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Progress in Science Education

2021, Vol. 4, No.2, 40-51

ISSN 2405-6057

DOI.10.25321/prise.2021.1079

© The authors, 2021

Published by CERN under the Creative Common Attribution 4.0 Licence (CC BY NC SA 4.0)

FOSTERING STUDENTS’ CONCEPTIONS ABOUT THE QUANTUM

WORLD – RESULTS OF AN INTERVIEW STUDY

Philipp Bitzenbauer1 and Jan-Peter Meyn1

1FAU Erlangen-Nürnberg, Germany

*Please address all correspondence to Philipp Bitzenbauer, philipp.bitzenbauer@fau.de

STRUCTURED ABSTRACT

Background: Quantum physics is both a highly topical and challenging topic of physics education. Learning quantum

physics is inherently difficult because it is unimaginative, counterintuitive and fundamentally different from what learners

know from their everyday life and classical physics. The results of recent studies underline that students are often not aware

of the relevance of quantum physics and its technologies for their own lives, which makes studying quantum physics even

more difficult. This is the starting point of this article: With the Erlanger teaching concept, we present an introductory

teaching concept for quantum physics at secondary schools with the aim, among others, to raise students’ awareness of the

importance of modern quantum technologies today and in the future.

Purpose: In order to evaluate which conceptions about the quantum world arise among students who are introduced to

quantum physics with the Erlanger concept, we conducted an interview study.

Sample/Setting: A random sample of N = 25 students was interviewed after the intervention (15 male, 10 female) in order

to answer the questions mentioned above. The interviews had a duration of 25 – 40 minutes. Prior to the intervention, none

of the students had any classroom instruction in quantum physics.

Design and Methods: The students’ answers were transcribed and then evaluated on the basis of deductive and inductive

categories using qualitative content analysis. The coding was done by independent coders (𝜅 = 0.84,95% −𝐶𝐼

[0.68; 1.00]). Additionally, a cluster analysis was performed and a three-cluster solution was extracted. The three clusters

could be interpreted in terms of content and thus facilitate the characterization of occurring types of students’ conceptions

after the intervention.

Results: After the intervention with our concept, we found elaborated conceptions about the quantum world with the

majority of respondents. 11 of the 25 students (cluster 1, labelled Primarily elaborate conception) are aware of the striking

differences between quantum and classical physics, as all students in this cluster characterize the quantum world via effects

or aspects that do not exist in classical physics. The importance of quantum physics for future technologies was named by

the students combined in the cluster 2, labelled Quantum world as the world of technology. 10 of the students interviewed

(cluster 3, labelled Quantum world as a classical world on a small scale) seem to stick to their pre-conceptions dominated

by classical ways of thinking.

Conclusions: Our article provides implications for both classroom practice and future research. For classroom practice, the

Erlanger teaching concept serves as a proposal to bridge the gap between quantum physics and the everyday life of the

learners. In addition, the results of the interview study presented in this paper make a contribution to the empirical research

on students’ conceptions about quantum physics. We not only find individual, independent conceptions of learners, but we

also show that there are dependencies between them, allowing us to extract types of conceptions. The extraction of such

types of student conceptions for various further concepts of quantum physics will be part of future research and could

contribute to our understanding of learning processes in quantum physics.

Keywords: quantum physics, interview study, cluster analysis, teaching concept

Received: September 2020. Accepted: March 2021.

1 INTRODUCTION

Quantum physics is both a highly topical and

challenging topic of physics education. Studying quantum

physics is inherently difficult because it is unimaginative,

counterintuitive and fundamentally different from what

learners know from their everyday life and classical

physics. Scholz et al. (2020) speak of a "knowledge

reboost" that is required for learning quantum physics.

In order to make such a reboost possible, learning

difficulties in quantum physics must be known. While

recent studies contribute significantly to our

understanding of the learners’ model understanding in

quantum physics (Ubben & Heusler, 2019) and our

understanding of patterns of student difficulties in modern

Bitzenbauer & Meyn 41

quantum physics in schools (Marshman & Singh, 2015),

the learner’s perspective on learning about quantum

physics remains unknown so far: A first study on the

importance of learning quantum physics from the

perspective of secondary school students revealed that

students are often not aware of the relevance of quantum

physics and its technologies for their own lives (Moraga-

Calderón et al., 2020). Moraga-Calderón et al. (2020)

therefore conclude that a stronger link between quantum

technologies or physics and the daily life of students must

be established in the teaching of quantum physics.

Teaching quantum physics must therefore be motivated in

terms of content by modern aspects of quantum

technologies as they influence the social lives of students

today, and will do so even more in the future - it is not

without reason that the European Quantum Flagship

initiative advertises its cause with the slogan "The Future

is Quantum" (EU, 2019).

