Problem-based structure for a teaching-learning sequence to overcome students' difficulties when learning about atomic spectra

Abstract

Research has highlighted difficulties experienced by students when studying quantum physics in introductory courses. In this paper, we present a teaching and learning sequence (TLS) aiming at introducing a quantum model of emission and absorption of radiation and we assess its impact on the students’ learning about atomic spectra. The TLS has been designed based on the contributions from physics education research and it was implemented among high school seniors. A detailed description of the TLS is also presented accompanied by a description of how it is implemented. Based on a pre- and post-assessment questionnaire and student interviews, we conclude that students are able to successfully use the models to reason about relevant phenomena.

Full text

Problem-based structure for a teaching-learning sequence
to overcome students’difficulties when learning about atomic spectra
Francisco Savall-Alemany *
Department of General and Specific Didactics, University of Alicante,
Sant Vicent del Raspeig, 03690 Alicante, Spain
Jenaro Guisasola
Department of Applied Physics, Polytechnic University College of Donostia,
University of the Basque Country, 20018 San Sebastian, Spain
Sergio Rosa Cintas
University Institute of Physics Applied to Science and Technology and Department of General
and Specific Didactics, University of Alicante, Sant Vicent del Raspeig, 03690 Alicante, Spain
Joaquín Martínez-Torregrosa
University Institute of Physics Applied to Science and Technology and Department of General
and Specific Didactics, University of Alicante, Sant Vicent del Raspeig, 03690 Alicante, Spain
(Received 18 February 2019; published 24 October 2019)
Research has highlighted difficulties experienced by students when studying quantum physics in
introductory courses. In this paper, we present a teaching and learning sequence (TLS) aiming at
introducing a quantum model of emission and absorption of radiation and we assess its impact on the
students’learning about atomic spectra. The TLS has been designed based on the contributions from
physics education research and it was implemented among high school seniors. A detailed description
of the TLS is also presented accompanied by a description of how it is implemented. Based on a pre- and
post-assessment questionnaire and student interviews, we conclude that students are able to successfully
use the models to reason about relevant phenomena.
DOI: 10.1103/PhysRevPhysEducRes.15.020138
I. INTRODUCTION
Quantum physics is an important part of introductory
physics courses at high school and university [1–5].The
study of quantum physics usually begins by analyzing
the phenomena of emission and absorption of electro-
magnetic radiation. Actually, a recent analysis of sec-
ondary school quantum physics curricula of 15 different
countries has shown that “discrete energy levels”and
“interaction between light and matter”are two of the
most commonly occurring items [6]. One of the intro-
ductory quantum physics goals is that students grasp a
quantum model of emission and absorption of radiation
in order to explain the emission and absorption spectra,
in terms of both frequencies and spectral line intensities.
This goal is relevant for two reasons. On the one hand,
explaining gas spectra helped to highlight the short-
comings of classical physics and to establish some initial
quantum ideas, in addition to having currently numerous
research and technological applications [7–9].Onthe
other hand, the introduction of quantum physics is an
extraordinary opportunity for students to work explicitly
on the construction and use of scientific models. By
doing so, their way of reasoning comes closer to that of
expert scientists. In fact, research has shown that model-
based reasoning is at the core of any scientific discipline
[10]. Models are representations used by scientists to
simplify complex phenomena, to reason, to visualize
abstract entities, and to interpret and predict experimen-
tal results [5,11–14].
Several studies have revealed persistent learning diffi-
culties regarding spectra and energy quantization in intro-
ductory quantum physics courses. Sinarcas and Solbes [15]
found that high school students had difficulties answering
the question “How does the Bohr model explain discon-
tinuous spectra?”, since more than 50% of the students did
not give any answer. Didis and Wang [16] interviewed 9
*pacosavall@gmail.com
Published by the American Physical Society under the terms of
the Creative Commons Attribution 4.0 International license.
Further distribution of this work must maintain attribution to
the author(s) and the published article’s title, journal citation,
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PHYSICAL REVIEW PHYSICS EDUCATION RESEARCH 15, 020138 (2019)
2469-9896=19=15(2)=020138(17) 020138-1 Published by the American Physical Society

university students who had taken a course in modern
physics, focusing on quantization of radiation and energy
and angular momentum quantization in the atom. They
found that only 2 students had learned a scientifically
correct model, while the remaining 7 students had diffi-
culties related to the key idea that every transition is
produced by the interaction between a single photon and
a single atomic electron. By analyzing other phenomena
related to energy quantization in atoms and radiation (not
atomic spectra), Didis, Eryilmaz, and Erkoç [17] stated
that, after following a whole course in modern physics,
only 10% of the university students acquired a scientifically
correct model. Likewise, research on the photoelectric
effect had detected learning difficulties regarding energy
quantization in radiation and in moving beyond the wave
model [18].
In a previous paper [19], we established the key concepts
(KC) that any quantum model of emission and absorption
of electromagnetic radiation should consider in order to
explain gas spectra in quantum physics introductory
courses (see Table I). Moreover, we identified the main
difficulties that high school students, university physics
students, and high school teachers had regarding this issue.
Specifically, we observed the following:
•Students have difficulties with energy quantization in
the atom (difficulties with KC1). They consider that an
atom can have any amount of energy. This difficulty
was also detected by Didis, Eryilmaz, and Erkoç [17].
We also found that some students and teachers
identified the base state with the energy level of
0 eV. This difficulty has also been detected by Ivanjek
et al. [20].
•Regarding the energy quantization in radiation (re-
lated to KC2), some students consider that a photon
can be partially absorbed (difficulties with KC2.1).
Some teachers and students attribute greater intensity
to radiation that is made up of higher energy photons,
regardless of the number of photons (difficulties
with KC2.3).
•The interaction between atoms and radiation (related
to KC3) leads to a higher percentage of incorrect
answers and a greater diversity of difficulties. As
Zollman et al. [3] and Ivanjek et al. [20] did, we
detected that some students and teachers consider that
emission and absorption of radiation can take place
without an atom transition between two stationary
states (difficulties with KC3.1). Likewise, some stu-
dents and teachers relate the emitted radiation energy
to only one of the states among which the atomic
transition takes place (difficulties with KC3.1). An-
other difficulty denote that transitions from higher to
lower energy stationary states take place directly to
the base state (difficulties with KC3.2). This difficulty
has also been detected by Ivanjek et al. [20].In
addition, we found a difficulty among both teachers
and students that is not strictly connected with
quantum physics: they do not apply the principle of
energy conservation to the interaction between atoms
and radiation, so that the energy transition in the atom
may not coincide with the energy of the emitted or
absorbed photon. Finally, it was detected that a
significant proportion of the teachers’group wrongly
state that atoms absorb more than one photon and
make successive transitions to higher energy states up
until they ionize (difficulties with KC3.4).
It should be emphasized that, although these KCs refer
to the emission and absorption of radiation and they can be
considered to be typical of quantum physics introductory
TABLE I. Key concepts that should be considered in any quantum model of emission and absorption of electromagnetic radiation to
explain the gas spectra [19].
KC1 (atomic model). Energy is quantized
in atoms.
KC1.1. Atoms can only be found in stationary states, characterized by discrete energy
values, in which they do not emit energy. Any energy change entails the transition of the
atom from one stationary state to another.
KC2 (light model). Energy is quantized
in radiation.
