Jesper Haglund, Fredrik Jeppsson
Using self-generated analogies in teaching of thermodynamics
Abstract
Introduction
Many concepts in thermodynamics are considered to be abstract concept and difficult for
novices to grasp. This is particularly the case for the concept of entropy. Sears (1944, p. 447)
claims that: ”There is no concept in the whole field of physics which is more difficult to
understand than is the concept of entropy, nor is there one which is more fundamental.” He
adds: “It has been said regarding some of the equations of thermodynamics, ‘Experience
indicates that it is much less difficult to use [certain] formulae than to understand them’. The
same may be said of the entropy concept; it is much less difficult to use it than to understand
it.”
One common approach to introduce abstract concepts in science education is to use analogies.
Gentner’s Structure Mapping Theory (1983) has been used extensively in science education
research to account for the nature of analogical reasoning. The purpose of teaching with
analogies is that the students are going to learn about a new domain by comparison with
another, more familiar domain. Conclusions are made with regards to the familiar context and
transferred to the taught context. In Gentner’s view, analogical reasoning depends on
structural similarities between the domains. As an example, ‘the atom is like a solar system’ is
an analogy where the abstract, invisible and presumably less familiar atomic structure is
compared to the more concrete and familiar domain of celestial bodies in motion. Structural
similarities are that electrons correspond to planets, which orbit around a larger atomic
nucleus and star, respectively, and that there is a large void space in between. Also the
mathematical formalism in Newton’s gravitational force and Coulomb’s law can be
compared, where electrical charges correspond to the mass of objects and the forces are
proportional to the inverse of the distance squared. However, attributes or surface features
should not be focused upon, such as drawing the conclusion that since the sun is yellow and
warm, so is the atomic nucleus.
Since an analogy is a representation of a phenomenon, where certain characteristics are
emphasised and other are played down, it is never a perfect image. There is a point where the
analogy breaks down, where conclusions from the source domain are not valid for the target
domain. As an example, the solar system as an analogue model of the atom structure does not
provide useful explanations from a quantum physics point of view. Spiro, Feltovich, Coulson
and Anderson (1989) argue that one way of handling the idiosyncratic features of individual
analogies is to present multiple analogies which complement each other. Heywood and Parker
(1997, p. 883) take a different perspective on the breakdown of analogies and argue that it
contributes to conceptual understanding, but also gives an authentic view of the scientific
enterprise: “[I]t is in the promotion of the critical scrutiny in challenging the analogy,
attempting to apply it and recognising when and why it breaks down that the opportunity for
learning really takes place.” They also show that an analogy where many corresponding
concepts are identified in the source and target domains produces a rich discussion.
In our interpretation, while analogies use explicit comparisons between the structures of the
concepts in the source and target domains, metaphors are more implicit and primarily
focusing on language. For instance, in thermodynamics teaching, the metaphor ‘entropy is
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Jesper Haglund, Fredrik Jeppsson
disorder’ is often made explicit by use of an analogy where a thermodynamic system and its
particles are compared to a messy room with its toys and pieces of clothing.
Blanchette and Dunbar (2000) have reviewed experimental studies of problem solving where
subjects are presented with problems in different domains but with similar underlying
structures, so that they would be suitable for analogical reasoning. However, the subjects tend
to focus on surface similarities, and fail to recognise the intended structural relations. This
may be contrasted with our everyday life, where analogical reasoning based on shared
structures often is used spontaneously. For instance, Clement (1987, 1988) has found that
scientists and students spontaneously come up with analogies in problem solving.
Spontaneous and self-generated analogies
The discrepancy between our spontaneous use of analogical reasoning and failure to recognise
structural relations in taught analogies may seem as a paradox. Blanchette and Dunbar (2000)
explain this discrepancy by contrasting a reception paradigm with a production paradigm. In
the reception paradigm, learners are supposed to receive an already existing analogy and
interpret and use it in an intended way. This brings along two challenges: firstly, that the
subjects are supposed to have in depth knowledge of the source domain, and secondly; that
they have to identify the similarity of the domains. In the production paradigm, on the other
hand, the learner him- or herself creates or generates analogies in order to organise what is
known about a studied phenomenon. By default, the source domain and how it is linked to the
target is grasped by the learner, otherwise it would not be considered as useful. We regard
spontaneous analogy as the use of analogy when exploring a new area spontaneously, without
being cued by a teacher or researcher. Self-generated analogy is the generation of a new
analogy, by request from a teacher or researcher. Pittman (1999) notes that the teaching by
analogy has been proposed by using argumentation along the lines of constructivism, with the
basic assumption that learning can take place only in relation to the pre-existing knowledge of
the learner. In spite of this constructivist stance, most studies in science education research
have been done on teacher-generated analogies, where the students’ previous knowledge is
only assumed implicitly. However, some studies have been performed on the use of
spontaneous or self-generated analogies in teaching, which seems to be a more natural fit with
the perspective of constructivism:
Middleton (1991) presented the strategy of requiring students to generate their own analogies
in biology teaching. By first coming up with analogies that make sense and later analogies
that seemingly do not, the students build skills in critical thinking and problem solving.
Wong (1993a, 1993b) performed an experimental study on 11 secondary school teacher
candidates who were asked to explain three air pressure phenomena, formulate areas where
their explanations were inadequate and come up with self-generated analogies as a tool to
attain a better understanding.
