A resource environment for preservice teacher education to introduce quantum
physics in secondary school
Lorenzo Santi †, Marisa Michelini ‡, Alberto Stefanel ‡‡, Giampiero Meneghin ‡‡
†Physics Department, University of Trieste, ‡Physics Department and ‡‡Interdipartimental Science
Educational Center, University of Udine
1. Introduction
Quantum Mechanics (QM) is one of the most important of the cultural achievements of the century
and the knowledge of its basis is nowadays an unrenounceable element in the citizen culture. Its
conceptual implications have, in fact, determined a new paradigm in physics [1] and its applications
have great social importance: electronic devices or employing light laser, for example, are
nowadays common and appear more and more often in the everyday phenomenology. The
educational research groups devote an increasing attention to the introduction of quantum physics in
the secondary school and in many basic courses scientific degrees [2]. Presently, there is no
common approach to the introduction on QM, especially at the basic level; for example, the
different possible formulations [3] and interpretation [4] of quantum theory has been used as
starting point for different didactic proposals, sometimes each other antithetical.
The praiseworthy experience to introduce quantum physics into schools have until now followed a
historical-problematic pattern which was more intended to introduce the physics of quanta than
quantum physics. In such approaches the discussions about experiments and the narrative treatment
of the discussions have prevailed over aspects relating to the subject itself.
Another choice used widely, both at the university level and for didactic approaches to the
formalism of the theory, is the ondulatory formulation [5]. It constitutes a rigorous method to
approach the new mechanics, but it demands strong prerequirement in physics and in mathematics,
that they can be only partially sized down by using computer simulation to ‘visualize’ quantum
phenomena [6]. The more general formulation of the quantum theory is the vector approach,
proposed by Dirac[7] and subsequently adopted by many other authors [8]. This approach points
out the central role of the formalism in QM and how it is strictly interlaced to the conceptual aspects
of the theory. It constituted a reference for the didactic proposals aiming to generate awareness of
the fundamental principia of the new mechanics and to offer hints on the formalism adopted in it [914]. In particular, this approach is very useful for didactics proposals in which the use of
simulations by means of computer modeling offers the opportunity to form children's theoretical
thinking and to analyze the microscopic world with the coherence of a theory.
Teachers need support in this task, which is a great innovation in the teaching of physics not only in
the contents, but also in the methods.
In this framework, multimedia may offer two types of contributions: it allows building up
environments with resources supporting the teachers’ training and offering materials and tools for
teaching innovation; it offers opportunities to use resources on the web in the conceptual analysis of
modeling activities and situations in which the most important aspects of the theory can be analyzed
by exploring hypothesis.
Within the framework of the SeCiF Research Project, teachers were given a web site with the
materials for work and study, which translate the didactic proposals produced in previous research
[10,12,13] into indications of how to operate. In this work we present the most important topics.
2. The need for innovation in schools and teacher education
The introduction of innovative proposals, like our proposal for quantum physics in the secondary
school, must be connected to a new teachers’ training [15]. In particular, teachers need support in
this task, which is a great innovation in the teaching of physics not only in the contents, but also in
the methods.
The increasing presence of ICT in our society stimulates deep and rapid changes, especially in the
styles of communication. These changes affect the ways we look at things, gather information and
learn. In the same way, a profound innovation in the ways of organizing and managing school
activity is a requirement that cannot be delayed [16].
A new professionalism on the part of teachers is required, made up by a complex set of subject,
technical, pedagogical, social and organizational skills [17,18]. Moreover, in the case of physics
teachers ICT are also educational tools: computer on-line measurements and computer modeling are
tools and methods in physics research today that must characterize also the didactic action of the
teacher [19, 20].
In order to produce qualified innovation, meta-cultural and experience-related models [21-25] must
be integrated into in-service and pre-service teacher training, in a process supported by research to
produce competent and qualified innovation [26-27].
Various elements, our investigations into teachers needs [28-29], their general tendency to
transform innovative proposals and return them to traditional didactic styles, their attitude of
reproducing a consolidated practice [30-32] and the lack, until 2000, in Italy of a professional
teacher training [33], have highlighted the need for operative proposals [23, 34-36], detailed
materials for teachers and cards for the students in class [37], so that a change can begin in the way
of teaching, strategies ways in which teachers interact with students [17, 38] .
In the framework of the Italian cooperation for research in physics education, from 1995 the Italian
Research Units in Physics Education are coordinated in
collaborative research into the problems above
summarized, with the particular aim to examine the
contribution to physics learning made by ICT and
teacher training [39].
