Teaching About Conduction Using the Domino Analogy: 
A Case Study of One Teacher's Approach


Allan G. Harrison


David F. Treagust


Science and Mathematics Education Centre
Curtin University of Technology
Box U1987 GPO  Perth,  Western Australia 6001





Paper presented at the Annual Conference of the Australian 
Association for Research in Education,  Fremantle. Western 
Australia, 22-25 November, 1993.



Abstract

This paper describes an investigation in which the researchers 
and an expert science teacher trialed a systematic approach for 
teaching analogies.  Science contains many abstract concepts that 
rely upon analogy for their explanation and while the shared 
attributes enhance may learning, unshared attributes may 
compromise student understanding.  This case study examines the 
process for integrating an innovation into a teacher's  strategy 
repertoire and also examines the resultant lesson from the 
perspective of student understanding of conduction.  The lesson 
discourse and teacher interview were tape recorded; for the next 
lesson the students completed an analogy mapping exercise and 
selected students were interviewed.  Analysis of the resultant 
data suggests that student understanding approaches the desired 
outcome when familiar analogies are systematically presented in 
science.


Teaching With Analogies
Whenever a teacher is challenged to explain a difficult or highly 
abstract concept, analogies may be employed.  This is 
particularly true when the abstract concept involves atoms and 
molecules or where the phenomenon cannot be easily described in 
purely scientific terms.  Throughout history, scientists such as 
Kepler (Bronowski, 1973), Huygens (Duit, 1991), Maxwell (Gee, 
1987) and Rutherford (Pimental, 1963) to name but four, have 
developed their theories and/or explained them using analogies.  
For instance, Oppenheimer (1955) and Starling and Woodall (1955) 
assert that light's wave nature can only be explained 
analogically and to this day (Hewitt, 1987, Serway, 1990) analogy 
remains the only satisfactory method for explaining the 
refraction of light.

Analogy is a culturally embedded means for explaining the 
difficult or inexplicable and its use ranges from children's 
stories through literature, religion, mathematics and science.  
While many teachers freely use analogies, there is a significant 
body of research indicating that analogies are "two-edged swords" 
as far as student cognition is concerned (Duit, 1991; Glynn, 
1991).  The central question when teaching with analogies is to 
ask, Do the students visualise the analogy in the way the teacher 

meant it to be understood? Can the students apply the analogy to 
the current phenomenon in a way that enhances their understanding 
of that scientific conception? and, Are the students able to 
recognise the analogy's limitations?  These and other concerns 
stemming from the random use of analogies in the classroom led us 
to examine the science education literature resulting in the 
identification of three valid models for teaching with analogies 
(Clement, 1987; Glynn, 1991; Zeitoun, 1984).
Subsequent analysis of these three models led us to conclude that 
Glynn's Teaching-With-Analogies (TWA) model had the greatest 
potential to enhance teacher presentation of analogies while 
reducing the incidence of alternative student conceptions.  Glynn 
developed his six step TWA model from an analysis of analogy use 
in science textbooks.  The concept familiar to the students is 
termed the analog, the science concept being studied is called 
the target, and the links between the analog and target are 
called mappings which have both shared and unshared attributes.  
While each step in GlynnŐs approach is important, the order in 
which the steps are used depends upon the teacher's style, the 
particular concept and the analogy being used.  We modified 
Glynn's TWA model by reversing steps 5 and 6 and the modified TWA 
model for teaching with analogies follows:
1.   Introduce the target concept to be learned - give a brief or 
full explanation depending on how the analogy is to be employed.  
2.   Cue the students' memory of the analogous situation - 
introduce the analog so that its familiarity to the students can 
be estimated by discussion and questioning.
3.   Identify the relevant features of the analog - explain the 
analog and identify its relevant features at a depth appropriate 
to the students' familiarity with the analog.
4.   Map out the similarities between the analog and the target - 
teacher and students identify the relevant features of the target 
concept and clearly link these with the corresponding features of 
the analog.