KC2.1 Radiation is composed of photons, understood as indivisible quanta.
KC2.2 Each photon’s energy is proportional to the radiation frequency.
KC2.3 The radiation intensity is proportional to the number and energy of photons that
form it.
KC3 (emission and absorption model).
Every transition is produced by the
interaction between a single photon
and a single atomic electron.
KC3.1 The frequency of the radiation emitted or absorbed by an atom is proportional to
the energy difference between the states from and to which the transition takes place.
KC3.2 Transitions to lower energy states are random, both in relation to the final state and
in relation to the moment they take place.
KC3.3 The spectral lines’intensity is proportional to the number of atomic transitions per
unit of time giving rise to them.
KC3.4 For a group of atoms at the lower energy level, the absorption of a photon pro-
duces transitions from that state to an excited state. Transitions from an excited state to
another higher energy state are possible but highly improbable.
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courses, research has found that some students’difficulties
in advanced courses are related to them and that incorrect
learning in introductory courses has a negative impact on
learning in later courses [21].
Some researchers have made proposals for teaching
introductory quantum physics, but a lack of results
concerning the learning outcomes has also been noted
[18]. In the specific case of atomic spectra, Zollman et al.
[3] present a sequence of computer-assisted activities
aiming at studying the spectra of several light sources.
They state that this sequence of activities brought
positive results concerning students’learning and atti-
tudes. McKagan et al. [4] test 18 computer simulations
from the physics education technology project [22] that
include several key features to help students build mental
models about quantum mechanics. Over the course as a
whole, where simulations were used extensively, the
researchers found high learning gains. However, the
researchers also indicate that students have difficulties
when using the acquired models to explain other phe-
nomena not contained in the simulations. Ivanjek et al.
[23] present a research-based tutorial for students to
correctly explain the frequencies of the emission spectra.
After putting it into practice, the students were capable of
applying the acquired concepts and reasoning skills in
cases that differ from any other used during the instruc-
tion and they significantly improved their understanding.
Hoehn and Finkelstein [14] use computer simulations to
teach some quantum phenomena and note an increase
in students’abilities to work with models, although they
also note that there are conceptual difficulties that they
are unable to overcome.
The fact that the learning difficulties are detected after
traditional instruction, plus the diversity of results pro-
vided after implementing the new proposals, led us to
design a teaching-learning sequence (TLS) to improve
students’learning. Our study expands the aims of the
aforementioned investigations in several respects. On the
one hand, the TLS that we present deals with emission
and absorption of radiation in a general way. It estab-
lishes a model that can explain not only the spectra but
also other phenomena such as the photoelectric effect,
fluorescence, and phosphorescence. Moreover, it also
shows how devices such as lasers or LEDs work and
other quantum interactions such as the Compton effect
or the Franck and Hertz experiment. On the other hand,
although we only analyze the impact on students’
learning about atomic spectra, we also include more
features than the previous research by addressing both the
frequency and intensity of spectral lines in emission
spectra and the absorption spectra.
II. CONTEXT OF THE STUDY
The TLS presented in this paper was implemented in the
last year (second year) of high school in Spain. High school
seniors (17–18 years old) who take the physics course
receive 4 hours of class per week throughout the school
year. The course is particularly intended for students who
wish to study science or engineering at university. The
curriculum content of this physics course is like the
curriculum offered on standard physics courses at
American colleges. In relation to quantum physics, the
Spanish high school curriculum [24] includes standard
learning aspects about the phenomena that give rise to
quantum theory such as “To relate the wavelength or
frequency of the radiation absorbed or emitted by an atom
to the energy of the atomic levels involved”and “To
interpret simple spectra, relating them to the composition
of matter.”In addition, other aspects related to the
limitations of classical physics, such as the photoelectric
effect, and Heisenberg and Schrodinger’s contributions,
such as “The quantum behavior of the particles. The need
for a more general model to explain their behavior: the
wave function and its probabilistic interpretation”are also
included. The part of the curriculum covering quantum
physics, nuclear physics, and relativity provides approx-
imately 30% of the subject grade in external assessment
tests taken by students to gain admission to Spanish
university for science and engineering degrees. For this
reason, teachers consider it important that students grasp
the appropriate knowledge concerning these topics.
By “modern physics,”the official syllabus and text-
books mean the scientific developments that gave rise to
relativistic physics and quantum physics at the beginning
of the 20th century. Regarding “quantum physics,”in the
introductory courses it is usually considered that it
“begins”with the explanation of the blackbody spectrum
by Planck in 1900. This is the sense that we give to the
term quantum physics in our work. However, historians
often reference “old quantum theory”as the period
between 1900 and 1927 (prior to Heisenberg and
Schrodinger’s developments). Research in physics edu-
cation classifies the atomic models introduced during this
period (e.g., the Bohr model or the Sommerfeld model)
as “semiclassical”or “quasiclassical.”Their study in
advanced quantum physics courses is controversial, as
they mix classical ideas with quantum concepts that later
makes it difficult to learn more current models, such as
the atom model with orbitals based on the resolution of
the Schrodinger equation [25–27].
All students had taken one semester of classical physics
(spring semester) and one semester of chemistry (fall
semester) in the first year of high school. The chemistry
syllabus includes the Bohr atomic model and the quantum
atomic model. However, the students had not studied the
quantum model of radiation based on the photon concept,
essential in interpreting the spectra. During this chemistry
course the de Broglie hypothesis, the uncertainty principle
or the probabilistic interpretation of the Schrodinger
equation are not introduced. In relation to the teaching
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of atomic models, the main objective of the chemistry
semester is an introduction to the study of the periodic table
and chemical bonds. Students learn to apply the “Moeller
rule”to fill atomic orbitals, predict the position of atoms on
the periodic table, and analyze the chemical bonds they
will form.
III. PROBLEM-BASED STRUCTURE OF THE
TEACHING-LEARNING SEQUENCE
In this section we describe first the theoretical tenets
of the TLS, then the pedagogical approach, and finally the
development of the TLS.
A. Theoretical framework of the TLS
Over the last decades physics education research has
repeatedly shown that students have failed to understand
the basic concepts in physics [28]. This has highlighted
the need for new learning strategies to replace the
transmissive teaching of scientific concepts. This has
resulted in a series of proposals that, disregarding minor
differences, basically agree that instruction involves the
active participation of the learner in the construction of
‘new’knowledge and that they will have to use their
previous knowledge as the basis for this [29]. Thus,
we might speak of the rise of a social-constructivism
psychological paradigm for the teaching and learning of
sciences which must integrate not only the different
teaching strategies but also those contributions coming
from other fields that have produced enriching elements
for science teaching, such as epistemology and ontology
of science. These theoretical elements of teaching and
learning show that students’meaningful learning of
concepts depends not only on conceptual understanding,
but also on students’procedures and attitudes [30,31].
This view of learning supposes that students inquire in
problems or scenario posed by the teacher. They must
use scientific skills, such as hypotheses, designing
experiments to test the hypotheses, etc., to solve the
problem and to build new knowledge guided by the
teacher.
B. Pedagogical approach
The idea that the teaching and learning of sciences
should recreate the scientific work is an old one [32].
