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The Importance of Being Interpreted: Grounded Words and Children’s Relational Reasoning


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Although young children typically have trouble reasoning relationally, they are aided by the presence of "relational" words (e.g., Gentner and Rattermann, 1991). They also reason well about commonly experienced event structures (e.g., Fivush, 1984). To explore what makes a word "relational" and therefore helpful in relational reasoning, we hypothesized that these words activate well-understood event structures. Furthermore, the activated schema must be open enough (without too much specificity) that it can be applied analogically to novel problems. Four experiments examine this hypothesis by exploring: how training with a label influence the schematic interpretation of a scene, what kinds of scenes are conducive to schematic interpretation, and whether children must figure out the interpretation themselves to benefit from the act of interpreting a scene as an event. Experiment 1 shows the superiority of schema-evoking words over words that do not connect to schematized experiences. Experiments 2 and 3 further reveal that these words must be applied to perceptual instances that require cognitive effort to connect to a label rather than unrelated or concretely related instances in order to draw attention to relational structure. Experiment 4 provides evidence that even when children do not work out an interpretation for themselves, just the act of interpreting an ambiguous scene is potent for relational generalization. The present results suggest that relational words (and in particular their meanings) are created from the act of interpreting a perceptual situation in the context of a word.
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published: 07 March 2012
doi: 10.3389/fpsyg.2012.00045
The importance of being interpreted: grounded words and
children’s relational reasoning
Ji Y. Son1*, Linda B. Smith2, Robert L. Goldstone2and Michelle Leslie3
1Department of Psychology, California State University Los Angeles, Los Angeles, CA, USA
2Department of Psychological and Brain Sciences, Indiana University, Bloomington, IN, USA
3School of Psychological Sciences, University of Indianapolis, Indianapolis, IN, USA
Edited by:
Haley Vlach, University of California
Los Angeles, USA
Reviewed by:
Elizabeth Goldenberg, University of
California Los Angeles, USA
Stella Christie, University of British
Columbia, Canada
Ji Y. Son, Department of Psychology,
California State University Los
Angeles, 5151 State University Dr.,
Los Angeles, CA 90032, USA.
Although young children typically have trouble reasoning relationally, they are aided by the
presence of “relational” words (e.g., Gentner and Rattermann, 1991).They also reason well
about commonly experienced event structures (e.g., Fivush, 1984).To explore what makes
a word “relational” and therefore helpful in relational reasoning, we hypothesized that these
words activate well-understood event structures. Furthermore, the activated schema must
be open enough (without too much specificity) that it can be applied analogically to novel
problems. Four experiments examine this hypothesis by exploring: how training with a label
influence the schematic interpretation of a scene, what kinds of scenes are conducive to
schematic interpretation, and whether children must figure out the interpretation them-
selves to benefit from the act of interpreting a scene as an event. Experiment 1 shows
the superiority of schema-evoking words over words that do not connect to schematized
experiences. Experiments 2 and 3 further reveal that these words must be applied to per-
ceptual instances that require cognitive effort to connect to a label rather than unrelated
or concretely related instances in order to draw attention to relational structure. Experi-
ment 4 provides evidence that even when children do not work out an interpretation for
themselves, just the act of interpreting an ambiguous scene is potent for relational general-
ization. The present results suggest that relational words (and in particular their meanings)
are created from the act of interpreting a perceptual situation in the context of a word.
Keywords: schemas, analogy, labels, relational reasoning, cognitive development
The importance of language to higher cognition is undisputed:
words help learners connect previously acquired ideas (Herbert
and Hayne, 2000) and move from concrete to more abstract
representations (Kotovsky and Gentner, 1996;Loewenstein and
Gentner, 2005). Effects of language on children’s cognition have
been demonstrated in several domains in cognitive development
(e.g., Miura and Okamoto, 1989;Choi and Bowerman, 1991;
Levine et al., 1992;Sinha et al., 1994) and appear particularly
potent in tasks that require more abstract encodings (Gelman,
1988;Waxman and Markow, 1995;Bloom and Keil, 2001)orrela-
tional reasoning (Kotovsky and Gentner, 1996;Loewenstein and
Gentner, 2005;Gentner et al., 2011).
Three metaphors are often used to discuss the effect of language
on cognition: (1) language as a lens, (2) language as an anchor or
guide, and (3) language as a cognitive tool. The lens metaphor is
related to classic Whorfian ideas, and captures the idea that the
words one knows influences the information that is detected and
how it is represented (Winawer et al., 2007;Boroditsky et al., 2011).
The anchor (Clark, 1998;Lupyan, 2005) or guide (Plunkett et al.,
2008) metaphor suggests that language aids category formation by
explicitly connecting related instances or by defining boundaries,
as when, for example, three dogs are all given the same label (e.g.,
Xu and Tenenbaum, 2007;Perry et al., 2010). The third, referred
to as the tool metaphor, captures how language leverages other
cognitive processes, for example, the comparison or alignment of
elements (Kotovsky and Gentner, 1996;Loewenstein and Gen-
tner, 2005;Gentner et al., 2011) such that similarity-based and
analogical processes may act on these newly encoded representa-
tions. These perspectives on language suggest two broad types of
words that may foster relational reasoning: novel words that can
be helpful despite the lack of associations and known words that
are helpful because of their rich semantic associations. The pur-
pose here is to explore what types of words facilitate thinking and
which situations benefit from the presence of those words.
The specific research questions are motivated by findings about
the difficulty of relational reasoning tasks for young children and
novices. Preschool children, in particular, have difficulty picking
out relevant relational information when there are other more
salient object features (e.g., Keil and Batterman, 1984;Gentner and
Rattermann, 1991). The literature on relational reasoning in young
children has repeatedly shown that words help children notice,
comprehend, and make use of relations (Gelman, 1988;Gentner
and Rattermann, 1991;Kotovsky and Gentner, 1996;Loewenstein
and Gentner, 2005). Many of these tasks make use of novel or arbi-
trary relational reasoning problems. For instance, in Rattermann
et al. (1990) work, they showed that labeling a series of objects
varying in size as “daddy, mother, and baby” helped preschool-
ers reason about size relations. The child might need to discover
that the “winner”in a choice task is always the middle-sized object March 2012 |Volume 3 | Article 45 | 1
Son et al. Words and relational reasoning
regardless of the specific objects or their absolute sizes. Thus, words
might help in these tasks because they help the child relate the
novel task to known relational structures (e.g., size differences in
families, Rattermann et al., 1990) or because words, even novel
words, help children discover the relational structure (Gentner
et al., 2011).
