To appear in a volume of readings to be edited by Joe Campione, commemorating

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1





A
NALOGICAL
R
EASONING IN
C
HILDREN


Usha Goswami

Centre for Neuroscience in

Education

University of Cambridge




Centre for Neuroscience in Education

Faculty of Education

184 Hills Rd

Cambridge CB2 2PQ, U.K.

Tel. 44 1223 767600/ Fax 44 1223 767602

Email:

ucg10@cam.ac.uk


To appear in a volume of readings to be edited by Joe Campione, commemorating
Ann L. Brown and her contribution to developmental psychology.


2

A
NALOGICAL
R
EASONING IN
C
HILDREN

Usha Goswami, Universit
y of Cambridge.


Reasoning by analogy is generally considered a core component of human
cognition. It is important for learning and classification, and for thought and
explanation. Analogy has been involved in key scientific discoveries and many argue
that

analogies are central to creative thinking. The contribution of analogical
reasoning to cognition has been defined in varying ways. In a recent definition of
analogy, Holyoak and Thagard (1995) introduced the engaging concept of “mental
leaps”. Holyoak an
d Thagard argued that the act of forming an analogy requires seeing
one thing as if it were another. The reasoner must make a kind of ‘mental leap’
between domains. These mental leaps are often evident in famous analogies in the
history of science.

A strik
ing example is the analogy that led to Kekule’s (1865) theory about the
molecular structure of benzene (see Holyoak & Thagard, 1995). In a dream, Kekule
had a visual image of a snake biting its own tail. This gave him the idea that the
carbon atoms in benz
ene could be arranged in a ring. The similarity between the snake
and the carbon atoms was at a purely structural/relational level
-

the level of circular
arrangement. Recognising abstract similarities such as these are the hallmark of
analogical reasoning
.

Another classic example of the role of abstract similarity in analogy is
Archimedes’ insight into the value of using water displacement to quantify the mass
of different substances. Archimedes had been asked to calculate whether base metal
had been subs
tituted for gold in an ornate and intricately
-
designed crown that had
been commissioned by his king. Archimedes knew the weight per volume of pure

3

gold, but the crown was so ornate that he could not measure its volume. Unable to
reach a solution, he went h
ome and had a bath. According to the legend, he then cried
“Eureka, I’ve got it”. When he stepped into the bath, he noticed that his body
displaced a certain volume of water. This gave him the mathematical solution to his
problem: immerse the crown in wate
r, and see whether the volume of water that was
displaced was equivalent to that displaced by pure gold. This kind of mathematical
solution really does seem to capture a very abstract kind of relational similarity that is
not evident to most people as they

get into the bath.

In addition to being an important mechanism for creative thinking, analogy is
the basis of much of our everyday problem solving. Small
-
scale ‘mental leaps’ are
made all the time by children (and adults), and form a core part of our ever
yday
mental repertoire. Ann Brown was one of the pioneers of the study of analogical
reasoning in children. She believed analogy to be central to children’s reasoning and
critical to educational innovation. She investigated both formal analogical reasoning

in laboratory
-
based settings, and children’s use of analogies in the “real worlds” of
their classrooms. This chapter will present an overview of research on analogical
reasoning by young children, illustrated
as often as possible
by examples of Ann’s
expe
rimental work.

Early Research on the Development of Analogical Reasoning

Historically, analogical reasoning was a neglected area in developmental
psychology. This was largely due to evidence from two different theoretical traditions,
suggesting that young
children could not reason by analogy. Piagetian theory held that
analogy was a late
-
developing skill, that was available only when the stage of formal
operations was attained at 11


12 years (Inhelder & Piaget, 1958). At the same time,
psychometric resear
ch showed that younger children were poor in the item analogy

4

tests used in intelligence testing. For example, 11


12 year olds completed analogies
like “pig:boar :: dog: ?” with word associations (“pig:boar :: dog:cat”, see Achenbach,
1971).

The item an
alogies used in psychometric testing were intended to measure the
fundamental aspect of analogical reasoning, the ability to reason on the basis of
relational similarity. Aristotle’s original definition of analogy was as an equality of
proportions “involvi
ng at least 4 terms.. when the second is related to the first as the
fourth is to the third” (Aristotle,
Metaphysics
). In item or classical analogies, the
reasoner is given the first 3 terms of the analogy. She must then use relational
similarity to genera
te or select the appropriate fourth term. In the example “pig is to
boar is dog is to ?”, the children must
generate

the fourth term “wolf”. In multiple
choice analogies, the child must
select

the appropriate completion term from a series
of distractors (e
.g., cat, wolf, bone, puppy).

Piaget also used a form of item analogy. He and his colleagues tested children
aged from 5 to 12 years with a pictorial version of the item analogy task (Piaget,
Montangero & Billeter, 1977). The experimental method was based

on picture sorting.
Children were given sets of pictures to sort into pairs, and then into sets of matching
pairs. The intention was that the children would extract analogies based on functional
and causal relations. If spontaneous sorting did not follow
this format, the
experimenter helped sort the pictures. For example, for the analogy “bicycle :
handlebars :: ship :?” the children were meant to select the picture of the
ship’s wheel
.
For the analogy “dog : hair :: bird : ?”, the children were meant to s
elect the picture of
the
feather
. Younger children (5
-

to 7
-
year
-
olds) often failed to select the correct
completion term. For example, one child offered ‘bird’ as the solution to the analogy
‘bicycle : handlebars :: ship :?’, saying “both birds and ships
are found on the lake”. In

5

another example, a 6
-
year
-
old child given the pictures “nurse: syringe :: barber : ?”
ignored the picture of
scissors

and told the experimenters “I’m looking for a
washbasin”. Piaget concluded that younger children solved analogi
es on the basis of
associations.