In this context have been developed: a protocol of
didactic experimentation on innovation [37] and a
model (framework) for on-site or remote teacher
training; various pilot experiments in Italian schools.
The last project was SeCiF (Studying and
Figure 1
Understanding Physics) [40,41]. Its main aim was to
produce materials for teachers to be offered over the
Web, as an environment of resources for didactic planning and classroom activity. Today we are reprocessing it for the pre-service education of teachers in the framework of the project Citizen's
Physics Training (FFC). In the context of SeCif Research the Udine Research Unit has produced
three web environments [41]: one on thermal phenomena for the base (primary) school; a physical
optics pillow [42] and one on quantum mechanics, for the secondary school [43] (fig 1).
Crisis elements of
3. The Environment: Approaching the Quantum
classical phisics
Theory.
The last of the above-cited environments consists of two
parts (fig. 2). The first contains a discussion of the
experiments that have constituted element of crisis for the
classical physics, and constitute a contribution to the
teachers that follow a more traditional approach to
Approach to
quantum physics. The second part, titled “Approaching the
Figure 2
quantum
Quantum Theory”, is centered on an innovative proposal to
introduce the QM, aimed to: propose a first didactic
approach to a synthetic point of view of quantum mechanics; present the basic formalism of QM.
In the following we will describe the main features of the proposal and the Java Applets used in the
past years during its experimentation in the school.
The site is offered as a resource environment for the teachers to build up their own didactic paths. It
is organized in many items, which illustrates: Introduction, Lay-out, Approach, Strategies and
methods, Pre-requisites, Maps, Path, Inter-disciplinary Characters, Resources, Contents,
Experiments, Simulations, Class Experimentation.
Among the working tools there are various proposals for experiments, simulations on pre-set
electronic broad-sheets and an inter-active environment for computer modeling on the interaction of
photons with polaroids and bi-refringent crystals.
The Introduction describes the didactic proposal, based on a direct approach to the main
principles of the theory and to the formal choices that determine the meaning of the entities, by
examinating the fundamental concepts and significant aspects of the QM. Some of the basic ideas
[10] have been used as a guide for the development of materials and the experimentations in the
school [12,13, 41, 44-45].
The aim of the introduction is the definition of the first steps toward a synthetic vision of quantum
physics and the formalism that supports it. It emphasizes the fundamental role of the superposition
principle. The mathematical apparatus for such formulation (vector spaces and linear operators), can
be approached in a simple way by using models, and it supplies a compact and unitary description
of the behavior of a simple spin system but also more complex quantum system.
The didactic strategy is based on the analysis of the phenomenology for simple situations ,
explored from the operative point of view and analyzed in terms of ideal experiments. This is done
in order to motivate and to support the hypotheses used to interpret the same phenomenology, in a
feed back that allows to gradually build the features of the formal entities of the interpretative
model and to study their consistency in an set of situations.
The Prerequirements for the didactic proposal are minimal. The polarization is considered as
property to be analyzed in its intrinsic features and an interpretation related to the description of the
light in terms of electromagnetic waves is not required. Instead, it is required the knowledge that of
the consistency of the description of the light in terms of photons, used to interpret the proposed
situations. The vector representation of physical entities and the most simple composition laws in a
bidimensional space are the main conceptual tools for the analysis and a minimal ability is
required.
The map presents and guides the exploration the conceptual organization quantum mechanics
proposed panorama. It points out the main nodes and the interconnection of the concepts. The map
has been studied as an integration (necessary for the teacher) of the conceptual maps and
organizational maps [41].
The didactical path is structured in two phases:
introduction to the quantum physics from the
superposition principle, starting from phenomenology:
polarization of photons interacting with polaroids and
Figure 3
birefringent crystals; a step by step make up of the
formalism, with a discussion of the basic concepts.
The polarization phenomenology, from the quantistic
point of view, is analyzed in simple ideal experiments of
interaction of photons on polaroids or birefringent
materials (calcite crystal).
The interpretation of the phenomena in terms of single photon interaction with apparatus allows to
learn how polarized photons are prepared and to recognize the Malus’ law (Figure 3). The simple
experimental framework allows to realize that the polarization properties characterize the (quantum)
state of light and that state can be described in a simple way by a vector. The concepts implied by
this formalization are discussed by identifying the mutual exclusive properties that characterize the
states described by mutual orthogonal vectors. The superposition principle, as a simple linear
combination of vectors, is the outcome of the conceptual synthesis and constitutes the base of the
new theory.