However, the proposals we are presenting differ from those
attempts in that the inquiry is not limited to learning how
to test principles and in that students are not regarded as
autonomous scientific researchers. In our proposal the
teacher has an essential role to pose the problems and to
guide both their resolution and the learning process. For
this reason we call the approach “problem based-structure
of learning and teaching”(PBSLT) [33–38]. For the
resolution of the problems, the class is divided into small
working groups (3–4 students) that develop a preliminary
inquiry, cooperate between them, and interact with the
scientific community, represented by the teacher and the
literature. Then, the students’teams will receive aid in
terms of clarifying questions, reformulate the partial results
obtained, extracting conclusions, etc.
In accord with the PBSLT, we design a TLS structured as
a succession of problems. At the beginning of the teaching
a core problem is raised, and the entire TLS is structured
around it. Next, the teacher proposes activities to make the
students aware that they are dealing with an important and
interesting problem. The teacher then asks what steps
would be logical to follow in order to solve it, so both
students and teacher should devise a plan, a sequence of
specific problems (or steps), aiming at figuring out the main
problem. Therefore, students progressively grasp the prob-
lem and the entire plan, so they feel that they have played
an important role in it [33,38]. Concepts and models are
introduced on a tentative basis, as informed hypotheses
that seek a solution to the specific problems being raised.
These hypotheses have to be tested through pencil and
paper problems, laboratory experiments, predicting new
results and problems, or analyzing their consistency with
the knowledge already acquired [35–38].
As a whole, guided problem-based TLS encourage stu-
dents to explain and confront their ideas in a hypothetical-
deductive environment involving many episodes of
argumentation, fundamental for learning both scientific
knowledge and science procedures [39,40]. Students dis-
cuss and work out activities in their small group. Then,
group answers are pooled (agilely) and analyzed by the
students and the teacher, coming to a reasoned consensus.
During group work, the teacher’s role is to encourage and
guide students, to question their answers, and to make them
think about it or provide additional information if neces-
sary. These teaching strategies have demonstrated a pos-
itive impact on students’learning at several educational
levels in fields such as optics [41,42], electromagnetism
[36,43], astronomy [34], problem solving [33],orexper-
imental chemistry work [44].
The design of the TLS includes an epistemological
analysis of the content established in the curriculum and
an analysis of the learning difficulties of the students
regarding that content. The epistemological analysis has
been performed for the period 1900–1927, considering the
physics level in university and college. This analysis covers
the problems, hypotheses, ideas, and experimental research
that make it possible to identify the key aspects and the
main difficulties that historically the scientific community
had to overcome in order to establish the scientific models
that we set as learning objectives [[45–48], among others].
With regard to the students’difficulties on the subject, a
review of previous research has been conducted [49,50].
Moreover, preliminary research was conducted on the
students’difficulties in relation to the objectives defined
in the TLS [19].
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C. TLS design phases
The main objective of the TLS is to establish a model that
explains how matter emits or absorbs radiation. This is the
problem posed to students at the beginning of the unit and it
guides the entire inquiry process. Before studying quantum
physics, students have studied the wave nature of light.
However, they have not considered how it interacts with a
material system on a microscopic scale. We begin, then, by
asking them about different ways of producing light and
about phenomena that occur when light interacts with matter.
In class, we produce combustion, incandescence, fluores-
cence, and phosphorescence phenomena (or show them on
video) and devices such as energy-saving light bulbs, LEDs,
and lasers are used. A spectroscope is introduced to analyze
the characteristics of the radiation emitted by the different
phenomena and/or devices in detail. It can be constructed
and calibrated by the students [51].
In this initial phase, we want students to become familiar
with the phenomena that we will try to explain later, which
is essential for achieving adequate learning [4,52]. Next, we
ask students for a tentative plan or strategy (which is the
sequence “index”) that we could follow to progress in terms
of inventing a mechanism to explain the emission and
absorption of radiation by material systems. After a short
debate between the students and the teacher we agree that
we should start with the apparently simplest situation: the
emission of light by a gas formed by atoms that are as
simple as possible. Thus, we begin the research by asking
students to develop a model that explains the visible
spectrum of hydrogen. As a hypothesis, students use the
classical model of emission and absorption of radiation: the
periodic movement of the electron in the atom might
generate an electromagnetic wave of the same frequency
as the vibration motion of the electron. However, they soon
realize that they cannot explain the hydrogen spectrum
observed earlier. Specifically, why it only has four frequen-
cies and why the atom does not collapse (resulting in a
continuous spectrum).
At this point, and after failing to find a solution to these
problems, we tell the students that a satisfactory model
cannot be found by using what classical physics establishes
for the emission of electromagnetic waves. In this way, we
make students participate in the crisis process that shocked
physicists at the beginning of the 20th century, which is
central for a correct understanding of the progress repre-
sented by quantum physics [53,54]. We ask the students
to consider, as a hypothesis, the Bohr’s postulates [55] and
try again to explain the formation of the visible hydrogen
spectrum:
•Electrons in atoms can only orbit in a few stationary
states, characterized by fixed energies. In them, they
orbit around the nucleus according to the laws of
mechanics but without emitting energy.
•Any change in the atom involves an electron transition
from one stationary orbit to another.
•The frequency of the emitted or absorbed radiation in
a single transition depends on the initial and final
energies, according to the expression jEf−Eij¼hν,
where Eiand Efare the energies of the atom in the
initial and final state, vis the radiation frequency and
his a constant.
Qualitative analysis leads them to consider the atom and
the emission of radiation model proposed by Bohr to be
adequate, but also to identify aspects that are contradictory
to the classic model of electromagnetic waves emission.
These contradictions force us to delve deeply into the
explanatory capacity of the model before accepting it. In
particular, we consider the following activities: (a) How can
we use the model to interpret the fact that to ionize the
hydrogen atoms, it will be necessary to illuminate them
with light at a minimum frequency of 3.28 ×1015 Hz?
(b) Can we deduce the frequencies of the hydrogen spectral
lines? (c) Can we predict the existence of more nonvisible
spectral lines? (d) How can we explain the hydrogen
absorption spectrum? (e) How can we explain any other
gas spectra (at least qualitatively)? (f) Energy quantization
only occurs when atoms interact with radiation or is it an
essential characteristic of the atom, regardless of how it
interacts (Franck and Hertz experiment)?
The model established at this point includes key con-
cepts KC1 and KC3, but the photon concept has not
yet been introduced. We use the connection between the
energy change in a single atom and the absorbed radiation
frequency to highlight a contradiction: experimentally it is
observed that each frequency of radiation can only produce
a certain electronic transition, a connection that classical
physics does not contemplate. This makes it reasonable,
even if it contradicts the wave model of electromagnetic
radiation, to think about the possibility that the energy in
the radiation may also be quantified, i.e., to come in
“packages”in which the amount of energy depends on
the radiation frequency.
Testing this hypothesis (based on Einstein’s in 1905)
involves using it to try to solve problems that could not be
solved with previous hypotheses and models. So, we start
by presenting one of them: the photoelectric effect. We
follow a similar strategy as previously: we familiarize the
students with the phenomenon, highlight what could not
be explained by classical theory, use Einstein’s hypothesis
to establish an interaction process between radiation and
the electrons in the metal, design experiments, analyze
data (obtained in experiments shown on video, if neces-
sary), compare to the initial hypotheses in light of the
results, and draw conclusions. This is how we came to
establish the KC2 key concepts, which we strengthen by
explaining the Compton effect, necessary to consolidate
the corpuscular nature of photons (with linear momen-
tum). Finally, we connect all the key concepts by
reviewing and completing the previous explanation for
the gas spectra.