We are taking up this point with this article: with the

Erlanger teaching concept for quantum physics (chapter 2

of this article), we make a proposal how modern quantum

physics can be taught in schools. This concept is

motivated by and connectable to the basics of quantum

technologies. In chapter 3 and 4 of this paper, we report

the results of an explorative interview study on clusters of

students’ conceptions that might be formed about the

quantum world, introducing students (without prior

knowledge) to quantum physics using the Erlanger

concept: By means of cluster analysis, we were able to

extract preliminary types of students’ ideas about the

quantum world. The results suggest that the Erlanger

teaching concept for quantum physics makes it possible to

explain the importance of quantum technologies in

secondary schools, and thus to create an awareness among

learners of the importance of modern quantum

technologies for their everyday life today and in the

future.

2 THE ERLANGER TEACHING CONCEPT

OF QUANTUM PHYSICS

2.1 Design principles

The Erlanger teaching concept on quantum physics

forms a proposal for teaching quantum physics at the

secondary school level (11th/12th grade). The underlying

design principles were derived from literature concerning

research on quantum physics education, specifically

including the following four perspectives:

1. Content perspective on the status quo of teaching

quantum physics in school: Stadermann et al.

(2019) derived an international core curriculum for

quantum physics in schools from a review of 15

different national physics school curricula and

summarised the status quo in terms of content for

today's quantum physics teaching. In another article,

Krijtenburg-Lewerissa et al. (2018) used a Delphi

study to investigate the question of which quantum

physics topics should be taught in quantum physics

classes at secondary schools from an expert’s

perspective. Both cited research papers are in

accordance regarding two key points: first of all,

quantum physics in school today is

predominantly taught by historical approaches and

topics, such as wave-particle duality which is seen

quite critically, because aspects of modern quantum

physics remain underrepresented. Consequently, as

a second key point, both call for research into the

feasibility of integrating modern findings of

quantum physics into physics lessons at school, far

beyond wave-particle dualism – and this demand is

not new at all. The proposal to avoid historical

approaches in introductory quantum physics

curricula was already put forward in a contribution

by Brachner and Fichtner as early as 1974 (Brachner

& Fichtner, 1974).

From a content perspective, the Erlanger

teaching concept is therefore based on the following

design principle: Provide modern insights into

quantum physics, avoiding historical approaches.

2. Learning difficulties in quantum physics: A

general overview of the current state of physics

education research on learning difficulties in

quantum physics is provided in the review article

published by Krijtenburg-Lewerissa et al. (2017).

Frequently reported learners’ difficulties are based

on mechanistic ways of speaking and thinking, e.g.

students think about electrons as haptic particles or

about photons as bright balls with a permanent

location (Masshadi & Woolnough, 1999; Mannila et

al., 2002; Hubber, 2006). These make it difficult to

build up quantum physics-based conceptions

(Müller & Wiesner, 2002).

Thus, taking into account results from research

into students’ difficulties in quantum physics, the

Erlanger concept is based on the following design

principle: Introduce quantum physics in a way that

is detached from mechanics.

3. Teachers’ perspective: In recently published results

of a Delphi study into teachers’ needs for teaching

quantum physics in the classroom (Weber, Friege &

Scholz, 2020), three points are crucial: firstly, the

authors report on the teachers’ need for quantum

physics experiments (esp. with single photons) for

classroom practice, or at least for simulations or

animations. Secondly, these experiments are

supposed to reveal the characteristic traits of quantum

physics as formulated by Küblbeck and Müller

(2003) from the teachers’ point of view. And thirdly,

teachers attach great importance to the practicality of

the material provided. The criterion of practicality is

difficult to fulfill with today’s real experiments with

individual quantum objects at schools (Kral et al.,

2016), but interactive screen experiments on single

photons are accessible (Bronner et al., 2009).

Thus, the Erlanger concept is based on the

following design principle: Integration of interactive

screen experiments from quantum laboratories

leading to the characteristic traits of quantum physics.

42 Fostering students’ conceptions about the Quantum world

4. Learners’ perspective: A study published in 2020

investigated the importance that students attach to

learning about quantum physics (Moraga-Calderón et

al., 2020). The key finding of the study was that while

learners considered quantum physics important for

society, they did not equally recognise the relevance

of quantum physics to their own lives. In their

summary, the authors conclude that students should

be taught the importance of applications of quantum

physics for society and for their everyday lives.

Thus, the Erlanger concept is based on the

following design principle: The new concept on

quantum physics must be motivated by modern

aspects of quantum physics as they influence the

social lives of learners today, and even more so in

future.