The main consequences of the superposition principle are discussed in order to emphatize that it
includes the uncertainty principle, and it allows to approach the problem of the measurement
process.
The representation of observables by means of operators is illustrated examinating the problem of
the calculation of the expected value for a physical observable. The polaroid, as a device that selects
a photon state, is used to represent a projecting operator. The generalization from a system with two
states to systems with an infinite number of states is proposed introducing the wave function, as a
probability amplitude for states, which defined locally in the space.
The two parts of the path are summarized in the following table.
I Part: phenomenology
Properties mutually exclusive
Interpretative hypothesis
Uncertainty principle
II Part: towards formalism
Amplitudes
Ortogonal states
Linear operators / Linear operetors and physical observables
Open questions
4. Resource, didactic materials, experiments, tools
In the section Resources are contained four Cards for the student, that can be used as material to
support the didactic activities:
the first regards the probabilistic interpretation of the results of ideal and real experiments of the
interaction of light with polaroids;
the second, regarding the interaction photons-polaroid, is a guide to the discussion of the conceptual
aspects of the superposition principle;
the third, regarding the interaction photons-birefringent crystals, is a tool for the discussion of
quantum uncertainty and the exploration of interpretative hypothesis;
the forth contains the approach to the construction of the quantum formalism.
A selected bibliografy completes the section, in order to offer to the teacher the references for
further studies.
A large collection of Experiments, contained in the proposals of the Udine Research Unit for the
Optics Pillow in the SeCif project [48], is offered in order to organize a laboratory for the
phenomenological exploration of the situations examined in the described didactic path.
Particular attention is given to the construction of formal thinking and the interpretation of
phenomena, principally because this work can be a prelude to quantum physics.
To this end, five electronic spreadsheets have been prepared, in the framework of didactic
experimentation [51], implementing Simulations to explore interpretative hypotheses. They allow
reconstructing interpretatively most of the experimental situations proposed, starting form the
interaction of single photons with polaroids.
4.1.The applet JQM
An environment for exploring hypotheses, to make prevision on phenomena related with the
interaction of polarized photons with polaroids and birefringent crystals, which we called JQM, was
written in Java script so that it could be used directly from the Web, as a conceptual gymnasium
(training), which could also be useful for developing an introduction to quantum physics.
In the graphical interface of JQM (fig.4), different objects are available. It allows setting up the
necessary projectors, polarizer filters, bi-rifrengent crystals, screens and sensors, using the mouse to
draw the icons of the objects in the simulation environment. Positioned bars represent the state of
polarization of the photons symbolically. The properties of the instruments are accessed by means
of a right click menu. The photons transmitted by the polarizers are selected with probabilities
deriving from Malus' law. It can be seen that photons that strike a bi-rifrengent crystal most
probably follow two separate paths.
Thanks to these software instruments of conceptual analysis, we can offer students the opportunity
to manipulate physics, which has been shown only in a narrative way before, and we give a
valuable contribution to the secondary school in training the student to theoretical thought.
The features of the applet are presented here The access to the properties
Differents objects
by illustrating how some of the situations of an instrument is by a
are availabe
discussed in the introduction of the menu (right click)
superposition principle [10] are represented
and simulated.
Figure 5 show how is represented a beam of
horizontally polarized photons, that interacts
with a polaroid, characterized by a
transmission plane at 45°. Transmitted
photons, with a 45° polarization, are detected
and counted by the detector: in the case of a
large number of photons in the beam, the
resulting photons beam intensity is given by
Malus’ law, and it does not depend on
interactions between the photons in the light
beam.
In such a way, one can assign to the photon Figure 4: The graphical interface of JQM
itself
the
corresponding
polarization
… the light beam is generated:
each photon is rapresented by a
segment oriented in the direction
which represents the state of
linear polarization of the photon
… the photons of the beam
interact with the polarizer with
diagonal permitted plane
Figure5: JQM - situation: light-polarizer-detector
The photons trasmitted by the
polarizer are selected with the
probability given by the Malus
law
The residual photons are detected by the
analizer where are detected and counted
properties and may recognize that the state of a physical system is well defined by the physical
properties measured for it. Photons, in state with vertical polarization (state v), always pass the
polarizer with vertical allowed direction and are always absorbed by the polaroid with orthogonal
allowed direction; photons, in state with horizontal polarization (state u), always pass the polarizer
with horizontal allowed direction and are always absorbed by the polaroid with orthogonal allowed
direction. The two states u and v are characterized by physical properties (direction of polarization)
that are mutually exclusive.