Cosgrove (1995) observed students at age 14 who studied the electric circuit, with the
intention that the students should devise a theory by means of analogical reasoning based on
two analogies provided by the teacher. One main issue was to address the belief that
electricity is consumed in the circuit. However, before the teacher presented the prepared
analogies, one student came up with another analogy: that the electric circuit is like a train
carrying coal. This spontaneous analogy was used throughout the teaching covering several
lessons. As more complex circuits were introduced, the analogy was modified through testing
ideas in discussions among the students to fit the phenomena.
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Jesper Haglund, Fredrik Jeppsson
Mason (1995) performed a study on a class of fourth graders, where the children were
introduced to three phenomena related to air pressure and instructed to generate analogies
through collaboration in small groups and full class discussions. The first set of analogies
were quite close to the studied phenomena and affected by the students’ alternative
conceptions, such as ‘water is like glue’ as an explanation for why a piece of cardboard sticks
to a glass filled with water when turned upside down. After studying the phenomena one by
one, the children were asked to look for similarities between them. As a conclusion: “It is
noteworthy that the more the children approached the scientific explanation of the
phenomena, the more they were able to recognize the structural similarity between the
three…” (p. 20).
Pittman (1999) performed a study on students in grade 7 and 8, who took a unit on protein
synthesis in regular science class during two weeks. After one week of regular instruction and
introduction to analogies, the students worked in groups of three or four to create own
analogies for protein synthesis. A majority of the analogies used sources from non-science
domains. As a conclusion, student-generated analogies were seen as a useful tool for
assessment of students’ conceptions and for formative assessment.
Blanchette and Dunbar (2000) performed a study on analogical reasoning, where the issue of
achieving zero budget deficit in financial politics was the target domain for learning.
Undergraduate students were found to be able to generate their own analogies that focused on
the relational structure, rather than on surface similarities. The result was the same after both
individual and group exercises.
Mayo (2001) compared teaching with teacher-generated analogies, student-generated
analogies and a no analogy set-up in a collage course on developmental psychology. The
teacher-generated analogy group was provided a set of common analogies, such as human
development is like climbing a staircase, which were matched with developmental theories
and discussed in class. The student-generated analogy group was instructed to generate own
analogies, which were criticised in class discussions, while the no analogy group read
additional texts on the topic. In multiple choice tests, the student-generated analogy group
performed significantly better than the teacher-generated analogy group, which in turn,
significantly outperformed the no analogy group.
Enghag and Niedderer (2005) performed a study on upper secondary school students working
with two week mini-projects in physics. A group of four girls chose to design a demonstration
of series and parallel electric circuits for lower secondary school students. In their work, they
expressed bewilderment regarding the observation that all light bulbs in a series circuit shone
with the same strength. This reflects a well known misconception about circuits: that current
is consumed as it goes around the circuit. They managed the situation by coming up with a
crocodile analogy, where positive and negative charges correspond to boys and girls at the
opposite banks of a river trying to reach the other side. First they said that crocodiles that eat
the children correspond to resistance. In order to explain the equal brightness of the bulbs,
however, they changed the explanation so that the children are not eaten by the crocodiles, but
the role of the resistance is to slow down the speed. Hence, there are fewer electrons going
through the bulbs per second.
James and Scharmann (2007) performed a treatment/control group study on a course on
methods for teaching science for preservice elementary teachers. The treatment group
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Jesper Haglund, Fredrik Jeppsson
participated in two class periods, where they were introduced to generation of analogies. They
were also asked to find analogies for rocket propulsion in order to explain Newton’s Third
Law in group exercises and to construct practice lessons based on the analogies. The control
group participants were taught to develop explanations by eliciting students’ ideas prior to
teaching, which was used to develop lessons for force and motion concepts in group
exercises. The outcome on conceptual understanding of Newtonian mechanics, as measured
by pre- and post-tests, using the Force Concept Inventory developed by Hestenes, et al. (1992)
was worth noting: “[A] remarkable difference in posttest measures of Newtonian conceptual
understanding was found as a result of two extremely brief demonstration lessons that were
presented to the treatment group to highlight the use of pedagogical analogies (James &
Scharmann, 2007, p. 581).”
In spite of these promising findings, Clark (2006) is cautious that in such constructivist
teaching, students spend too much time on their idiosyncratic explanations, rather than
building a conception in line with the position in science.
Ownership of learning
Enghag, Gustafsson and Jonsson (2009) presented small-group work with content-rich
problems, “open-ended physics problems related to everyday life situations that lack some
information” (p. 455), as an approach to make students assume ownership of learning. Group
ownership of learning is characterised by choice and control of the task, which is manifested
in exploratory talk, where “students have subject-mattered focused talk and use language in
an exploratory fashion, such as questioning, challenging, and encouraging” (p. 457).
Individual ownership of learning relates to individual students’ commitment to their own
questions in the group discussion and to their gradual development of insight.
Learning of thermodynamics and entropy
Baierlein (1994) suggests that there are generally two approaches to teach introductory
thermodynamics and therefore, the concept of entropy. On the one hand, a historical and
macroscopic approach can be adopted that focuses on properties of cyclic processes and, in
line with Clausius, introduces entropy as a state function in relation to these processes. This
provides good opportunities for problem solving in engineering, but a limited understanding
of the nature of entropy. On the other hand, a microscopic approach involves the introduction
of a system-particle model and microstates that uses Boltzmann’s statistical approach. Here,
the challenge is how to proceed from the abstract physical model to macroscopic applications.