2.2 Key ideas of the Erlanger teaching concept

The design of the Erlanger teaching concept takes

into account the requirements derived from the literature

(chapter 2.1). Table 1 shows how they are addressed in

the design of the new concept: in a Delphi study, physics

teachers expressed a need for experiments in quantum

physics classes (Weber et al., 2020). Especially, single

photon experiments, among others, proved to be

thematically interesting for teachers.

The treatment of single photon experiments in class

is in accordance with

1. the requirement not to introduce quantum

physics as an extension or generalisation of

classical mechanics, so that mechanistic ways of

speaking become superfluous in quantum

physics lessons and

2. the requirement to include modern quantum

physics in schools.

In this way, quantum physics is formulated as an

extension of classical optics instead of as an extension of

mechanics, using the quantum object photon as an

example. The treatment of quantum physics with single

photon experiments thus leads to a doctrine of quantum

physics that is founded in optics - quantum optics

(Bitzenbauer & Meyn, 2020a).

The key ideas used in the Erlanger concept are as

follows:

Prevention of mechanistic ways of speaking and

thinking: the avoidance of wave-particle dualism

from teaching quantum physics makes a

discussion about the mechanistic trajectories in

quantum physics redundant, and the meaning of

the property position in quantum physics is

addressed in the context of measurement.

Notion of preparation instead of transmitter-

receiver-concept: instead of talking about photon

sources, the preparation of quantum states by

coincidences is emphasized.

Highlighting effects that cannot be explained

semiclassically: Data from quantum optics

experiments are used to understand the quantum

nature of light.

Talking about photons: emphasis on the model

character, esp. on the QED model (Jones, 1991),

defining photons as elementary excitation of the

electromagnetic field.

2.3 The new curriculum

Modern quantum technologies, such as quantum

computing, quantum cryptography and so forth, exploit

the control and manipulation of individual quantum

objects, e.g. single photons. As an introduction to the

teaching concept, a self-developed explanatory video is

shown (Donhauser, Bitzenbauer & Meyn, 2020). The

explanatory video motivates to deal with quantum

objects and phenomena using the examples of quantum

computers and data security and thus incorporates the

significance of quantum technologies for the students’

lives from the very beginning: The importance of data

security is discussed with the students beforehand and the

influence of quantum physics on data security is

addressed in the explanatory video.

In order to lay the foundations for understanding

modern quantum technologies with the students, the

Erlanger concept deals with the essential traits of

quantum physics (Küblbeck & Müller, 2003) using single

photon experiments in interactive screen experiments

(Bronner et al., 2009) based on the experiment from the

publication of Grangier et al. (1986).

Requirement from literature review (chap. 2.1)

Implementation in the new concept with/by…

1. Integration of modern quantum physics

Single photon experiments leading to a QED model of

photons

2. Detach quantum physics from classical mechanics

Introduction into quantum physics from classical optics

3. Explain characteristic traits of quantum physics with

real experiments, simulations or animations

Providing interactive screen experiments and adaptable

working material

4. Emphasis on importance of quantum technologies

Starting point data security / quantum computers

Tab. 1. Requirements for a new teaching concept on quantum physics derived from literature and their implementation in the

Erlanger concept of quantum physics.

Bitzenbauer & Meyn 43

With this experiment, the indivisibility of photons

(anti-correlation effect) as well as single photon

interference can be shown simultaneously. The results of

this experiment mean that the idea of the photon as a

localized particle must be dropped. In this way, a

transition from classical to quantum physics is made

possible.

The concept can be carried out in four lessons (90

min. each):

Chapter 1: Single photon detectors

Chapter 2: Preparation of single photon states

Chapter 3: Anti-correlation at a 50/50-beam

splitter cube

Chapter 4: Single photon interference.

Further details of the concept are published in

(Bitzenbauer & Meyn, 2020).

Fig. 1. Schematic experimental set-up of the experiment from

the publication by Grangier et al. (1986). The individual

components of the experiment are dealt with in the individual

chapters of the teaching concept.

3 DESIGN OF THE STUDY

3.1 Research questions

The new curriculum was formatively evaluated during

its development by means of acceptance surveys

(Bitzenbauer & Meyn, 2020a). For the summative

evaluation of the Erlanger concept, a mixed methods-

design is used. Different qualitative and quantitative

methods of empirical research are used to investigate the

learning effectiveness of the concept. However, our

research questions go beyond a mere learning gain:

Providing a modern picture of quantum physics at the

level of the upper secondary school is a central goal of the

Erlanger teaching concept of quantum physics. We are

therefore particularly interested in the conceptions of the

quantum world that are developed by students who are

introduced to quantum physics with this new curriculum.

