contexts. The third by designing the course around a modelling process that engages students in epistemic practices of the theoretical physicist, such as generating and/or running thought experiments, and mathematical modelling in a purely theoretical setting. All is aimed to help students accept the quantum description of the world as a plausible product of their own inquiry. This process is assisted by the discussion of the facets of the foundational debate that are triggered by each of the suggested interpretive choices, with the goal to promote an awareness of its cultural significance, of the limits the chosen stance, of the open issues. Data on the cycles of refinement illustrate how a set of activities have been made effective in addressing the challenges at a local level.
We present a study of student understanding of energy in quantum mechanical tunneling and barrier penetration.This paper will focus on student responses to two questions that were part of a test given in class to two modern physics classes and in individual interviews with 17 students.The test, which we refer to as the Quantum Mechanics Conceptual Survey (QMCS), is being developed to measure student understanding of basic concepts in quantum mechanics.In this paper we explore and clarify the previously reported misconception that reflection from a barrier is due to particles having a range of energies rather than wave properties.We also confirm previous studies reporting the student misconception that energy is lost in tunneling, and report a misconception not previously reported, that potential energy diagrams shown in tunneling problems do not represent the potential energy of the particle itself.The present work is part of a much larger study of student understanding of quantum mechanics.