For instance, Reif (1999) argues in favour of a microscopic, atomistic, approach and
emphasises the need to understand the underlying mechanisms of physical phenomena. In
addition, he points out the difficulty among students to build visualizable mental models with
a macroscopic approach. In contrast, Kautz, Heron, Shaffer, & McDermott (2005) claim that
students tend to apply microscopic models in inadequate ways, and propose that concepts
have to be firmly understood in macroscopic contexts first, using for example bicycle pumps.
Several metaphors and analogies are used in teaching about entropy, among these seeing
thermodynamic phenomena as a waterfall, along the lines of Carnot’s reasoning (e.g. Fuchs,
1987; Kaper & Goedhart, 2005), and as a messy room, where disorder corresponds to high
entropy.
In previous studies, we have shown that the word entropy and words commonly used as
sources in metaphors for entropy have many senses. This semantic ambiguity adds further to
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Jesper Haglund, Fredrik Jeppsson
the challenge of learning abstract concepts, such as entropy (Haglund, Jeppsson, &
Strömdahl, 2010; Jeppsson, Haglund, & Strömdahl, 2010).
Purpose of research
This article is part of an ongoing investigation of how self-generated analogies may be used to
express and develop the understanding of thermal phenomena among university students,
particularly of the concept of entropy. In a separate article, we have described six challenges
that students encountered when they generated own analogies for two thermodynamic
processes and how they confronted these challenges (Jeppsson & Haglund, In progress).
In the present study, we aim to explore how the use of self-generated analogies may be used
to express and develop the understanding of thermal phenomena.
Method
Participants
The participants were eight student teachers (N = 8), specialising in mathematics and physics
teaching at upper secondary school, at the fourth year of the teacher education program at a
Swedish university. Previously, they had taken courses in maths and maths teaching for one
year and a half. In the weeks before the study, they had all taken a course in mechanics and
thermodynamics, including a brief introduction to particle models in the kinetic theory of
gases and the concept of microstates by use of University Physics (Young, Freedman, &
Sears, 2003), but not an in depth account of statistical mechanics including the connection
between energy levels and microstates. The participants were familiar with each other and
used to work together. The study was not part of the standard coursework and the student
teachers volunteered freely, but received a small token of appreciation for the participation.
Data collection
The participants were given a short introduction by the researchers on the use of analogies in
teaching and two processes representing thermal phenomena were presented: reversible,
adiabatic expansion of an ideal gas, and; free, adiabatic expansion of an ideal gas. The student
teachers were provided with the rather extensive descriptions given in Figure 1 and Figure 2
in writing.
Process 1. Adiabatic expansion
An ideal gas is kept in a container by a frictionless piston. The gas has amount of substance n,
temperature T, internal energy U, pressure p, volume V and entropy S. Let the gas expand slowly,
adiabatically (i.e. no heat Q is exchanged with the environment) and reversibly (i.e. so that the process
“can go in the other way” to restore the original state) by retracting the piston. As the piston retracts,
work W is performed by the gas on the environment, which means that the internal energy U of the gas
decreases. At the same time, the volume V increases and the pressure p decreases. The temperature T
decreases. The average velocity of the gas particles decreases, because they will have a lower velocity
after collisions with the withdrawing piston. The entropy does not change during the process, since no
heat has been exchanged with the environment and the process is reversible, a situation represented by
the following relation: dS = dQ/T.
Fig. 1. Description of the adiabatic, reversible expansion given to the student teachers.
Process 2. Free expansion
An ideal gas is kept in one half of an isolated container separated by a thin wall. There is a vacuum in
the other half. The gas has amount of substance n, temperature T, internal energy U, pressure p, volume
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Jesper Haglund, Fredrik Jeppsson
V and entropy S. After the instantaneous removal of the wall, the gas expands freely in the entire
container. No work W or heat Q is exchanged with the surroundings, and hence, the internal energy
remains constant. As a result, the volume of the gas is doubled and the pressure is halved. Since the
particles collide with the stationary walls, their average velocity does not change. The temperature T is
constant, but the entropy S increases.
Fig. 2. Description of the adiabatic, free expansion given to the student teachers.
The intended level of the descriptions was that they should bring across what happened in the
processes, by the use of terms familiar to the student teachers, but leave as a ‘stretched target’
for the subjects to figure out how and why it happened. As a hypothesis, we expected that it
would be challenging for the student teachers to account for why the entropy remains
unchanged in Process 1, in spite of increased volume. In Process 2, the main challenge for
them was expected to be explaining why the temperature remains the same, even though the
volume increases. The design of the task adheres to the instructional tactic of completion
problems, where the participants are supposed to fill in a gap on the way to a given end state,
in combination with high contextual interference in the form of comparisons between source
and target domains in group discussions (van Merriënboer, Shuurman, de Croock, & Paas,
2002).
The participants were divided in two groups of four in each, S1, S2, S3 and S4 in Group A
and S5, S6, S7 and S8 in Group B. The student teachers were given the instructions to
establish a shared view on the processes within the group and identify what is difficult to
understand. They were also instructed to come up with analogies for the processes, with a
particular emphasis on entropy, and select a few of them for presentation to the researchers
and to the other participants. This group work section lasted for one hour and the researchers
were not present, except for short check-ups on the progress.
For half an hour, the groups presented the selected analogies and gave feed-back to each
other. After the presentations, the groups got a hint from the researchers that microstates
relate not only to spatial configuration of particles, but also to energy states, since this was
perceived by the researchers as a necessary input for further progress.