By the term conception we mean representations and

notions that people give to phenomena or their underlying

patterns (Rickheit & Sichelschmidt, 1999).

In this article, we consequently address three research

questions:

1. Which conceptions about the quantum world do

students have who are introduced to quantum

physics with the Erlanger teaching concept?

2. Which types of learners’ conceptions about the

quantum world can be found?

3. Is it possible to make learners aware of the

importance of quantum technologies for their

everyday lives with the Erlanger concept?

3.2 Methods and participants

During the summative evaluation a total of 171

learners (12 classes of grade 11/12) were introduced to

quantum physics with the Erlanger concept. The

participants’ prior knowledge was controlled with the

help of a pre-test on declarative knowledge in quantum

physics. From the results of a post-test, it was found that

the students recorded significant increases in declarative

knowledge of quantum physics. These (and further)

findings are presented in (Bitzenbauer & Meyn, 2020b).

In order to address the above-mentioned research

questions, a random sample of N = 25 students out of the

total sample was interviewed after the intervention (15

male, 10 female). The interviews had a duration of 25 –

40 minutes and were scheduled as individual interviews.

The interview guideline was prepared according to the

requirements of a “good interview guideline” (Niebert &

Gropengießer, 2014) including the procedure to be

followed by the interviewer, as suggested by Bolderston

(2012):

keywords for a preamble in which

confidentiality and consent issues are addressed

with the participant,

questions on the agenda,

enquiry questions to help participants deepen

their answers and

a closing statement of thanks

Our guideline is the result of a multi-step development

process, including a pilot interview and expert discussion,

as recommended by McGrath, Palmgren & Liljedahl

(2019).

The interview questions provide insights into the

associations the learners have with quantum physics in a

number of ways. For example, the interviewees were

asked to describe what constitutes quantum physics for

them, they were supposed to distinguish between quantum

physics and classical physics, or they had to characterize

the quantum world.

3.3 Data analysis

3.3.1 Analysis carried out to answer research question 1

The students’ answers were evaluated on the basis of

deductive and inductive categories using qualitative

content analysis (Mayring, 2000). The definitions of the

five categories found are presented in table 2, including

Chapter 1

Chapter 3

Chapter 2

Chapter 4

44 Fostering students’ conceptions about the Quantum world

anchor examples. The coding off all students’ answers

was carried out by independent coders using a coding

manual with a high level of agreement (𝜅 = 0.84,95% −

𝐶𝐼 [0.68; 1.00]).

In this study, we consider a student to have a certain

conception if at least one statement was made during the

interview that could be assigned to the associated

category. In the process of coding, each category is treated

equally. Subsequent occurrences of the same category in

the transcript of one participant are not coded, since

repetitions of the same expression or the repeated use of a

similar explanation do not provide new insights into the

participants’ conceptions. Frequency analysis is applied

to count the occurrence of a category and helps to clarify

research question 1.

3.3.2 Analysis carried out to answer research

questions 2 and 3

As we are not only interested in isolated ideas

(discussed in research question 1) but also in the

underlying structure of students’ conceptions about the

quantum world, cluster analysis was conducted in order to

address research question 2. Cluster analysis is an

explorative method of empirical research to identify

groupings within a sample (Eshghi et al., 2011).

To conduct cluster analysis based on the qualitative

data from our interview study, the categories were used as

binary variables (0 = "Student did not address category

during the interview", 1 = "Student did address category

during the interview") because a published simulation

study provides evidence that hierarchical cluster analysis

and K-means perform well with dichotomous data (Henry

et al., 2015). In this research article, it was found that

hierarchical clustering can produce valid solutions with

samples as small as 𝑁 = 20 (ibid.).

1

This approach is justified by the fact that there is a lack of empirical

physics education research on learning modern quantum physics. As

there no research has been published on the learning processes in

Thus, hierarchical-agglomerative clustering methods

were used in this study to determine the optimal number

of clusters, namely using the Manhattan metric and

Ward’s fusion algorithm (Strauß & Maltitz, 2017). On the

basis of the cluster solution found using a dendrogram

(Backhaus et al., 2016; Denis, 2020), a partitioning K-

Means cluster analysis was used to classify clusters.

Interpreting cluster analysis results, we go along with the

suggestions provided by Henry et al. (2015) according to

which, for smaller samples (in our study 𝑁 = 25), the

solution with few clusters should be given priority over

the solution with many clusters, since “in addition to

taking parsimony into account, the assignment accuracy

is higher with fewer clusters, but can decrease rapidly as

the number of clusters increases” (ibid., p. 1014).