Slightly older children (aged approximately 7 to 12 years)
given the same
picture sorting task
formed good analogies, but were then easily dissuaded by
“counter
-
suggestions” supplied by the experimenter. For example, they
were happy to
accept a picture of a
pump

to complete the ship/bicycle analogy (‘ship : ship’s wheel ::
bicycle : pump’). They apparently did not realise that the associative response was less
acceptable than the response based on relational similarity. Pia
get thus argued that
true understanding of analogy did not develop until early adolescence, during the
formal operational stage. According to his theory, formal operational reasoning
required children to operate mentally on the results of simpler operation
s. A simpler
operation was finding relations between A and B terms in an analogy (‘first
-
order’
relations). To recognise the relational similarity between the relations linking A to B,
and C to D, children required ‘second
-
order’ relational understanding.

How robust is Piaget’s conclusion that young children cannot reason on the
basis of relational similarity? A child who accepts
pump

as the solution to the analogy
‘ship : ship’s wheel :: bicycle : ?’ does not appear to understand the concept of
analogy. H
owever, the child could accept
pump

because of a failure to appreciate the
functional and causal relations on which Piaget’s analogies were based (for example,
the relation ‘steering mechanism’). If such relations are not yet specified in the child’s
conce
ptual system, then the child could fail in the analogy task despite being able to
reason by analogy. As noted often by Ann in her work, when uncertain about a new or
unusual problem, novice learners are likely to fall back on simpler solution strategies

6

su
ch as associative reasoning and matching on the basis of surface similarity. Hence
the younger children in Piaget’s studies may have been quite capable of using
relational similarity as a basis for analogical solutions. However, they may not have
been fami
liar with the relations intended by the experimenter to form the basis of the
picture analogies.

The Role of Relational Knowledge in Solving Item Analogies

To explore this possibility, Ann and I set out to
examine

performance in
classical item analogies w
hen the problems were based on relations that we knew
were familiar to young children. For example, relations between real world objects
such as ‘trains go on tracks’ and ‘birds live in nests’ are very familiar to 4
-

and 5
-
year
-
olds. We therefore reasoned
that item analogies such as ‘train is to track as ship is to
?’ could be used to examine whether even 4
-

to 5
-
year
-
olds (the youngest age group
tested by Piaget) have the ability to reason by analogy. We also devised an
experimental method based on a pictu
re format (Goswami & Brown, 1990). We gave
children picture sequences in the multiple choice format familiar from psychometric
tests. For example, the initial pictures might comprise a
train

(A), some
traintracks

(B), and a
ship

(C). We then offered the ch
ild a variety of picture solutions, such as
some
water

(D), a
sailor
, a
car
, and a different
ship

(see Figure 1). The correct choice,
which would indicate analogical ability, was the
water
. The associative choice was the
sailor
. Selection of the sailor wou
ld be expected if younger children rely on
associative reasoning to solve item analogies, as had been believed. The other choices
were a ‘surface similarity’ match (the second ship, surface similarity matching is a
simpler solution strategy), and a categor
y match (the car).



Figure 1 about here


7

In the experiments, the children watched while the experimenter presented the
first three terms of a given analogy. As the pictures were presented, the child was
asked to name each one to ensure that they were fami
liar. The child was then asked to
predict the picture that was needed to finish the pattern. The prediction task was
included to see whether the children could generate an analogical solution
spontaneously, without seeing the solution pictures. This would
be evidence for truly
‘mental’ operations. Following the request for a prediction, the experimenter showed
the child the choice of solution terms. The different choices were designed to test
different theories of analogical development.

The analogy matchi
ng game showed that all children tested (4
-
, 5
-

and 9
-
year
-
olds) performed at levels significantly above chance. The 4
-
year
-
olds selected the
correct completion term on 59% of occasions, the 5
-
year
-
olds on 66% of occasions,
and the 9
-
year
-
olds on 94% of oc
casions. There was no evidence of a reliance on
simpler solution strategies such as associative matching or matching on the basis of
surface similarity. Many of the younger children were quite shy about making
predictions prior to seeing the solution choic
es. However, those who were more
confident showed clear analogical ability on this measure as well. For example, when
4
-
year
-
old Lucas was given the analogy
bird is to nest as dog is to

?,

he first predicted
that the correct solution was
puppy
. He argued,
quite logically, "Bird lays eggs in her
nest [the nest in the B
-
term picture contained three eggs]
-

dog
-

dogs lay babies, and
the babies are
-

umm
-

and the name of the babies is puppy!" Lucas had used the
relation
type of offspring

to solve the analogy.

This was an equally valid relation
given pictures A to C, but was not represented among the solutions on offer. He
continued "I don't have to look [at the solution pictures]
--

the name of the baby is

8

puppy!" Once he looked at the different picture choice
s, however, he decided that the
doghouse

was the correct response.

The picture matching game also included a control task to ensure that the
correct solution to the analogy was not simply the most attractive pictorial match for
the C term picture. In this
control task, the children were simply shown the C term
picture along with the correct solution term and the distracters, and were asked to
choose which picture ‘went best’ with the C term picture. For example, the children
were shown the picture of the do
g, and were asked to choose the best match from the
pictures of the
doghouse
,
bone
, second
dog

and
cat
. In this unconstrained task, the
children were as likely to select the associative match (bone) as the analogy match
(doghouse). Additionally, although t
he children readily agreed that another match
could be correct in the control condition (9 year olds: 76%, 4 year olds: 82%), they
were not so flexible in the analogy condition, where most of them said that only
one

answer could be correct (9 year olds: 89
%, 4 year olds: 60%). This shows awareness
of the relational similarity “constraint” that governs truly analogical responding. The
children understood that the correct completion term for the analogy had to link the C
and D terms by the
same

relation that
linked the A and B terms. Notice also that Lucas
was using the relational similarity constraint when he generated the solution ‘puppy’
for the
bird/dog

analogy. This provides evidence of truly mental operations, thereby
meeting Piaget’s original criteria f
or the presence of ‘true’ analogical reasoning.

The Relationship between Relational Knowledge and Use of the Relational Similarity
Constraint

The picture analogy game shows that the ability to reason by analogy in formal
tasks is present by at least age 4.