Next, the participants reassembled in the original small groups to modify the analogies or
come up with new ones, based on the feed-back from the researchers and the other group.
Finally, everybody gathered for a round-table discussion on how analogies can be used in
education, assuming a teacher perspective.
In all, the exercise took three hours and the sessions were audio and video recorded.
Data analysis
The audio records were transcribed. In addition, the coding and analysis was managed
through using the MAXQDA (2010) software. Quantitative measures, such as the number of
concepts and challenges covered by each analogy were analysed in Excel pivot tables.
We followed the approach of Blanchette and Dunbar (2000) in analysing the following
dimensions of the generated analogies:
• Degree of similarity between source and target. We used the following categories for
the source domain: anthropomorphic; dead objects, and; physics.
• Structural depth. To discern between different relational structures, we used Gentner’s
(1983) distinctions between attributes, first-order relational structure and higher-order
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Jesper Haglund, Fredrik Jeppsson
•
relational structure. Attributes are statements only taking in one argument and
focusing on surface similarities. In the example ‘the hydrogen atom is like our solar
system’, attributes would be that the sun is yellow or hot. First-order relational
structures are comparable to a causal reasoning, e.g. if X thus Y. Higher-order
relational structures are characterized by several interrelated concepts, e.g. if X, given
that Y and Z fulfil certain condition, then W. When we analysed the depth of relational
structure we also analysed the awareness of limitations and break-down of the
generated analogies.
The explicitness of the analogies were coded as: not developed, if only one utterance
with no explicit connection to the target was mentioned and not further elaborated;
implicit, for which no elements of the target were mentioned; partially explicit, if a
few elements stated in the source had counterparts in the target, and; explicit, if all (or
a large majority of the) elements stated in the source had an identified counterpart in
the target.
In addition, the following categories were used to code the analogies:
• Initiating group. Did group A or group B bring up the analogy? Separate records were
made if both groups came up with a similar analogy.
• Origin. Whether the analogies were originated by the group itself or provided
previously by teacher or from literature. Several analogies were explicitly taken from
the previous course on thermodynamics. Some other analogies may have been heard in
previous teaching, but without being mentioned in the group exercises.
• Process covered. Did the analogy correspond to the reversible and/or the free
expansion?
• Number of physical quantities covered in the analogy (e.g. entropy, number of
microstates and pressure)
• Number of other concepts covered (e.g. reversibility and the ideal gas law)
• Number of challenges (a combination of difficult issues, e.g. explaining the constant
temperature at free expansion, and misconceptions, e.g. the belief that collisions are
required to maintain the temperature)
• Number of statements. A statement is our smallest unit of text excerpt, corresponding
to verbal output from one individual person.
Six challenges with which both groups spent a lot of the time, such as grasping the concepts
of entropy and microstates and the constant temperature in free expansion, have been reported
in a separate article (Jeppsson & Haglund, In progress).
Apart from these dimensions, prior to the data collection, we were particularly interested in
looking at what senses of entropy (Haglund, et al., 2010) the groups focused on. Did they
assume a macroscopic perspective, a microscopic particle perspective or use the disorder
metaphor implicitly?
Results
General overview
Overall, the discussions in the two groups went on well and the teacher students came up with
many analogies for the two processes. In all, group A initiated the discussion of 20 analogies
(out of which four were not elaborated and are excluded in the further analysis) and group B
initiated 12 (one not elaborated and excluded).
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Jesper Haglund, Fredrik Jeppsson
As seen in table 1 below, about half of the analogies used by the groups focused on relational
structures, and not on attributes, a profile shared by both groups. Group A came up with more
analogies than B, but on average their analogies were slightly less elaborated, as can be seen
in the lower numbers of average concepts and challenges covered. Group B’s considerably
larger total amount of statements related to analogies reflects that they spent most of the time
elaborating one analogy (‘angry bees’, which covered 857 of the statements), while group A
spent more time of their group session on understanding the processes without relating them
to analogies.
Table 1
Group
Number of analogies - attributes
Number of analogies - first order
structure
Number of analogies - higher order
structure
Total number of analogies
Average number of quantities
Average number of other concepts
Average number of challenges
Total number of statements
A
8
B
6
5
3
3
16
2.4
0.4
0.9
622
2
11
2.7
0.9
1.7
1081
The analogies can be classified by origin as shown in Table 2. A majority of the analogies
were originated by the groups themselves, but 10 out of 27 were taken from previous
teaching. Interestingly, however, the groups elaborated the new, own analogies more than the
previously known analogies, as seen in the larger amount of concepts covered, the
qualitatively deeper structural level and the considerably larger amount of statements.
Table 2
Origin
Number of analogies - attributes
Number of analogies - first order
structure
Number of analogies - higher order
structure
Total number of analogies
Average number of quantities
Average number of other concepts
Average number of challenges
Total number of statements
By groups
8
From
teacher/literature
6
5
3
4
17
2.8
0.8
1.5
1506
1
10
2.1
0.3
0.8
197
In Table 3, data is shown by domains used as sources. The anthropomorphic and dead objects
domains are far from the thermodynamics processes studied, as are some of the physics
models (e.g. bouncing balls in space). The anthropomorphic domain stands out as the most
productive in generating higher order structure analogies. Particularly, the large number of
challenges touched upon shows the potential of rich discussions, but also indicates the risks of
overly complex models.