It is noteworthy that in this study, the cluster analysis

neither leads to generalizable results, nor is it conducted

with the aim to yield valid types of students' conceptions

about the quantum world. Instead, clusters that are

interpretable in terms of content yield preliminary groups

of students with similar conceptual structures regarding

the quantum world. Thus, they may function as a starting

point for further investigations. In subsequent studies with

larger samples and quantitative approaches, the findings

of this first exploratory investigation will have to be

validated

1

.

A discussion of the results of our exploratory study

against the background of published literature is presented

in chapter 5 of this paper. This supports the approach and

offers a first justification for the students’ conceptions

found.

this field yet, explorative approaches are necessary to open up the

field.

Category

Definition

Anchor example

Continuous transition to ever

smaller objects [ContTrans]

(Wiesner, 1996)

Text passages that refer to micro-objects

or the "smallest"

"When I think of the quantum world, I imagine [...] a

fairly empty space that only contains a few small [...]

particles, quantum objects."

Quantum world as a world of

dualism / the model

description [Dualism]

(Wiesner, 1996)

Text passages that make clear that the

quantum world requires a model

description.

"The quantum world is difficult to put into words,

simply because we can only make it imaginable

through models, whereby none of these models really

applies [...]."

Quantum world as a world of

effects or facts that do not

appear in the classical world

[Quaneff]

(Wiesner, 1996)

Relate effects or facts that exist in the

quantum world but not in the classical

world (e.g. quantum randomness,

anticorrelation, quantization, ...).

"[...] really the quantum randomness, that it is simply

completely random and you can't say in advance [...]

what will happen next, because that [...] is completely

random and not like in the real world.”

Quantum world with

opportunities for technology

and research (new)

[TechnRes]

Text passages that relate to quantum

physics and its potential for technology

and research, e.g. Quantum computers.

"With [...] quantum physics and technology, we can

also develop these quantum computers so that we can

[...] calculate a little faster with them and [...] create a

better view of all of our data."

Quantum world as a world

without concrete

imaginability (new)

[Unimaginable]

Text passages that refer to the fact that

the quantum world and / or its elements

cannot be imagined visually.

"In the classical world [...] everything has a position

and for everything you can imagine what it looks like,

and in the quantum world that's just not the case, so

you couldn't say what a photon really looks like [...]."

Tab. 2. Categories that were used to analyze the interview data. In brackets we indicate an acronym for the categories, respectively.

Bitzenbauer & Meyn 45

4 RESULTS

4.1 Results of qualitative content analysis

The most common category was Quantum world as a

world of effects or facts that do not appear in the classical

world [Quaneff]. 68% (17 of 25) of the respondents

named aspects such as quantum randomness, anti-

correlation or non-locality to define what constitutes the

quantum world for them (see figure 2). It is noticeable that

48% (12 of 25) of the students described quantum objects

in the sense of a replica concept and also spoke about them

in that way (Continuous transition to ever smaller objects

[ContTrans]), but that 56% (14 of 25) of the respondents

also expressed the need for restrictions: One cannot

imagine quantum objects as classical particles (Quantum

world as a world without concrete imaginability

[Unimaginable]). At least 24% (6 out of 25) of the learners

made statements for both categories at the same time, e.g.:

I: “[...] What actually is quantum physics, what

defines quantum physics and the quantum world

for you, what would you say?”

B20: “Yes, I think [...] the working with the, I

say, the smallest parts that you can imagine, or

that you actually can't imagine [...] so, […] those

smallest sub-components of the smallest

components, so to speak”

In 48% of the cases (12 out of 25) respondents made

statements that fall into the categories [Quaneff] and

[Unimaginable], and so it can be assumed that these two

conceptions seem not to occur independently of one

another. That means: Learners who characterize the

quantum world via quantum effects are also often aware

that quantum objects cannot be assigned a shape in the

classical sense.

At least 28% (7 out of 25) of the respondents stated

that quantum theory provides potential for technology and

research. The respondents referred to quantum computers

and cryptography in particular:

I: “[...] Then I would say we are about to start

and my first question would be that you could

please describe what the quantum world actually

means for you.”

B9: “I remember quite well the introduction to

the topic, that of data security and quantum

computers, and that's why I believe that quantum

physics will actually be our future too, that at

some point we can no longer be without it. And

the understanding behind it.”

Such considerations indicate the student’s awareness

of the importance of quantum physics for modern

technologies today, and especially for the future. In order

to get a more precise overview of the types of students’

conceptions that arose from the introduction of the

Erlanger teaching concept of quantum physics, it must be

analyzed which categories apply particularly frequently

synchronously with learners. This was investigated using

cluster analysis.

