Symbols and Similarity 1
Running Head: SYMBOLS AND SIMILARITY
Manuscript under review (11/11/02)
SYMBOLS AND SIMILARITY:
YOU CAN GET TOO MUCH OF A GOOD THING
Judy S. DeLoache
University of Virginia
and
Tanya Sharon
Emory University
This research was supported by NICHD grant HD25271 to the first author and NRSA
postdoctoral fellowship HD08599 from NIH to the second author. Address for
correspondence: Judy S. DeLoache, Department of Psychology, University of Virginia,
P.O. Box 400400, Charlottesville, VA, 22904-4400. The author may also be reached via
email: jdeloache@virgina.edu.
Phone: 434-243-3577
Fax: 434-924-4546
Symbols and Similarity 2
Abstract
Surface similarity generally promotes reasoning by analogy, and physical
similarity has been shown to have a powerful effect on very young children's use of a
scale model as a source of information about another space. The research reported here
investigated 2-1/2-year-old children's performance when asked to reason from one space
to a second, perceptually identical one. Contrary to the expectation that increased
surface similarity would improve the children's performance, it actually had a negative
effect. Children were less successful in three different identical-spaces tasks than in a
similar-scale task. Close analysis of the results indicated that the children’s relatively
poor performance was largely due to memory problems; the identical spaces made it
difficult for them to keep track of the current hiding place from trial to trial. The results
of the research were interpreted as suggesting that part of the power of symbols derives
from the fact that they are virtually never identical to their referents, thereby enabling
one to use one to draw inferences about the other without danger of confusing them.
Symbols and Similarity 3
The identification of similarity between separate entities is a pervasive and
powerful tool of human cognition. Its power derives in part from its remarkable
flexibility. We can recognize similarities between bald heads and golf balls, digital
clocks and sundials, dobermans and dachshunds, the solar system and an atom. We
interpret things as alike based on appearance, function, kind, and relational structure, as
in the above examples, as well as an unlimited list of other factors--material
composition, size, smell, ownership, geographical origin, and so on. Without an
appreciation of similarity, fundamental cognitive processes such as categorization,
induction, generalization, and analogical reasoning would be impossible (e.g., Gentner,
1983; Holyoak, 1984; Medin, Goldstone, & Gentner, 1993; Vosniadou & Ortony, 1989).
Perceptual or surface similarity is relatively salient and easy to recognize. As a
result, it is often a useful index of deeper conceptual or structural similarities and can
provide access to more complex relations (Gentner & Toupin, 1986; Medin & Ortony,
1989; Ross, 1989; Smith, 1989). Thus, in spite of the great difference in their size, the
fact that dobermans and dachshunds look alike in many respects makes it easy to
identify both as dogs and to draw inferences about other, nonobvious ways in which they
are likely to be similar.
Although surface similarity can help individuals of any age appreciate deeper
structural similarities, it is especially important for young children. In the absence of
other information, even young children will assume that two entities that look alike are
the same kind (e.g., Gelman & Markman, 1987; Smith, 1993a, 1993b). Perceptual
Symbols and Similarity 4
similarity between the characters that play comparable roles in two stories helps children
appreciate the analogical relation between the stories (Gentner & Toupin, 1986).
Perceptual similarity can also be helpful for detecting the relation between
symbols and their referents. An iconic symbol is one that bears some degree of physical
similarity, or resemblance, to its referent. Clearly, many symbols and symbol systems
(such as mathematics and alphabets) are purely abstract, with no iconicity whatsoever
between symbol and referent. Indeed, some theorists reserve the term "symbol" for just
such wholly abstract relations (Pierce, 1932, 1955). Others appreciate that many
symbolic entities are iconic (e.g., Goodman, 1976), that symbols often enjoy some
degree of similarity to their referents. It is important to note that similarity alone does
not make one entity a symbol for another; something is a symbol only if someone
intends for it to stand for or represent something other than itself (DeLoache, 1995,
2002).