However, it does not show that older children were
failing in the item analogies devised by Piaget because they lacked knowledge of the

9

particular relations required to apply the relational similarity “constraint”. Our picture
analogy game may in fact hav
e
underestimated

analogical ability. This is because
relational knowledge was not measured independently of analogical success. Ann and
I had simply assumed that familiar relations had been selected for the analogies. This
leaves open the possibility that
the younger children may have failed in some trials
because the relations used in those particular analogies were unfamiliar to
them
.
Alternatively, some children may have failed some analogies because they were
actually reasoning about relations that were

different

from those that we had intended
-

like Lucas.

The idea that children’s analogical performance depends on their relational
knowledge has been called the ‘
relational familiarity’ hypothesis’

(Goswami, 1991,
1992)
.

On this theoretical account, ana
logical development depends critically on the
conceptual knowledge of a particular child. As knowledge develops and is linked to
knowledge in other domains in different ways, the ability to use more sophisticated
analogies develops. According to the relati
onal familiarity hypothesis, analogical
reasoning is available from early in development, in fact it is a core cognitive skill
present even in infancy (Goswami, 1998). Analogies in young children are only
“perceptually bound” (see Gentner, 1989) or associa
tive in nature (Sternberg & Nigro,
1980) when the relational knowledge needed to reason on the basis of relational
similarity is missing.

To explore this hypothesis empirically, Ann and I decided to change the
control task in the picture matching game. We
designed a new control task, intended
to measure children's knowledge of the relations being used in the particular analogies
that we were presenting in the item analogy task. This time, we used item analogies
based on physical causal relations like
meltin
g
,
cutting

and
wetting
. These relations

10

are known to be available to children by 3
-

4 years of age, if not earlier (Bullock,
Gelman & Baillargeon, 1982). Children aged from 3 to 6 were given analogies like
“chocolate is to melted chocolate as snowman is t
o ?”, and “playdoh is to cut playdoh
as apple is to ?”. The distractors were (1) a different object with the same causal
change (e.g., cut bread for the
cutting

analogy), (2) the same object with a different
causal change (e.g., a
bruised

apple), (3) a sur
face similarity match (e.g., a small ball),
and (4) a semantic associate of the C term (e.g., a banana). Knowledge of the causal
relations required to solve the analogies was measured in the new control condition. In
this condition, the children were shown

three pictures of items that had been causally
transformed (e.g., cut playdoh, cut bread, cut apple). They were then asked to select
the causal agent responsible for the transformation from a set of pictures of possible
agents (e.g., a knife, water, the s
un).

The results of these experiments (Goswami & Brown, 1989) showed that both
analogical success and causal relational knowledge increased with age. The 3
-
year
-
olds solved 52% of the analogies and 52% of the control sequences, the 4
-
year
-
olds
solved 89% o
f the analogies and 80% of the control sequences, and the 6
-
year
-
olds
solved 99% of the analogies and 100% of the control sequences. By far the most
frequent error was to select the correct object with the wrong causal change (e.g., the
bruised apple, a di
rty snowman). This suggested that the children knew that relational
similarity depended on a causal transformation, but did not always select the correct
one. The next most frequent error was to select the correct causal transformation of
the wrong object.

Again, this suggests some attempt to use the relational similarity
constraint. There was also a significant
conditional

relationship between performance
in the analogy condition and performance in the control condition. This is important
for the relationa
l familiarity hypothesis. The conditional relationship arose because

11

individual children’s performance on particular items in the analogy task was linked
to their knowledge of the corresponding causal relations. The data suggested that
analogical reasoning

in children is highly dependent on relational knowledge.

Measuring the Relational Similarity Constraint in Problem Solving Paradigms

A complementary approach to studying the development of analogical
reasoning in young children is to give them “real worl
d” problems to solve by using
analogies. In this approach, children are typically given a “base” problem that is
intended to illustrate a potential solution to a new problem, the “target” problem. For
example, if a magic genie must move his precious jewels

from one bottle to another,
he might solve this problem by rolling up his magic carpet and using it as a tube to
transfer the jewels. When children are then given a new problem of moving some
small rubber balls from one bowl to another bowl on a table, th
ey might realise that a
sheet of paper lying nearby can be rolled up to form a tube (Holyoak, Junn & Billman,
1984). If the relational similarity between the two problems is recognised, then the
application of analogy should be simple. If instead the child
ren ignore the paper and
try to find similar objects to help them (e.g., a rug), then it is argued that they are
unable to focus on the underlying relations because they are drawn to surface
similarities (a simpler form of reasoning). In the problem analog
y literature, Gentner
(1983, 1989) has argued that young children focus on object similarity at the expense
of relational commonalities.

In the original
study

by Holyoak et al. (1984), the 5
-
year
-
olds tested were not
very good at reasoning by analogy in th
e genie paradigm. Almost 70% of them
ignored the sheet of paper when trying to work out how to move the little rubber balls.
Ann Brown was not convinced by this apparent failure to use analogies. She pointed
out that in another problem analogy involving a
stick (a “magic staff”), Holyoak et al.

12

(1984) had found that giving 5
-
year
-
olds a hint to use analogy had led to all of the
children reasoning successfully. This led Ann to investigate systematically the factors
that influence whether young children will
notice relational similarities between
problems in problem analogy paradigms (e.g., Brown & Kane, 1988; Brown, Kane &
Echols, 1986; Brown, Kane & Long, 1989). She showed that while the core ability to
reason on the basis of relational similarity is present
, many performance factors can
impede the flexible use of analogy by young children.

In her first study of performance factors, Ann gave 4
-

and 5
-
year
-
olds the
'Genie' problem invented by Holyoak et al. (1984) (see Brown et al., 1986). The
children were sh
own the Genie problem via a toy scenario with toy props. They then
enacted the correct solution with the experimenter, rolling up a piece of paper that
represented the magic carpet, and rolling the jewels through the paper tube. In order to
help the childr
en to extract the
goal structure

of the problem, a series of questions
were asked including "Who has a problem?", "What did the genie need to do?", and
"How does he solve his problem?". The children were then shown another problem
intended to be analogous
to the genie's, which also involved toy props. This was the
'Easter Bunny' problem. An Easter Bunny needed to deliver a lot of eggs to children in
time for Easter, but had left things a bit late. A friend had offered to help him, but the
friend was on the
other side of a river, and so the eggs had to be transported across the
river to this friend without getting wet. The idea was that the Easter Bunny could use
an analogous solution to the genie by rolling his blanket (a piece of paper) into a tube
and roll
ing the eggs across the river through this tube.