Fig. 2. Percentage of respondents making statements that fall into the respective category.

46 Fostering students’ conceptions about the Quantum world

Tab. 3. Summary of the three clusters on the students' conceptions about the quantum world and quantum physics. Numbers shown are

those of learners per cluster (#Students) and the percentage (rounded) of respondents within the cluster who made statements in their

responses that can be assigned to the respective categories.

4.2 Results of cluster analysis

In a first step, the results of the coding of all student

responses were subjected to a hierarchical-agglomerative

cluster analysis using Manhattan metrics and Ward's

fusion algorithm (3.3.2). Taken together, the dendrogram

(see figure 3) and the arguments in terms of content led to

a 3-cluster solution. A partitioning K-Means cluster

analysis was calculated on the basis of the cluster solution

found.

If one compares the statements of the respondents

within the clusters with those of the total sample, striking

differences between the clusters are revealed. These

enable the content description of the extracted

imagination types (see chapter 5).

Table 3 therefore shows which percentage of the

respondents of each cluster made statements that can be

assigned to the respective categories.

In figures 4-6, we also show this graphically in

comparison to the distribution within the total sample, i.e.

in comparison to the results from figure 2. In the next

chapter, we give an interpretation of the clusters and

discuss the results with previous findings from physics

education research.

Cluster

# Students

[ContTrans]

[Dualism]

[Quaneff]

[TechnRes]

[Unimaginable]

1

11

0%

19%

100%

27%

64%

2

4

50%

25%

0%

100%

25%

3

10

100%

30%

60%

0%

60%

Fig. 3. Dendrogram with the three clusters.

Fig. 4. Comparison of response behavior of students from cluster 1 with the total sample.

Bitzenbauer & Meyn 47

5 DISCUSSION

5.1 Research question 1

We carried out an interview study with N = 25

students. These were introduced to quantum physics with

the Erlangen teaching concept for quantum physics (see

Chapter 2) and had no prior knowledge. A goal associated

with the new teaching concept was to emphasize the

importance of quantum physics and its technologies. In

this way, a contribution to the learning of quantum

physics should be made.

Based on the interview data, we found five categories

among the student responses, which can be found in Table

1. These ideas do not arise independently among the

learners, as we have seen for the two concept categories

[Quaneff] and [Unimaginable] and from the results of a

cluster analysis.

5.2 Research question 2

Using cluster analysis, we extracted three types of

student conceptions about the quantum world (chapter

4.2). In this discussion. we intend to give an interpretation

of these clusters.

Cluster 1 – Primarily elaborate conception

Students in this cluster characterize the quantum world

in 100% of the cases via effects or aspects that do not exist

in classical physics, for example with a lack of

determinism or anti-correlation. None of the learners in

this cluster talks about quantum objects as “smallest

particles” in the classical sense. Instead, seven of the

respondents in this cluster explicitly emphasize that

quantum objects cannot be compared with objects from

classical physics, and that a visual illustration may

therefore be allowed, but must not be confused with

reality. 27% (3 out of 11) of the learners in this cluster

Fig. 5. Comparison of response behavior of students from cluster 2 with the total sample.

Fig. 6. Comparison of response behavior of students from cluster 3 with the total sample.

48 Fostering students’ conceptions about the Quantum world

include the importance of quantum physics for technology

and research in their answers, e.g.:

I: “My first question to you is, why don't you just

describe in principle what quantum physics is for

you.”

B2: “For me, quantum physics cannot be

described with things from our world, because

you might think of things in our reality in

miniature, but it's not that simple. So in our

world there are laws that are practically

different in quantum physics.”

I: “Can you describe a little more precisely what

you mean when you say that you can't just make

things smaller?”

B2: “Yes, e.g. in our classical world every object

has a place; that is not the case in the quantum

world. Electrons and photons do not have a fixed

location, so they are not localized and [...] you

can actually only measure them with such a

detector.”

In this cluster, 11 of the students are incorporated,

which corresponds to 44% of the total sample. 60% (6 out

of 10) of all females have such elaborate ideas about the

quantum world, but only a third of males (5 out of 15).

Cluster 2 – Quantum world as the world of technology

Students in this cluster characterize the quantum world

in 100% of the cases through its importance for

technology and research, for example, in relation to

quantum computers or quantum cryptography. None of

the learners in this cluster express thoughts that

specifically relate to quantum effects, but 50% make

statements that speak in favour of the continuous

transition to “smaller and smaller particles”. Only one

student in the cluster explicitly emphasizes that quantum

objects cannot be compared with objects from classical

physics and that a visual illustration may therefore be

allowed, but must not be confused with reality. One

example for a student from this cluster is B9:

B9: “So for me, these are just the smallest

particles that still determine our whole world

and our lives, including technology. So quantum

particles are e.g. even electrons and nowadays

without electricity you can tell that you can't do

anything. Or when you think of data security and

quantum computers, I already think that

quantum physics will be our future [...]”