However, there is another context in which young children
have been shown to reason relationally and with relative ease:
well-understood events, such as buying fast food or going to the
movies. The research in that literature suggests that children’s rela-
tional reasoning derives from their schema-like representations of
event structure (Fivush, 1984;Gobbo and Chi, 1986;Bauer and
Mandler, 1989;Hudson et al., 1992). Schemas are “abstract” or
“variable-ized” cognitive entities (Schank and Abelson, 1995). For
example, buying fast food has a common structure that is captured
in a “fast food restaurant schema” across the variety of specific
fast food experiences in a young child’s life but each visit also
has unique features. In brief, schemas are theoretical constructs
that can be roughly defined as structured representations that
bring order to emotions, perceptions,and experiences (Rumelhart,
1975;Rumelhart and Ortony, 1977). Schemas and closely related
notions of frames (Minsky, 1975) and scripts (Schank and Abelson,
1977, 1995) are organized slots filled by different units of knowl-
edge suitably representing information required for responding to
structurally similar situations.
Given these contexts in which children are able to reason
relationally (in the presence of words or with well-understood
“schematized” events), these experimental questions emerge: do
words benefit children’s performances in situations such as arbi-
trary relational tasks used in laboratory studies because they foster
schema-like interpretations? If so, is there, a “sweet spot” in the
knowledge structures that words might activate – not so empty (as
might be the case with novel words), that the word provides no
relational structure, but also not so specific that the knowledge is
of a rich and detailed experience rather than a variable-ized and
therefore generalizable relational structure?
To answer the first question, wepropose the Schema hypothesis:
words that draw upon rich past experiences evoke schemas, well-
understood, structure-sensitive event structures, and these enable
relational thinking. Standard relational tasks used with young chil-
dren are (particularly so from the child’spoint of view) ambiguous.
Words, through their meanings and through their associations
with previously experienced relational structures, might invite par-
ticular interpretations that resolve the ambiguity in some mean-
ingful way. These interpretations – if properly structured in terms
of their relations – may then enable children to reason analogically
about structural similarities despite surface differences.
If the Schema Hypothesis holds, one might expect that calling
upon a highly familiar event structure would be most helpful in
promoting relational interpretations. However, if children recall
a highly fixed and specified narrative rather than a story-schema
with slots in its structure, they may be unable to apply it to the
present relational problem and thus less likely to respond accord-
ing to relational similarity (Brown et al., 1986). More generally, for
any evoked relational structure to benefit reasoning, it may have
to have open slots and not be so specific that the slots are already
filled in. Accordingly, there might be a need for optimal openness
in the activated schema in order to support relational reasoning:
children must know enough about the event structure to make
inferential use about it but without too much specificity so that it
can be applied analogically to novel problems. This idea fits with
recent findings showing that children have difficulty attending to
relations when they are distracted by more vivid concrete infor-
mation (Kaminski et al., 2008;Son et al., 2008, 2011;McNeil et
al., 2009). Thus, the experiments test what we call the Optimal
Vagueness hypothesis: the key prediction is that less specified, less
concrete, and sparsely detailed schemas may better direct attention
to relational structure than richly detailed concrete situations.
The four experiments that follow tested the Schema hypoth-
esis and the Optimal Vagueness hypothesis by examining 4- and
5-year-old children’s relational reasoning in a task that has been
commonly used to study relational reasoning in children. Our ver-
sion is based on a prior study by Kotovsky and Gentner (1996).
In that study, 4-year-olds were presented with a triad of cards, a
standard and two answer choices – the relational match and a non-
relational foil. The standard presented a relation among a set of
three objects (e.g., a symmetry relation as in oOo). The elements in
the answer choices were similar to each other (e.g., xXx and xxX)
but differed from the standard to ensure that the only commonal-
ity shared by the standard and the relational answer was a relation.
When the relational answer was in the same dimension (i.e. size
symmetry, oOo and xXx), they found that 4-year-olds succeeded
in responding to relations such as symmetry. However when the
relational dimension changed (i.e., oOo and light blue-dark blue-
light blue) or the relational polarity changed (i.e., oOo and XxX),
children’s performance did not statistically differ from chance. In
order to help these children respond relationally on these more dif-
ficult cross-dimensional triads, Kotovsky and Gentner introduced
the task by categorizing triads using linguistic labels (e.g., “even” to
indicate symmetry). They found that children who succeeded on
the labeling task were then more likely to make relational choices
on the difficult cross-dimension triads. The relational patterns in
the studies that follow are made from three objects and are, like
those of Kotovsky and Gentner, abstract–asymmetrical arrange-
ment (ABA) or an asymmetrical arrangement (BAA). In contrast
to the Kotovsky and Gentner methods, we used a lexical gener-
alization task, first teaching children names for one instance of a
pattern and then asking how they generalized that name to new
instances. Across experiments, we manipulate the kinds of words
used to understand how words might evoke schemas that aid in
the interpretation of these relations structures.
Experiment 1 tested the Schema hypothesis by labeling the cards
with words whose meaning and associated referents might evoke
the proper relational interpretation and comparing the effects of
these potentially meaningful labels to the effects of two kinds of
novel words. The schema-evoking labels were chosen to be words
that (1) refer to well-organized events for young children and (2)
have potentially relevant relational meanings that might help chil-
dren interpret the stimulus arrays in an appropriate way. The ABA
pattern, as shown in Figure 1, is made of two matching objects on
either side of a unique center object. We conceptualized this center
object as a toy potentially worthy of sharing. For the symmetric
Frontiers in Psychology | Developmental Psychology March 2012 | Volume 3 | Article 45 | 2
Son et al. Words and relational reasoning
FIGURE 1 | Named instances of ABA and BAA shown to children
during training.
pattern, the word chosen to evoke the relevant relational interpre-
tation was “sharing” because sharing events are well-understood
by children in terms of balance, fairness, and the sameness of
two compared entities. This may have been the intuition that led
Kotovsky and Gentner (1996) to use the term “even”(for their ABA
figures) which evokes a similar set of concepts. The asymmetric
BAA pattern, as shown in Figure 1, always includes one item on the
left that is different from the rest. We conceptualized this unique
object to be a vehicle that might be pulling the other two objects.
Thus to support this relational interpretation, we chose the word
“pulling”because this word (perhaps especially to young children)
might evoke ideas of a lead object and followers such as an engine
pulling freight cars. Note that these words (like “daddy, mommy,
baby” in previous studies of labels and relational learning, Rat-
termann et al., 1990) are merely evocative. The relational displays
do not actually show an object being shared or an engine being
engaged in pulling. However, if children possess schemas that are
sufficiently abstract concerning these kinds of events, then the
words “sharing” and “pulling” might elicit the relevant relational
The two control conditions used novel words that might
be expected to help relational reasoning by the guide or tool
metaphors. In the Arbitrary Word condition, two novel nonsense
words were used (i.e., “koli” for ABA; “teemo for BAA); this
condition serves as a control for any general effects of naming.
Because the arbitrary words could be hard to learn and to link to
the relations (which is presumably not the case for “pulling” and
“sharing”), the second control condition provided iconic words
that were mimetically related to the relations they labeled (Imai
et al., 2008;Yoshida, in press) in terms of their phonetic form.