5.   Indicate where the analogy breaks down - note alternative 
conceptions that the students may be developing and known areas 
where the analog and target do not correspond.  Point these out 
to the students to discourage incorrect conclusions about the 
target from the analogy. 
6.   Draw conclusions about the target concept - summarise the 
important aspects of the target concept.
Our current empirical data indicate that Steps 2, 4 and 5 are the 
points where student understanding often fails to match the 
teacher's expectations.
At Step 1, three approaches are possible.  When the analogy is 
used as an advance organiser, the target concept is introduced 
after the analogy.  When the analogy is used to develop the 
concept, the concept should be taught in sufficient detail to 
make the analogy relevant.  When the analogy is to be used as 
revision, the concept is fully taught.  Overall, teachers can 
enhance analogical instruction by choosing an appropriate analogy 
before the lesson and by carefully planning how it will be 
taught.
It is generally recognised that analogies generate meaning 
through a constructivist pathway (Duit, 1991).  Students come to 
science instruction with tenaciously held preconceptions about 
their world; however, these intuitive ideas are often ignored by 
teachers.  Similarly, students have their life-view of each 
analog used by their teacher and when the meaning a student 
attributes to an analog differs from that intended by the 
teacher, the studentŐs subsequent understanding of the target 
concept will probably be scientifically inappropriate.  We 
believe that it is imperative that teacher and student hold a 
common view of the analog before analog-target mapping commences.  

Thus, at Step 2, if the student visualises the analog in a 
different way to the teacher, is it any wonder that the student 
generates alternative conceptions?  Teachers draw on a far richer 
knowledge base than do the students and there may be distinct 
cultural and socioeconomic differences between the teacher and 
the students.
Steps 3 and 4 may unite as a single step and our research 
indicates that as a teacher becomes proficient in the use of this 
teaching sequence, this does occur (Harrison, 1992).  As relevant 
features of the analogy are identified (Step 3), they are often 
mapped immediately as the first of the shared attributes (Step 
4).  Our in-class observations showed that student mapping of the 
shared attributes cannot be taken for granted.  Additional shared 
attributes that were not immediately apparent appeared as the 
analogy was discussed in class and, on several occasions, weaker 
students made valuable contributions to the mappings that had 
been overlooked by more able students.
Post-lesson interviews highlighted the value of examining the 
unshared attributes.  Every analogy breaks down somewhere and 
many of the analogies employed in science are used for phenomena 
that are foreign to the student.  It is unreasonable to expect 
novices to make expert judgments on structures or functions they 
cannot see or even visualise.  Neither the teachers nor the 
students interviewed felt that the extra time spent delineating 
the unshared from the shared attributes was excessive even though 
the analogy sometimes occupied 15-20 minutes of the lesson.  
Students stated that because the teacher had identified the 
unshared attributes for them, they were much more comfortable 
with their understanding.  It also is expected that many teachers 
will perform Steps 4 and 5 as a parallel exercise because as 
students propose analog-target mappings, shared and unshared 
attributes will emerge side-by-side.  
The summary at Step 6 is necessary to articulate what has been 
found by carefully relating the familiar to the unfamiliar.

The Domino Analogy for Conduction of Heat in Solids
The account that follows describes a lesson with a mixed ability 
Year 8 class that was studying the topic Heat in which the 
teacher, Mrs Kay (not her real name), used the domino analogy.  
The students were familiar with the kinetic theory from their 
previous topic on Atomic Structure.   The observed lesson was the 
third lesson on Heat and was dealing with methods of heat 
transmission, in particular, conduction.  The lesson itself was 
audiotaped and the researchers' role was that of "observer as 
participant" (Merriam, 1988, p. 93).  Following the lesson, the 
teacher was interviewed and during the next science lesson, 
students completed a worksheet on which they were asked to map as 
many of the shared and unshared attributes they could recall.  
Students were then selected for interview if they provided 
relatively full responses on the analogy mapping worksheet.



