In this cluster, 4 of the learners are incorporated,

which corresponds to 16% of the total sample. 20% (2 out

of 10) of the females in this cluster have such ideas about

the quantum world, and 13% of the males (2 out of 15).

Cluster 3 - Quantum world as a classical world on a small

scale

Students in this cluster characterize the quantum world

in 100% of the cases using a clearly articulated notion of

scaling. They think of quantum objects as the "smallest

particles" that are "too small to be seen" and are the

“components of the smallest building blocks”. These

associations of quantum physics to small particles

indicate a misunderstanding of quantum physics, but it

should be emphasized that this does not always go hand

in hand with the idea of quantum objects as classical

“particles”. At least 60% (6 out of 10) of those surveyed

in this cluster even emphasize that pictorial

representations of quantum objects are not adequate.

None of the learners in this cluster express thoughts that

specifically relate to the importance of quantum physics

for technology and research. An example of one of the

students’ answers is the following of B11:

I: “And now I would just ask you, what makes the

quantum world for you.”

B11: “Well, it's all pretty small. [...] When I think

of the quantum world, I just imagine a pretty

empty space with just a few small particles,

quantum objects.”

I: “So what makes the difference between the

classical world and the quantum world for you?”

B11: “[...] That we just can't really say anything

because as soon as we try to read it, the property

changes. The classic world is a little more

robust.”

In this cluster, 10 of the test persons are incorporated,

which corresponds to 40% the total sample. Only 20% (2

out of 10) of all females have such ideas about the

quantum world, but at 53%, more than half of the males

do (8 out of 15).

5.3 Research question 3

11 of the 25 test persons can be assigned to cluster 1,

which combines the most elaborated view on the quantum

world. Four more students can be sorted into cluster 2.

The conceptions of these students are predominantly

influenced by the importance of quantum physics for

technology. Taken together, 15 of the 25 students develop

conceptions about the quantum world that seem to be

detached from classical ways of thinking mainly. From

these results, one might deduce that introducing learners

to quantum physics with the help of the Erlanger concept

can successfully promote elaborate conceptions of the

quantum world, and especially create an awareness of the

importance of quantum technologies for the everyday life

of learners today and in the future. However, in order to

finally clarify this research question, more suitable

instruments and quantitative study designs must be

chosen, as already indicated in chapter 3.3.2.

5.4 Comparison of the results with literature

on students’ conceptions of the quantum

world

Using data from a questionnaire survey of physics

students on quantum physics, Ireson (1999) conducted a

cluster analysis and was able to identify three types of

students’ conceptions of quantum physics. These clusters

were labelled quantum thinking, intermediate thinking

and mechanistic thinking. As an example of mechanistic

thinking, Ireson (ibid., p. 197) specifies the students’

imagination of the photon as a small, spherical entity. On

Bitzenbauer & Meyn 49

the other hand, the imagination of the photon as a “’lump'

of energy transferred into or out of the electromagnetic

field” represents an example of quantum thinking for

Ireson (ibid., p. 197). These three levels in the learners’

conceptions between classical thinking to quantum

thinking are repeatedly reported in further articles, with

only the naming of the three types varying (Ke et al.,

2005).

The three clusters of students’ conceptions about the

quantum world extracted in this article using data from an

interview study fit into this scheme: Cluster 1 “Primarily

elaborate conception” can, for example, be well

associated with Ireson's (1999) cluster quantum thinking

in terms of content: While students in this cluster

characterize the quantum world by quantum effects

[Quaneff] (100%, 11 out of 11) or the lack of a visual

representation of quantum objects (64%, 7 out of 11,

category [Unimaginable]), scaling conceptions or particle

notions are not expressed (0%, 0 out of 11, category

[ContTrans]) by these students.

Students of cluster 2 “Quantum world as the world of

technology” may be associated with the intermediate

thinking in the regime of Ireson (1999). While all four

students in this cluster describe quantum physics in terms

of its potential for technology and research (category

[TechnRes]), particle conceptions are not entirely absent

here (50%, 2 out of 4, category [ContTrans]). Of course,

a larger number of participants and different instruments

would be necessary to validate this type of imagination

(chapters 3.3.2 and 5.5).