Brown et al. found that 70% of the children in the experimental group noticed
this analogy spontaneously. However, only 20% of children in a control group noticed
the analogy by themselves. Although the con
trol group had also experienced the

13

Genie's problem, they had not been questioned about the goal structure of the story.
Ann concluded from this and a series of similar studies that the key to performance
was whether children had represented the relational

structure of the previously
-
encountered problem in memory. When they had represented relational or goal
structure, they found it easy to recognise relational similarities between previously
-
encountered problems and novel ones. When they had not, noticing
relational
correspondences was more difficult. Questioning by the experimenter facilitated this
representational process, as it encouraged the children to represent the important
relations that enabled the character to achieve his goal.

Another performanc
e factor that could impede noticing relational
correspondences was “functional fixedness”. The negative effects of functional
fixedness on creative problem solving were first observed by the Gestalt
psychologists. They argued that failures of ‘insight’ wer
e due to ‘functional
fixedness’. Potential solution tools to particular problems (like the sheet of paper for
the rubber balls problem) were ‘burdened’ by their habitual use, and this rendered the
tools unavailable to the reasoner. In fact, potential solut
ion tools were not even
recognised because of ‘cognitive embeddedness’
-

they were too embedded in their
familiar context. Both functional fixedness and cognitive embeddedness were argued
by the Gestalt psychologists to
interfere

with inductive reasoning.
Ann Brown showed
that the same constraints applied to young children. She also went further,
demonstrating that attempts to generate inverse mechanisms can enable cognitive
flexibility and promote inductive learning.

To investigate functional fixedness in
young children, Ann again used the
analogy paradigm involving the genie. In her experiments, various tools were made
available to solve this problem, including glue, string, tape and a sheet of paper.

14

Children aged 5 and 9 years were tested in two conditio
ns. In the Functional
Fixedness condition, the children were first asked to make drawings on 3 sheets of
paper prior to receiving the Genie problem. Following this experience (that the
function of paper is for drawing on), only 20% of the 5
-
year
-
olds and 3
5% of the 9
-
year
-
olds thought of rolling the paper into a tube to help the Genie. In the Cognitive
Flexibility condition, the children used the 3 sheets of paper to make a tent, to make a
drawing and for a communication game. Here, 75% of the 5
-
year
-
olds a
nd 80% of the
9
-
year
-
olds in the Cognitive Flexibility condition spontaneously generated the rolling
solution in the analogy test. Brown and Kane (1988) argued that the experience of
using the paper for drawing fixed its function for the Fixedness group, i
mpeding
analogical reasoning. For the Cognitive Flexibility group, experiencing a variety of
uses for the paper freed it from its specific role as paper, making it available for other
solutions.

In related studies aimed at exploring how analogies could be
best used in
teaching and learning, Ann found that relational representation could be enhanced by
experiencing a
series

of analogies, and by being
taught

to look for analogies during
problem
-
solving ('learning
-
to
-
learn'). She devised two novel paradigms in

this work,
labelled the A
-
B
-
A
-
C paradigm and the A1
-
A2/B1
-
B2/C1
-
C2 paradigm. In the first
paradigm, children were introduced to problem A and asked to solve it by themselves
(which they were typically unable to do). They were then given an easier problem
B,
which was actually similar in terms of relational correspondences to problem A.
Following successful solution of B, problem A was re
-
administered, along with gentle
hints about its similarity to problem B. A novel problem C was then given, to measure
sp
ontaneous analogical transfer. In the A
-
B
-
A
-
C paradigm, the solution to be
transferred was always the same. In the A1
-
A2/B1
-
B2/C1
-
C2 paradigm, the children

15

were transferring three different solutions, one each for problem pair A, B and C. The
solution to p
roblem A1 was related to problem A2, the solution to problem B1 was
related to problem B2, and the solution to problem C1 was related to problem C2. The
children were forming a “learning set” to look for analogies.

The A
-
B
-
A
-
C paradigm was explored experim
entally by Brown et al. (1989).
Again, the Genie paradigm formed the core of the procedure. Children aged 7 were
given the Genie problem to solve by themselves with toy props including a real toy
carpet, and when they failed, they were given the Easter Bun
ny problem described
above. The experimenter helped them to solve problem B before re
-
presenting the
Genie problem, telling them that problem B would help them as the two problems
were “just the same”. Finally, a novel problem C (involving a farmer who had

to
transfer ripe cherries across an obstacle without damaging them) was administered.
Ann was most interested in performance with problem C, as success would indicate
that children had extracted “meta
-
knowledge” about trying to use analogies.
Children’s p
erformance was compared to that of controls who simply got the same
problems in the A
-
B
-
A
-
C order without any of the help or hints given to the
experimental group.

The results showed that 98% of the children in the instructional group solved
problem C by
rolling up paper, whereas only 38% of children in the control group
generated this solution. The children were “learning
-
to
-
learn”, learning to use analogy
even though they were never instructed in how the problems were alike. Similar
“learning
-
to
-
learn” e
ffects were demonstrated in the A1
-
A2/B1
-
B2/C1
-
C2 paradigm
with even younger children. Here children aged 3, 4 and 5 years learned to transfer
different solutions (stacking objects, pulling objects, swinging over ob
stacles)
between problem pairs. A
t the sa
me time
,

as they progressed through the problem

16

sequence they
extracted an abstract notion of the usefulness of problem solving by
analogy. When performance on the final problem, C2, was assessed, 85% of 3
-
year
-
olds, 95% of 4
-
year
-
olds and 100% of 5
-
year
-
o
lds were succes
sful (Brown, Kane &
Long, 1989).
These findings highlight the factors that are important when designing
instructional analogies for young children. Teachers need to present a series of
examples of a particular concept within an explicit fram
ework that emphasises
relational similarity, making the goal structure of the exercise transparent. However,
related work by Ann showed that even very young children can do all this for
themselves when they have rich conceptual representations of the domai
n being
studied, and are interested in the subject matter.