Figure 1: Books and dominoes represent respectively, particles 
and mobile  electrons in a solid.
The audiotape of the lesson  was transcribed verbatim and 
analysed to identify the six steps of the modified TWA model and 
the shared and unshared attributes mentioned by Mrs Kay and her 
students.  All the interviews were similarly transcribed and Mrs 
Kay's interview was analysed to obtain her evaluation of the 
model's efficacy.  The student interviews were scrutinised to 
assess the degree to which the selected students understood the 
analogy and to identify their mental image(s) of conduction of 
heat.  The interpretations are discussed under the six steps of 
the modified TWA model as they apply to this analogy.


1.   Introducing the Target Concept to be Learned 

Mrs Kay introduced conduction by referring back to the previous 
lesson and by describing a commonplace phenomenon (which "feels 
the colder", the tap or the wooden bench) and by performing a 
simple experiment using two thermometers to measure the 
temperature of the tap and the wooden bench.  This phase closed 
with her asserting, "would you all agree that the metal tap is 
transferring heat better"? .

2.   Cueing Students' Memory to the Analogous Situation 
     
Mrs Kay proposed the analogy by saying, "Now we have a little 
example here [row of books and a row of dominoes" - see Figure 
1].  The visual impact of the line of identical books and the row 
of dominoes in front of the books quickly focussed the student's 
attention onto this analogy.

3.   Identifying the Features of the Analog that are Relevant 

Mrs Kay introduced the analogy by saying that, "a row of books 
and a row of dominoes is like particles in a solid."  She 
followed with "these books, they're meant to represent the 
particles in a solid that are quite close together."  It appears 
that Mrs Kay saw this comparison as being obvious and 
unambiguous.  Her approach matches Gentner's criterion (1988, p. 
76) that "access to memory is heavily influenced by surface 
similarity between [analog] and target ... in judging soundness, 
it is systematic structural overlap that counts."  In-class 
observations, the lesson transcript and the student interviews 
suggest that the students understood this likeness and found it 
attractive.
For Mrs Kay, this was the appropriate time to check whether or 
not the students were familiar with the analog.  During the post-

lesson teacher interview, she indicated that the students' 
reaction at this stage encouraged her to further map the shared 
attributes: "I thought today the kids probably got the idea by 
seeing that without getting any more complex."  Later in the 
interview, when the unshared attributes were being discussed, she 
maintained her confidence that the class were happy with the 
initial proposition by stating "I still think they got the 
general idea", and "this lot did seem certain ... they did seem 
to be with it."  When the student interview responses to the 
specific propositions were discussed, it appears that, at this 
stage, the students were comfortable with this comparison.

4.   Mapping the Similarities Between the Analog and the Target 
Concepts 
The book/particles dominoes/free electrons analogy contained 
eight propositions relating to the conduction of heat.  These 
propositions were analysed in the order in which they occurred.  
The student worksheets also provided information which is 
summarised in Table 21

Table 1:  Incidence of shared and unshared attributes in Year 8 
class that studied conduction of heat using the domino/book 
analogy  (n = 22)      
                    SHARED ATTRIBUTES                             
POSITIVE         NEGATIVE
     Books in the line represent particles                       
21        1
     Dominoes are like mobile electrons                     22
     Books bumping is like particles bumping           2
     Books too far apart is like a liquid                    1
     Only first book fell is like a gas             1
     Size: dominoes<books::electrons<particles     3 
     Dominoes falling is like heat passing through           1
     Books falling is like heat passing through         2
                UNSHARED ATTRIBUTES
     Books are similar in size to particles                      
19
     Domino speed is similar to electron speed          14        
3
     Gas particles vibrate like solid particles               1
     Books & dominoes stop after hitting suggests
     particles & electrons stop after hitting                      
1
     Book speed is like particle vibration speed         1  
                                                                 
On the student worksheet, spaces were provided for five shared 
and five unshared analog-target attribute mappings.  For the 
first two spaces (of both shared and unshared attributes) either 
the analog or the target attribute was provided.  For the 
following spaces, the student was required to provide the analog 
and the target attribute.  In the following discussion, the items 
(i), (ii), etc, refer to the valid and invalid propositions 
contained in each analog-target link and are in the order they 
appeared in the lesson transcript unless otherwise stated.