Table 3
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Jesper Haglund, Fredrik Jeppsson
Domain
Number of analogies - attributes
Number of analogies - first order
structure
Number of analogies - higher order
structure
Total number of analogies
Average number of quantities
Average number of other concepts
Average number of challenges
Total number of statements
Anthropomorphic Dead objects
1
6
Physics models
7
1
3
4
3
5
5.8
1.4
3.6
1266
0
9
1.6
0.3
1
145
2
13
2
0.5
0.5
292
Surprisingly, all analogies used a microscopic approach with sources that shared the structure
of components comprising a system or a whole. In addition, many of the analogies used the
idea of entropy as disorder, but the implicit nature of the metaphor makes it difficult to
quantify the extent of its use. However, none of the analogies was based on quantitative
relations between central macroscopic quantities. For instance, none of them is similar to
Carnot’s waterfall analogy, where extensive quantities (mass of water vs. entropy) and
intensive quantities (height vs. temperature) are compared and related quantitatively (by
multiplication). This microscopic approach was adopted in spite of the primarily macroscopic
focus of the previous course on thermodynamics.
Overall, both groups demonstrated the capability of coming up with more than one higher
relational structure analogy and several more first order relational structure analogies,
primarily from domains far from the studied phenomena.
Examples of analogies
In the section below, we present four analogies with which the teacher students spent most
time and elaborated to the greatest depth. In addition, they represent a large variety across
many of the different dimensions identified in the study, e.g. self-generated vs. teacher
generated analogies.
Angry bees
When group B began the work of coming up with analogies, S6 immediately suggested the
analogue model of angry bees in a can. The group spent the majority of the time in the group
work sessions on the analogy, as seen in the large number of statements, 857, and chose it for
their presentations. It covered the largest amount of quantities, other concepts and challenges
of all analogies provided by both groups. It was categorised as explicitly expressed, of higherorder relational structure and from an anthropomorphic domain. The category
anthropomorphic domain was chosen, since the bees were discussed as if having emotions
and a free will to act. The ‘angry bees’ analogy was only used to reflect the process of
adiabatic expansion.
The central characteristic of the bees is the angriness, which the group after some discussion
found to correspond to temperature in the thermodynamic model. The angriness is related to a
number of factors, such as the volume (the more crammed, the angrier the bees), the flight
speed (the angrier the bees, the faster they fly) and the frequency of crashing into each other
and the walls. In the following text excerpt, I6 tries to establish what angriness corresponds to
in the thermodynamic systems:
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Jesper Haglund, Fredrik Jeppsson
S6: But the angriness has to be the same as the temperature, right…?
S7: Yes, it has to be that…
S6: Internal energy…
S7: It could be pressure… but that also depends on the temperature…
S6: No, the pressure has to be the result of how many times they run into the walls. /…/
S5: …but then… it has something to do with volume… because, I mean… the less the volume, the
more…
S6: It depends on that… I just mean, exactly what is the angriness… it has to be the temperature…
S7: The temperature, right…
S6: The temperature or the internal energy.
Here, S6 persists in establishing the physical quantity that corresponds to the angriness in the
source domain, while S5 and, to some degree, S7 look for causal relationships between the
angriness and other quantities within the angry bees model.
In the excerpt below, Group B explores how collisions are related to the ‘angriness’ of the
bees, i.e. the temperature of the corresponding thermodynamic system:
S7: They fly a certain… at a certain velocity… they can fly to certain positions…
S8: And then they get more positions they can fly to… as you pull out the piston.
S7: But they don’t get as pissed off when they get more space.
S8: No.
S6: …so they don’t run into each other… because that is what makes then pissed off.
S7: …run slower… so then, they don’t use it, in any case…
S8: No, they won’t meet with each other so often, either… so they are not so cramped… then they don’t
get that angry.
S6: Well, then we have to explain that first.
S8: They have more places where they may end up, but not… they are not so angry with each other…
S6: Well, we have to explain that first, also… that they get angry if they meet with each other.
S8: Yes, right.
S6: Or what keeps… what keeps them angry.
S8: Yes, right.
S5: Uhum.
S6: Because they don’t get angry, but they are kept angry, right, when they meet with each other… a
constant angriness… [laughter]
S7: A constant angriness.
S5: The angriness is constant.
S6: It’s like an isoangy. [laughter]
This idea that the bees have to be kept angry by a constant frequency of crashing into each
other is probably a consequence of identification with the bees as living organisms. If we are
not hit by our fellow humans after some time of rough-and-tumble, we will slowly calm
down. The remoteness of the domains yields a humorous effect when the formal prefix ‘iso’ is
applied to the angriness of the bees. Another instance of anthropomorphic reasoning, although
not seen in this particular excerpt, is the idea (although followed by moderating laughter) that
the can has to be dark, so that the bees won’t be able to see the walls and each other (and
supposedly slow down before the impact).
Throughout the work, Group B (seemingly only partially playfully) expressed the spirit that
they should not themselves explore where the analogy breaks down, but that it’s up to the
other group and the researchers to find the weak points of their analogy. This was expressed
most clearly regarding their puzzlement of the constant entropy of the adiabatic process:
S6: But what am I going to say [in the presentation] about the entropy? That there are more microstates,
but the velocity decreases, so the probability that they end up in a state is the same…? And therefore the
entropy is the same…? Do you think I should say that it’s a guess…? Should we appear to…
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Jesper Haglund, Fredrik Jeppsson
S7: No, we claim.
S6: Ok, we claim.