That is,“ko-li-ko”was used for ABA patterns and “tee-mo-mo”for
BAA. These words, however, are not expected to evoke relational
events that are well-known to children.
Participants and design
Forty-four children, average age 57months (range 46–68 months)
from daycares in a Midwest community participated in this
experiment. Three additional children were tested but two were
excluded from analysis due to unfavorable testing conditions (fire
alarms) and the other child had difficulty during the label training
(described in the procedures section). Children were randomly
assigned to one of the label conditions: Arbitrary (n=15), Iconic
(n=16), or Schema-evoking (n=13). In this experiment (as well
as the studies that follow), informed parental consent was obtained
before data collection and all protocols were approved by local
institutional review boards.
Materials and procedure
Training consisted simply of naming cards that were constructed to
encourage a schematic construal (e.g., sharing or pulling). All par-
ticipants were shown the training instances, two unique cards for
each relation for a total of four training instances. The ABA rela-
tion cards were cross–penguin–cross and triangle–bear–triangle;
the BAA cards were boat–rectangle–rectangle and car–diamond–
diamond as shown in Figure 1. ABA cards were labeled with the
same word/phrase, either “koli, “ko-li-ko,” or “sharing” depend-
ing on the condition, and BAA cards were labeled with another
word/phrase, either “teemo,”“tee-mo-mo,” or “pulling.”
Experimenters showed each training card separately and said,
for example, “This is a koli card. See, this card is koli. Can you
say koli?” Note that all of the words were used in the adjective
form so that the same grammatical frame could be used in all con-
ditions. After waiting for the child to repeat the word or phrase,
the card was put away and the next card was named. The labels
and cards were not counterbalanced because the schema-evoking
and iconic words were specific to the particular relation that the
children were being shown (Experiment 4 will further address this
issue). Because we could not counterbalance the words in some of
the conditions without changing the intent of the experiment, we
also did not do so for the arbitrary labels.
After children were trained in both types of relations, the exper-
imenter began the testing phase of the study. Testing trials asked
children to find a matching card to a given linguistic label (e.g.,
“Can you give me the sharing card?”). There were two kinds of
testing trials: memorization and generalization. All trials involved
a two-alternative forced choice.
Memorization trials were made up of the same objects as the
training instances (e.g., bears and triangles, penguins and crosses).
A memory trial consisted of two answer choices: a card that was
identical to the original learning instance and a distracter that
contained the same objects in a different pattern (e.g., respectively,
cross–penguin–cross and penguin–cross–cross). On memory tri-
als, children were always asked to retrieve the card that was iden-
tical to its taught label. When children were taught that the card
depicting cross–penguin–cross was “koli/ko-li-ko/sharing,” they
were correct when they chose that card over the distracter (i.e.,
penguin–cross–cross). The memory trials were designed to test
whether children were simply able to learn the association between
words and their referents from the brief training segment.
Generalization cards consisted of three simple geometric
shapes, as in Kotovsky and Gentner’s (1996) tasks, that re-created
the ABA and BAA relations with variations on color, shape, or
size dimensions (see Figure 2). The size dimension cards will be
referred to as “opposite polarity” cards because they had two large
objects and one small one, while all training instances were made March 2012 |Volume 3 | Article 45 | 3
Son et al. Words and relational reasoning
FIGURE 2 | Test trials from Experiments 1 and 2.
up of two small objects and one large one. All generalization cards
were novel to the participants because they were not named or
shown during training. Pilot testing with generalization materials
showed that children did not systematically prefer the appropriate
relational example when asked for “sharing” and “pulling” cards
without training (n=7, M=0.48, SD =0.33).
After the brief four-card training (labeling of the exemplars),
children completed 8 memory trials and 12 lexical generaliza-
tion trials with the testing cards. On half of all of these trials,
children were asked to get theABA card (“Can you get the koli/ko-
li-ko/sharing card?”) and shown two answer choices, an ABA
(relational match) and BAA card (distracter) made of the same
objects. Children were asked for the BAA card on the other trials.
The testing order started off with four memory trials to make
the goal of the task clear, that is, to retrieve the object corre-
sponding to a particular name. Then they received three blocks of
generalization trials interspersed with two memory trials. Color,
shape, and opposite polarity trials were not blocked but instead
presented in two pseudo-random orders.
Children’s memory and generalization performances are shown in
Tab l e 1 . A 2 (test: memory, generalization) ×3 (label condition:
Arbitrary, Iconic, Schema-evoking) repeated-measures ANOVA,
revealed a main effect of test, F(1, 41) =20.69, p<0.001, par-
tial η2=0.34, and label condition, F(2, 41) =18.22, p<0.001,
partial η2=0.47, but no interaction, F(2, 41) =0.62. As with
most tests of learning, memorization performance exceeded novel
Bonferroni corrected post hoc comparisons revealed that chil-
dren trained with Schema-evoking labels showed significantly bet-
ter memorization than children in either the Iconic, t(28) =11.68,
p<0.05, or Arbitrary conditions, t(27) =14.91, p<0.01. These
two conditions did not differ significantly, t(30) =0.42. Perfor-
mance in each of the three conditions exceeded chance levels on
the memorization test, ts>4.31, ps<0.001.
Table 1 | Means (and SDs) from the label conditions tested in
Experiment 1.
Memory trials Generalization trials n
Arbitrary label
0.71* (0.19) 0.54 (0.12) 15
Iconic label
0.75* (0.17) 0.64* (0.12) 16
Schema-evoking label
0.94* (0.12) 0.85* (0.20) 13
*Performance that statistically differed from chance (0.5) at p<0.001.
The analyses of generalization trials also revealed that children
in the Schema-evoking condition made significantly more rela-
tional matches than children in either the Iconic, t(28) =12.20,
p<0.01, or Arbitrary conditions, t(27) =28.82, p<0.001. These
results support the schema hypothesis that words have their
effect by evoking relationally relevant interpretations. Addi-
tionally, children in the Iconic label condition chose relational
matches to the given label more often than those with Arbi-
trary label training, t(30) =6.34, p<0.05. Although the Iconic
and Schema-evoking generalization performances reliably differed
from chance, ts>5.86,ps<0.001, the Arbitrary condition did not,
t(14) =1.7. This pattern suggests some benefit to Iconic labels,that
is, a sensitivity by the children to the correspondence of the sound
to visual patterns.
The advantage of the Schema-evoking condition on general-
ization test could, as hypothesized, be due to increased relational
interpretations; however, because children in the Schema condi-
tion also performed better on the memory trials, better general-
ization performance could simply reflect more robust memory for
the trained label. To examine this issue, the following analyses on
generalization performance included memory performance as a
covariate. Memory performance was only a marginally significant
covariate, F(1, 40) =3.34, p<0.10, and there was still a signif-
icant effect of label condition even when memory performance
was included first in a stepwise linear regression, F(2, 40) =8.75,
p<0.01, partial η2=0.30.