(i)  "books ... represent the particles in a solid which are 
quite close together." 
The interviews revealed that the students recognised and readily 
accepted this initial premise.  Referring to this initial link, 
the opening question in the interview asked each student "What do 
you think of that idea?"  Each girl easily recalled the analogy 
expressing both interest and understanding at this superficial 
level.  Comments further into the interviews revealed that each 
student understood that the books represent atoms and that atoms 
are closely packed in solids.  Lizzy's comment was typical: "the 
dominoes were the electrons and the books were the particles, the 

atoms." 
When discussing the fact that particles vibrate and disturb the 
ones next to them, Sally and Lizzy stated that

     Mrs Kay made the point and I think the book does too, that 
the movement of the free electrons [dominoes] passes the heat 
better than the movement of the molecules.  [Sally] 

     When she showed us the books and the dominoes, how they fell 
onto each other, it was because the vibrating atoms bump into 
each other passing heat and energy, it was clear.   [Lizzy]
None of the interview comments and only one worksheet statement 
was found that disconfirmed the proposition that "books are like 
particles."

(ii) "When we heat particles, [they] start to move and spread out 
the relationship between heat and motion in the following way:  
"it sort of gets heated up and moves a bit faster and it sort of 
it moves faster and then it is heated up."
While this was the only statement that mirrored the teacher's 
idea, the thread of the idea that getting hotter meant that the 
particles moved faster, ran through most of the interviews.  
However, the following comment by Sally suggests an alternative 
conception: "When they are heated, how they expand, they move 
when they're heated, they vibrate."  Sally may have thought that 
the analogy was saying that the added heat starts the particle 
moving.  Later when she was asked about insulators, she asserted 
that: "They don't move, the particles don't move so they can't 
conduct heat."  This girl was the least talkative of all the 
interviewees and was the least sure of the four.

(iii)   All particles move, when heat is added they move faster.  
Mrs Kay inferred this propositional statement when she said to 
the class,  "I'm heating this end of the solid (pushes over first 
book)" which hits the next, making it move like transferring heat 
to the next particle.  This idea that heat is analogous to motion 
was consistently evident throughout the interviews and the 
student worksheets.   During the student interview, Tina, made a 
very perceptive remark when asked to describe the analogy.
     
Tina  It's, it sort of got me thinking that they sort of stop 
after they move. So they move and they hit something and transfer 
the heat and they just stop where they lose the heat, sort of 
just passes through.
Int. Like the book is lying there still, once it's done its job?
Tina It's done its job and it stops.
Int. Do you think that's how it really works?
Tina No.
Int. How do you think it really works then?
Tina All the particles move around and they hit each other and 
they keep moving on so the heat transfers into other particles 
which keep moving and hitting the other ones and keep 
transferring the heat to everything.
Int. So if you have this long piece of copper wire, and you heat 
this end, what happens?
Tina It heats the next [particle] and the next one and the next 
one and it carries through.
Int. What about the one that was moving that did the bumping, is 
it still going to be moving?
Tina No. In a piece of copper wire it's not ...
Int  So in a piece of copper wire, if you heat one up, it moves 
quickly, bumps something else, so it's not moving quickly?
Tina No.  It still is, but the example shows that it's not.
Int. So you're saying to me - the example says it moves, then 
stops, but you know that it keeps moving?
Tina Yes. 

Tina recognised this limitation in the analogy that, if you take 
the analogy literally, the particle starts, hits, stops.  
However, she could disregard this misconception, but the research 
did not determine whether or not other students were equally 
perceptive.  This observation makes a powerful case for examining 
the unshared attributes, and especially, from the students' 
cognitive viewpoint. 