S7: You shouldn’t give… /…/ We’re going to claim… You should never show your weaknesses. It’s up
to them, in that case…
S6: What if [the researcher] starts to laugh…? [laughter] Then we say that [the lecturer] taught us so. /…/
S7: We take a chance, OK. We go: ‘Everybody knows that’ /…/ We go in hard.
S5: ‘But how did you get to that…?’ ‘Come on! Logic!’ [laughter] ‘Common sense!’
S6: ‘We actually derived it.’ /…/ That’s our bet.
S7: OK.
S5: We go for that.
S7: We just cheat.
S5: Cheat.
Overall, the ‘angry bees’ analogy encompassed some concepts that were not found in the
other analogies. For instance, the different degrees of freedom of thermodynamic systems
(corresponding to translational, rotational and vibrational motion) were discussed in terms of
the motion of the bees, particularly the varying ease with which they loop or spin along
different axes. The individual character of each bee was reflected in pointing out that they can
have different masses (mother, father and baby bee), different speeds and something similar to
personality or temper in that some bees get angry more easily than others.
After the researchers introduced the concept of energy levels as a complementary contribution
apart from spatial configuration to the number of microstates, the group elaborated the ‘angry
bees’ analogy in coming up with four (humorously named) corresponding levels of angriness.
Party
The analogy that group A spent most time with (297 statements) was built on comparison of
both processes with a party scenario. As a parallel to the ‘angry bees’ analogy of the other
group, the party analogy was categorised as explicitly expressed, of higher-order relational
structure and from an anthropomorphic domain. In addition, it almost encompassed the same
number of concepts and challenges as the ‘angry bees’ analogy. In the ‘angry bees’ analogy,
the temperature, corresponding to angriness, was the most prominent physical quantity. This
was the case also for the party analogy, where temperature corresponded to the eagerness to
get a seat. S4 introduced the analogy:
S4: Well, imagine that we’re at a party or a pub or something. And then, we have a number of seats
here… a number of tables located… People are moving all the time at a party. They don’t want to get
stuck too long… but you still want to be able to sit down sometimes. I mean, you just can’t stand up an
entire evening. So some people have seats and others don’t. And then, when people get up, people are
very quick at trying to take the seat. When you have few tables, people are more eager trying to find a
seat. /…/ If we now add tables, we are expanding… Then there are more seats available and then people
don’t have to rush to these seats.
They saw a contrast in that a deliberate effort is needed to bring in more tables in the scenario
corresponding to adiabatic expansion, but not for free expansion where empty tables in an
adjacent room suddenly become available. In addition, there were two types of locations for
the people, standing up or sitting down:
S4: In the other example [free expansion]… if we imagine a big hall like this and a partition-wall
between… we have a lot of tables here and a lot of tables there…
S2: …empty tables from the beginning.
S1: Exactly.
S4: All the people are gathered here… then it’s like pretty crowded…
S3: Yes, people are standing and don’t have any seats.
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Jesper Haglund, Fredrik Jeppsson
S4: But then, if you remove [the partition-wall], there will be more seats
S3: Yes, more microstates.
S4: Well, but then again, people will have to be just as eager to get a seat.
S1: Right.
S4: …since the temperature is constant.
In all, this resulted in a rich analogy that encompassed many of the desirable dimensions of
both processes, but as a result also was highly complex. Another point is the anthropomorphic
idea that the eagerness of individuals corresponding to temperature is affected by the
knowledge whether or not there are available tables, which makes a difference between the
two processes. This complexity made it at times difficult to identify correspondences between
the source and target domains at higher levels:
S3: But doesn’t the entropy change then [at adiabatic expansion/addition of seats]?
S1: That’s what I think is so strange…
S2: No, they have less seats… they have a smaller volume for their seats…
S3: What? I mean, now we have just looked at the microstates of the seats…
S4: Mhm…
S3: But if we take away seats and nothing else happens… if we take away seats and decrease the
volume… /…/ the volume increases or the volume decreases… well, that depends on which way it goes…
Here, S3 has difficulties sorting out if taking away seats in the party setting corresponds to
increased or decreased volume. In our view, the reason is that there is no correspondence to
different types of locations or microstates in the ideal-gas model. There is only one type of
location that is either occupied or not. This characteristic of the model would have been more
suitable for other thermodynamic phenomena, such as phase changes like condensation on a
wall, but makes the problem at hand overly complex.
Models of balls
While the party analogy resulted in high complexity, the tactic of using idealised models of
one or a few balls bouncing against walls in a frictionless way proved more helpful for both
groups. This was particularly useful when it came to explaining the constant temperature in
the free expansion process, which initially was seen as puzzling. In contrast to the bee and
party analogies, these analogies where similar to taught models and taken primarily from the
domain of mechanics within physics. For example, S2 contrasts the situations of one ball that
bounces on a wall that moves slowly away in the adiabatic expansion with the case where a
wall suddenly disappears in the free expansion:
S2: If we imagine that we only have one big ball that flies around at a certain speed… then, at first, it has
a high velocity… and then we pull out to get, like, a dropshot… it bounces softer against the wall, which
is nudged away a little bit by it… and then, afterwards it has less energy… it has lower velocity. But in
that case [free expansion], it has high velocity… and then, this wall disappears suddenly… now, the
velocity hasn’t decreased, but it just flies around in this great space at high speed.
Here, S2 manages to make sense of the constant temperature in free expansion, by reference
to the constant velocity of individual particles. As a contrast, the velocity and kinetic energy
decrease when particles bounce on a wall that flees away.