Interpretative hypothesis may be done in the case of photons with 45° polarization, involving the
superposition principle: the phenomenology states that in this case the photon u+v is not a statistical
mixture of photons characterized by the two different physical properties (horizontal and vertical
polarization), neither it is formed by photons carrying each one simultaneously the two properties,
equally weighted.
The physical properties associated to the horizontal and vertical direction of polarization are
mutually exclusive and each of them is incompatible with the property associated to the 45°
polarization (incompatible osservables): they correspond to two orthogonal physical states.
The JMQ applet also allows simulating simple experiments in which linearly polarized photons
interact with bi-refringent crystals. These situation are proposed in order to explore furthermore the
consequences of the superposition principle: for example, one may discuss the impossibility to
assign a definite path to the single photon during its propagation or, in a different theoretical
framework, to recognize that the photon does not
evolve classically during the interactions (figure 6)
The simulations carried out with JQM may be used
also in the part of the proposal regarding the
introduction of the formalism of QM. The central
concepts of the formalism are introduced by
discussing the previous phenomenological context: for
example, the representation of photon states by
versors in the transverse plane, indicating the
polarization directions, and the abstract vector space
of states. Starting from the proposition that classic
physics correctly describes the average evolution of a
Figure 7: JQM- Interaction of photons
large number of photons, one establish the
with birefringet crystals
corrispondence between the dot product of two state
vectors and the transition probability between the two
.
corresponding physical states: P(u,v)= Itr/Iin = cos2q = (u. v)2
The superposition principle results a natural consequence of the vector rappresentation for the
polarization state, decomposed in amplitudes: u = y1 H + y2 V, and this rappresentation allows to
extend these results to a more general physical system.
Moreover, simulations of interaction of arbitrarly linerarly polarized photon with a bi-refringent
crystal, carried out with JQM, introduce the discussion of the problem to determine the expected
value for an observable, leading to the representation of observables by means of linear operators
(fig. 7).
4. Conclusions
The quantum physics, due to its relevence in the present physical framework, is an unrenounceable
item of the citizen culture. New ways to introduce this topic in the curricula are needed, with
particular care for the reference ideas of the new mechanics and giving at least some indications on
the formalism involved.
One must also provide new tools to the teacher, allowing them to carry out these innovation in the
classroom activities. Netherless, the teacher is acked to acquire a new professionalism because the
new methods of communication are changing our ways of learning and require great changes in the
school and in the way teachers work. Research carried out in collaboration with an extensive
network of Italian didactic research units has allowed us to perfect instruments and methods for
training physics teachers in the innovations introduced by the ITC. In the SeCiF project, recently
concluded, these research units have studied materials for a radical change in the curriculum. In the
FFC project, still in progress, these materials are re-processed and proposed to train new physics
teachers for what could be defined as a great turning point in scientific didactics.
The didactic materials, produced by Udine Unit and regarding the introduction of quantum physics,
are base on a direct quantum way of thinking, following the Dirac approach.
These materials are organized in a resource environment for teachers and contain multimedia tools
that can be used to explore hypothesis, to build concepts and, more generally, they help to introduce
the theory and the characteristic features of QM.
Included in the materials offered to teachers there is the documentation of the experiments carried
out at the Marinelli High School in Udine, which also supported the development of the SeCiF
project. In the framework of the FFC project, this material has started to be used in the training of
graduates specializing in secondary school teaching.
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Modena, Napoli, Palermo, Pavia, Torino, Udine are: 1) National Project financed by Ministerium_1996_In-service
secondary school teacher education for new curricula based on ITC experimented in school, 2) National Project
financed by CNR_1996-1997-1998__ITC in physics education and teacher education l, 3) National Project financed by
CNR_1999_ ITC in physics and in teacher education l, 4) Relevant National Project financed by Ministerium_19992000_Spiegare e Capire in Fisica (SeCiF) – Explaining and understanding in Physics.
[40] Studied and implemented for SeCiF project, by Italian community: http://pctidifi.mi.infn.it/SeCiF
[41] Studied and implemented for SeCiF project, by the research unit in physics education of the University of Udine,
see: www.uniud.it/cird/SeciF/
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[43] In the SeCiF project are contained three different contribution to teacher’s training regarding QM: one based on
Feynmann paths (Torino); one based on quantum fields (Milano); the third one is described here (Udine).
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