(iv)  The particles are further apart in the liquid phase.   This 
propositional statement emerged from the following comment made 
by Mrs Kay during the lesson.  "A little bit further apart ... 
that was more like a liquid wasn't it?"
This proposition emanated from the failure of the first attempt 
to apply the domino effect to the line of books.  The fact that 
the books were too far apart was seized upon to analogically show 
why liquids are poor conductors.  Sally understood this point 
when she said: "like in liquids they're too far apart, like they 
hardly bump into each other, so it's difficult to conduct." 
Several students such as Lizzy, focussed upon gases which have 
even greater interparticle distances:  "in the solid they pass 
heat better than in a gas because in a solid the atoms are very 
close together, so not as much heat can be passed through in 
gases."
(v)  One book hitting the next is like conduction.   The 
statement by Mrs Kay that led to this propositional statement 
was, "all the particles are close enough to pass on the 
vibrations" and "now this way of transferring heat by particles 
passing on vibrations is called conduction."
This mechanism is the central issue in this analogy for 
conduction.  The interviews demonstrated that each student had 
absorbed this idea.  In describing this mechanism, three of the 
four girls produced over half a page of transcript each.  The 
fourth girl, Tina, provided ten full lines of information.  The 
following four excerpts from the student interviews show how 
these students understood the domino-effect analogy for 
conduction of heat in a solid:
When they vibrate they knock the next ones, and that vibrates too 
and it knocks the next one, and it vibrates as well, and in a 
solid [the atoms] pass heat better than in a gas ...   [Lizzy]

It makes the rest of  [the atoms and electrons] move because one 
bumps into the other.  [Sally]

The particles, they vibrate and ... pass the energy on ... when 
it bumps into the other ones.  [Peta]

The first [particle] heated bumps the next one and then that one 
gets the heat, and the next gets it and so on.  [Tina]
(vi)  The books represent atoms and the dominoes represent free 
electrons.  This propositional statement came from the following 
comments by Mrs Kay,  "these books are our atoms here and these 
dominoes, these little ones, are meant to represent free 
electrons."  The proposition that the dominoes represented the 
"free electrons in a metal" was also well received as evidenced 
by the following remarks.
The dominoes were the electrons and the books were the particles, 
the atoms ...  [Lizzy]

Dominoes probably move faster because they're smaller ... there'd 
be more of them to the number of books ... electrons would move 
faster than the particles.  [Tina]

(vii)  Both electrons and atoms transfer heat energy.  Mrs Kay 
had said that  "free electrons also vibrate, so we've got a 
double way of passing on the vibrations."  This propositional 
statement is important when discussing conduction in solids 

because it explains why some solids (metals) are good conductors 
while others (wood, plastic) are not.  The interviews again 
indicated that these two girls understood this idea.
Substances with many free electrons convey heat more faster than 
those that don't have free electrons.   [Tina]

Int.      Why are metals good conductors?
Tina  They have free electrons which move faster than particles 
but do sort of the same thing ... there's more things doing it.  
[Peta]
The comment from Tina in (vi) above also supports the idea that 
Free electrons, that's just in metals and they move all around 
the place because they're free. ... they're moving faster because 
they're smaller ...  [Tina]

(viii)  Because dominoes are smaller than books, free electrons 
are smaller than atoms.  This propositional statement arose from 
seeing the model and the fact that Mrs Kay explicitly identified 
the books as being like atoms and the dominoes being like 
electrons throughout the lesson.  Mrs Kay stated both before and 
after the lesson that this was her reason for choosing books and 
dominoes as the analogs.  The relative size of atoms and 
electrons was not discussed in the lesson and this idea was 
encountered on only three of the student worksheets.  Several 
students mentioned this point during the interviews.
I thought that the electrons had to be smaller since, because all 
atoms have electrons inside them ... so I thought they must be 
smaller, I thought the dominoes were a good idea.    [Lizzy]


But Tina interpreted the relative size of books and dominoes and 
suggested that there is less difference between electrons and 
atoms than there is between dominoes and books.  This is evident 
from the following interview statement: "... a bit nearer in size 
maybe?"