Perceptual similarity, or iconicity, has been shown to have a powerful effect on
the understanding and use of symbolic artifacts by young children. This result has
emerged from studies of very young children's use of a scale model as a source of
information about a larger space (for reviews, see DeLoache, 1995; DeLoache, 2002;
DeLoache, Miller, & Pierroutsakos, 1998)
In the standard task used in this research, children watch as a miniature toy is
hidden in a scale model of a room. They are then asked to retrieve a larger version of
the toy hidden in the corresponding location in the room itself.1 Across numerous
studies, 3-year-olds have performed very well, using their knowledge of the location of
Symbols and Similarity 5
the smaller toy to find the larger one approximately 80% of the time. In contrast, 2-1/2year-olds’ success rate is only about 20%.
The failure of the younger children occurs even though there is a very high level
of perceptual similarity between the model and room, with the large and small items
being of highly similar shape, material and color. The children's difficulty with the task
is not a simple problem of memory. When asked to retrieve the miniature toy that they
observed being hidden in the model, 2-1/2-year-olds' success rate is around 75-85%,
almost as high as that of 3-year-olds. Nor is it a problem of motivation; children usually
enjoy the task, and 2-1/2-year-olds' performance is equally poor when they are asked to
locate a highly prized item--their own mother—instead of a toy (Troseth & DeLoache,
1998). Rather, young children’s difficulty is specifically with achieving representational
insight, that is, with recognizing and using the symbol-referent relation (DeLoache,
1995).
When the degree of perceptual similarity between room and model is
manipulated, the pattern of performance is markedly affected for both age groups
(DeLoache, Kolstad, & Anderson, 1991). Decreasing the level of surface similarity
between the items of furniture in the two spaces causes 3-year-olds to be quite
unsuccessful (only 21% correct in the above study). At the same time, increasing the
level of similarity between model and room makes leads to successful performance by 21/2-year-olds. This age group is quite successful (70% correct in the above study) in the
similar-scale task, in which the larger space is not a full-sized room, but only twice as
big as the model. Figure 1 summarizes the effects of similarity for 2 ½-year-olds in
several versions of the model task. With low similarity, children perform very poorly,
Symbols and Similarity 6
but their performance rises with increased similarity between the model and the larger
space.
One possibility for how similarity affects performance in the model task is that
the effect occurs because surface similarity helps young children match the items of
furniture in the two spaces. Matching these items is clearly essential for successful
performance. It would be impossible for children to succeed if they did not realize that
the miniature couch is like the full-sized couch, the small chair like the larger chair, and
so on.
An alternative possibility is that children must also notice the higher-level
representational relation between model and room to reason from one to the other.
According to this view, noticing the lower-level similarities is necessary, but not
sufficient, for success. Prior research supports this alternative. For example, in a study
by Troseth and DeLoache (1998) the experimenter simply pointed to each item of
furniture in the model, asking the child to "show me the one like this in the room." The
2-1/2-year-old children readily indicated the matching items. However, when the same
children were then given the standard model task, they performed poorly. Thus, being
able to do the lower-level mapping between individual items in the two spaces is
necessary, but not sufficient, for success in the model task. Only if children have access
to the higher-level relation between the two spaces do they use what they know about
one to draw inferences about the other.
The goal of the two studies presented here was to investigate further the role of
similarity in young children's performance in the model task. The steady improvement
in performance as a function of similarity that is shown in Figure 1 suggests that if
Symbols and Similarity 7
similarity were increased even more, performance would improve accordingly. Indeed,
performance could be expected to be best if the two spaces were identical in appearance,
making it maximally simple to achieve representational insight into the relation between
the two spaces and also making it easier to map between them. Accordingly, we report
two studies that were conducted using the symbolic retrieval task with identical spaces.
Preliminary Study
The goal of this study was to examine 2-1/2-year-old children's ability to reason
from one space to another identical one. To provide a strong test of the predicted
superior performance with identical spaces, two quite different identical-spaces tasks
were used. A pair of commercial dollhouses enabled us to assess children's ability to go
from one small-scale space to another, identical one. The second task involved
transferring information from one full-sized room to another.
