Analogical Reasoning in Children
Usha Goswami, Institute of Child Health, University College London.
Analogical thinking lies at
the core of human creativity. It has been argued that the very act of forming
an analogy requires a kind of ‘mental leap’, as it necessitates seeing one
thing as if it were another (Holyoak & Thagard, 1995). Famous analogies in
science frequently reveal their inventor’s ability to make these mental leaps.
However, as well as being an important cognitive mechanism in creative
thinking, analogy is the basis of much of our everyday problem solving.
Small-scale ‘mental leaps’ are being made all the time by children and adults
and form a core part of our everyday mental repertoire. This chapter examines
the availability of analogical reasoning to young children. Far from being a
sophisticated reasoning strategy characteristic of older children and adults,
it will be argued that analogical reasoning is available from infancy onwards.
‘Analogy pervades all our thinking, our everyday speech and our trivial
conclusions as well as artistic ways of expression and the highest scientific
achievements’ (Polya, 1957).
The Development of
Analogical Reasoning
The Relational
Similarity Constraint
Even though analogies
require mental leaps, they are guided by certain basic constraints. The most
important is the need for relational similarity. In many analogies, the
objects in the analogy are not similar at all. Their similarity is at a purely
relational level. A striking example of this 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 benzene could be
arranged in a ring. The similarity between the snake and the carbon atoms was
at a purely relational level - circular arrangement. The fact that the
objects being compared in an analogy should be linked by the same
relations is widely accepted to be the hallmark of analogical reasoning, and
has been called the ‘relational similarity constraint’ (Goswami, 1992).
Quite frequently, objects in
the two situations being compared in an analogy do bear some resemblance to
each other - they share ‘surface’ similarity. This similarity of appearance can
support the analogical mapping. An example is the invention of Velcro, which
followed the observation by Georges de Mestral that burdock burrs stuck to his
dog’s fur (see Holyoak & Thagard, 1995). The surface similarity in
the appearance of the small hairs coating burdock burrs and the fuzz on Velcro
supports the relational similarity of ‘effective sticking mechanism’. These two
factors - relational similarity and surface similarity - both affect analogical
reasoning (e.g., Gentner, 1989). Gentner’s work shows clearly that surface
similarities between objects can support relational mappings and hence affect
analogical performance. In order to examine the development of analogical
reasoning in children, therefore, we need to examine their understanding of the
relational similarity constraint in the absence of surface similarity.
The Item Analogy
Task
The standard test for
analogical reasoning (used in IQ testing) is the ‘item analogy’ task. In item
analogies, two items A and B are presented to the child, a third item C is
presented, and the child is required to generate a D term that has the same
relation to C as B has to A. Successful generation of a D term requires the use
of the relational similarity constraint. For example, if the child is given the
items ‘cat is to kitten as dog is to ?’, she is expected to generate the
solution term ‘puppy’. The response ‘bone’, which is a strong associate of dog,
would be an error. Another example is the analogy ‘Bicycle is to handlebars
as ship is to ?’. Here the relation constraining the choice of a D term is
‘steering mechanism’, and so a child who offered the completion term ‘bird’
would not be credited with understanding the relational similarity constraint.
The first developmental
psychologist to study analogical reasoning, Piaget, used a pictorial version of
the item analogy task, and his data suggested that understanding of the
relational similarity constraint did not develop until early adolescence (Piaget,
Montangero & Billeter, 1977). Younger children tested by Piaget offered
solutions like ‘bird’ to the bicycle/ship analogy, giving reasons like
‘both birds and ships are found on the lake’. Piaget concluded that younger
children solved analogies on the basis of associations (see also Sternberg
& Nigro, 1980). He argued that children only became able to reason on the
basis of relational similarity at around 11-12 years of age. This conclusion
was accepted in developmental psychology for many years. Piaget’s conclusions
about analogical development fitted neatly into his influential theory of the
development of logical reasoning in children. Analogies appeared to be
characteristic of the final stage of logical development - the stage of ‘formal
operational’ reasoning. Formal operational reasoning required children to
operate mentally on the results of simpler operations. A simpler operation was
finding relations between objects (‘first-order’ relations). As analogies
required children to reason about similarities between the relations
between objects (‘second-order’ relations), it appeared to be a typical formal
operational skill.
The Role of
Relational Familiarity in Analogical Development
Closer inspection of
Piaget’s experimental methods, however, suggest that his conclusions about
analogical development were too negative (Goswami, 1991). A key methodological
problem was that Piaget did not check whether the younger children in his experiments
understood the relations on which his analogies were based (for example, the
relation ‘steering mechanism’ in the bicycle:handlebars::ship:rudder
analogy). This failure to ensure that the first-order relations were familiar
means that the younger children’s failure to solve the item analogies in
Piaget’s experiments could have arisen from a lack of knowledge of the
relations being used. Item analogies based on unfamiliar relations would
obviously underestimate analogical ability.
One way to test this
possibility is to design analogies based on relations that are known to be
highly familiar to younger children from other cognitive developmental
research. Simple causal relations such as melting, wetting
and cutting are known to be acquired early in development, and to be
available for use in picture-based tasks by the ages of 3 and 4 years.
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. Item analogies such
as ‘playdoh is to cut playdoh as apple is to cut apple’ and ‘bird is
to nest as dog is to doghouse’ can thus be used to examine whether 3- to
5-year-olds have the ability to reason by analogy.
For this young age group, a
picture-based version of the item analogy task is required (Goswami, 1989,
Goswami & Brown, 1989, 1990). The analogy task can then be presented as a
‘game’ about matching pictures. In our studies, the children were shown a ‘game
board’ with four slots for pictures, the slots being grouped into two pairs for
the A:B and C:D parts of the analogy (see Figure 1). As the children watched,
the experimenter presented the first three terms of a given analogy (e.g.,
pictures of a bird [A], a nest [B], and a dog [C]). As the pictures were
presented, the child was asked to name each one to ensure that they were
familiar. 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.
----------------------
Figure 1 about here
----------------------
Following the request for a
prediction, the experimenter showed the child a choice of solution terms. For
the bird/dog analogy, these were pictures of a doghouse, a cat,
another dog, and a bone (see
Figure 1). The different choices were designed to test different theories of
analogical development. The correct choice, which would indicate analogical
ability, was the doghouse. The associative choice was the bone.
Selection of the bone would be expected if younger children rely on associative
reasoning to solve analogies, as Piaget and Sternberg had claimed. The other
choices were a ‘mere appearance match’ choice (the second dog), and a category
match (the cat). ‘Mere appearance’ matching is a term coined by Gentner (1989)
to refer to the matching of object or ‘surface’ similarities when attempting to
solve analogies (such as choosing another dog to match the dog in the C term,
or choosing something that looks like a nest to match the B term). Gentner has
suggested that younger children might rely quite heavily on object similarity
in reaching analogical solutions (Gentner, 1989).