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Although the established model satisfactorily explains
emission and absorption of radiation, there are aspects
that it cannot explain and that limit its validity. These
limitations, which students should be aware of, are,
among others, the existence of two contradictory models
for electromagnetic radiation and the problem of predict-
ing the existence of discrete energy states of atoms
without resorting to ad hoc introductions from exper-
imental data.
Before tackling these problems, we propose to the
students activities in which they should use the quantum
model of emission and absorption of radiation to explain
phenomena such as fluorescence and phosphorescence or
the operation of common technological devices such as
neon lights, energy-saving lamps, LEDS, and lasers. These
activities allow students to consolidate the established
model, delve into the phenomena it can explain, and
appreciate its predictive capacity.
After applying the established model, the TLS proposes
activities for students to address one of the problems that
limits its validity: the existence of two contradictory
models for electromagnetic radiation. Specifically, the
activities ask them to seek an interpretation for the
phenomenon of radiation interference through a double
slit to establish a single model that accounts for the
behavior of photons. When they analyze what would
happen if they carried out this experience with a single
photon, the different groups of students realize that the
place on the screen where this photon can be detected is
indeterminate and subject to probabilistic interpretations.
The final discussion in the class, guided by the teacher,
concludes that the photon is generated as a corpuscle, is
detected as a corpuscle, but in order to know where it can
be detected it is necessary to analyze its movement as if it
was a wave that indicates where it is more likely to be
detected. This model can satisfactorily explain both
radiation emission and absorption phenomena, as well
as the interference phenomena. The TLS proposes activ-
ities to delve deeper into this same phenomenon, by
analyzing how the distribution of radiation on the screen
changes by modifying the characteristics of the double slit.
The final discussion, guided by the teacher, comes to
define the uncertainty principle.
Once the problem of the nature of radiation has been
overcome, the TLS poses the problem of quantization in
the atom: How to predict which orbits are stable for the
electron? We ask the students to consider de Broglie’s
hypothesis, which states that the electron exhibits ondula-
tory behavior. The hypothesis implies that the stable orbits
would be those in which the wave would be found as a
standing wave. Testing the hypothesis requires demonstrat-
ing that the electron shows such wave behavior. The
students, according to their previous experience with the
wave model of light, suggest conducting a double-
slit interference experiment. After analyzing the results
(photographs) in each group and after a discussion guided
by the teacher, the students concluded that electrons (and
by extension all particles) have a quantum wave behavior as
described above for photons.
Finally, the TLS proposes activities to reflect on why
we do not observe the particle’s wave behavior regularly.
Such activities provide opportunities for students to revisit
previous experiments. After a group discussion, the stu-
dents conclude that in all the experiments they have
conducted before it has been necessary to make use of
slits (or obstacles) of very small width, similar to the
wavelength of the particles under study. Quantum phenom-
ena will not manifest without such conditions, which are
practically impossible in daily life. However, the dimen-
sions of the atom are similar to the wavelength of the
electron. From this conclusion, the teacher suggests that the
wave function of the electron around the nucleus can be
represented as a shaded area that tells us, depending on its
“lightness”or “darkness,”what is the probability of finding
the electron. The teacher explains that this shaded area is
called the “orbital.”
The problem of studying in detail the atomic structure
that arises from this electron model remains open. This
aspect is no longer an objective of this course, according
to the curriculum. Despite this, the TLS presents activities
for students to reflect on the concept of orbital from the
perspective of the “dual”or “corpuscle-wave”nature of
the electron that defines quantum physics. This allows us,
in our opinion, to connect and give a first physical
foundation to the atomic model that the students used
the previous year when studying chemistry and applying
Moeller’srule.
The TLS was developed over 12 sessions, each lasting
55 minutes (3 weeks). Three sessions focused on atomic
spectra and up to 8 on quantum phenomena of radiation
emission and absorption. At the end of the TLS we expect
the students to have acquired a quantum model of emission
and absorption of radiation based on the Bohr model for the
atom and on the photon concept for radiation. We also
expect them to be able to identify which phenomena can be
explained by using that model, under which conditions
it was established and what its limitations are: to give
response to other problems, such as the position or move-
ment of an electron in the atom, this model is not sufficient
and models based on the concept of the atomic orbital need
to be used.
In Table II we present a summary of the TLS, relating
how each problem contributes to build up the quantum
model of emission and absorption of radiation and to
address the aspects of scientific work for the students’
methodological training.
IV. METHODOLOGY
To assess the effectiveness of the TLS we compared the
learning outcomes achieved by students treated with the
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TLS (experimental group) and students who learned
quantum physics through habitual teaching (control group):
•The TLS was implemented with 5 cohorts of physics
students from the last year of high school, featuring a
total of 74 students, over 4 years, in two high schools
in the province of Alicante (Spain). One of them is a
city-center school located in Alicante, the provincial
capital city with 330 000 inhabitants, while the other is
a city-center school in a city of 100 000 inhabitants
located less than 100 km from Alicante. Four out of
the five groups were taught by the lead author of this
paper and the other was taught by a collaborating
teacher who has expert knowledge of the TLS. The
collaborating teacher used the program of classroom
activities with the students [57] and the teacher’s guide
[56,58]. This teacher’s guide includes justification of
the sequence of activities, the goal of each activity,
expected answers for each activity, and the answers
given by the students in the first year of implementa-
tion. The collaborating teacher had the opportunity to
discuss all aspects of the TLS with the lead author of
this paper, before and during implementation. Both
teachers have over 10 years of experience as high
school physics teachers and for most of this time they
have been teaching using problem-based teaching and
learning strategies.
TABLE II. Problem-based structure of TLS on the quantum model of emission and absorption of radiation.
Problem sequence
Procedures regarding science
to be learned by the students
Explanations to be understood
by the students
Activities
(see Ref. [56])
Which phenomena produce
light? How can we change the
characteristics of the light
emitted in each of them?
Become familiar with experimental
phenomena. Grasp the importance
of studying light emission and
absorption and its applications.
Need to plan a logical strategy for
moving forward.
Highlight three key elements to
consider when searching for an
explanation: the substance or
material which emits or absorbs
radiation, the radiation (its spectrum
of frequencies and intensities),
and the interaction mechanism
between them.
A1 to A4
Establishing a model that
explains the gas spectra.
- Models must be tested in terms of
their ability to predict or explain.
Key concepts KC1 and KC3 A5 to A14
Is the energy in the radiation
quantified?
- Before being accepted, a model must
prove its universality by explaining
and predicting phenomena that differ
from any used to establish it.
Key concepts KC2 A15 to A23
Review of progress—Limits on
the validity of the established
model
The scientific models have a limit of
validity. They have been set after
accepting idealizations and
simplifications. They cannot be used
when the conditions under which
they were set are not met.
- We cannot predict the energy values
for stationary atomic states. The
model is an ad hoc construction.
Recapitulation
- We cannot explain wave phenomena
such as interference or light
diffraction.
Possible applications of the
developed model
Scientific models are representations
that allow us to simplify complex
phenomena, reason, visualize
abstract entities and interpret and
predict results.
Emission and absorption phenomena
can be explained using the same
model: this requires analyzing the
structure of energy states of the
atoms, molecules or crystals
involved, determining the energy
and quantity of photons that make up
the radiation and establishing an
interaction mechanism between
them.