Similarly, group B uses a model of balls bouncing on walls in free space to come to terms
with the constant temperature of the free expansion process:
S7: Maybe it’s in… in space… you shoot out a ball… then they go… [gesture of crossing and bouncing
balls]
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Jesper Haglund, Fredrik Jeppsson
S5: Airlocks…?
S7: No, you get… in space… of weightlessness… then they just go like this… ‘ding’, ‘ding’ [sound
effect and gesture of crossing balls]
S5: Airlocks… /…/
S8: You put up two walls on the moon and then we send in a ball...
S7: Yes, but then you have the gravity…
S8: Yes…
S7: A corridor…
S8: …in space… or two solar systems…
S7: A corridor in the middle of space... then you throw in balls that start to bounce like this... [gesture of
bouncing and crossing balls with sound effects] ‘ding’, ‘ding’ ….and then, like: ‘poh’ [a wall is suddenly
removed] /…/ Then, they will start to go in this way instead [gesture of travelling a longer distance] …at
the same speed.
S8: Yes.
S7: Because here they have…
S5: But then you mean that…
S6: But if the temperature is constant, of course they have the same speed.
S7: OK, but how… We have to be able to explain it in some way… why it is so…
By introducing weightlessness and ignoring air resistance, they realise that the speed of the
particles will remain unchanged when a wall is removed. Although reminding of ideal models
of elastic collisions in mechanics, the situation of the problem in free space makes them aware
of the idealisations made, as compared to an earth scenario. S6 sees it as self-evident that
constant temperature implies constant velocities, probably based on previous teaching on the
kinetic theory of gases, but S7 expresses that the ball model could provide a deeper
explanation.
Flees
Beside the ideal models of balls, Group A used an analogy of flees jumping from one person
to another to explain the constant temperature in free expansion. In contrast to the three
examples above, the flees analogy is not a self-generated analogy, but it was presented by the
lecturer in their previous course in thermodynamics in order to explain thermal equilibrium.
All elements stated in the source had an explicit counterpart in the target and, in the group
presentation, they aimed to capture both the energy and the spatial configuration contributions
to entropy:
S1: Yes, but this is the same as the one [the lecturer] brought up in the lecture... about energy
conservation... or the energy problem ... that you can see ... see entropy as if I have fleas in my hair... and
[S2] has no fleas... So now we are in example 2 [free expansion], right... and then, if we bump into each
other, then half of the fleas will jump over to [S2]... and then the disorder is higher, so the entropy has
increased...
S2: Uhum…
S1: …because they are distributed... and the pressure is halved, because they don’t bite me as hard, since
they are not as many... and what more did we say...?
S2: Pressure per square unit… there will be more space…
S3: They jump just as fast throughout...
S1: ...so it is the same speed, too…
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Jesper Haglund, Fredrik Jeppsson
In spite of this promising start where they found many correspondences and did not run into
any great inconsistencies between the source and target domains, this analogy was not
elaborated much further. They did not deal with other challenges apart from the constant
temperature (in contrast to the 8 challenges in relation to the angry bees and the 7 challenges
of the party analogy).
Discussion
Discussion of results
Enghag et al. (2009) use ownership of learning to analyse the responsibility taken collectively
by the group and individually by the students in small-group problem solving. By using illdefined context-rich problems, the students are encouraged to make choices and state
assumptions in order to be able to reach a result. In our view, the use of student-generated
analogies, as presented in this study, is an even more direct way to induce students to choose
their object of study. The students have to assume ownership of the analogy, since it has to be
either explored, with assessment of its merits and shortcomings, or discarded. This ownership
of the analogy is emphasised most clearly in the ‘angry bees’ analogy, where it even develops
to a protective stance, i.e. that it is up to people outside the group to find the weaknesses of
the analogy. This required responsibility may be one of the reasons for the students spending
so much time and coming to such structural depth with their own analogies. In addition, the
emotional and motivational aspect of identifying and exploring your own analogy should not
be forgotten. This type of creative exercise, as proposed by Middleton (1991), is likely to
encourage ownership of learning both by the individual students who come up with analogies
and by the groups who work with them.
In our view, the low degree of elaboration of the analogies originated in previous education is
probably not due to the subjects not understanding the relational structures of these analogies.
For example, in the presentation of the ‘flees’ analogy, the teacher students quickly pointed
out the correspondences between the source and target domains. If they had only discerned
the surface attributes of the presented analogy during teaching, they would not have found it
helpful and use it in this subsequent setting. The reason is probably instead that they take for
granted that the other group members have understood the analogy in the same way as
themselves, and that therefore there is no need to elaborate it further and negotiate the finer
details. By selecting a particular analogy in teaching, the teacher has sanctioned it and it
becomes less likely that the students will scrutinise it and explore where it breaks down. With
own analogies, on the other hand, the students are more aware that the sources are not
perfectly identical to the targets. By engaging in exploration and assessment of the analogy, a
group assumes ownership for it. In this way, we support the view of Heywood and Parker
(1997) that the identification of analogy break-down is an important trigger for engagement of
an analogy, rather than a sign of a poor analogy. The ‘flees’ analogy in the present study is an
example of an analogy with an almost too good match between the source and target domains.
No break-down or challenges are encountered, and consequently, the discussion does not take
off. However, we found that also the establishment of the structural features of a new selfgenerated analogy can give rise to creative discussions, even if the point of analogy breakdown is not reached. For example, in case of the ‘angry bees’ analogy, the group engaged in
creative discussion, even though the protective attitude was an obstacle for them to identify
points of break-down.