Analogies in Foundational Domains

One area of knowledge that is inherently interesting to young children is
biology. The natural world surrounds the young child and knowledge acquisition
about livi
ng things has been considered a “foundational domain” (Wellman &
Gelman, 1997). Ann was always interested in how young children reasoned when
everything was in their favour. She was impatient of the classical view that reasoning
is age
-
dependent and conten
t
-
independent (see Brown, 1990). Ann did not believe that

children gradually became increasingly efficient all
-
purpose learning machines,
acquiring and applying general reasoning strategies irrespectiv
e of the domain in
which they a
re reasoning. Rather, sh
e spent a large part of her career trying to
demonstrate that when children are reasoning in familiar domains, they have both
inductive and deductive logic at their disposal.

Ann thus extended her ‘functional fixedness’ studies to the developmentally
“pri
vileged” domain of biology and natural kinds. She taught 4
-
year
-
old children
about different mimicry defence mechanisms in real animals (Brown, 1989). Children

17

in the Fixedness condition learned about one such defence mechanism, visual mimicry
of a more da
ngerous animal. They learned about the capricorn beetle, which reveals
wasp
-
like markings when attacked, the hawkmoth caterpillar, which has underside
markings like a poisonous snake, and the crested rat, which can part its hair to show
skunk
-
like markings
. Children in the Flexibility group learned about three different
mimicry mechanisms. They learned about the hoverfly, which makes a sound like a
bee, the opossum, which can freeze and play dead when attacked, and the
walkingstick insect, which can change
shape to look like a twig or a leaf. Both groups
were then tested for their ability to learn a novel mimicry solution, camouflage by
colour change.

In this test phase of the experiment, the children were told about two novel
examples of mimicry. These wer
e Peppered moths, whose natural mixed white/grey
colouring had been predominantly white prior to industrialisation in Northern
England, but were now grey/black, and Pocket mice, who had been predominantly
light
-
coated rather than red
-
coated when they had l
ived in a sandy
-
floored forest, but
who had been forced to move into a forest with reddish soil. The children were asked
what had happened to the moths/mice. The correct answer was that over time the
moths had evolved to be predominantly grey/black (making

them less visible in the
polluted air), and the mice had evolved to be predominantly red
-
coated (making them
less visible against the reddish soil).

Ann found that the Fixedness group, who had learned only one mechanism of
camouflage (look like something

scary), were poor at inventing the new solution
(colour change), with only 10% thinking of this possibility. In contrast, children in the
Flexibility group were very good, with 82% inventing the colour change solution.
Given that 4
-
year
-
olds are close to
ceiling in this particular test of inventive flexibility

18

(albeit in optimal contexts of learning), it seems unlikely that older children will
perform more poorly. Again, Ann had come up with a clever and natural way of
demonstrating that as long as childre
n are reasoning in familiar domains, they are not
inductively ‘perceptually bound’, as had been believed for so long. Children are not
limited to simpler reasoning strategies, restricted to using analogies when surface
appearances suggest that transfer is
appropriate. Rather, they can reason on the basis
of deep principles and relational structure.

Analogical Reasoning in Toddlers?

Finally, Ann’s interest in how young children reason in optimal conditions led
her to push her age of enquiry younger and young
er. One of her most innovative
contributions to the field was in devising ways to study analogical reasoning in 1
-
, 2
-

and 3
-
year
-
olds. For example, in her work with Maria Crisafi, Ann found ways of
demonstrating analogical transfer in children aged from 2



4 years. In her work with
tool use with Anne Slattery, she was able to explore analogising in pre
-
verbal infants.

Crisafi and Brown (1986) devised a series of problems in which 2
-

and 3
-
year
-
olds had to extract different types of candy from different m
achines. For example,
with the “gumball” machine, they had to learn to insert a particular token into a
particular location to receive a gumball. A visually quite different apparatus, a plastic
golden box in three sections with separate doors and a window,

required the
identification of a different location using a different token (a nut) to get some candy.
Finally, a third automated machine, a different kind of box with windows and slots,
required an analogous solution involving a marble. The three problem
s thus differed
in surface similarity, but the underlying goal structure was the same. The children
could get the candy by working out which was the correct token, and which was the
correct location at which to use the token.


19

The three problems
just

descr
ibed

were designed to

foll
ow an “easy
-
to
-
hard”
sequence. T
he gumball machine is the easiest problem, the golden box comes next,
and the automated box is the most difficult. Only 10% of 3
-
year
-
olds solved the most
difficult automated box problem if it was p
receded by two irre
levant non
-
analogous
problems. In contrast, p
resenting the problems in an easy
-
to
-
hard sequence resulted in
42% of 2
-

and 3
-
year
-
olds solving the most difficult “box” problem.
If

the problem
similarities were pointed out as part of a gam
e to help Miss Piggy to get candy, via a
hint, performance
reached

100%. The children were given hints like “Okay, when
Miss Piggy knows how to play the first candy game, she will know how to play all the
candy games because they are all the same”. The aim

of the hint was to try to help the
children to reflect on the goal structure of the problems and thereby notic
e their
structural similarity. Ann found s
imilar results in a second study involving the
gumball machine, a toy dumper truck which looked quite d
ifferent, and the automated
box. Although surface similarity was now reduced, 87% of the children solved the
most difficult box problem when given hints. In a final study using this apparatus, in
which children had to instruct Kermit the Frog in how to get

the candy from each
machine, solution of the box problem was achieved by 90% of children, compared to
less than 10% of controls who simply practiced getting the candy. Crisafi and Brown
argued that the difficulty for young children lay not in applying ana
logies, but in
noticing task similarity. Either telling them that problems were similar (via hints), or
inducing them to state problem similarity for themselves (by helping Kermit) led to
very early competence in analogy tasks.