The superior generalization performance by children who
heard meaningful event-related words supports the hypothesis
that schema-evoking words enhance childrens ability to appre-
hend the common relational structure across novel instances. The
choice of schema-evoking words such as “sharing” and pulling”
to refer to ABA and BAA patterns is similar to Gentner and Rat-
termann’s (1991) and Rattermann et al.’s (1990) use of the word
“daddy” and “baby” to help young children respond to size rela-
tions. Words like “sharing” or “daddy” may foster analogical rea-
soning by reminding children of relevant event structures. These
words conveniently emphasize relations because the schemas they
activate are both well-known and consist of well-structured rela-
tions that have been applied to multiple individual instances in the
past, though never to such abstract displays as used in this exper-
iment. Nonetheless, evoking these relational frames may facilitate
processes such as alignment and comparison and thereby provide
an interpretive context within which to understand even novel or
perceptually ambiguous information.
Frontiers in Psychology | Developmental Psychology March 2012 | Volume 3 | Article 45 | 4
Son et al. Words and relational reasoning
Children’s poor performance in the arbitrary and iconic con-
ditions suggests that word meaning does matter. However, the
comparison in Experiment 1 was between familiar words with
some meaning and novel made up words with none. The schema
hypothesis, however, implies that the meaning should be rela-
tionally relevant, not just familiar. Accordingly, Experiment 2
compared schema-evoking words with other meaningful, known
English words (also gerunds) that provide no obvious schematic
interpretation of the relational structures displayed in the stimulus
This experiment replicates the Schema-evoking condition of
Experiment 1 and compares performance to a new control group.
In this new condition, the labels were known English words that
were unrelated to the situation depicted on the card. Children saw
the training cards from Experiment 1 labeled as “boiling”for ABA
cards and “eating” for BAA cards.
Participants and design
Forty children, average age 60.5months (range 51–68 months)
from daycares in a Midwest community participated in this exper-
iment. None of the children had participated in Experiment 1.
Five additional children were tested but three were excluded from
analysis because they exclusively chose an option on one side and
two for unfavorable testing conditions. Children were randomly
assigned to one of the label conditions: Unrelated (n=20) or
Schema-evoking (n=20).
Materials and procedure
The Schema-evoking condition was a replication of Experiment
1. In the Unrelated condition, ABA cards were labeled as “boiling”
and BAA cards were labeled as “eating.”
Label training, memory, and generalization testing procedures
were similar to Experiment 1 with a few minor changes. There were
two pseudo-random orders for label training, half of the children
learning ABA cards first (order: bear, penguin, boat, car) and the
other half learning BAA cards first (order: boat, car,bear, penguin).
After the brief four-card training (labeling of the exemplars), chil-
dren began the testing trials which consisted of 8 memory trials
and 12 lexical generalization trials with the testing cards. On half of
all of these trials, children were asked to get theABA card (“Can you
get the boiling/sharing card?”). Children were asked for the BAA
card on the other trials (“Can you get the eating/pulling card?”).
The testing order began with four memory trials. Then each child
received three blocks of generalization trials interspersed with two
blocks of memory trials. Generalization trials were blocked into
dimension-specific groups (color, shape, and opposite polarity)
and were presented in one of three orders (color–shape–polarity,
shape–polarity–color, and polarity–color–shape).
A 2 (test: memory, generalization) ×2 (label condition: Unre-
lated, Schema-evoking) repeated-measures ANOVA revealed a
main effect of test, F(1, 38) =30.94, p<0.001, partial η2=0.45, as
well as a significant interaction, F(1, 38) =5.30, p<0.05, partial
η2=0.12. Although, label conditions showed no differences on
memory test trials (see Ta b le 2 for group means), there were sig-
nificant differences in generalization performance, t(38) =2.55,
Bonferroni corrected p<0.05. Comparisons to chance perfor-
mance supported this analysis: generalization performance in the
Schema condition exceeded chance, t(19) =3.12, p<0.01, while
generalization by the Unrelated condition did not, t(19) =0.48.
Typically, developmental studies of analogy and language
examine the effect of particular labels on structural sensitivity
(e.g., Loewenstein and Gentner, 2005,seeGentner and Ratter-
mann, 1991 for a review). The results here demonstrate that it is
not the mere use of a known word that cues relational judgments
but that words foster relational interpretations by dint of their
meanings. However, the question of the schematized meaning is
still open – must the use of the word evoke a schema-like represen-
tation, that is a representation that is variable-ized, with slots, and
thus not too specific? Or can any related meaning, including highly
concrete and specific meanings, also foster relational generaliza-
tion? This is the crux of the Optimal Vagueness hypothesis tested in
Experiment 3. Additionally, Experiment 3 implemented an alter-
native method for controlling for meaningfulness by applying the
labels “sharing” and“pulling” to unrelated training cards.
By the Schema hypothesis, providing the words “pulling” and
“sharing” helped children because they activated relevant knowl-
edge about events with the relevant relational properties. Although
we used a central toy for “sharing” and a right-most vehicle for
“pulling” to foster a relational interpretation, the geometric forms
on the training instances are not actually good illustrations of
either “sharing” or “pulling” situations. Further, we know from
the performance of the children in the previous unrelated-control
conditions that the stimulus cards alone apparently are not suffi-
cient to evoke the relevant schemas without the schema-evoking
labels. The relations that are presented by these cards, at best,
vaguely resemble – or could be seen as roughly similar to – pulling
or sharing events. Although these scenes can be interpreted as shar-
ing or pulling, this act of interpretation requires prompting – for
instance, by the provision of a relationally applicable label. The
Optimal Vagueness hypothesis suggests that the vagueness of the
resemblance – being evocative rather than highly similar – is a
virtue. The idea is that a well-specified example might empha-
size the objects in the example causing children not to see the
Table 2 | Means (and SDs) from the label conditions tested in
Experiment 2.
Memory trials Generalization trials n
Unrelated label
0.72* (0.23) 0.46 (0.23) 20
Schema-evoking label
0.74* (0.19) 0.63(0.20) 20
Performance that statistically differed from chance (0.5) at p<0.01.
*Performance that statistically differed from chance (0.5) at p<0.001. March 2012 |Volume 3 | Article 45 | 5
Son et al. Words and relational reasoning
schema as having open slots and thus minimizing generalization.
That is, although the label “sharing” may evoke a familiar event
context to young children, the perceptual situation that receives
the label can lead to a vague and general idea of sharing or to a
specified instantiation of sharing. A vague and schematic under-
standing of sharing might be multiple parties equally wanting or
distributing something. Such a vague conceptualization might be
better for emphasizing relations rather than the specific objects
in the example. A more specific interpretation, for example, that
Sally and Susie want to share a teddy bear, might not help gener-
alization. Alternatively, one might argue that more specific (and
better understood) narratives might benefit learning because it
would better activate the relevant underlying knowledge. Exper-
iment 3 tests these alternatives by training all children with the
schema-evoking labels (“sharing” and “pulling”) but applying
them to instances that richly, vaguely, or poorly, fit with these
Thirty-eight children, average age 57 months (range 50–
68 months) from local daycares in a Midwestern town participated
in this experiment. Five additional children were excluded (three
for unfavorable testing conditions; one reported by the teacher
to have developmental delays; one who exclusively chose cards
presented on one side). Children were randomly assigned to one
of three training card conditions: Unrelated (controls, n=12),
Specifically related (n=14), or Vaguely related (n=13).