A24 to A28
Light is ondulatory or
corpuscular?
- Several models may be necessary to
represent entities and phenomena
(i.e., atoms).
- Each model responds to a well-
defined set of problems.
- Experts use different models,
identifying the problems to which
they give response and their limits of
validity.
Photons are emitted and absorbed as
corpuscles. Predicting at what point
they will be detected requires
understanding their propagation as
that of a wave.
A29 to A31
How to predict stable orbits? Electrons are detected as corpuscles.
Predicting at what point they will be
detected requires understanding their
propagation as that of a wave.
A32 to A35
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•The control group is made up of 67 students, from 4
cohorts, who studied the unit following the usual
teaching methodology: they follow a textbook (similar
to the textbooks for college [59]) that contemplates in
a unit the contents and objectives established by the
official curriculum. Of the 4 weekly class sessions,
2 hours are devoted to lectures and 2 hours to
recitation (problem solving). No time is devoted to
experimental work. In the course, students do not
normally have the opportunity to participate actively
and limit themselves to taking notes from the teacher’s
explanations, both in lectures and in problem sessions.
The students’role was limited to asking questions for
clarification after teacher explanations.
The 67 students receiving conventional teaching (con-
trol) and the 74 students who followed the TLS attend
similar schools and devote the same amount of instructional
time to the quantum phenomena of emission and absorption
of radiation.
To evaluate the learning achievement reached by the
experimental and control students, a pretest and post-test
were designed with very similar open questions. The post-
test questions, that have already been validated in another
study [19], are attached as the Appendix. It includes three
questions:
•The first question Q1 (see the Appendix) looks at
understanding the absorption of radiation phenome-
non. KC1, KC2, and KC3 are assessed in it. A correct
answer should state that atoms can only be found in
stationary states (KC1) and that the transitions be-
tween them are caused by the absorption of indivisible
photons (KC2). In addition, the energy of a single
photon cannot be absorbed by more than one atom,
nor can an atom absorb several photons in a single
transition. Following this line of reasoning, an atom in
the fundamental state will make a transition to a higher
energy state if it absorbs a photon with energy that is
equal to the difference between the initial and final
states (KC3). For question Q1, photons of 10.2 eV
will be absorbed, producing a transition from the
−13.6eV state to the −3.4eV state. Photons with
13 eV may not be absorbed because they would move
the atom to an energy state that does not correspond to
any stationary state.
•In question Q2 (see the Appendix), we analyze
whether students can predict the emission spectrum
detected after hydrogen atoms are excited to a well-
defined state. The correct answers should take into
account that atoms in an excited state can only make
transitions to lower energy states (KC1). These
transitions are random, i.e., they can occur to any
lower energy state. When a single hydrogen atom
makes a transition, it emits a single photon (KC3).
For the case stated in the question, transitions can
take place from −1.51 to −3.4eV or from −1.51 to
−13.6eV. A single photon is emitted in each one.
Atoms that have moved to the −3.4eV state will later
make a transition to the −13.6eV state, emitting a
second photon. In the emission spectrum, photons
with three energies, and therefore three frequencies,
will be detected. Three lines will appear, with an
intensity that depends on the probability of each
transition.
•Question Q3 (see the Appendix) focuses on the
interpretation of spectral lines intensity and explores
key concepts KC2 and KC3. A correct answer to the
question should involve matching a more intense line
to a higher energy per unit of time of the amount of
photons that have the frequency of the spectral line
(KC2). As each photon has been generated in a
random transition, a line of higher intensity also
indicates that the transition which generates these
photons is more likely to occur than the others (KC3).
In the case considered, the most intense line is the
yellow one and its frequency corresponds to the lowest
photon energy, so the number of photons with that
frequency emitted in a second should be higher than
the others. This is equivalent to considering the atomic
transition that gives rise to the photons with the yellow
line frequency to be more probable than the others.
A similar analysis will explain the other spectral line
intensities.
Although the students had not previously studied a
quantum model of emission and absorption of radiation,
we carried out a pretest to assess their initial knowledge
before starting the TLS. The phenomena being presented and
the conceptual questions were the same in the pretest and
post-test, so that the objectives of each question can be
considered equal, but in the post-test, numerical aspects were
included that it did not make sense to include in the pretest.
The pretest was validated by four teachers (three high school
teachers and one university teacher). All the high school
teachers stated that they expected that no student would give
a single correct answer before studying the quantum physics
unit. The questionnaire was handed out by the lead author of
this paper to all the groups, in the presence of the group’s
teacher and during a session prior to starting the study of the
quantum physics unit. The students answered the question-
naire under examination conditions (without the possibility
of consulting peers, textbooks, or other materials) and did
not experience any difficulty in understanding the state-
ments, although they did not know what to answer. They
spent about 10 minutes on the questionnaire.
One month after finishing the TLS, we gave a ques-
tionnaire to the students as a post-test. The questionnaire
was handed out during a session by the lead author of this
paper. The students answered with interest, under test
conditions, and spent about 20 minutes on it. In general,
they did not experience any difficulties in understanding the
text or the content of the questions.
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Two days after the questionnaires were completed, we
interviewed 5 students from the experimental groups who
had obtained particularly good results in the unit’sevalu-
ation exams and who had answered the post-test question-
naire correctly. For the interviews among the experimental
students we used the answers they gave to the question-
naires. At the beginning of each interview, students were
shown the answers they had given in the questionnaires and
were asked questions such as “What do you mean by this
answer?”,“How do you imagine the atoms that make up the
gas and what happens to them when they interact with
radiation?”,“Could you explain this phenomenon consid-
ering that atoms are made up of particles like protons,
neutrons, and electrons?”. These interviews intended to
analyze in greater depth the understanding of the quantum
model of emission and absorption of radiation acquired by
the students. It also pretends to assess whether they had
memorized how to use it or, on the contrary, they have
understood the phenomena and their own explanations
about it. The interviews lasted about 10 minutes and were
conducted by the lead author of this paper.
The answers obtained in the pretest and post-test ques-
tionnaires were initially analyzed by the first author of this
paper. The kappa intrarater reliability coefficient was
calculated by this researcher three weeks later, obtaining
a value of 0.86 on average for all questions, satisfactory for
a level of confidence of 95%. Then, the lead researcher
proposed a draft set of categories for each of the questions.
Subsequently, all researches read the answers and each
response was tentatively assigned a category. Then, the
results were discussed with the other members of the
research team. The interrater kappa Cohen reliability
coefficient averaged 0.84 for the questions, indicating a
very significant degree of agreement in the judges’criteria
for assigning the categories used to interpret the responses.
When there was disagreement about a description category
or the location of responses to a specific category, this was
resolved by just using evidence of students’understanding
as a reference [60].
The answers to the questions were grouped into the
following categories:
A. Correct answer and explanation to the question.
B. The answer includes one or more of the difficulties:
B1. Difficulties related to KC1
B2. Difficulties related to KC2
B3. Difficulties related to KC3
And/or a new difficulty.
C. Unclassifiable. Explanations without logical con-
sistency.
D. No answer.
The classification was necessary to analyze the impact of
the TLS in a qualitative way, as we do in the next section.