An alternative or complementary interpretation is that the previously encountered analogies
have already been worked with and have contributed to learning as part of the previous
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Jesper Haglund, Fredrik Jeppsson
course, so that it is not necessary to do it again. In addition, it should not be ignored that an
explanation for the lower structural level of the teacher-generated analogies is that the
subjects may well have interpreted the task in the way that own analogies are seen as better
and more appreciated by the researchers than the teacher’s analogies. Therefore they
dedicated more time and effort to them. In this way, our data supports Blanchette and
Dunbar’s (2000) results that deeper relational structures are focused on in the work with selfgenerated analogies, compared to work with teacher-generated analogies. However, while
they find the reason primarily in the learner’ abilities in interpreting the teacher-generated
analogies, we think that other meta-cognitive, emotional and epistemological aspects are more
decisive. Nevertheless, the conclusion is the same: the work with self-generated analogies
provides a fertile soil for focus on deep relational structures of analogies.
In line with Heywood and Parker (1997), the ‘angry bees’ analogy was an example of how an
analogy with many correspondences between the source and target domains generated a rich
discussion. However, as seen in the less successful party analogy, the number of dimensions
and concepts involved in an analogy should not be too large. At some point, it becomes too
complex and cumbersome, so that clear inferences cannot be made in the target domain.
As Clark (2006) argues, students need guidance in order not to focus too much on their
idiosyncratic explanations when trying to reconcile their previous understanding and new
experiences. In the current study, a case in point was the anthropomorphic idea that collisions
are required for angry bees to remain angry. This idea was transferred to the domain of
thermodynamics where Group B argued that particles have to collide to keep the temperature
constant. As argued in Jeppsson and Haglund (In progress), the idea that collisions are
required to maintain the temperature may be seen as a parallel to the view that an external
force is required to maintain the velocity of an object. This is a misconception commonly
found in relation to the teaching of Newtonian mechanics and similar to pre-Newtonian
theories, such as the medieval impetus theory or Aristotelian explanations (Clement, 1982).
Here, a teacher would have to intervene and point out that the analogy is taken too far. At
some times, the participants can assume the responsibility of sorting the matter out
themselves, but at other times, teacher interventions are necessary in order to avoid
misleading idiosyncratic explanations.
The fact that student teachers in both groups in our investigation were able to generate and
handle many different analogies which emphasised different characteristics of the same
phenomena shows that self-generated analogies is a possible way to generate multiple
analogies, as proposed by Spiro, Feltovich, Coulson and Anderson (1989).
The surprising result that all self-generated analogies in this study were built on microscopic
models of thermodynamic systems lends support to Reif’s (1999) view that it is difficult to
visualise concepts in macroscopic thermodynamics. In contrast to the suggestion of Kautz et
al. (2005), the student teachers do not use macroscopic models in their explanations. Instead,
the idealised microscopic models of balls proved particularly useful in coming to terms with
the constant temperature in the free expansion process.
Method discussion
The study as a whole was a small, primarily qualitative, exploratory study on self-generated
analogies. As a consequence, what has been found is a set of different ways of approaching
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Jesper Haglund, Fredrik Jeppsson
this type of task, but there are limited possibilities to generalise the results to other areas of
study or contexts.
In relation to the data analysis, it should be mentioned that one of the researchers had taken
the same course in thermodynamics a couple of years prior to the study. This was particularly
useful in the categorisation and analysis of the analogies that were brought up. For instance, it
assisted in categorising particular analogies as either self- or teacher-generated. On the other
hand, this may have limited the perspective as a researcher, giving an insider point of view.
The formulation of the two processes in writing, and the oral introduction of the tasks by the
researchers may well have influenced the interpretation of the exercise by the participants,
and thereby given a bias in the study. For example, the fact that the average velocity of the
particles was mentioned in the text may have induced the student teachers to apply particle
models.
The approach of letting the participants work together in groups with minimal intervention by
the researchers corresponded to an ambition of designing an authentic setting.
Educational implications
In the present study, we show that the use of self-generated analogies is a possible way to
make students assume ownership of their learning, by engagement in group work.
Specifically, self-generated analogies tend to be elaborated into a greater structural depth than
teacher-generated analogies, and are therefore in line with Gentner’s (1983) structural
perspective on analogy. In addition, we have previously found that the use of self-generated
analogies is a potential approach for identifying challenges to learning thermodynamics
concepts, but also for learners to come to terms with such challenges (Jeppsson & Haglund, In
progress). In this way, student-generated analogies may provide both a useful instructional
tactic and a research tool.
Another result is that often more questions are raised by the students than answers given.
Consequently, the use of self-generated analogies can be seen as a method for generating
hypotheses in a constructivist framework and for inquiry based learning. In this respect, we
adhere to the view of Harwood and Parker (1997) that richness of the discussions is one of the
main objectives of the exercise, rather than finding the analogy with the perfect match
between the source and target domains. On the other hand, the teacher is crucial in managing
the process of learning and will have to intervene when analogies tend to become too complex
or when they direct the students into idiosyncratic explanations which are not in line with the
intended view of science.
As a final remark, all student-generated analogies in this study related to microscopic
explanations of thermal phenomena. In this respect, Baierlein’s challenge of how to relate
macroscopic and microscopic concepts in thermodynamics remains in science education.
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