Materials and procedure
In this experiment, the children were shown cards labeled as either
“sharing” or “pulling.” If these words (and whatever representa-
tions are activated) are powerful enough to promote relational
generalization, children in all three conditions should perform
equally well in the tasks. The difference among the conditions is
that there were three different types of cards that were labeled. If
the perceptual situation that receives the label contributes to the
interpretation of the activated schema, then there should be dif-
ferences in performance. Examples of the three types of training
cards are shown in Figure 3.
FIGURE 3 | Training cards for Experiment 2.
In the Specifically related condition, the training cards were
designed to concretely support children’s notions of “sharing”
(or “pulling”), with attention drawn to the specific entities par-
ticipating in the relation. “Sharing” cards portrayed scenes with
two children flanking a stuffed animal in the middle. Instead of
vaguely being interpretable as a sharing situation, this perceptual
scene depicts a specific interpretation of sharing, namely that the
two children must be sharing the toy in the middle. However, the
training cards shown in the Vaguely related condition only evoke
an ambiguous sense of “sharing” because two geometric shapes
are flanking a toy in the middle. This scene could be interpretable
in a number of ways, from the two shapes sharing the toy to more
generally activating notions of balance or dividing evenly. Unre-
lated training cards were similarly vague (two geometric shapes
flanking an object in the center) but contained objects that would
be less interpretable by the label. For instance, an unrelated “shar-
ing” card depicted a cross–tree–cross. Presumably, this scene is
less related to “sharing” than cross–toy–cross because young chil-
dren probably think about sharing toys more often than sharing
Label training, memory, and generalization testing procedures
were similar to Experiment 2 with one major change. During
memory trials, each participant chose between condition-specific
cards (e.g., Specifically related participants chose between girl–
penguin–girl and penguin–girl–girl while Vaguely related partic-
ipants chose between cross–penguin–cross and penguin–cross–
cross cards). All children were asked for either “sharing” or
“pulling” cards in both memory and generalization trials because
they were all trained with these labels.
A 2 (test: memory, generalization) ×3 (training card condition)
repeated-measures ANOVA revealed no main effect of test, F(1,
36) =2.18, nor condition, F(2, 36) =0.6, but a significant interac-
tion, F(2, 36) =4.64, p<0.05, partial η2=0.21. A series of Bon-
ferroni corrected post hoc comparisons were conducted to examine
this interaction (see Tab l e 3 for all group means). Although, the
three training conditions showed no differences on memory test
trials, they were significantly different in generalization. Vaguely
related participants made significantly more relational general-
izations than those in both Unrelated, t(24) =4.83, p<0.05,
and Specifically related conditions, t(26) =7.12, p<0.05. This
provides direct support for the Optimal Vagueness hypothesis.
Table 3 | Means (and SDs) from the training conditions examined in
Experiment 3.
Memory trials Generalization trials n
Unrelated label 0.75(SD =0.18) 0.63(SD =0.20) 12
Specifically related label 0.72(SD =0.29) 0.60 (SD =0.19) 14
Vaguely related label 0.70(SD =0.22) 0.75(SD =0.18) 13
Performance that statistically differed from chance (0.5) at p<0.05.
Performance that statistically differed from chance (0.5) at p<0.01.
Different cards were all labeled as “sharing” or “pulling.
Frontiers in Psychology | Developmental Psychology March 2012 | Volume 3 | Article 45 | 6
Son et al. Words and relational reasoning
Like Experiment 2, when known words are used, children are
able to remember the associated instances. Performance on mem-
ory trials showed that children were just as willing to attach
“sharing” and “pulling” to cards that were not quite obviously
related (the Unrelated and Vaguely related training instances) as to
cards that exemplified these labels (Specifically related instances).
The same words were used in all three conditions so the differ-
ence in generalization scores suggests that the interpretive match
between the words and instances is critical. Thus, we can conclude
that relational generalization is not solely fostered by the use of a
particularly apt word. Words associated with familiar, structurally
organized schemas are only part of the story; how those words
interact with the displays is also critical.
Relational generalization depends on the schematic interpre-
tations that join words and referents. Perceptual instances that
are appropriately vague, ones that can be interpreted in terms
of those familiar schemas but require effort to do so, allow chil-
dren to attend to relations within the schema. Displays that match
the well-known schema too well do not lead to relational gen-
eralizations; and neither do displays that are not interpretable in
terms of the schema. Thus, the match between a known schema
and a sufficiently ambiguous instance reflects optimal vagueness,
a “sweet spot” for transfer, because there is enough similarity
between label and referent to evoke relevant past instances but
enough abstractness to enable generalization to future instances.
Thus the problem with Specifically related training instances
may be this: what is interpretable using an obvious and literal
meaning of a word activates only a narrow understanding. Apply-
ing the word sharing” to a specifically related instance may have
activated a concrete and specific notion of “sharing” such that
children did not engage in the act of adapting and interpreting,
and instead simply adopted the narrow construal. This conser-
vative strategy may simply be a prudent strategy because this
is also the least assumptive understanding (see also Medin and
Ross, 1989). The Vaguely related training instances may have fos-
tered generalization by engaging children in broadening their own
understanding of sharing, one that would also encompass future
Another possible benefit of vagueness may be that it requires
interpretive work and optimal vagueness allows this additional
processing to yield a relational schematic perspective that can
be applied to future instances (McQuarrie and Mick, 1999). The
vaguely related situation (the combination of the word and visual
stimulus) may engage children in figuring out why the cross–
penguin–cross situation is a sharing situation. In the Specifically
related condition, the flanking girls are readily interpreted as shar-
ing the penguin, so relatively little cognitive gain is achieved
by using the “sharing” terminology. Consistent with this idea,
researchers have found shallow learning when children (Martin
and Schwartz, 2005;Martin, 2009) and adults (Ross and Kennedy,
1990;Chi et al., 1994) are not given the opportunity to do the
work of re-interpreting something as something else. Text com-
prehension research has also found that poorly written text that
forces knowledgeable readers to cognitively work to find coher-
ence promotes comprehension (McNamara et al., 1996). Perhaps
a too literal instantiation of a schema may not necessitate adequate
cognitive work.