Method
Participants. There were 24 30-month-old participants in the identical-rooms
condition, (M = 30.3, range 29.0-32.0) and 16 in the identical-dollhouses condition (M =
29.9, range 29.0 – 30.0), including approximately equal numbers of boys and girls.
Stimuli and Apparatus. The rooms condition used two adjacent rooms of the
same shape and size (4.8 x 2.7 x 2.5 m.) furnished with several identical items, including
a chair, desk, floor pillow, large box fan, and wastebasket. The toys used for hiding and
retrieving were two stuffed toy dogs (15 cm long), identical except for a blue or red
ribbon around the neck. The dollhouses condition employed two identical commercial
dollhouses (55 x 25 x 30 cm) open on one side. Each had 7 rooms with identical items
of plastic furniture. The dollhouses sat in the same orientation on two tables
Symbols and Similarity 8
approximately 1 meter apart. The toys used for hiding and retrieving were two small
plastic dogs with red and blue ribbons.
Procedure. Children were tested individually. A brief warm-up period was
followed by an extensive orientation. First, children were introduced to the two toy
dogs, labeled as “Red Dog” and “Blue Dog” (based on their ribbons). The experimenter
then referred to one of the spaces as “Red Dog’s room” (or, for half the children, Blue
Dog's room). Each item of furniture was pointed out and labeled as belonging to Red
Dog. Next, the experimenter explained that Blue Dog “has a room just the same as Red
Dog’s.” In the dollhouses condition, the experimenter directly compared all the items of
furniture in the two spaces, placing each item from the one dollhouse by the
corresponding piece in the other, while commenting on the correspondence between
them. This direct comparison could not be done in the rooms condition, but the
experimenter emphasized the similarity between the items of furniture in the two spaces.
Next was a placement trial. The experimenter explained that the two dogs like to do the
same things in their rooms. She placed Red Dog on the shelves in one space and
instructed the child to put Blue Dog in the same place in his room. If the child had
difficulty, the experimenter placed the toy correctly. The last part of the orientation was
one or two practice trials in which the experimenter labeled the toy's hiding location as
she placed it (locations were never labeled once the test trials began).
The orientation was followed by 4 retrieval trials, each of which involved three
parts: (1) Hiding event: The child watched as the experimenter hid one of the dogs in its
space. The experimenter called the child’s attention to the act of hiding, but without
naming the location: “Look, Red Dog is going to hide here.” She then told the child that
Symbols and Similarity 9
she would hide Blue Dog “in the same place in his room.” The child was unable to see
this hiding event in either condition. (2) Symbol-based retrieval: Then the experimenter
led the child to the second model and asked him or her to find the toy. Before
permitting the child to search, the experimenter provided a reminder: “Remember, he’s
hiding in the same place as Red Dog.” If the toy was not found on the first search, the
experimenter provided increasingly explicit prompts until the child found the toy. Only
the first, unprompted search was counted in calculating correct performance. (3)
Memory-based retrieval: After Blue Dog was found, the child was taken back to the first
model and asked to retrieve Red Dog. The child was again prompted to continue
searching if the first search was incorrect.
The toy was hidden in a different location on each of the 4 trials (none of which
was used in the orientation trials), and half the children in each condition received one of
2 orders of hiding places.
Results and Discussion
The results did not reveal the expected benefit of increased similarity. Indeed, as
seen in Figure 2, the children in the identical-dollhouses and identical-rooms conditions
succeeded in retrieving the toy on only 41% and 43% of the symbol-based retrievals,
respectively. This is well below the average of 66% that has been found for this age
group in various studies using the similar-scale task. Interestingly, performance in the
memory-based retrievals--66% in the dollhouses and 64% in the rooms conditions--was
also lower than the 80% to 90% expected based on previous research. Clearly, the
children were not helped by having identical rather than highly similar spaces. Indeed,
Symbols and Similarity 10
the use of identical spaces seemed to have a negative effect on their performance on both
types of retrievals.