In her work with pre
-
verbal
infants, Ann built upon babies’ early focus on
causal information. She noted that a search for causation or mechanism is
fundamental to learning (Brown, 1990). When you are an immobile baby, a pressing

20

need is to learn how to use tools to bring desired obj
ects into reach. Indeed, Piaget
(1952) himself pointed this out, noting many instances of how his own children pulled
on blankets or table cloths to bring toys within reach. Ann therefore proposed that if
analogical problems were posed to infants using (a)

similarity at the level of causal
structure, and (b) a type of causality that had been differentiated within the infants’
emerging theory of the world, rapid learning and transfer by analogy would be
expected. In Brown (1990), she reported a series of stu
dies with infants aged 18
months and older based on the relation of “pulling”. The child sat restrained in an
infant
-
seat next to its mother, with a highly desirable toy (like a toy carousel) just out
of reach. Within reach lay an assortment of potential t
ools for reaching the toy. All
tools were painted with red and white stripes (high surface similarity). At least one
potential tool was long enough and had a head that was rigid enough to enable pulling
(e.g., a toy rake, a toy walking cane). Other potenti
al tools were too short, or were not
rigid, or had unsuitable heads for pulling (e.g., a feather duster). The dependent
measure was which tool the infant reached for first.

Below 24 months of age, Ann reported that the infants usually required their
mothe
rs to demonstrate the first solution. Only 21% of this age group solved the
reaching problem without help. However, on the transfer problem (for which the
desirable toy and the tool set were changed), 92% solved the problem first time if
there was only one

tool of suitable length, and 54% solved the problem first time if
there were 2 tools of suitable length but only one with a rigid head for pulling. Further
studies showed that the main factors explaining tool choice were length, rigidity and
effective pul
ling heads. Surface similarity (candy stripes, shape) were not influential.
Once again, Ann had demonstrated that as long as children understand a particular
schema or domain, they can reason on the basis of deep principles and relational

21

structure. In the

right circumstances, they can learn by analogy very efficiently. Ann’s
conclusion was that “even 1
-
year
-
olds can override surface features of physical
similarity and respond in terms of causal relations if they know what kind of thing it is
that they are
deal
ing with” (Brown, 1990, p. 127). In other words, even babies can use
analogies

if they understand the causal mechanisms in question.

Analogies in Reading and Mathematics

Analogies in the classroom do not
often

depend on causal mechanisms,
although in
subjects like physics and biology
,

causal analogies
may be

quite
pervasive. Yet children can apply their ability to use analogy to the acquisition of
basic
skills like
reading and mathematics.
The key to analogy use in these domains is
the recognition of s
hared relational structure.
I will focus here on reading, which has
been an area of interest to m
e for a long time (see English
, 2004
, for a
recent
survey

of
analogies in mathematics). As w
e have seen
,

instructional analogies for young
children work best w
hen teachers present a series of examples of a particular concept
within an explicit framework that emphasises relational similarity, making the goal
structure of the exercise transparent. What are the relevant concepts and relational
similarities in learn
ing to read?

The strongest predictor of how well a child will learn to read and spell their
language is their “phonological awareness”.
Phonological awareness

refers to the

child’s

ability to reflect on the sound patterns of the
ir

native language,
and is
m
easured by the
ir

facility in detecting and manipulating the component sounds in
words. For example, a child might be asked to detect which words rhyme out of “cat,
pat, fit”, or to say “
star” without the “s” sound, requiring

the response “tar”. As
children

acquire language, they become aware of the sound patterning characteristic of
their particular language, and use similarities and differences in this sound patterning

22

as one means of organising the mental lexicon (see Ziegler & Goswami, 2005). For
learnin
g to read and write English, an important unit of phonological similarity is the
rhyme (see De Cara & Goswami, 2002). Rhyme awareness measured prior to entering
school is a strong predictor of reading and spelling acquisition, and children who are
dyslexic

appear to have rather weak rhyming skills (Bradley & Bryant, 1978, 1983).

From an analogy perspective, this means that rhyme is an important kind of
relational similarity for learning to read. A child who is sensitive to rhyming similarity
will already be

organising words in the language into rhyming categories, such as “cat,
hat, mat, fat” or “light, night, sight, fight”. A key concept in acquiring reading is the
“alphabetic principle”, the concept that letters represent
units of sound that are smaller
th
an words
. In many of the world’s languages, letters represent distinct single sounds
(called phonemes), and reliably and consistently represent the same phoneme in every
word in the language. In a language like German, for example, the letter A always has
the same sound. It makes the same sound in the

German

words
Ball, Sand and Garten.
Compare this to English, in which the letter A does not make the same sound in
exactly the same words (ball, sand and garden). For the English child learning to read,
the al
phabetic principle is more difficult to understand, as it only works some of the
time. What is the English child to do?

One useful strategy is to use higher
-
order consistencies in the spelling system
of English.
In fact, the spelling patterns of English ar
e more consistent in their links to
sound at the level of the rhyme than at the level of the phoneme (Treiman, Mullennix,
Bijeljac
-
Babic, & Richmond
-
Welty, 1995).
The inconsistency of spelling
-
to
-
sound
correspondence
s

at the
letter
level means that childre
n learning to read English need to
supplement the use of letter
-
sound recoding with strategies like using analogies
between
groups of shared letters
. A word like “light” is difficult to recode to sound if

23

the child tries to sound out each
individual letter

and blend these sounds

into a word.
However, if the child recognises the similarity between “light”, “fight” and “night”,
then the child can use a rhyme analogy to predict that all these words will be
pronounced
in
the same way.
In fact, there are 90 diff
erent words in English that use
the
letter

pattern “
-
ight”, and in all of them this pattern is pronounced as in “light”.