Experiment 4 further explores the issue of how much interpre-
tive work is necessary: are schematic interpretations effective only
when children form one for themselves or even when children are
simply told how to interpret a scene? How much cognitive work is
necessary to foster future relational generalization? Perhaps sim-
ply the act of interpreting an ambiguous scene is cognitive work
When the label“sharing” is applied to these scenes, children may be
interpreting the scene based on their past experiences with sharing
and the scenes in the Vaguely related condition have enough com-
ponents to foster a relevant interpretation. In Experiment 4, we
made it highly difficult for children to interpret scenes accord-
ing to the labels themselves. This was done by switching the
meaningful labels (used in previous experiments) and scenes such
that the word “sharing” was applied to the pulling cards and the
word “pulling” used with the sharing cards. To examine whether
schematic interpretations are effective when children are simply
told how to interpret a scene, in one condition (the Story-Schema
condition), we provided an appropriate interpretation for the chil-
dren. For each training card, the experimenter briefly told a“story”
that explained the fit between the label and the perceptual situa-
tion. As a control to this condition, in the Unrelated condition,
children were given the same switched labels and cards as the
Story-Schema condition, but critically were not provided with a
relevant interpretation.
Twenty-four children, average age 59 months (range 49–
67 months) from Indiana daycares participated in this experiment.
Children were randomly assigned to either the Unrelated (control,
n=12) or Story-Schema condition (n=12). Two additional chil-
dren were tested but presented a side bias, only choosing cards
presented on one side.
Materials and procedure
The training cards were the same cards used Experiments 1 and 2 as
well as the Vaguely related condition of Experiment 3. In contrast
to previous studies, the symmetrical cards picturing stuffed ani-
mals (e.g., cross–penguin–cross) were now labeled “pulling” while
the asymmetrical cards depicting vehicles were labeled “sharing”
in both conditions of the current experiment. In the Unrelated-
control condition, experimenters labeled these cards with the same
procedure as previous studies. In the Story-Schema condition,
experimenters gave a one-sentence story to go along with the label.
For example, an experimenter would hold up the asymmetrical
car–diamond–diamond card and say, “This is a sharing card. See,
this card is sharing. Look, the diamonds are going to share the car.”
For a symmetrical card, such as the cross–penguin–cross card,the
experimenter would say, “This is a pulling card. See, this card is
pulling. Look, the penguin is pulling the crosses closer.”
After the training sequence, the testing phase of the study
began. The memory and generalization trials were similar to
previous experiments. Participants in both conditions were pre-
sented with the same cards and asked the same questions. As in March 2012 |Volume 3 | Article 45 | 7
Son et al. Words and relational reasoning
the previous experiments, generalization trials were blocked into
dimension-specific groups and were presented in one of three
pseudo-random orders. The critical difference in this study was
that the relationally matching“sharing” cards are all asymmetrical
and “pulling” cards are symmetrical.
A 2 (test: memory,generalization) ×2 (training: Unrelated, Story-
schema) repeated-measures ANOVA revealed no main effect of
test, F(1, 22) =0.32, nor an interaction, F(1, 22) =0.51, but
there was a significant main effect of condition, F(1, 22) =18.99,
p<0.001, partial η2=0.46. Children performed significantly
better in the Story-schema condition (see Tabl e 4 ).
Less than half of the children in the Unrelated condition (n=5)
were able to answer more than 0.75 (6 out of 8) of memory
trials correctly compared to 11 out of 12 children in the Story-
schema condition, χ2(1, n=24) =4.11, p<0.05. Like Experiment
1, these significant differences in memorization could be driving
differences in generalization. An ANCOVA revealed that mem-
ory performance was not a significant covariate, F(1, 21) =1.13,
and training condition was a marginally significant factor, F(1,
21) =4.23, p<0.06, partial η2=0.16. The Schema-story training
facilitated both children’s memorization of the initial instances
and their generalization of the learned pattern.
The Schema-story apparently enabled these children to inter-
pret the pictured events in new ways and to generalize those
interpretations, a result that provides support for both the Schema
Hypothesis and the Optimal Vagueness hypothesis. Children in the
Schema-story condition were told how to interpret the cards rather
than having to form an interpretation themselves (although apply-
ing this interpretation most likely did require some mental work)
and they exhibited superior performance to children who simply
received the labels. This result strongly suggests that the key is hav-
ing an interpretation that makes sense. One of the difficulties for
the Unrelated condition may be that it was too difficult to interpret
a car–diamond–diamond scene as a“sharing” scene without some
additional information. So, the insight of the Schema hypothe-
sis still holds, that children need some background information
(either from their own experiences or provided by an external
source) to interpret a scene relationally. Although applying the
given interpretation to the perceptual situation at hand may be
slightly odd (diamonds sharing a car?), it may be that the oddness
provides some opportunity for the child to work out how this per-
ceptual situation instantiates sharing. Therein lies the contribution
of the Optimal Vagueness hypothesis: perhaps to appropriately
make use of a schema, the fit between the story and the situation
may be better left vague and unexplained in order to promote
Table 4 | Means (and SDs) from the training conditions of
Experiment 4.
Memory trials Generalization trials n
Unrelated label 0.61 (0.26) 0.62 (0.20) 12
Story-schema with label 0.92* (0.17) 0.86* (0.14) 12
*Performance that statistically differed from chance (0.5) at p<0.001.
interpretation and thus generalization. This experiment suggests
that the benefit of work may not be the sheer effort exerted in find-
ing an interpretation but simply the mental work of interpreting a
scene, even if that interpretation is provided by someone else.
The studies in this paper used lexical generalization as a measure
of how much young children represent the deep structural simi-
larities present in an array when learning how words relate to these
arrays. The key hypothesis was that words promote the discovery of
relations by evoking well-known event structures, thereby relating
this phenomena in relational reasoning to children’s flexible rea-
soning about well-known events. However, the key for relational
generalization is to represent the relation in a variable-ized way
such that very different kinds of entities can be seen as standing in
the same relational role. This suggests that an event structure that
fits too well with the depicted situation, with stereotypic entities in
the relational roles, does not promote generalization. The present
results provide support for both the Schema-evoking hypothesis
and the Optimal Vagueness corollary. By using words and scenes
that vaguely evoke event structures familiar to young children,
label training boosted attention to relations and fostered relational
Two aspects of schemas motivated the design of these exper-
iments: using words to activate schematic interpretations and
using scenes conducive to schematic interpretation. The con-
nection between language, schemas, and generalization is an old
one but the direction of application in these experiments is new.
Originally in the 1970s, schemas (and scripts and frames) were
hypothesized as constructs to explain language comprehension
(e.g., Minsky, 1975;Rumelhart, 1975;Schank and Abelson, 1977;
Charniak, 1978). Individuals could interpret ambiguous language
in the context of these schemas that represented events in terms of
actors, actions, and objects in highly likely spatial or temporal rela-
tions. These classic ideas motivated the Schema hypothesis, which
was supported by our results showing how the use of well-known
words with structured meanings can bring about generalizable
interpretations of ambiguous situations.