Two logistical factors may have contributed to the children's low performance. In
the identical-rooms condition, the large scale of the spaces precluded surveying the entire
space in one glance, which may have increased the chances of a child first noticing and
searching an incorrect location. In the identical-dollhouses condition, the individual
rooms were very small and the items of furniture closely spaced, making it easy for the
children to impulsively search multiple locations. In addition, the children sometimes
knocked over or otherwise displaced items of furniture while searching, possibly
disrupting their search.
Given the unexpected and nonintuitive nature of the results of the preliminary
study and their significance for young children's symbol use, it seemed prudent to see if
they could be replicated in a task not subject to the problems just mentioned. Hence, a
new study was conducted employing the same small-scale space that has often been used
in numerous studies with both the standard and similar-scale model tasks.
Study 1
In Study 1, 2-1/2-year-old children were asked to reason from one small scale
space to another, identical one. One of the small spaces was the model used in previous
replications of the similar-scale task; the second space was identical to it.
Method
Participants. Twenty-four 30-month-old children participated (M = 30.7, range =
28.5 – 32.5; 12 boys and 12 girls), and 24 children previously tested in the similar-scale
task (DeLoache et al., 1991) served as a comparison group (M = 30.6, range = 29.5-32.0;
Symbols and Similarity 11
12 boys and 12 girls). (The performance of 2-1/2-year-old children has been assessed in
this task in 8 separate replications in which performance on the symbol-based retrievals
has ranged from 58% to 75%, with an overall average of 66%.)
Stimuli and Apparatus. For the identical condition, the identical models (63 x 48
x 38 cm) were constructed of white cloth walls supported by plastic pipes.
Corresponding objects in the two models (floor pillow, shelf unit, wastebasket, chair,
chair pillow, dresser, and rug) were identical in appearance and were in the same relative
positions. The models were placed in the same orientation on the floor approximately 1
meter apart in a large room. A divider between them prevented children from being able
to see both spaces at once. The hiding objects were two small plastic dogs (2 cm long),
one with a blue ribbon around its neck and the other with a red ribbon.
In the similar-scale condition, the smaller space was one of the models used in
the identical condition. The larger space was approximately twice as large (92 x 70 x 61
cm) and was also constructed of white cloth walls supported by plastic pipes. It
contained larger versions of the furnishings (same shape, color, and texture) in the
smaller space, all in the same relative positions. Finally, the toys were plastic toy dogs
(3 cm and 7 cm high).
Procedure. The procedure was the same as that in the preliminary study, except
that there were no practice trials.2
Results
The results basically replicated those of the preliminary study. As can been seen
in Figure 2, the children's symbol-based (51%) and the memory-based retrievals (70%
93%). These differences in performance were evaluated with a 2 (condition: identical vs.
Symbols and Similarity 12
similar scale) x 2 (retrieval type: symbol-based vs. memory-based) x 4 (trials) doubly
repeated measures mixed-model ANOVA, with condition as a between-subjects factor
and retrieval type and trial as the within-subject factors. (Note that the analyses were
conducted on raw scores.)
The analysis confirmed main effects for condition, F(1,46) = 10.42, p < .005, and
retrieval type, F(1,46) = 24.44, p < .001. A Helmert contrast showed that first-trial
performance was significantly higher than performance on later trials, F(1,46) = 40.42, p
< .0001. Performance on the second trial was significantly lower than on later trials,
F(1,46) = 4.23, p < .05. No interactions were significant, because the pattern of best
performance on the first trial and worst on the second trial held for both conditions and
both types of retrieval. However, it is worth noting that the drop from the first to the
second trial was more than twice as large for the identical condition (from 79% to 24%)
than it was for the similar-scale condition (from 88% to 63%).
To further assess the pattern of performance by the two groups, perseverative
searching was examined for all but the initial trial.3 This analysis compared the number
of times children in the two groups searched at the location that had been correct on the
preceding trial. Only the first search on each trial was counted. Perseveration was more
common in the identical condition than in the similar-scale condition—on the symbolbased retrievals, 47% for the children in the identical task versus only 28% for those in
the similar-scale task, t(1,46) = 5.66, p < .05. For the memory-based retrievals, the
respective figures were 32% compared to 7%, t(1, 46) = 11.54, p < . 005.