However, to conduct a quantitative comparison of the
percentage of correct and incorrect answers in each group,
we have calculated the χ2value in each question and the
associated pvalue. To do so, a contingency table was
obtained by collapsing the categories B, C, and D into one
unique “incorrect answer”category to meet chi-square
assumptions. Moreover, we have also calculated the p
value using Fisher’s exact test and we have analyzed the
odds ratio and the Cohen’shvalue.
The interviews were transcribed and everything that the
students wrote and drew was kept for subsequent analy-
sis. The interviews were analyzed independently by three
authors of this paper. Passages were classified in two
initial groups, based on the degree of understanding
regarding the model of emission and absorption of
radiation. By doing this initial separation, some doubts
in the evaluation process were solved and, moreover,
some examples of how students use the model could be
assessed [61].
V. RESULTS
A. Results from the questionnaires
In the pretest, no student, either from the control group or
from the experimental one, answered any of the questions
correctly. Only a small percentage of students in both
groups gave answers that match classical interpretations
of spectra. In addition, a few students used terms from
quantum physics incorrectly, showing that they remem-
bered memorized knowledge on atomic theory studied in
chemistry. The vast majority of students in both groups did
not answer the questions or their answers were not logical.
In accordance with the results obtained, we can state that
the students in both groups had no knowledge of quantum
physics. So, in terms of previous knowledge of the topic,
the control and experimental samples are uniform.
In Table III we present the percentage of students’
correct responses in the experimental and control group
to post-test questions, as well as the values obtained for the
statistics used. The statistical parameters used are suited to
compare the effect of an innovation in the experimental
and control groups [62]. We have calculated the χ2value in
each question, and the associated pvalue, by using a
contingency table with the number of students that
answered correctly and incorrectly. Although the sample
size is sufficient to apply χ2, we have also calculated the p
value using Fisher’s exact test. Finally, we calculated the
odds ratio and the size of the effect using Cohen’sh.
No statistical differences have been observed between
the students in the 5 experimental cohorts so they have
been grouped together into a single experimental group
(N¼74). The same happens with the students from the
control cohorts and the results have also been grouped
together into a single control group (N¼67). Figure 1
shows the percentage of correct answers of the experi-
mental and control group to each question.
In the question referring to absorption (Q1) the applied
statistics show that there is a statistically significant
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difference between the results obtained by the experimental
group and the control one. By comparing the percentage of
correct and incorrect answers in each group we obtain a
χ2¼48.46, higher than the critical value for 1 degree of
freedom χ2
0.95 ¼3.84, and p<10−5. The result is con-
sistent with that obtained by applying the Fisher’s test,
which also provides a p<10−5. We obtain an odds ratio of
19.93, which means a large gain of the experimental group
compared with the control group. Also, the value of
Cohen’sh¼1.29 indicates a large effect size. In question
Q2, referring to emission, the differences between the
results of the experimental and control group are significant
when applying the statistics. By comparing the percentage
of correct and incorrect answers for each group, we obtain
χ2¼41.93 and p<10−5(critical value for 1 degree of
freedom χ2
0.95 ¼3.84). Fisher’s test also indicates that
p<10−5. The calculated odds ratio value is 18.19. The
size of the effect achieved in this aspect when applying the
TLS is large, as shown by the Cohen’shvalue, h¼1.21.
In Q3 (referred to the intensity of the spectral lines), we
observe that the differences are also statistically significant
when comparing the percentage of correct and incorrect
answers given by each group using the three statistics. We
obtain a χ2¼46.51 higher than the critical value (critical
value for 1 degree of freedom, χ2
0.95 ¼3.84), correspond-
ing to p<10−5. Fisher’s test also indicates that p<10−5.
The odds ratio value is 18.77. Cohen’shhas a value of
h¼1.26, indicating a large effect size [63].
After analyzing the percentage of correct answers to each
question separately, we carried out a global analysis. In
order to do this, we have assigned the students one point
for each question that they have answered correctly. In
Table IV we show the percentage of students who respond
correctly to 0, 1, 2, or 3 questions (getting 0, 1, 2, or 3
points, respectively) for the experimental and control
groups. 41% of the experimental students answer the three
questions correctly, while no control student manages this.
In addition, we should highlight that the mode for the
experimental students corresponds to have three correct
answers, while it corresponds to 0 correct answers in the
case of the control students.
We have conducted a Shapiro-Wilk test to assess to what
extent the quantity of correct answers for the experimental
and control group match a normal distribution. We have
obtained WExp ¼0.815 and WCont ¼0.54 for the exper-
imental and the control group, respectively. Both values
correspond to a pvalue lower than 10−5and are not
included into the interval of confidence of 95% of prob-
ability (0.9670, 1), so we have to conclude that the
distributions do not match a normal distribution. Taking
that result into account, we have conducted a Mann-
Whitney nonparametric test to compare the results. The
value obtained for this statistic was U¼661.5. It corre-
sponds to a pvalue lower than 10−5. It is equivalent to a
Z¼7.5in a normal distribution, higher than the critical
value of 1.9599 for two tails. Although the occurrence of
only 3 correct answers may weaken the value of the statistic,
we consider that the statistically significant differences are
consistent with the results presented above for each indi-
vidual question and show the global impact of the TLS.
FIG. 1. Percentage of correct answers given to each of the
questions by the 74 experimental students (E) and the 67 control
students (C).
TABLE III. Percentage of correct answers to each question by the experimental groups (E group) and control groups (C group).
Statistical comparison between them.
Question
Percentage of correct
answers (E group)
Percentage of correct
answers (C group)
X2(χ2
0.95 ¼3.84;
df ¼1)P(from χ2)
P(from
Fisher test) Cohen’sh
Q1 66.2 9.0 48.46 <10−5<10−51.29
Q2 59.5 7.5 41.93 <10−5<10−51.21
Q3 64.9 9.0 46.51 <10−5<10−51.26
TABLE IV. Percentage of students from each group categorized
by the quantity of correct answers.
Quantity of correct
answers (punctuation)
Experimental
percentage of
students
Control
percentage of
students
0 17.6 77.6
1 17.6 19.4
2 24.3 3.0
3 40.5 0.0
Mean (SD) 1.88 (1.13) 0.25 (0.50)
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Regarding students’difficulties in learning the key
concepts of the TLS (see Table I), we are interested in
looking at how learning difficulties have changed in
relation to the key concepts. We have classified the
incorrect answers (Table V). Category B comprises the
ties in relation to the key concepts. We also found some
incorrect answers not clearly related to any key concept.
In many cases these lacked internal logic. None of them
were detected with a percentage higher than 3%, so we have
classified them in category C as “unclassifiable.”Finally,
category D corresponds to answers left blank.
The difficulty B1 (related to KC1) was found mainly in
questions Q1. It includes answers that explicitly show not
understanding that the energy is quantized in the atoms
(KC1). Students who gave those answers mostly consider
that the atom can absorb any photon and reach an energy
different from that of the stationary states. The percentage
of students for difficulty B1 is about 10% in both groups.
There does not seem to be any progression between
experimental and control regarding this difficulty.
The difficulty B2 was mainly found in question Q3. It
corresponds to answers where the intensity of the radiation
is not related to the quantity of photons within it, always
attributing higher intensity to the radiation formed by
photons with higher energy.
Regarding the difficulty B3, the students use alternative
explanations depending on the context of the question
(Q1, Q2, and Q3) but in all cases, the answers show that
students did not understand KC3.