The matching game showed
that all children tested (4-, 5- and 9-year-olds) performed at levels
significantly above chance in the analogy task, selecting the correct
completion term 59%, 66% and 94% of the time respectively. There was no
evidence of mere appearance matching. Although many younger children were shy
of making predictions prior to seeing the solution choices, 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, and
was quite certain that he was correct. He continued "I don't have to look
[at the solution pictures] -- the name of the baby is puppy!" Once he
looked at the different solution options, however, he decided that the doghouse
was the correct response.
The 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 the
control task, the children were simply shown the C term picture along with the
correct solution term and the distractors, and were asked to choose which
picture ‘went best’ with the C term picture. For example, the children were
shown the picture of the dog, 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 the 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 cognitive flexibility
displays a full understanding of analogy, and provides evidence of truly mental
operations, thereby meeting Piaget’s original criteria for the presence of
‘true’ analogical reasoning.
The Relationship
between Relational Knowledge and Analogical Responding
From the picture analogy
game, we know that the ability to reason by analogy is present by at least age
4. However, the analogy game may still have underestimated analogical
ability. This is because relational knowledge was not measured independently
of analogical success. Instead, it was simply assumed that familiar relations
had been selected for the analogies, leaving 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 intended by the
experimenter - like Lucas.
The idea that children’s
analogical performance depends on their relational knowledge has been called
the ‘relational familiarity’ hypothesis’ (Goswami, 1992). In order to establish whether
children's use of analogical reasoning is knowledge-based, dependent on
relational familiarity rather than analogical ability, relational knowledge as
well as analogical ability needs to be assessed. This can be done by
changing the control task in the picture matching game. The appropriate control
task measures children's knowledge of the relations being used in the analogies
that are presented in the item analogy task.
A second set of analogy
experiments using the picture matching game were thus carried out to test the
relational familiarity hypothesis. This time, item analogies based on physical
causal relations like melting, cutting and wetting were used. These relations are known to
be available by 3 - 4 years (Bullock, Gelman & Baillargeon, 1982). Children
aged from 3 to 6 were given analogies like ‘chocolate is to melted chocolate
as snowman is to ?’, and ‘playdoh is to cut playdoh as apple is to ?’.
This time 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 mere appearance
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 a control condition. Here the children were shown three pictures of
items that had been causally transformed (e.g., cut playdoh, cut bread, cut
apple), and were asked to select the causal agent responsible for the
transformation from a set of pictures of possible agents (e.g., a knife, water,
the sun).
The results 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% of 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 dirty snowman). This suggested that
the children knew that a causal transformation was required, but did not always
select the correct one. The next most frequent error was to select the correct
causal transformation of the wrong object. There was also a significant conditional
relationship between performance in the analogy condition and performance in
the control condition, as would be predicted by the relational familiarity
hypothesis. This conditional relationship arose because individual children’s performance
in the analogy task was linked to their knowledge of the corresponding causal
relations. Analogical reasoning in children is thus highly dependent on
relational knowledge. This raises the possibility that children younger than 3
years of age may be able to reason by analogy - as long as they have the
requisite relational knowledge.
Analogical Reasoning in
Infants and Toddlers
It is difficult to use the
item analogy format to demonstrate analogical competence in children younger
than 3 because of the abstract nature of the task. Researchers working with
very young children have thus devised ingenious problem analogies in
order to show analogical reasoning at work. In problem analogies, a young child
is faced with a problem that they need to solve. Let us call this problem B.
The use of an analogy from a previously-experienced problem, problem A, offers
a solution. The measure of analogical reasoning is whether the children think
of using the solution from problem A in order to solve problem B.
Chen and his colleagues
devised a way of giving problem analogies to infants as young as 10 months of
age, using a procedure first developed by Brown (1989) for 1 1/2- to
2-year-olds. Brown's procedure depended on seeing whether toddlers could learn
how to acquire attractive toys that were out of reach. Different objects (such
as a variety of tools, some more effective than others) were provided as a means
to a particular end (bringing the desired toy within grasping distance).
The analogy was that the means-to-an-end solution that worked for getting one
toy in fact worked for all of the problems given, even though the problems
themselves appeared on the surface to be rather different. Brown and her
colleagues used this paradigm to study analogical reasoning in children aged
17-36 months. Chen, Campbell and Polley (1995) were able to extend it to
infants.
In Chen et al.'s procedure,
the infants came into the laboratory and were presented with an Ernie doll that
was out of their reach. The Ernie doll was also behind a barrier (a box), and
had a string attached to him that was lying on a cloth (see Figure 2). In order
to bring the doll within reach, the infants needed to learn to perform a series
of actions. They had to remove the barrier, to pull on the cloth so that the
string attached to the toy came within their grasp, and then to pull on the
string itself so that they could reach Ernie. Following success on the first
trial, two different toy problem scenarios were presented, each using identical
tools (cloths, boxes and strings). However, each problem appeared to be
different to the problems that preceded it, as the cloths, boxes and strings
were always dissimilar to those encountered before. In addition, in each
problem two strings and two cloths were provided, although only
one pair could be used to reach the toy.
----------------------
Figure 2 about here
----------------------
Chen et al. tested infants
aged 10 and 13 months in the Ernie paradigm. They found that although some of
the older infants worked out the solution to reaching Ernie on their own,
others needed their parents to model the solution to the first toy acquisition
problem for them. Once the solution to the first problem had been modelled,
however, the 13-month-olds readily transferred an analogous solution to the
second and third problems. The younger infants (10 months) needed more salient
perceptual support in order for reasoning by analogy to occur. They only showed
spontaneous evidence of using analogies when the perceptual similarity between
the problems was increased (for example, by using the same goal toy, such as
the Ernie doll, in all three problems).
Freeman (1996) devised a
series of analogies for 2-year-olds using real objects and models. Her
analogies were based on the simple causal relations of stretching, fixing,
opening, rolling, breaking and attaching. For
example, a child might watch the experimenter stretching a loose rubber
band between two plexiglass poles in order to make a 'bridge' that she could
roll an orange across ("Look what I'm going to do, I'm going to use this
stuff to roll the orange! Stretch it out, put it on - wow, that's how I roll
the orange!"). Following an opportunity to roll the orange by themselves,
the children were given a transfer problem involving a loose piece of elastic,
a toy bird and a model with a tree at one end and a rock at the other. They
were asked "can you use this stuff to help the bird fly?". The
intended solution was to stretch the elastic from the tree to the rock, and to
'fly' the bird along it. In a third analogy problem, the children were asked to
"give the doll a ride" by stretching some ribbon between two towers
of different heights that were fixed to a base board. Children in a control
condition were simply asked to "help the bird fly" and "give the
doll a ride" without first seeing the base analogy of rolling the orange.