In their original conception, schemas were generalizable
because of the presence of mental variables or slots that could be
filled in by a set of options. Developmental researchers have found
that children’s knowledge for familiar events are often formu-
lated in such ways, highlighting relational structure and including
optional and variable information (i.e. Nelson and Gruendel, 1981;
Mandler, 1983;Hudson and Nelson, 1986). For well-understood
events such as birthday parties, children provide general knowl-
edge, such as expectancy that games will be played, and provide
specific options, such as pin-the-tail-on-the-donkey as filler for the
“games” slot. This was the motivation for the Optimal Vagueness
hypothesis; that schemas were useful because they were meaning-
ful but at the same time, not fixed nor too specific. In the present
experiments, we used arrays with simple abstract elements in the
roles. The benefit of these arrays – over richer ones – for children’s
relational reasoning supports the idea that too much emphasis on
specific fillers draws attention away from the schematic structure.
Thus, less vibrant and loosely fitting fillers seems to leave more
attentional resources available for processing relational structure.
Frontiers in Psychology | Developmental Psychology March 2012 | Volume 3 | Article 45 | 8
Son et al. Words and relational reasoning
The Schema and Optimal Vagueness hypotheses, when con-
sidered together, suggest a “sweet spot” for generalization. The
Optimal Vagueness perspective suggests that there should not be
too many particulars or concrete details involved in the labeling
experience else generalization may suffer. But the Schema hypoth-
esis shows a need for enough cues to activate relevant background
information to provide appropriate interpretation and facilitate
learning. The following discussion explores these two ends and
their implications.
Generally, concrete and rich representations have more informa-
tion than sparse ones and the natural consequence is that only
some of this information gets learned. Concreteness is relevant to
Experiment 3, in which a perceptually more detailed depiction of
an event called “sharing” (or“pulling”) results in less transfer than
a more schematic depiction. Although learning from concrete rep-
resentations can be beneficial, it can also be problematic for three
reasons. First, learners may not understand that these details are
optional, creating a characterization of the situation that is unnec-
essarily tied to its originating context (Goldstone and Sakamoto,
2003). The second reason, related to the first, in that specific inter-
esting details may compete against, and often overwhelm, subtle
relational information (Uttal et al., 1997;DeLoache, 2000). Lastly,
even relevant details may affect the appreciation of similarity to
other isomorphic instances (Sloutsky et al., 2005;Kaminski et al.,
Children and other learners do not a priori realize what they
are supposed to learn from an experience. Given that concrete
details of objects are typically more salient than relational infor-
mation, particularly for young children (Gentner and Rattermann,
1991), when these details are available, they are encoded more
readily. Young childrens immediate recall memory for specific
details is better than recall of general structure (Slackman and
Nelson, 1984;Sloutsky and Fisher, 2004). Studies of young chil-
dren’s attention, such as the often used card sort task devised by
Zelazo et al. (1995, 1996), show that when attention is already
directed toward some feature or dimension, it is difficult for
children to overcome this “attentional inertia” (Kirkham et al.,
2003) when they are required to switch to another dimension.
In the card sort task, the dimensions (typically color and shape)
are initially fairly equal in saliency. If information is unequal
in saliency, as in the case of concrete details versus relations,
it is reasonable to think that young children will have an even
harder time focusing their attention on the less salient relations.
In the case of highly detailed training cards, children may not
have even noticed the perceptual symmetry portrayed in the situ-
ation in lieu of more salient object details. The mere presence of
many features in the Specifically related girl–penguin–girl scene
that overlapped with the label “sharing” may have made it dif-
ficult for children to notice the symmetrical structure also in
the scene. Thus, picking out and responding to relational infor-
mation is often easier with sparser instances (Rattermann et al.,
1990;Gentner and Rattermann, 1991). Conflating concrete details
and abstract relations makes relational reasoning difficult even
for adults (Goldstone and Sakamoto, 2003;Son and Goldstone,
DeLoache and colleagues (DeLoache, 1995, 2000;Uttal et al.,
1999) have stressed the importance of competing concrete and
symbolic construals. Concrete objects can be considered as inter-
esting objects in their own right or as symbolic stand-ins for
something else, and when concrete properties are intensified, then
symbolic construals suffer. In schema terms,this sy mbolic“stands-
for” insight is the idea of a slot to be filled in by something
else. This representational insight may be the key step to gen-
eralization, with learners’ appreciation that many fillers can be
placed in a slot. A particularly relevant example of this compe-
tition between interesting details and relational information is
in the domain of math manipulatives. Although educators are
generally in favor of concrete manipulatives (Ball, 1992;Moyer,
2001;Kennedy et al., 2007), some researchers suggest that this
growing enthusiasm should be paralleled with a better under-
standing of what children actually learn and generalize from
manipulatives (Uttal et al., 1997). Stevenson and Stigler (1994)
observe that American math teachers will use anything inter-
esting, from “marbles, Cheerios, M&Ms, checkers, poker chips,
or plastic animals, sometimes even in a single lesson. The gen-
eral attitude seems to be that more information, more detailed
examples, and more interest in math activities (i.e., counting
M&Ms matters to children more so than counting notches on
paper) are important. However, if the goal of math education is
to direct attention to structure, perhaps less interesting and less
concrete learning examples may serve better. The Optimal Vague-
ness hypothesis is more consistent with the simple tiles used by
Japanese teachers (Stevenson and Stigler, 1994). The tiles are con-
crete and familiar in that they are physical manipulatives and used
repeatedly, however they are not vivid or particularly interesting
One might object to these criticisms of concrete details, claim-
ing that the reason richly interesting items, such as M&Ms,
do not benefit learning is that what is interesting about these
items is irrelevant to the structure of the learning situation.
This criticism, however, cannot account for the findings from
Experiment 3 (see also Kaminski et al., 2008). In that experi-
ment, the relations between the rich objects were highly relevant
to understanding the schema and could have even fostered a
better understanding of the balance or asymmetry in the situa-
tion. That is, the Specifically related training cards were designed
to be more accurate instances of “sharing” and “pulling” than
the other training cards. The Specifically related training cards,
having three objects concretely related to “sharing,” provided
an excellent example of sharing, yet did not allow the label
to generalize to sparser versions of the same relation such as
One of the fundamental problems with specificity may be that
the presence of specific details changes the similarity relations
between the learning cards and the generalization cards. In this
study, the dissimilarity was obvious: there were no simple shapes
on the Specifically related training cards and all generalization
cards consisted of three simple shapes; all other training cards
had at least two simple shapes. But more generally, the addition
of details introduces more dissimilarity to future instances. The
simplicity of abstract formalisms or simplified representations,
only expressing sparse structure, allows them to be equally similar March 2012 |Volume 3 | Article 45 | 9
Son et al. Words and relational reasoning
to (and equally far from) many instances (Son and Goldstone,
2009). Because abstractions have less information, and in par-
ticular less contrasting dissimilarities (Tversky, 1977;Bassok and
Holyoak, 1989), they capture a prototype-like representation that
anchors many instances, which may be dissimilar from each other
but equally similar to the prototype (see Son et al., 2008 foratest
of this hypothesis in children’s shape generalization). The cen-
tral role of vague, simplified representations for learning may also
explain why heavy reliance on specific examples often leads to poor
understanding (Chi et al., 1989).