Research exploring children’s ability to use rhyme analogies in reading
suggests that even beginning readers can use analogies if th
ey have good phonological
skills. For example, in a series of experiments using monosyllabic words, Goswami
(1986, 1988) taught beginning readers a “clue” word to use as a basis for analogy,
such as “beak”, and then gave them new words to try to read such
as “peak” and
“weak”. The children made many analogies, although they did not use analogy on
every occasion when it made sense to do so. They even made
some
analogies when
reading stories, when the clue and test words were part of the text of the story. In

a
series of
further
studies exploring individual differences in the tendency to draw
analogies,
it was shown

that phonological awareness of rhyme appeared to be the key

(Goswami, 1990; Goswami & Mead, 1992)
. Children with good rhyming skills made
more ana
logies than children with poor rhyming skills.
Rhyme analogies are

used

less
frequent
ly by children

in orthographies where letters have a more consistent
correspondence to sound. For example, Goswami, Ziegler, Dalton and Schneider
(2003) compared English a
nd German children’s use of rhyme analogies. They did
this by asking the children to read “nonsense” words, words with spelling patterns that
could be recoded to sound but that had no meaning, like “dake” or “mirn”. The
English children made use of rhyme a
nalogies, and the German children did not.
English children were better at reading nonsense words like “dake” when they were
spelled by analogy to real English words (bake, make, lake) than when the same sound

24

pattern was spelled using a
letter

pattern tha
t did not exist in English (such as “daik”,
there are no English words with the letter pattern “
-
aik” at the end). For German
children, there was no difference

between these two types of nonsense word
.
German
children

were so used to letters always making
the same sounds that they were equally
accurate
at

reading nonsense words like “dake”
and

nonsense words like “daik”.

More recently, work by educational psychologists like Walton has
demonstrated that when teachers set out to use analogy as an instructiona
l mechanism
for reading in English, it works very well. Walton and his colleagues compared the
effects of teaching beginning readers to read by using a “rhyme analogy” strategy
(‘beak’
-

‘peak’) with the effects of teaching beginners to read by using a
let
ter
-
sound

recoding strategy

(Walton,
Walton & Felton
, 2001)
. All the children were pre
-
readers.
Reading ability was assessed following 3 months of training, and four different kinds
of words were used to assess different skills (analogy
-

irregular pattern
s [
fight
-
sight
],
analogy
-

regular patterns [
bed
-
ted
], letter recoding [
bat
-
bet
] and nonwords [
hib
]).
Walton et al.
(2001)
found that both training groups showed broadly equal reading
acquisition gains. However, whereas the rhyme analogy group could also r
ead new
words requiring letter
-
recoding skills, the letter
-
recoding group could not read new
words requiring rhyme analogy skills. A recent meta
-
analysis of

early

literacy
instruction
al

programmes in the United States comparing the effectiveness of “large
unit” programmes (like analogy) with “small unit” programmes (
like
letter
-
sound
recoding) has
also
shown that
their effects are broadly similar (Ehri, Nunes, Willows,
Schuster, Yaghoub
-
Zadeh & Shanahan, 2001). Both types of programme were
preferable to a “
whole language” instructional system, where little direct instruction
concerning the alphabetic principle was provided.

Conclusion


25

Analogy can be effortless if measures of analogical reasoning in children
involve familiar relations that are embedded in dom
ains whose causal structure is
familiar to the child. Analogy can be effortful or absent if measures of analogy are
based on unfamiliar relations embedded in unfamiliar domains. Such measures will
seriously underestimate children’s analogical skills. The f
ailure to appreciate the
importance of domain
-
specific knowledge

led early researchers to conclude that
analogical reasoning was absent until early adolescence. The paradigms chosen (the
picture sorting task of Piaget et al., 1977; the verbal multiple choi
ce paradigm of
Sternberg & Nigro, 1980) depended on analogical relations that were unfamiliar to
young children. Ann Brown’s research demonstrated clearly that analogical reasoning
is used by children as young as 1, 2 and 3 years of age. She argued convinc
ingly that
analogy was particularly likely if there was similarity across problems at the level of
causal structure, and if the type of causal mechanism involved had been differentiated
by the child. With the right domain knowledge, young children are insi
ghtful and
flexible learners, and use analogies all the time.

Nevertheless, it is important to note that there is still a role for development.
As children learn more about the world, the type of analogies that they make will
change. Their knowledge about
the world will become richer, and so the structure of
their knowledge will become deeper, with more complex relationships represented.
Such development enables deeper and more complex analogies.

The important
relations for analogy can also be taught. In th
e reading analogies considered, children
can be taught about rhyme, and can be taught to use rhyme analogy as a recoding
strategy.

There is also a
n outstanding

developmental question about whether changes
in analogy use
are dependent solely on changes in t
he knowledge base, or whether
information processing factors, such as the number of relations that can be represented

26

in primary memory at any one time, determine these changes (e.g., Halford, Wilson &
Phillips, 1999). Nevertheless, analogies at all ages p
rovide a powerful logical tool for
explaining and learning about the world
, contributing

to the acquisition
and
restructuring of knowledge
. Analogies play an impo
rtant role in conceptual change,
and

this is particularly clear in the history of science (e.g
, the Benzene analogy). In the
history of developmental cognitive science, the pioneering work of Ann Brown has
made a particular contribution to our understanding of the development of analogical
reasoning in children.




27

Tribute
.

I would like to record
my gratitude to Ann, whom I was very lucky to have as my
mentor for my year in Champaign
-
Urbana (1987
-
1988, supported by a Harkness
Fellowship). It was so intellectually exciting to work with Ann and her husband Joe
Campione, but it was also memorable beca
use of Ann’s warmth and welcome
-

I was
simply treated like one of the family. Ann’s ingenious mind and the depth and breadth
of her grasp of learning and transfer in children has been rivalled by few if any. Her
commitment to the importance of rigorous re
search to improve the learning and
education of young children lives on in her published work.


28

References


Achenbach, T.M. (1971). The children’s associative responding test: A two
-
year
follow
-
up.
Journal of Educational Psychology
,
61
, 340
-
348.

Bradley L
. and Bryant P. (1978). Difficulties in auditory organization as a possible
cause of reading backwardness.
Nature,

271,

746

747
.

Bradley, L. and Bryant, P.E. (1983). Categorising sounds and learning to read: A
causal connection.
Nature
,
310
, 419
-
421.

Bro
wn, A.L. (1989). Analogical learning and transfer: What develops? In S.
Vosniadou & A. Ortony (Eds.)
Similarity and Analogical Reasoning
, (pp. 369
-
412). Cambridge: Cambridge University Press.

Brown, A.L. (1990). Domain
-
specific principles affect learning a
nd transfer in
children.
Cognitive Science
,
14
, 107
-
133.