Freeman found that whereas
only 6% of the children in the control condition thought of the stretching
solution to the transfer problem, 28% of 30-month-olds in the analogy condition
did so, and this figure rose to 48% following hints to use an analogy
("You know what? To help the bird fly, we have to change this", said
while pointing to the elastic). When the same hint was given to the children in
the control condition, only 14% thought of the stretching solution.
Although these performance levels may appear modest, they are comparable to the
spontaneous levels of analogical transfer found in adults. Problem analogy
studies conducted with adults typically find spontaneous transfer levels of
around 30%, at least in unfamiliar problem scenarios (e.g., Gick & Holyoak,
1980).
The studies reviewed above
suggest that analogical reasoning is available at 1 and 2 years of age.
Children younger than about 1 year may need the support of perceptual or
surface similarity in order to use analogies successfully (see Gentner, 1989).
However, the degree of surface similarity required may depend on the extent to
which the relations relevant to the analogy have been represented by the
infant. Remarkable research evidence from studies of babies suggests that a
focus on relations in the absence of surface similarity is strong even in the
first year of life.
The Origins of Relational
Reasoning
The knowledge that children have
about objects and events in their worlds, and the knowledge that they have
about the causal and explanatory structures underlying relations between
these objects and events, is known to expand at a terrific rate from the very
first months of infancy. Infants and young children gain a lot of their
knowledge by observing and interacting with the world around them. Equally
importantly, they seek to explain their everyday worlds to themselves.
The result is that the knowledge base is continually restructured and revised
in the light of experience. Analogy may play an important role in this process
of acquisition and self-explanation of knowledge (Goswami, 1998). This process
of revision and restructuring is aided by the development of abstract knowledge
structures (schemas and scripts) for representing the temporal and causal
frameworks of events, frameworks that facilitate the storage and organisation
of incoming information and presumably also the application of analogy.
However, the recognition of relational similarity does not appear to depend
on the development of such abstract representations. The ability to recognise
relational similarities appears to be present from very early in development.
This has been called the ‘relational primacy’ hypothesis (Goswami, 1992, 1996).
Relational
Processing in Infants: The Physical World
The roots of relational
competence can be found in the mechanisms that infants use to process
perceptual information. The early representation of perceptual prototypes,
for example, appears to depend on the extraction of correlational information
about visual features, suggesting sensitivity to the relations between those
features (see Goswami, 1996, 1998). For example, infants who were shown a
series of ‘cartoon’ animals attended not only to the distinctive features of
these animals (e.g., their necks and legs), but to the correlations between the
features (long legs went with short necks, short legs went with long necks, see
Younger & Cohen, 1983). New exemplars were then categorised according to
their relational similarity to the prototype. Structural similarities among
perceptual stimuli can also be demonstrated, and these may well form the basis
of relational representations of those stimuli at a conceptual level (e.g.,
Smith & Heise, 1992). For example, structural similarities in auditory and
visual perceptual events can convey relational information. A tone of music may
be ascending because of acoustic properties such as timbre. A visual stimulus
may have properties that convey ascension, such as a locus of highest density
at its uppermost point (e.g., an arrow). Infants who are shown a choice between
two visual stimuli, an arrow pointing upwards and an arrow pointing downwards,
and who hear an ascending tone of music coming from the mid-line,
preferentially look at the ‘up’ arrow (Wagner, Winner, Cicchetti & Gardner,
1981). This is a form of analogy. These inherent perceptual properties
of rising tones of music and of arrows pointing upwards could convey the shared
relation 'ascending', which is part of our mental representation of
these physical events. Infants may first be sensitive to the similarity between
the inherent structure of physical events, and then come to represent
them as relationally similar (see Goswami, 1998, for further discussion).
Further support for the
notion that infants are sensitive to relations from early in development comes
from evidence that infants preferentially attend to changes in the
visual scene. Change is informative, because change signals the occurrence of events.
Events in the visual world are usually described by relations between
objects (such as ball collides with teddy, child pushes friend).
The ability to detect structural regularities in these relations (to notice
relational similarity) would be cognitively powerful in terms of knowledge
acquisition, as events in the visual world are frequently causal in
nature. The detection of regularities in causal relations like collide, push
and supports between different objects (such as ball collides with teddy,
toy car collides with toy garage, mummy collides with daddy) would involve a
rudimentary form of analogical reasoning.
There is quite a lot of
evidence that infants are sensitive to cause-effect relations by about 6 months
of age (see Goswami, 1998, for a review). Other types of relations, such as
spatial relations (above and below) and quantitative relations (more
than and less than) are also detected by this age. One way of
measuring infants' ability to process and represent spatial, numerical and
causal relations is to introduce violations of typical regularities in
the relations between objects, which then result in physically 'impossible'
events. For example, an object with no visible means of support can remain
stationary in mid-air instead of falling to the ground. The experimental investigation
of infants' ability to detect such violations is the main source of evidence
for infants’ ability to process relations between events.
Consider the causal
relations involved in support. Adults are well aware that if they put a box
of cookies down on a table and the box protrudes too far over the table’s edge,
the cookies will fall onto the floor, whereas if only a small portion of the
bottom surface of the box protrudes they will not. The recognition of how much
contact is required to support an object in different situations must require a
degree of relational comparison between one situation and the next. Baillargeon,
Needham and DeVos (1992) studied 6.5-month-old infants' expectations about when
a box would fall off a platform. The infants were shown a box sitting at the
left-hand end of a long platform, and then watched as the finger of a gloved
hand pushed the box along the platform until part of it was suspended over the
right-hand edge. For some infants, the pushing continued until 85% of the
bottom surface of the box protruded over the platform, and for others the
pushing stopped when 30% of the bottom surface of the box protruded over the
platform. In a control condition the same infants watched the box being pushed
to the right-hand end of the platform, but the bottom surface of the box
remained in full contact with the platform. The infants spent reliably longer
looking at the apparatus in the 85% protrusion event than in the full-contact
control event. This suggests that they expected the box to fall off the
platform (the box was able to remain magically suspended in mid-air via a
hidden hand). The infants in the 30% protrusion event looked equally during the
protrusion event and the control event. Baillargeon et al. argued that the
infants were able to judge how much contact was required between the box
and the platform in order for the box to be stable. In fact, Baillargeon has repeatedly
found that infants reason on the basis of relational information before they
reason on the basis of absolute information when making judgements about the
physical properties of objects. Bryant (1974) has reported a similar precedence
for relational over absolute information in young children. The ease with which
infants and young children process relational information suggests that
relational processing is present in the cradle, and that relational comparisons
are an important source of information about the physical world. No-one has so
far devised a direct experimental test of this idea, however.