•In all the questions, a set of explanations are based on
the fact that the energy diagram represents both the
energy of the stationary states and the energy of the
photons that can be absorbed (as an absolute value).
So, only photons that match the energy values shown
in the diagram are emitted or absorbed.
•In question Q1, a set of explanations ignores the fact
that the energy conservation principle must be accom-
plished in the interaction processes between photons
and electrons: students that answer in this way
indicate that the atom, when it absorbs the photon,
performs a transition that takes it to a stationary state,
whose energy difference from the initial state does not
coincide with the photon’s energy. Moreover, they do
not give any explanation of what happens with the
“missing”or “exceeding”energy.
•In question Q2, a set of explanations omit that
transitions between stationary states are random and
it indicates that the spectrum will have a single line,
corresponding to the light emitted by the atoms when
making the transition from the excited state directly to
the fundamental.
•In question Q3, a set of explanations consider that
the most intense radiations are those emitted by the
atoms found in the states of higher energy (in absolute
value), without considering that the atom has to make
a transition when it emits radiation.
Fluctuations in the percentages are not considered in
absolute values, no statistical differences are sought, but
an attempt is made to observe changes in the difficulty
distribution shown in Table V. The percentage of answers
left blank by control students is particularly high compared
to an insignificant percentage in the experimental group.
The lack of answers, also detected by other previous studies
[15,19], can be attributed to the lack of an explanatory
model that helps them find and/or justify their answers.
Regarding the difficulties related to the key ideas, we
observe that the percentage of difficulties detected in the
experimental students is lower in all cases, except for
difficulty B3 for question Q3 that remains constant. The
differences related to difficulty B3 in question Q1 and the
differences related to difficulty B2 in question Q3 are
particularly noteworthy. This analysis gives us clues about
the weakest parts of the TLS, pointing to possible improve-
ments in both its design and its implementation.
B. Interviews with the experimental students
After reviewing the answers given in the questionnaire
by the experimental students, we interviewed five of them
to assess the quality of the students’argumentation when
explaining their answers and the scientific model they use.
Consequently, five students who had answered the three
questions correctly where selected, to assess to what extent
they really understood their given answers or, in contrast, if
they had simply given algorithmic answers, without under-
standing the processes involved.
The answers given by the students in the interviews
show that they can use various representations of the atom
coherently (establishing relationships between them) to
explain what happens when radiation interacts with atoms.
Student 7 (we used numbers to preserve anonymity)
answers as follows when asked to use another representa-
tion of the hydrogen atom to Q1 [Fig. 2shows the answer
(s)he gave in the questionnaire and the picture (s)he draws
in the interview]:
TABLE V. Percentages of learning difficulties in experimental
students (E) and control students (C).
Q1:
absorption
Q2:
emission
Q3:
intensity
(% of
answers)
(% of
answers)
(% of
answers)
Category E C E C E C
B1. Difficulties with KC1 8.1 9.0 1.3 1.5  
B2. Difficulties with KC2 0.0 3.0   4.0 23.9
B3. Difficulties with KC3 12.2 31.3 12.2 20.9 14.9 13.4
C. Unclassifiable 10.8 16.4 25.7 28.3 14.9 23.9
D. Did not answer 2.7 31.3 1.3 41.8 1.3 29.8
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“Interviewer: What image do you have of atoms? What
do you imagine, a lot of energy diagrams inside the
vessel?
Student 7: No, I suppose that a single diagram. A single
diagram for a given gas.
I: Then, regarding those atoms in there, considering that
they are formed by protons, neutrons, and electrons,
would you be able to draw any of those atoms?
St7: I suppose it would be an atom containing its
corresponding protons and electrons. But together
[(s)he draws a point and an orbit around it representing
an electron that orbits a nucleus, as happens with
hydrogen]. And when emitting light, it would propagate
accordingly.
I: So, when the atom absorbs light, what would happen
to the atom?
St7: Well, by absorbing light, if the light is sufficient for
the electron to go into a stationary state, then I suppose
the electron will absorb it and later, it will shift to a state
of lower energy and emit light [he draws an arrow that
refers to the radiation incident on the atom and, by
means of another arrow, the transition of the electron
into a more external orbit, then (s)he adds a line
that represents the transition back into the internal
orbit, which would correspond to the aforementioned
emission].
I: If the atom you drew was the atom in the base state,
what would it be like after absorbing radiation?
St7: It will shift to a…to another stationary state if the
light is enough for it to do so. Then it will shift again to
any other lower energy state.
I: What if the light weren’t absorbed?
St7: Nothing would happen. I suppose the light would
pass by and have no effect on the atom.”
Two of the students interviewed go one step further and
refer to the quantum model of the atom instead of using
Bohr’s model, using the concept of orbital instead of orbits.
As an example, we are showing the answers given by
Student 22. Here we can observe that (s)he uses different
representations to refer to the atom according to the
situation being approached and the feature (s)he intends
to emphasize:
“Interviewer: The atoms in there, the hydrogen atoms
inside the vessel, how do you imagine them?
Student22: Dispersed, scattered over there. No?
I: Lots of scattered atoms? Could you draw those
atoms?
St22: I don’t know, like it’s all filled up, like this, a lot
[(s)he represents small dots inside a vessel, a repre-
sentation that looks like the kinetic-corpuscular model
of a gas].
I: And when those atoms receive radiation, what do you
think happens to them?
St22: Well, then that happens [(s)he points out his
answer in the questionnaire, the energy diagram], that
the electron changes from…well, it makes a transition,
doesn’t it?
I: That’s the answer you gave. But I would like you to
think of atoms made up of protons, neutrons and
electrons, or do you imagine that there are energy
diagrams in the vessel?
FIG. 2. Student 7’s answer to Q1 (left) and representation of the atom made during the interview (right). (S)he draws a nucleus and an
electron that makes a transition to a more external orbit when it absorbs a photon (represented by an arrow coming from below). (S)he
uses a line to represent the transition that will result in emission of radiation. Student 7’s written response: “Subparagraph a) The atoms
absorb the photons from light and they will jump to the stationary state of −3.4eV, then they will go down again emitting light.
Subparagraph b) There will be no jump, it is impossible because there is no stationary state of the hydrogen atom
at −0.6eV, so the photon will pass by.
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St22: No, no, no.
I: Protons, neutrons and electrons, how do you imagine
them in the atom? What do you think that happens to the
atom?
St22: I know they’re not going to be moving in circles,
but it’s more like they’re in one of those orbitals….
I: Could you represent the atom in any way?
St22: Let’s see, we represent it like this [(s)he draws an
electron making a circular movement around a proton]
but really, apart from the fact that there is no [orbit
as the electron’s path] the electron is where there is
more…you see, the orbital is where the electron is most
likely to be, isn’t it? There are different ones.
I: So, there are no orbits, there are orbitals.
St22: Yes.
I: And using this atom model, when that atom absorbs
radiation, what happens to it?
St22: That…It sort of gets bigger [(s)he draws the
electron further from the nucleus]. Because of the
attraction, it goes down again and emits radiation.”