Brown, A.L., & Kane, M.J. (1988). Preschool children can learn to transfer: Learning
to learn and learning by example.
Cognitive Psychology
,
20
, 493
-
523.

Brown, A.L., Kane, M.J., & Echols, C.H. (1986
). Young children’s mental models
determine analogical transfer across problems with a common goal structure.
Cognitive Development
,
1
, 103
-
121.

Brown, A.L., Kane, M.J., & Long, C. (1989). Analogical transfer in young children:
Analogies as tools for commu
nication and exposition.
Applied Cognitive
Psychology
,
3
, 275
-
293.

Bullock, M., Gelman, R., & Baillargeon, R. (1982). The development of causal
reasoning. In W.J. Friedman (Ed.),
The Developmental Psychology of Time
, pp.
209
-
254. New York: Academic Press.


29

Crisafi, M.A. & Brown, A.L. (1986). Analogical transfer in very young children:
Combining two separately learned solutions to reach a goal.
Child Development
,
57
, 953
-
968.

De Cara, B., & Goswami, U. (2002).
Statistical Analysis of Similarity Relations
amon
g Spoken Words: Evidence for the Special Status of Rimes in English.
Behavioural Research Methods and Instrumentation
,
34

(3),

416
-
423
.

Ehri, L.C., Nunes, S.R., Willows, D.A., Schuster, B.V., Yaghoub
-
Zadeh, Z., &
Shanahan, T. (2001). Phonemic awareness ins
truction helps children learn to
read: Evidence from the National Reading Panel’s Meta
-
analysis.
Reading
Research Quarterly
,
36
, 250
-
287.

English, L. (2004
)
Mathematical and Analogical Reasoning of Young Learners
.

Mahwah, NJ:
Lawrence Erlbaum Ass.


Gentner
, D. (1983). Structure
-
mapping: A theoretical framework for analogy.
Cognitive Science
,
7
, 155
-
170.

Gentner, D. (1989). The Mechanisms of Analogical Learning. In S. Vosniadou & A.
Ortony (Eds.)
Similarity and Analogical Reasoning
, (pp. 199
-
241). London:
Ca
mbridge University Press.

Goswami, U. (1986) Children's use of analogy in learning to read: A developmental
study.
Journal of Experimental Child Psychology
,
42
, 73
-
83.

Goswami, U. (1988) Orthographic analogies and reading development.
Quarterly
Journal of
Experimental Psychology
,
40A
, 239
-
268.

Goswami, U. (1990) A special link between rhyming skill and the use of orthographic
analogies by beginning readers?
Journal of Child Psychology and Psychiatry
,
31

(2),
301
-
311.


30

Goswami, U. and Mead, F. (1992). Onset a
nd Rime Awareness and Analogies in
Reading.
Reading Research Quarterly
,
27

(2
),
152
-
162.

Goswami, U. (1991). Analogical reasoning: What develops? A review of research and
theory.
Child Development
,
62
, 1
-
22.

Goswami, U. (1992).
Analogical Reasoning in Chil
dren
. Hillsdale, NJ: Lawrence
Erlbaum Associates.

Goswami, U. (1998).
Cognition in Children
. Hove: Psychology Press.

Goswami, U., & Brown, A.L. (1989). Melting chocolate and melting snowmen:
Analogical reasoning and causal relations.
Cognition, 35
,
69
-
95.

Goswami, U. & Brown, A.L. (1990). Higher
-
order structure and relational reasoning:
Contrasting analogical and thematic relations.
Cognition
,
36
,
207
-
226.

Goswami, U., Ziegler, J. C., Dalton, L., & Schneider, W. (2003). Nonword reading
across orthographies
: How flexible is the choice of reading units?
Applied
Psycholinguistics
,
24
, 235
-
247.

Halford, G.S., Wilson, W.H., & Phillips, S. (1999). Processing capacity defined by
relational complexity: Implications for comparative, developmental and cognitive
psych
ology.
Behavioural & Brain Sciences
,
21

(6).

Holyoak, K.J., & Thagard, P. (1995).
Mental Leaps
. Cambridge, MA: MIT Press.

Holyoak, K.J., Junn, E.N., & Billman, D.O. (1984). Development of analogical
problem
-
solving skills.
Child Development
,
55
, 2042
-
2055
.

Inhelder, B., & Piaget, J. (1958).
The growth of logical thinking from childhood to
adolescence
. New York: Basic Books.

Piaget, J., Montangero, J. & Billeter, J. (1977).
La formation des correlats. In J. Piaget
(ed.)
Recherches sur L'Abstraction Reflechi
ssante I
, pp. 115
-
129. Paris: Presses
Universitaires de France.


31

Sternberg, R.J., & Nigro, G. (1980). Developmental patterns in the solution of verbal
analogies.
Child Development
,
51
, 27
-
38.

Treiman, R., Mullennix, J., Bijeljac
-
Babic, R., & Richmond
-
Welty,

E. D. (1995). The
special role of rimes in the description, use, and acquisition of English
orthography.
Journal of Experimental Psychology
:
General
,
124
(2), 107
-
136.

Walton, P.D., Walton, L.M., & Felton, K. (2001). Teaching rime analogy or letter
recodin
g reading strategies to pre
-
readers: Effects on prereading skills and word
reading.
Journal of Educational Psychology
,
93
, 160
-
180.

Wellman, H.M., & Gelman, S.A. (1997). Knowledge acquisition in foundational
domains. In D. Kuhn & R.S. Siegler (Eds),
Handbo
ok of Child Psychology,
Volume 2
:
Cognition, Perception and Language
, pp. 523
-
573 (4
th

Edition).

Ziegler, J., & Goswami, U. (2005). Reading Acquisition, Developmental Dyslexia,
and Skilled Reading Across Languages: A Psycholinguistic Grain Size Theory.
P
sychological Bulletin
,
131

(1),

3
-
29
.



32

Figure Captions.

1. The analogy terms, correct answer and distractors for the analogy
train:traintracks::ship:sea

(Goswami & Brown, 1990).