Relational
Processing in Infants: The Psychological World
As noted above, one powerful
aspect of relational information is that it frequently provides information
about causality. Causal relations are not only particularly powerful
relations for understanding the everyday world of objects and events, they also
provide an insight into the psychological world. For example, recent work with
infants has suggested that a sensitivity to causal relations may partly
underlie the development of a notion of agency. Things that move on
their own are agents, and things that move because of other things obey certain
cause-effect, or mechanical, laws (see Leslie, 1994). Infants' interest in
things that move helps them to sort out the source of different cause-effect
relations in the physical world. Again, this seems likely to require a form of
relational comparison.
For example, Gergely,
Nadasdy, Csibra and Biro (1996) have shown that 12-month-old infants can
analyse the spatial behaviour of an agent in terms of its actions towards a
goal, and will apply an ‘intentional stance’ to this behaviour when it appears
rational, thereby attributing a mental cause for the goal-directed behaviour.
The adoption of an ‘intentional stance’ towards agents entails an assumption of
rationality - that the agent will adopt the most rational action in a
particular situation to achieve his or her goal. To examine whether
12-month-old infants would generate expectations about the particular actions an
assumed agent was likely to perform in a new situation to achieve a desired
goal, Gergely et al. designed a visual habituation study in which a computer
display gave an impression of agency to the behaviour of circles. The infants
saw a display in which two circles, a large circle and a small circle, were
separated by a tall rectangle (see Figure 3). During the habituation event,
each circle in turn expanded and then contracted twice. The small circle then
began to move towards the large circle. When it reached the rectangular barrier
it retreated, only to set out towards the large circle a second time, this time
jumping over the rectangle and making contact with the large circle. Both
circles then expanded and contracted twice more. Adult observers of this visual
event described it as a mother (large circle) calling to her child (small
circle) who ran towards her, only to be prevented by the barrier, which she
then jumped over. The two then embraced.
--------------------
Figure 3 about here
--------------------
Following habituation to
this event, the infants saw the same two circles making the same sequence of
movements, but this time without a barrier being present. However, although the
relations between these objects were the same, the absence of a barrier meant
that the causal significance of the relations differed - in analogy terms, the
‘relational structure’ was no longer comparable. In a ‘new action’ event, the
small circle simply took the shortest straight path to reach the large circle.
Gergely et al. predicted that, if the infants were making an intentional
causal analysis of the initial display, then they should spend more time
looking at the ‘familiar action’ event than the ‘new action’ event, as even
though the former event was familiar it was no longer rational (nor
analogous). This was exactly what they found. A control group who saw the same
habituating events without the rectangle acting as a barrier (it was positioned
to the side of the screen) showed equal dishabituation to the old and new
action events. This intriguing result shows just how powerful the ability to
represent and compare causal relations between objects may be for the young
infant. Causal analyses of the everyday world of objects and events supply
information about the physical world of inanimate objects and also about
the mental world of animate agents.
Relational
Processing in Infants: Imitation
Relational processing and
relational comparison may also lie at the heart of the early facial imitation
of gestures such as tongue protrusion, which has been reported in infants as
young as 1 - 3 days (e.g., Meltzoff & Moore, 1983). Meltzoff and Moore
(1997) describe the essential puzzle of facial imitation as follows: ‘Infants
can see the adult’s face but cannot see their own faces. They can feel their
own faces move, but have no access to the feelings of movement in the other. By
what mechanism can they connect the felt but unseen movements of the self with
the seen but unfelt movements of the other?’ (p. 180). Meltzoff and Moore
suggest that the solution to this puzzle depends on the appreciation of the
similarity of ‘organ relations’. They suggest that infants might compute the
configural relations between organs, such as ‘tongue-to-lips’, and use these to
represent both their own behaviour and that of the adult. These
perceived organ relations provide the targets which the infants attempt to
match. On this account, imitation involves an early form of analogising.
Interestingly, Piaget also
suggested a role for analogy in explaining imitation behaviour in infants. He
noted the occurrence of ‘motor analogies’ in his own babies, in which the
infants imitated certain spatial relations that they had observed in the
physical world with their own bodies. For example, they imitated the opening
and closing of a matchbox by opening and closing their hands and mouths. Piaget
suggested that this behaviour showed that the infants were trying to understand
the mechanism of the matchbox through a motor analogy, reproducing a
kinesthetic image of opening and closing. Again, the infant is suggested to be
representing relations, and analogy is suggested as a mechanism for
knowledge acquisition and for explaining events in the everyday world.
The coding of ‘organ
relations’ proposed by Meltzoff and Moore (1997) would also allow infants to
recognise when they are being imitated by an adult. Such recognition is found
by at least 14 months (Meltzoff, 1990). Recognising that someone else is
imitating you implies a recognition of the structural equivalence (or
relational similarity) between another agent’s behaviour and your own (see also
Meltzoff, 1990; Meltzoff & Moore, 1995). Again, this is a form of analogy.
Such analogies may play an important role in the growth of psychological understanding.
For example, Meltzoff has argued that imitation, broadly construed, serves as a
discovery procedure for understanding persons. Although the links between
imitation, analogy and the development of an understanding of the psychological
world noted here must remain speculative given the current absence of detailed
research, it is perhaps not a coincidence that imitation, analogy and the
understanding of mental states (‘theory of mind’) are absent in the animal
kingdom (with the possible exception of highly ‘language-trained’ chimpanzees
(e.g., Thompson, this volume; Heyes, 1996, 1998; Tomasello, 1990; Visalberghi
& Fragaszy, 1990)
Analogies in Foundational Domains
Recently, a number of
developmental psychologists have argued that the developing knowledge base can
be divided into three foundational ‘domains’ or sets of representations
sustaining different areas of knowledge. These are the domains of naïve biology, naïve
physics, and naïve psychology (e.g., Wellman & Gelman, 1997). Of
course, many concepts will be represented in more than one of these
foundational frameworks (for example, persons are psychological entities,
biological entities and physical entities). Nevertheless, Wellman and
Gelman suggest that children will use at least two levels of analysis within
any framework, one that captures surface phenomena (mappings based on
attributes) and another that penetrates to deeper levels (mappings based on
relations). This means that analogies should be at work within foundational
domains. We have already seen that evidence from infancy research suggests that
analogies play a role in helping the child to understand the physical and
psychological worlds. We turn now to an examination of the role of analogies in
developing knowledge in these foundational domains in early and later
childhood.