Cluster 3 “Quantum world as a classical world on a

small scale” can, consequently, be associated with

Ireson's (1999) cluster mechanistic thinking: all of the 10

students in this cluster remain in classical imaginations,

e.g. thinking of quantum objects as the "smallest

particles" (100%, 10 out of 10, category [ContTrans]).

Thus, a successful conceptual change towards quantum

thinking cannot be observed in the context of our

interview study for students in this cluster.

Furthermore, the results of Wiesner’s (1996) interview

study with 𝑁 = 27 students from secondary school into

differences between classical objects and quantum objects

can directly be compared with the types of conceptions

reported in this article, as for the category system used in

our interview study, we resorted to categories by Wiesner

(1996). There are certain similarities between the results

reported then and the results of the interview study

reported here but also differences: If one summarizes

statements on energy quantization, Heisenberg’s

indeterminacy relation, the property location of quantum

objects, as well as effects that only occur in quantum

physics, as the category quantum effects, 49% of

Wiesner’s respondents fall into this category, as cited in

Müller (2003, p. 22) - this percentage is higher in the

investigation reported here (68 %). In addition, in this

study, the category Quantum world with opportunities for

technology and research [TechnRes] is one that was not

documented in the study by Wiesner (1996), but with

regard to which 28% of the respondents make statements

here.

In both studies, around a quarter of the respondents

describe dualism, i.e. the need for model descriptions, as

the central difference between classical physics and

quantum physics: 26% of the respondents in Wiesner’s

study, as cited in Müller (2003, p. 22), and 24% of the

participants in the study presented in this article.

In summary, the results of the cluster analysis reported

in this article fit well with previous findings from physics

education research – this contributes to the justification of

the results presented in this study. Although the clusters

found can still only be described as preliminary types of

students' conceptions about the quantum world, the results

indicate that fostering quantum thinking could be

promoted by introducing learners to quantum physics

with the Erlangen teaching concept (cf. chapters 5.2 and

5.3). However, in order to draw more valid and reliable

conclusions of this kind, certain limitations must be

tackled in subsequent studies.

5.5 Limitations

To assess the results reported in this paper, the

following note is essential: Each of the five categories

presented in table 1 was coded dichotomously for each

student. If several statements were made that are suitable

for assignment to the same evaluation category, they were

still only coded once, since repetitions of the same

expression or the repeated use of a similar explanation do

not provide new insights into the participants’

conceptions (chapter 3.3.1). For each respondent, it can

only be determined whether or not statements were made

that fall into the corresponding categories. If the

respondent did not make any statements that could be

assigned to category X, it must not be concluded from this

that the respondent does not have the idea X – he/she

simply did not express it. To minimize the likelihood of

learners’ conceptions remaining unarticulated during the

interview, we used the procedure of internal triangulation:

we referred to the same aspects at different points during

the interview, increasing the chance that learners would

express all their ideas about the topic during the interview.

This is an accepted procedure to ensure validity in

interview studies (Niebert & Gropengießer, 2014). A

solution that could better differentiate between the various

manifestations of several students’ conceptions could lie

in using a questionnaire with different items concerning

the quantum world, where participants can indicate their

agreement or disagreement on a rating scale, as it was

done in various studies on similar topics (Ireson, 1999;

Ubben & Heusler, 2019). However, in order to develop

suitable items for such a questionnaire, a deeper insight

into students’ conceptions on the topic is required. Thus,

we argue that while this must be desirable for subsequent

investigations, an exploratory approach, as presented in

this article is suitable to open up the field.

Taking into account all the above-mentioned points,

the types of students’ conceptions extracted by cluster

analysis in this article are not to be understood as fixed,

strict types, but rather as preliminary imagination

patterns. Of course, this applies not least because the

sample size of 𝑁 = 25 does not allow generalized

conclusions.

50 Fostering students’ conceptions about the Quantum world

6 CONCLUSION

In this article, we presented the results of an interview

study. We surveyed conceptions about the quantum world

of 25 students from 11th and 12th grade of German

secondary schools who were introduced into quantum

physics with the Erlanger teaching concept. The presented

results provide implications for both classroom practice

and future research. For classroom practice, the Erlanger

teaching concept serves as a proposal to bridge the gap

between quantum physics and the everyday life of the

learners. In addition, the results of the interview study

presented in this paper make a contribution to the

empirical research on students’ conceptions about

quantum physics. Not only do we find individual,

independent conceptions of learners, but we also show

that there are dependencies between them so that we are

able to extract types of conceptions. The extraction of

such types of student conceptions for various further

concepts of quantum physics will be part of future

research and could contribute to our understanding of

learning processes in quantum physics.

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