We observe that the student combines up to 4 repre-
sentations for the atoms contained in the vessel according to
the feature he intends to describe: (s)he imagines the set of
atoms as dispersed points inside the vessel (according to
the kinetic-corpuscular model), (s)he uses the energy
diagram to reason about the transitions taking place in
the atom, (s)he refers to electrons orbiting the nucleus to
interpret the change in the structure of the atom after
absorbing radiation, but (s)he refers to the atomic orbitals
when referring to the position and absence of trajectory of
the electron. We observe, moreover, that the representations
are not mixed in an unreflective way, but that each one
responds to a different problematic aspect.
We get similar explanations by asking students for more
details about question Q2, as shown in the following example.
In Fig. 3, we show the drawings made by the student:
“Interviewer: In this second question about emission, if
we take into account that atoms are made up of protons
and electrons, as you have represented before, can you
explain what would have to happen to the atom for
radiation to be emitted? In this case, what’s happening
to the atoms?
Student 20: They’re returning to their minimum energy
state.
I: Could you represent this in some way with drawings?
St20: Let’s see, if…if this is where it is once the electric
discharge takes place [(s)he draws an atom with a proton
and an electron and, with an arrow, represents the
transition to a more external orbit] well, it would return
to its state…Idon’tthinkIwilldoitthesameasthe
previous one [in reference to the size of the drawings].
I: Yes, we admit that the drawings are approximate.
St20: Yes [(s)he uses an arrow to represent transition
from the outermost to the innermost represented orbits].
I: Would it return to its fundamental state?
St20: Exactly.
I: But here you tell me that there are three transitions [in
reference to his written response to the question].
St20: Three possible, that is, it could go either directly
or through the −3.4eV state, let’s pretend there is
another electron, we know there isn’t but…[(S)he adds
an intermediate orbit between the previous two and an
electron that makes a transition from it to the innermost
orbit. [(S)he says he does so to avoid representing
another atom but (s)he recognizes that hydrogen only
has one electron].
I: Would it be another atom?
St20: Oh, well, yes. Exactly. Firstly, It’d do the…. The
shift to the middle state, so to speak, and then It’dgo
back to the base state.”
We can see that the student correctly relates the energy
diagram to the pictorial representation of the atom and that
(s)he is able to pass from one to the other according to the
feature (s)he wants to emphasize [(s)he uses the energy
diagram to work with quantitative values and the repre-
sentations based on the Bohr model to qualitatively explain
what happens to the atoms].
VI. CONCLUSIONS
In this research, we set out to design and evaluate a
problem-based TLS to improve teaching and learning of
quantum physics in introductory courses, specifically
focusing on atomic spectra. We have designed the TLS
considering difficulties that students are unable to over-
come when studying atomic spectra in regular education.
FIG. 3. Drawing by student 20 to explain atomic transitions and
how they relate to the emission spectrum. At the top, (s)he shows
the absorption of energy produced by the electrical discharge and
at the bottom, (s)he shows the possible transitions back to the
fundamental state.
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In addition, we have developed a teacher’s guide [56,58]
that explains the goals of each activity, the main students’
difficulties when carrying them out, and the strategies to
overcome these difficulties.
Results from the administered questionnaire show that
there is a significant improvement in the students’learning,
which has been analyzed in light of the key ideas of the
quantum model of emission and absorption of radiation.
This improvement is characterized by a significant increase
in the students’ability to use the quantum model of
emission and absorption of radiation to interpret frequen-
cies and intensities of radiation in emission and absorption
phenomena. By interviewing some experimental students
we have shown that they understand the quantum model of
emission and absorption of radiation and they are able to
select the representation of the atom they use taking into
account the aspects they want to analyze or emphasize.
They use energy diagrams to deal with the quantitative
aspects. They use pictorial representations to explain what
happens to subatomic particles during emission and absorp-
tion. Likewise, they resort to the Bohr model due to its
simplicity but recognize that the quantum model of the
atom, with atomic orbitals, must be used to interpret
magnitudes such as the position of the electron in the atom.
Results also show the necessity for some changes in the
TLS. Three are the main points we are working on to
improve its efficacy:
•Reducing the percentage of incorrect answers corre-
sponding to KC3. It seems that a further insight on the
emission and absorption of radiation processes is
required in order to overcome those difficulties. We
should require the students to use the energy diagram
to represent and discuss each phenomenon avoiding
direct interpretations using unique equations or quan-
titative operations.
•Increasing the emission phenomena interpretation
capability. Q2 referring to the emission spectrum
registered the lower correct answers’percentage and
the higher nonclassifiable amount of response. Match-
ing electrons’transitions in the atom and spectral lines
is hard for the students, as other studies have shown
[23]. An effort should be made to introduce activities
aiming at reinforcing that point.
•Improving the use of the orbital atomic model. Almost
all devices and applications of the emission and
absorption of light have been studied after introducing
the quantum model of emission and absorption of light
and before introducing the orbital model of the atom.
We consider that some “application activities”could
be moved to the end of the unit, bringing the students
opportunities to use the recently introduced atomic
model and to overcome the use of quasiclassical
models.
We are aware that the student samples in this study are
not extensive, but some of the students’difficulties that we
detected concerning emission spectra match to other inter-
national previous studies [15–17,20]. In addition to them,
we have also focused on absorption phenomena and on
emitted light intensity. Because of the difficulty of finding
control groups that perform classroom analysis of the
quantum phenomena of emission and absorption of radi-
ation other than gas spectra and the photoelectric effect,
we have limited the learning evaluation questionnaire to
gas spectra. We are currently working on extending this
research to assess the impact of the unit more extensively,
including the students’capability to explain more quantum
phenomena and expanding student samples to university
degrees.
As we mentioned in the introduction, the use of the
Bohr model in teaching quantum physics is controversial
[25–27,64–68]. This and other quasiclassical models have
been identified to be the origin of difficulties and alternative
ideas held by the students in advanced quantum physics
courses and that are difficult to overcome [25–27]. The
importance of the correct learning of Bohr’s model on
subsequent learning of quantum concepts has also been
noted [68]. Despite all this controversy, we must bear in
mind that using atomic models based on Schrodinger’s
equation can be excessively complicated for introductory
quantum physics courses in high school. By following the
TLS, the students have learned to use Bohr’s model to
interpret radiation emission and absorption phenomena.
They have done so by facing a path of problems that allows
them to recognize the experimental situations to which it
responds, the simplifications on which it has been estab-
lished, and the problems that it cannot explain and that limit
its use. This helps students to choose it as suitable for
explaining certain phenomena, but they resort to other more
suitable models or representations when this model fails.
This ability corresponds to expert thinking [5,10–14].
As we stated in the introduction to this paper, scarce
research has been done in physics education on quantum
phenomena of emission and absorption of radiation, and
the little research in this field focuses on gas spectra and
on the photoelectric effect [18]. Concerning introductory
quantum physics, computer-assisted activities have been
reported to have brought positive results on students’
learning [3,4,14]. However, these studies also report
persistent student difficulties when working with models
[4,14]. Focused only on emission spectra, the research-
based tutorial of Ivanjek et al. [23] brought positive results
on students learning. Our research provides a new proposal
to address this subject that considers a greater diversity of
emission and absorption of radiation phenomena and that
has, as we have shown, a positive impact on learning about
models and atomic spectra. The similarities and differences
between our results and previous research lead us to think
that our experience may be useful in educational contexts
for introductory quantum physics courses, in both high
school and college.
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APPENDIX: POST-TEST QUESTIONNAIRE
In Fig. 4we present the questions and figures used in the post-test.
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