Discussion
Symbols and Similarity 13
The results of Study 1 thus clearly replicate those of the preliminary study: the 21/2-year-old children in the identical condition performed worse than children of the
same age in the similar-scale version of the task. Not only was it not easier for the
children to reason from one space to another identical one than to a highly similar one, it
was actually harder. The overall pattern of performance in the identical and similar-scale
conditions in Study 1 offers clues to the reason for the this outcome.
First, the results indicate that the relatively poor performance in the identical
condition is not due to failure to appreciate the higher-level relation between the two
spaces, nor is it attributable to difficulty mapping between them. The symbol-based
retrieval performance of the children in this condition on the first trial was 79%, only
slightly lower than the 88% achieved by the children in the similar-scale condition. Thus,
the children in the identical condition started with enough awareness of the model-room
relation to map a hiding event from one space onto the other.
Second, the children’s performance was lower in the identical than in the similarscale condition on both the symbol-based and the memory-based retrievals. This similar
pattern implicates memory, and two particular aspects of the results—the difference
between the two conditions in performance over trials and the rate of perseverative
searching—point to greater memory problems in the identical condition.
To search successfully in either task, children must (a) base their search on their
representation of where they most recently observed the toy being hidden by the
experimenter, and (b) avoid basing their current search on their memory representation of
where they most recently found the toy. This is true for both the symbol-based and
memory-based retrievals.
Symbols and Similarity 14
In the similar-scale and standard model tasks, the difference in the sizes of the
two spaces offers children a readily available way to keep track of their different memory
representations. Success is achieved by following a relatively simple rule: always rely
on the memory representation of the most recent hiding event of the miniature toy in the
model. The primary memory demand (after the initial trial) would then be remembering
which of the observed hiding events in the model is the most recent one. This presents
somewhat of a challenge, even in the similar-scale condition, as shown by the decline in
performance after the first trial. Performance dropped between trials a and 2 by 25% for
the symbol-based retrievals and by 21% for the memory-based retrievals. (Similar
changes between the first and second trial have sometimes been reported in symbolic
retrieval tasks—O’Sullivan et al., 2001; Schmitt & Anderson, 2002; Troseth &
DeLoache, 1998.)
The identical group faces additional memory demands. The absence of a size cue
to differentiate between the spaces makes it more difficult to keep track of which memory
representation should guide the current search. Thus, children might be uncertain
whether to rely on their memory of seeing one toy dog behind a chair (where it had most
recently been placed by the experimenter) or their memory of seeing the other dog under
the floor pillow (where they had most recently found it on the previous trial). Consistent
with this analysis, the change in performance from trial 1 to trial 2 was much larger in the
identical condition than in the similar-scale condition, a 55% drop for the symbol-based
retrievals and a 33% drop for the memory-based retrievals. In addition, the lowest level
of performance occurred on the second trial, the trial on which there is the greatest
imbalance of memory representations. In the identical condition, children who searched
Symbols and Similarity 15
correctly on the first trial (as most of the children did in the studies reported here) began
the second trial with no less than three memory representations involving the first hiding
place—for example, the first toy hidden under the chair by the experimenter in space 1,
the second toy found by the child under the chair in space 2, and the first toy found under
the chair in space 1. Against this, they began their first search on the second trial with
only one representation of the toy in the new location. By this analysis, it is not
surprising that many children searched in the previously correct location, that they did so
most often on the second trial, and that children in the identical condition—who lacked
the simplifying size cue—were particularly inclined to make this error. In subsequent
trials, however, as additional memory representations are formed for the hiding and
finding events, a child’s memory representations of the most recent location would no
longer constitute such a disproportionate part of the set of representations. The same
general problem holds in the similar-scale and standard tasks, although it is not so severe
as in the identical task.