Analogy as a Mechanism for
Understanding Biological Principles
Evidence that analogy is an important mechanism for
understanding biological principles comes from a series of studies by Inagaki
and her colleagues (Inagaki & Hatano, 1987; Inagaki & Sugiyama, 1988).
They were interested in how often children would base their predictions about
biological phenomena on analogies to people: the personification analogy.
As human beings are the biological kinds best known to young children, it seems
plausible that children should use their biological knowledge about people to
understand biological phenomena in other natural kinds. For example, Inagaki
and Sugiyama (1988) asked 4-, 5-, 8- and 10-year-olds a range of questions
about various properties of 8 target objects, including "Does x breathe?", "Does x
have a heart?", "Does x feel pain if we prick it with a needle?",
and "Can x think?". The target objects were people, rabbits, pigeons,
fish, grasshoppers, trees, tulips and stones. Prior similarity judgements had
established that the target objects differed in their similarity to people in
this order, with rabbits being rated as most similar and stones being rated as
least similar. The children all showed a decreasing tendency to attribute the
physiological properties ("Does x breathe") to the target objects as
the perceived similarity to a person decreased. Apart from the 4-year-olds,
very few children attributed physiological attributes to stones, tulips and
trees, and even 4-year-olds only attributed physiological properties to stones
15% of the time. A similar pattern was found for the mental properties
("Can x think?"). This study supports the idea that preschoolers'
understanding of biological phenomena arises from analogies based on their
understanding of people.
Analogy as a Mechanism for
Understanding Physical Principles
Evidence that analogy is an important mechanism for
understanding physical principles comes from a series of studies by Pauen and her
colleagues. Pauen has studied children’s understanding of the principles
governing the interaction of forces by using a special apparatus called the
‘force table’ (Pauen, 1996). The force table consists of an object that is
fixed at the centre of a round platform. Two forces act on this object, both
represented by plates of weights. The plates of weights hang from cords
attached to the central object at either 45', 75' or 105' to each other. The
children's job is to work out the trajectory of the object once it is released
from its fixed position. Their predictions concerning this trajectory are
scored in terms of whether they consider only a single force (one plate of
weights), or whether they integrate both forces in order to determine the
appropriate trajectory. The force table problem is presented to the children in
the context of a story about a King (central object) who has got tired of
skating on a frozen lake (the platform) and who wants to be pulled into his
royal bed on the shore (see Figure 4). Children aged 6, 7, 8 and 9 years of age
were tested.
----------------------
Figure 4 about here
----------------------
Pauen found that most of the younger children (80 - 85%)
predicted that the king would move in the direction of the stronger force only
(the larger plate of weights). An ability to consider the two forces
simultaneously was only shown by some of the 9-year-olds (45%). Such
integration rule responses were shown by the majority of the adults tested
(63%). Pauen speculated that this may have been because the children who
received the plates of weights applied a balance scale analogy to the force
integration problem. A balance scale analogy gives rise to one-force-only
solutions, which are incorrect.
This idea about the balance scale analogy was prompted by the
comments of the children themselves, who said that the force table reminded
them of a balance scale (presumably because of the plates of weights). This led
Pauen to propose that the children were using spontaneous analogies in their
reasoning about the physical laws underlying the force table, analogies that
were in fact misleading. To investigate this idea further, Pauen and Wilkening
(1997) gave 9-year-old children a training session with a balance scale prior
to giving them the force table problem. One group of children received training
with a traditional balance scale, in which they learned to apply the
one-force-only rule, and a second group of children received training with a
modified balance scale that had its centre of gravity below the axis of
rotation (a 'swing boat' suspension). This modified balance scale provided
training in the integration rule, as the swing boat suspension meant that even
though the beam rotated towards the stronger force, the degree of deflection
depended on the size of both forces.
Following the balance scale training, the children were
given the force table task with the plates of weights. A third group of
children received only the force table task, and acted as untrained controls.
Pauen and Wilkening argued that an effect of the analogical training would be
shown if the children who were trained with the traditional balance scale
showed a greater tendency to use the one-force-only rule than the control group
children, while the children who were trained with the modified balance scale
showed a greater tendency to use the integration rule than the control group
children. This was exactly the pattern that they found. The children's
responses to the force table problem varied systematically with the solution
provided by the analogical model. These results suggest that the children were
using spontaneous analogies in their reasoning about physics, just as we have
seen them do in their reasoning about biology. At the present time, studies of
children’s use of analogy in the domain of naïve psychology (theory of
mind) do not feature in the research literature. However, given the promising
developments noted in infancy research, this is surely only a matter of time.
Analogies in Piagetian Tasks
Halford’s
Structure Mapping Theory of Logical Development
Most neo-Piagetian theorists
of cognitive development incorporate the concept of relational mapping (e.g.,
Case, 1985; Halford, 1987, 1993; Pascual-Leone, 1987). However, Halford is the
only neo-Piagetian who has formally proposed that analogy plays a central role
in the development of logical reasoning, and who has linked analogical
processes to performance in traditional Piagetian tasks. In his
structure-mapping theory of cognitive development (1987, 1993), Halford
proposed that most logical reasoning was analogical. He also proposed that
limitations in primary memory (the memory system that holds any information
that is currently being processed) constrained the kinds of analogy that
children could use at different points in cognitive development. He suggested
that this explained the relatively late emergence of the Piagetian ‘concrete
operations’. Piaget used the term ‘concrete operations’ to refer to children’s
symbolic or representational understanding of the properties of concrete
objects and the relations between them (such as transitivity and class
inclusion). His argument was that capacity limitations prevented children from
representing and mapping transitive or class inclusion relations prior to
approximately 5 years of age.
Halford suggested that the
critical capacity limitations governing the use of analogy in logical reasoning
concerned the number of relations that could be represented in primary memory
at any one time (see also Halford, Wilson & Phillips, in press). The number
of relations determined the processing load entailed in solving the
analogy. A simple causal inference analogy of the kind used by Goswami and
Brown (1989, e.g., vase:pieces of vase::egg:broken egg) was thought to entail
a relatively low processing load, as it required the child to represent and map
a single relation (breaking) from one object (vase) to another (egg).
These relational mappings were said to be within the
information-processing capacity of children as young as 2 years of age. An
analogy that required two relations to be processed jointly was thought
to entail a higher processing load (e.g., A above B above C :: Tom
happier than Bill happier than John). The information-processing capacity
capable of supporting such system mappings was thought to emerge between
4 and 5 years of age. Prior to this, it was hypothesised that even familiar
pairs of relations could not form the basis of an analogy, as there was
insufficient capacity in primary memory to hold and compare the representations
of both relations simultaneously. Analogies based on pairs of relations were
thought to be necessary for the successful solution of Piagetian concrete
operational tasks. In order to test this theory, evidence that young children
can solve analogies based on pairs of relations and evidence that they use
analogies in Piagetian tasks such as transitive reasoning and class inclusion
is required.