One student identified an extra shared attribute not mentioned by 
Mrs Kay.
(ix) The speed of the particles.  The line of dominoes fell over 
faster than the line of books showing that electrons transfer 
heat faster than particles.  This similarity was recognised by 
Lizzy as evidenced by the following interview comment:

Dominoes will fall over a long time before the books.  It is 
showing that a substance with many free electrons convey heat 
more faster than those that don't have free electrons. ... The 
dominoes fell faster than the books ... electrons move faster 
than the atoms. 

5.   Identify Analog-Target Links Where the Analogy Breaks Down
No invalid analog-target links were mentioned by Mrs Kay during 
the lesson, though unshared attributes were discussed at length 
during the post-lesson interview with Mrs Kay when she stated 
that
Yes, I could have talked about the unshared attributes a bit 
more.  I probably should have said that the particles are 
obviously a lot smaller ... we have talked about that before ... 
about the structure of the atom. ... I think they ... know 
they're smaller, but probably I should have said, ... obviously 
the particles aren't this size.  I know I didn't do the unshared 
attributes.  But to me it seemed a quick little thing [the 
analogy], that it wasn't really worth it.

Nevertheless, the students identified three instances in which 
the analogy breaks down  These unshared attributes were:


(i)  The particles stop moving after they hit the particle next 
to them. When the book or domino fell over it ceased moving, thus 
particles and electrons stop once they have transferred energy to 
other particles. This difference was volunteered by two students 
during the interviews.
Int.      Once the book had fallen over it was still.  Do you 
think that matches?
Liz  No, I think they keep on vibrating, and just keep on moving. 
on heat, not what they did after they passed on the heat.  

      I thought they'd still keep vibrating, because after they 
bump into the other ones ... they'd be all round the place ...    
[Peta]
Tina's comment on this item is described fully in the discussion 
of propositional statement (iii) which says that "all particles 
move, when heat is added they move faster."
(ii)  Size difference between books and electrons was 
inappropriate.  This difference was given by Tina when she said 
that: "you need bigger books because the particles are much 
bigger than the electrons."
 
(iii)  Free electrons are far superior to particles for 
transferring heat.  The real difference is far greater than the 
model indicates.  This generated a alternative conception for 
Sally because she was led, when discussing insulators, to say: 
"well solids don't have particles and like plastic, is not as 
good a conductor ..."
     
6.  Summarise, Drawing Conclusions About the Target Concept 
The conduction concept was rounded off by Mrs Kay saying:  "So 
metals are the best, then solids, then liquids and gases are 
pretty poor."
Conclusions
This was the second lesson in which Mrs Kay used the modified TWA 
model to present an analogy in a systematic maner.  At her first 
attempt she covered each of the six steps in a linear fashion 
but, as is evident above, she failed to overtly discuss the 
unshared attributes of the domino analogy.  In reflecting upon 
her performance, Mrs Kay stated that "I had written [the model] 
down, but I hadn't really looked at it last night which I 
probably should have ... I should have looked at it, ... I could 
have talked about the unshared attributes a bit more."  
Based on four lessons in which we observed Mrs Kay implimenting 
the modified TWA model, and from the student interview responses, 
it appears that three teacher actions are essential for effective 
teaching with analogies.  These are, one, ensuring that the 
teacher and the students visualise the analog in the same way; 
two, developing the shared attributes to plausibly elucidate the 
target; and three, clearly identifying the unshared attributes 
for the students.  When these three cognitive activities are 
performed in a manner that is intelligible, plausible and 
fruitful for the students, it is most likely that the resultant 
student understanding will be compatible with the teacher's 
expectations.


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