Most current models of perseveration posit that memory limitations play a
prominent role in the tendency to repeat a previous response or to continue to rely on an
outdated mental representation (Diamond, 1991). In the research reported here, the
children in the identical condition were significantly more likely than those in the similarscale condition to search (incorrectly) at the location that had been correct on the
previous trial. Again, this difference held for both symbol-based and memory-based
retrievals. (For further discussion of the role of perseveration in children’s performance
in the scale model task see O’Sullivan, Mitchell & Daehler, 2001; Sharon & DeLoache,
in press.)
Symbols and Similarity 16
It is worth considering the role of similarity in the broader context of reasoning in
the general domains of analogy and symbolization. As in the research reported here, the
effect of similarity is not as straightforward as might be assumed. Contrasting effects of
surface similarity have been reported for analogical reasoning. On the one hand, as noted
earlier, superficial similarity among entities often promotes analogical transfer by
initiating a comparison process that then reveals the underlying abstract similarity
(Gentner, 1989; Goldstone, Medin, & Gentner, 1991; Medin & Ross, 1989). On the other
hand, very salient superficial similarities sometimes impede transfer by discouraging
people from looking for deeper-level similarities (Goldstone & Sakamoto, in press).
Another case in which surface similarity impairs analogical mapping is when highly
similar elements play different roles in two analogues; in this case, transfer is worse than
if there were a lower level of similarity (Gentner & Toupin, 1986; Lowenstein &
Gentner, 2001; Ratterman & Gentner, 1998).
With respect to symbolization, the identical spaces conditions in the present
research represents an anomalous situation. A symbol is never identical to its referent;
symbolic relations are fundamentally asymetrical (Goodman, 1976). Often the basis of
the asymmetry is the fact that they do not share the same affordances (DeLoache, 2002):
One can sit in a chair, but not in a photograph of a chair or a miniature replica of a chair.
A symbol and its referent are qualitatively different kinds of entities.
It may be that the extraordinary power of symbols derives in part from this fact.
A symbol brings to mind its referent (and vice versa), making it possible to draw
inferences about one of them from what is known about the other. At the same time, the
Symbols and Similarity 17
qualitative difference between them prevents confusion, making it unlikely that
inappropriate inferences will be drawn.
Symbols and Similarity 18
Footnotes
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young children's understanding of scale models. Child Development, 62, 111-126.
DeLoache, J. S., Miller, K. W., & Pierroutsakos, S. (1998). Reasoning and
problem-solving. In D. Kuhn & R. S. Siegler (Eds.), Handbook of child psychology: Vol.
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Symbols and Similarity 22
Footnotes
1
Some children experience the opposite order, watching the larger toy hidden in the room
and searching for the miniature toy in the model. There is no effect on performance, so
for ease of communication only the ‘hide-model, search-room’ case will be used in
descriptions of the task.
2
Practice trials were used in some early studies with the standard model task in an effort
to make the model-room relation clearer. However, these trials had no beneficial effect
and were eventually dropped from the standard task.
3
It was not possible to examine perseverative searching in the preliminary study because
only correct searches were recorded, mainly due to the difficulty of precisely scoring the
rapid sequence of incorrect searches in the dollhouses condition.
Symbols and Similarity 23
Figure Captions
Figure 1: Symbol-based retrieval performance in the model task increases as a function
of physical similarity. The three sources of similarity include the surface appearance of
the items of furniture, the material of which the walls of the model were constructed
(rigid versus cloth), and the size ratio between the two spaces.
(Data from DeLoache, Kolstad, & Anderson, 1991, and unpublished research).
Figure 2: Performance on both types of retrievals in the preliminary study (Identical
Rooms and Dollhouses) and study 1 (Similar Scale and Identical Models).
Symbols and Similarity 24
Effects of Similarity on the Performance of 2 1/2 year-olds
100
% Errorless Retrievals
80
60
40
20
0
Similarity
Symbols and Similarity 25
% Errorless Retrievals
100
80
60
40
Similar Scale
Ident. Models
Ident. Rooms
Ident. Dollhouses
20
0
Symbol-based
Retrievals
Memory-based
Retrievals