Analogies based
on Pairs of Relations
In order to examine whether
young children can solve analogies based on pairs of relations, Goswami,
Leevers, Pressley and Wheelwright (1998) designed a set of analogies based on
pairs of physical causal relations (extending the technique used by Goswami &
Brown, 1989, described above). They asked 3-, 4-, 5- and 6-year-old children to
make relational mappings based on either single causal relations like cut,
paint, and wet, or pairs of causal relations, like cut + wet
and mend + paint. Their experiment had four conditions, a
single-relation analogy condition (e.g., apple: cut apple:: hair: cut hair),
a double-relation analogy condition (e.g.,
apple: cut, wet apple:: hair: cut, wet hair), a single-relation
control condition and a double-relation control condition. The 4 distractors in
both analogy conditions were the same (representing two double relational
changes and two single relational changes respectively). The child was thus
forced to attend to the A:B pairing in each condition in order to select the
correct solution term to each analogy. In the control conditions, the children
were asked to select the picture of the causal agent or the pair of causal
agents responsible for the causal changes shown in the analogies, following
Goswami and Brown (1989).
Children's performance in
the analogy and the control conditions was then examined as a function of
Condition and Age. The pattern of the results was remarkably similar to the
pattern found in the causal relations analogies used by Goswami and Brown
(1989). There was a close correspondence between analogy performance and
performance in the relational knowledge control conditions for both the single
relation and the double relation analogies. For the single relation conditions,
the 3-year-olds solved 33% of the analogies and 46% of the control sequences,
the 4-year-olds solved 51% of the analogies and 63% of the control sequences,
the 5-year-olds solved 72% of the analogies and 76% of the control sequences,
and the 6-year-olds solved 89% of the analogies and 88% of the control
sequences. For the double relation conditions, the 3-year-olds solved 13% of
the analogies and 31% of the control sequences, the 4-year-olds solved 50% of
the analogies and 50% of the control sequences, the 5-year-olds solved 62% of
the analogies and 74% of the control sequences, and the 6-year-olds solved 78%
of the analogies and 91% of the control sequences. Analyses demonstrated no
interaction between age and number of relations, although the main effect of
number of relations almost reached significance, reflecting the fact that
children of all ages found the double relation analogies and control sequences
more difficult than the single relation analogies and control sequences.
Goswami et al. concluded that the ability to solve analogies based on pairs of
relations was governed by relational familiarity. As long as familiar
relational structures are chosen as a basis for analogy, therefore, young
children should be able to use analogies to help them to solve Piagetian
reasoning tasks.
Analogies in a
Transitive Mapping Task
Halford has suggested that
familiar ordered structures may provide useful analogies for transitive
reasoning tasks. For example, a transitive sequence such as Tom happier than
Bill happier than John may be solved by using an analogy to a familiar
series of height relations such as A above B above C. As relational
familiarity is known to determine analogical reasoning in young children, we
need a familiar instantiation of height relations for the children to use as a
basis for analogy. The family provides a familiar example of an ordering structure
based on size, as in most families the father is taller than the mother, and
the mother is taller than the child or baby. According to Halford’s
structure-mapping theory, young children who have mentally represented the
relational structure Father > Mother > Baby should be able to use
this structure as a basis for analogies in transitive tasks using less familiar
relations.
Goswami (1995) examined this
hypothesis using Goldilocks and the Three Bears as a familiar example of family
size relations (Daddy Bear > Mummy Bear > Baby Bear). Three- and
4-year-old children were asked to use the relational structure represented by
the Three Bears as a basis for solving transitive ordering problems involving
perceptual dimensions such as temperature, loudness, intensity, and width. The
transitive mapping test was presented by asking the children to imagine going
to the Three Bears' house, and then to imagine looking at their different
belongings. This imagination task constituted a fairly abstract test. For
example, the imaginary bowls of the Three Bears' porridge could be either boiling
hot, hot, or warm, and the child had to decide which bowl of
porridge belonged to which bear. In order to give the correct answer, the child
had to map the transitive height ordering of Daddy, Mummy, and Baby Bear to the
different porridge temperatures, giving Daddy Bear the boiling hot porridge,
Mummy Bear the hot porridge, and Baby Bear the warm porridge (these mappings do
not follow the original fairy tale, in which Daddy Bear's porridge was too
salty, and Mummy Bear's was too sweet).
The results showed that the percentage
of correctly ordered mappings approached ceiling for the 4-year-olds for most
of the dimensions used. The lowest levels of performance occurred for width
(of beds, 62% correct), and hardness (of chairs, 76% correct), and the
highest occurred for temperature (of porridge, 95% correct). Performance
with the width dimension (wide bed, medium bed, narrow bed) was possibly
affected by worries that a baby could fall out of a narrow bed, as many
children allocated the medium bed to Baby Bear. They were then left without a
bed for Mummy Bear. The 3-year-olds produced correctly ordered mappings for
only some of the dimensions, performance being above chance (17%) for the
dimensions of temperature of porridge (31% correct), pitch of voice (31%
correct), and height of mirrors (62% correct, but an isomorphic relation).
Relational familiarity and real-world knowledge about family size relations seem
to have helped the 3-year-olds with these particular dimensions. The children
are unlikely to have based their correct mappings on the story, as none of
these dimensions was mentioned in the Three Bears book that was read to
them as part of the study. Note that this mapping task did not require a
transitive inference, however. Evidence for the use of analogies by 3-
and 4-year-olds in a ‘Daddy, Mummy, Baby’ paradigm has also been demonstrated
in a mapping task requiring the recognition of monotonic size ordering for
successful performance (Gentner & Ratterman, 1991; Ratterman & Gentner,
1998).
Analogies in a
Class Inclusion Task
Halford also suggested that
families provide potentially useful
analogues for class inclusion tasks (Halford, 1993). His argument was that
families were very familiar entities to young children, that they fulfilled the
criteria for inclusion of having two clearly defined sub-sets (parents and
children), and that they typically had a small set size, making it easy for
children to represent the relevant relations in order to make an analogy. In
order to see whether the family could act as a basis for successful performance
in Piagetian class inclusion tasks, Goswami, Pauen and Wilkening (1996) devised
the ‘create-a-family’ paradigm.
The children in Goswami et
al.'s study (4- to 5-year-olds) had all failed the traditional Piagetian class
inclusion task, which was given as a pretest ("Are there more red flowers
or more flowers?"). In the ‘create-a-family’ paradigm, children were shown
a toy family, for example a family of toy mice (2 large mice as parents, 3
small mice as children). Their job was to create analogous families (2 parents
and 3 children) from an assorted pile of toys (such as toy cars, spinning tops,
balls and helicopters). After the children had correctly created 4 analogous families,
they were given 4 new class inclusion problems involving toy frogs, sheep,
building blocks and balloons. As ‘family’ is also a collection term, and as
collection terms are known to influence class inclusion reasoning, the class
inclusion problems were posed using collection terms (‘group’, ‘herd’, ‘pile’,
‘bunch’). A control group of children received the same class inclusion
problems using collection terms, but did not receive the ‘create-a-family’
analogy training session.
Goswami et al. found that more
children in the 'create-a-family' analogy condition than in the control
condition solved at least 3 of the 4 class inclusion problems involving frogs,
sheep, building blocks and balloons. This effect was particularly striking at
age 4, in which no improvement at all was found in the control group with the
collection term wording, but criterion was reached by 50% of the experimental
group. It should be remembered that all of the children had previously failed the
standard Piagetian class inclusion task. Goswami et al. argued that this change
was due to the use of analogies based on a representation of family structure.
Goswami et al.’s data suggests that Halford’s structure-mapping theory of how
analogies might contribute to the development of logical reasoning is both
powerful and plausible. However, further research is required, particularly
regarding the developmental appropriateness of the notion of capacity
limitation as an upper limit on children’s use of analogies (see Gentner &
Ratterman, in press; Goswami, in press).
Conclusion
It is not unusual in
developmental psychology for researchers to demonstrate that apparent changes
in children’s cognition are in reality changes in the knowledge that children
have available as a basis for exercising a particular skill. Analogical reasoning
appears to be no exception. If measures of analogy are based on unfamiliar
relations, then these measures seriously underestimate children’s analogical
skills. Hence early research concluded that analogical reasoning was absent
until early adolescence because it depended on experimental tasks that used
analogical relations that were unfamiliar to younger children. Later research
has demonstrated that analogical reasoning is used by children as young as 1, 2
and 3 years of age. It has also been shown that forms of relational reasoning
which probably involve relational comparisons are present in young infants.
Nevertheless, it is
important to note that the nature of a cognitive skill measured at time 1 may
differ completely from the nature of a cognitive skill measured at time 2. For
example, Strauss (in press) has argued that the kind of analogies made by
infants may be completely different from the kind of analogies made by older
children. He suggests that the kind of analogies made by young infants are perceptual
in nature, whereas those made by young children use conceptual
knowledge. Such questions about the continuity of cognitive skills are
important ones for answering the question of ‘what develops’ in analogical
reasoning.
My argument here has been
that the early age at which analogies appear suggest that they provide a
powerful logical tool for explaining and learning about the world. Analogies
also contribute to both the acquisition and the re-structuring of knowledge,
and play an important role in conceptual change. As children's knowledge about
the world becomes richer, the structure of their knowledge becomes deeper, and
more complex relationships are represented, enabling deeper or more complex
analogies. This means that, as children learn more about the world, the type of
analogies that they make will change. Another important developmental question
is whether these changes are driven solely by changes in the knowledge base, or
whether information processing factors, such as the number of relations that
can be represented in primary memory at any one time, determine these changes.
Finally, it may be worth
noting that the developmental role of analogy in cognition is not limited to
childhood. The role of analogy in the history of science can also be explained
in a knowledge-based fashion. Scientific breakthroughs often depend on the
right analogy (Gentner & Jeziorski, 1993; Gordon, 1979), but the scientists
who make the breakthroughs seldom have extra information that is unavailable to
their colleagues. Instead, the analogy occurs to them and not to their fellow
scientists because of the way that their conceptual understanding of their
field is structured, and the richness of their representations. This in turn
may be correlated with their intelligence. If intelligence is important, then
its importance may explain why classical analogy performance is a good
correlate of I.Q. It has been reported that more efficient processing of
stimuli as a neonate (using a habituation paradigm) is related to performance
on a test of analogical reasoning at age 12 (e.g., bread is to food
as water is to beverage, Sigman, Cohen, Beckwith, Asarnow &
Parmelee, 1991). There is clearly still much research to be done before we can
claim to understand the role of analogical reasoning in cognitive development
in all its complexity.
References
Baillargeon,
R., Needham, A., & De Vos, J. (1992). The development of young infants'
intuitions about support. Early Development & Parenting, 1,
69-78.
Brown,
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.
Bryant,
P.E. (1974). Perception and Understanding in Young Children. London:
Methuen.
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.
Case,
R. (1985). Intellectual development: Birth to adulthood. New York:
Academic Press.
Chen,
Z., Sanchez, R.P., & Campbell, T. (1997). From beyond to within their
grasp: Analogical problem solving in 10- and 13-month-olds. Developmental
Psychology, 33, 790-801.
Freeman,
K.E. (1996). Analogical reasoning in 2-year-olds: A comparison of formal and
problem-solving paradigms. Unpublished Ph.D. thesis, University of
Minnesota, 1996.
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: Cambridge University Press.
Gentner,
D., & Jeziorski, M. (1993). The shift from metaphor to analogy in western
science. In A. Ortony (Ed.), Metaphor and thought, 2nd edition (pp.
447-480). Cambridge, England: Cambridge University Press.
Gentner,
D., & Ratterman, M. J. (1991). Language and the career of similarity. In S.
A. Gelman & J. P. Byrnes (Eds.), Perspectives on thought and language:
Interrelations in development (pp.
225-277). London: Cambridge University Press.
Gentner,
D., & Ratterman, M.J. (in press). Deep thinking in children: The case for
knowledge change in analogical development. Behavioural & Brain Sciences.
Gergely,
G., Nadasdy, Z., Csibra, G., & Biro, S. (1995). Taking the intentional
stance at 12 months of age. Cognition, 56, 165-193.
Gick,
M.L., & Holyoak, K.J. (1980). Analogical problem solving. Cognitive
Psychology, 12, 306-355.
Gick,
M.L., & Holyoak, K.J. (1983). Schema induction and analogical transfer. Cognitive
Psychology, 15, 1-38.
Gordon,
W. J. J. (1979). Some source material in discovery-by-analogy. The Journal
of Creative Behaviour, 8, 239-257.
Goswami,
U. (1991). Analogical reasoning: What develops? A review of research and
theory. Child Development, 62, 1-22.
Goswami, U. (1992). Analogical Reasoning in Children. Hillsdale,
NJ: Lawrence Erlbaum Associates.
Goswami, U. (1995). Transitive Relational Mappings in 3- and
4-year-olds: The Analogy of Goldilocks and the Three Bears. Child
Development, 66, 877-892.
Goswami, U. (1996). Analogical Reasoning and Cognitive Development. Advances
in Child Development and Behaviour, 26,
pp. 91-138. San Diego, California: Academic Press.
Goswami, U. (1998). Cognition in Children. Hove: Psychology
Press.
Goswami, U. (in press). Is relational complexity a useful metric for
cognitive development? Behavioural & Brain Sciences.
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., Pauen, S., & Wilkening, F. (1996). The effects of a
'family' analogy on class inclusion reasoning in young children.
Unpublished manuscript, Institute of Child Health, University College London.
Goswami, U., Leevers, H., Pressley, S., & Wheelwright, S. (1998).
Causal reasoning about pairs of relations and analogical reasoning in young
children. British Journal of Developmental Psychology, 16,
553-569.
Halford,
G.S. (1987). A structure-mapping approach to cognitive development. International
Journal of Psychology, 22, 609-642.
Halford,
G.S. (1993). Children's Understanding: The Development of Mental Models.
Hillsdale, NJ: Erlbaum.
Halford,
G.S., Wilson, W.H., & Phillips, S. (in press). Processing capacity defined
by relational complexity: Implications for comparative, developmental and
cognitive psychology. Behavioural & Brain Sciences.
Heyes,
C.M. (1996). Genuine imitation? In C.M. Heyes & B.G. Galef (Eds.), Social
learning in animals: The roots of culture, pp. 371-389. San Diego:
Academic.
Heyes,
C.M. (1998). Theory of mind in non-human primates. Behavioural & Brain
Sciences, 21, 101-134.
Holyoak,
K.J., & Thagard, P. (1995). Mental Leaps. Cambridge, MA: MIT Press.
Inagaki,
K., & Hatano, G. (1987). Young children's spontaneous personification as
analogy. Child Development, 58, 1013-1020.
Inagaki,
K., & Sugiyama, K. (1988). Attributing human characteristics: Developmental
changes in over- and under-attribution. Cognitive Development, 3,
55-70.
Leslie,
A.M. (1994). ToMM, ToBY and Agency: Core architecture and domain specificity.
In L.A. Hirschfeld & S.A. Gelman (Eds.), Mapping the Mind, pp.
119-148. New York: Cambridge.
Meltzoff,
A. (1990). Foundations for developing a concept of self: the role of imitation
in relating self to other and the value of social mirroring, social modeling,
and self-practice in infancy. In D. Cicchetti & M. Beeghly (Eds.), The
Self in Transition: Infancy to Childhood, pp. 139-164. Chicago: University
of Chicago Press.
Meltzoff,
A.N. (1995). Understanding the intentions of others: Re-enactment of intended
acts by 18-month-old children. Developmental Psychology, 31,
838-850.
Meltzoff,
A.N., & Moore, M.K., (1983). Newborn infants imitate adult facial gestures.
Child Development, 54, 702-709.
Meltzoff,
A.N., & Moore, M.K., (1997). Explaining facial imitation: A theoretical
model. Early Development & Parenting, 6, 179-192.
Pascual-Leone,
J. (1987). Organismic processes for neo-Piagetian theories: A dialectical
causal account of cognitive development. International Journal of Psychology,
22, 531-570.
Pauen,
S. (1996). Children's reasoning about the interaction of forces. Child
Development, 67, 2728-2742.
Pauen,
S., & Wilkening, F. (1996). Children's analogical reasoning about
natural phenomena. Journal of Experimental Child Psychology, 67,
90-114.
Piaget,
J., Montangero, J. & Billeter, J. (1977). Les correlats. In J. Piaget (ed.)
L'Abstraction Reflechissante. Paris: Presses Universitaires de France.
Polya, G. (1957). How to Solve It. Princeton: University Press.
Ratterman,
M.J., & Gentner, D. (1998). The effect of language on similarity: The use
of relational labels improves young children’s performance in a mapping task.
In K. Holyoak, D. Gentner & B. Kokinov (Eds)., Advances in Analogy
Research: Integration of theory and data from the cognitive, computational and
neural sciences, pp. 274-282. Bulgaria: New Bulgarian University.
Sigman,
M., Cohen, S.E., Beckwith, L., Asarnow, R., & Parmelee, A.H. (1991).
Continuity in cognitive abilities from infancy to 12 years of age. Cognitive
Development, 6, 47-57.
Smith,
L.B., & Heise, D. (1992). Perceptual similarity and conceptual structure.
In B. Burns (Ed.), Advances in Psychology: Percepts, concepts and categories,
pp. 233-272. Amsterdam: Elsevier.
Sternberg, R.J., & Nigro, G. (1980). Developmental patterns in the
solution of verbal analogies. Child Development, 51, 27-38.
Strauss,
S. (in press). Review of Goswami, U.: Analogical reasoning in Children. Cognition
& Pragmatics.
Tomasello,
M. (1990). Cultural transmission in the tool use and communicatory signalling
of chimpanzees? In S. Parker & K. Gibson (Eds.), Language and
intelligence in monkeys and apes: Comparative developmental perspectives
(pp. 274-311). Cambridge: Cambridge University Press.
Visalberghi,
E., & Fragaszy, D. (1990). Do monkeys ape? In S. Parker & K. Gibson
(Eds.), Language and intelligence in monkeys and apes: Comparative
developmental perspectives (pp. 247-273). Cambridge: Cambridge University
Press.
Wagner,
S., Winner, E., Cicchetti, D., & Gardner, H. (1981). Metaphorical mapping
in human infants. Child Development, 52, 728-731.
Wellman,
H.M., & Gelman, S.A. (1997). Knowledge acquisition in foundational domains.
In D. Kuhn & R.S. Siegler (Eds), Handbook of Child Psychology, Volume 2:
Cognition, Perception and Language, pp. 523-573 (4th
Edition).
Younger,
B.A., & Cohen, L.B. (1983). Infant perception of correlations among
attributes. Child Development, 54, 858-867.
Figure Captions.
1.
The gameboard (top row), analogy terms (middle row) and correct answer and
distractors (bottom row) for the analogy bird:nest::dog:doghouse
(Goswami & Brown, 1990).
2.
Depiction of the problem scenarios used to study analogical reasoning in
infants by Chen, Campbell & Polley, 1995.
3.
Schematic depiction of the habituation events shown to the infants in the
rational approach group by Gergely, Nadasdy, Csibra & Biro (1995),
depicting (a) the expansion and contraction events and the first approach, and
(b) the retreat, jump and eventual contact events.
4.
Schematic depiction of the force table used by Pauen (1996).