After listing the disadvantages of highly specific learning scenar-
ios, one might conclude that for generalization, the more abstract,
the better. However, the present results as well as other studies
clearly document children’s (and adults’) difficulties with abstract
formalisms (e.g., Lave, 1988;Nunes et al., 1993). After all, merely
including two simple shapes in the training cards was not enough
to foster generalization to cards with simple shapes (the Arbi-
trary and Iconic label conditions from Experiment 1, and the
Unrelated conditions from Experiments 2–4). The notion of
optimal vagueness offered here suggests that learning instances
can be too vague. For example, future studies should address
whether applying “sharing” to simple shapes such as diamond–
circle–diamond would be effective for generalization. After all,
if generalization is merely a case of similarity, then such train-
ing should produce the best levels of generalization to new cards
with triples of simple shapes. If such training is ineffective, it
may be that such a situation is difficult to organize according
to relational information because it does not sufficiently evoke
richly relevant information. One immediate advantage of hav-
ing toys in sharing” scenes and vehicles in “pulling” scenes is
that they provide scaffolding that partly overlaps with children’s
past experiences with these actions. Exactly because the struc-
tural information conveyed to the young participants is hidden
among these details, children could have simply remembered
that the label “sharing” goes with the toy cards and “pulling”
with vehicle ones. However, that alone could not have resulted
in better generalization to scenarios that do involve toys or
An additional disadvantage of “too much vagueness” is demon-
strated by Experiment 1’s iconic label condition. As useful as
a slot-like variable representation of a situation might be, a
highly impoverished one, such as the ko-li-ko” label, did not
foster as much generalization as a meaningful label. The iconic
labels made use of syllabic isomorphism for things that are the
same on the ends (“ko”) and something different in the mid-
dle (“li”). But perhaps the relation is not even noticed, as seems
likely in the present case (that is, that children did not even
notice the parallel relational structure of the mimetic forms). This
notion of too much vagueness might similarly explain Gick and
Holyoak’s (1983) results showing less analogical generalization
when participants were provided with an explicit (but abstract)
statement of the underlying principle of a story than from expo-
sure to multiple analogs. This abstract principle for these adults
and “ko-li-ko” for children may just be too vague to activate
relevant knowledge. Thus, the key to relational insights more
generally may be building up or activating relevant past knowl-
edge with slot-like schemas. Consistent with this idea, Gick and
Holyoak found that when learners produced their own state-
ment of the underlying principle after exposure to multiple
analogs, this schema was highly predictive of subsequent transfer.
Thus, in their study, a general schema created from more spe-
cific instances produced transfer. Perhaps in the current studies,
the use of “sharing” allowed multiple past instances to be acti-
vated and thus aided the formation of a relationally appropriate
The real advantage of initial concreteness may be this: that
schemas can be created from them. The process of forming a
schema may be important to benefits in generalization. If this
is the case, the advantages of concreteness may be particularly
critical early in learning. Goldstone and Son (2005) have pro-
posed a pedagogical method of “concreteness fading”where initial
instances are highly concrete but are gradually idealized over time.
By initially presenting easily understood concrete ideas along with
more abstract ideas, and then fading away those concrete details,
this method eases a learner into a more abstract construal. This
may be an effective teaching methodology because it instantiates
a schematization process. Initially, during label training, our par-
ticipants may have been more reliant on the concrete details but
taking away the toy in the middle during the impoverished gener-
alization trials may have fostered a “faded” understanding of the
learning instances.
A related idea is “progressive alignment” by Gentner and col-
leagues (Kotovsky and Gentner,1996;Gentner and Medina, 1998)
which uses alignment of concretely similar situations to foster
comparison, a process shown to highlight commonalities, discard
deviations, and result in schema-like representations (Markman
and Gentner, 1993). Presumably,if children have experiences shar-
ing desirable toys, they may be able to effectively align their past
experiences with the ambiguous one in front of them in order to
create a schematic interpretation. However,if alignment of parts is
critical for schematic interpretation, the relational construal cre-
ated here may not be flexible enough to generalize to less alignable
instances. For example, if lining up objects is critical to under-
standing ABA relations, then“sharing” as applied to ABA instances
may not extend to instances such as AABAA or even ABBA or
ABCBA. If alignment is not critical, optimally vague learning may
be less “slot-like” and instead more like an image. In such a case,
perhaps any instance with something vaguely different in the mid-
dle, such as a single large isosceles triangle, could be considered
The present studies, in addition to expanding on the role of
words and schemas in fostering relational construals, are poten-
tially important to a fundamental understanding of the meaning
of words. In other studies where words benefit relational reason-
ing (i.e., “Daddy” from Gentner and Rattermann, 1991;“Even
from Kotovsky and Gentner, 1996; “Top/Middle/Bottom” from
Loewenstein and Gentner, 2005), it might be tempting to think
that the meaning of particular words is the source of the facilita-
tion. The present results suggest that while meaning matters, the
relevant meaning for generalizing relational concepts may be an
Frontiers in Psychology | Developmental Psychology March 2012 | Volume 3 | Article 45 | 10
Son et al. Words and relational reasoning
“interpretation” that can be bent to fit multiple instances. Words
that are related to well-ordered schemas allow children to take on
a relational perspective – but that perspective must be applied to
a situation that is conducive to developing relational meaning. As
accounts of language can contribute to a better understanding of
analogical reasoning, so also can an account of creating relational
similarity contribute to better accounts of language.
We thank Stacy Einikis, Jennifer Dold, and Elizabeth Hannibal
for their invaluable assistance in collecting data. We also want
to express our gratitude to the participating daycares (includ-
ing the children, teachers, and parents). This work was funded
by National Science Foundation REESE grant 0910218 and NIH
grants, HD007475 and HD28675.
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Conflict of Interest Statement: The
authors declare that the research was
conducted in the absence of any com-
mercial or financial relationships that
could be construed as a potential con-
flict of interest.
Received: 31 October 2011; accepted:
07 February 2012; published online: 07
March 2012.
Citation: Son JY, Smith LB, Goldstone
RL and Leslie M (2012) The impor-
tance of being interpreted: grounded
words and children’s relational rea-
soning. Front. Psychology 3:45. doi:
This article was submitted to Frontiers in
Developmental Psychology, a specialty of
Frontiers in Psychology.
Copyright © 2012 Son, Smith, Gold-
stone and Leslie . This is an open-access
article distributed under the terms of
the Creative Commons Attribution Non
Commercial License, which permits non-
commercial use, distribution, and repro-
duction in other forums, provided the
original authors and source are credited.
Frontiers in Psychology | Developmental Psychology March 2012 | Volume 3 | Article 45 | 12
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... Teachers help students make connections between pictorial and symbolic representations, and even connections with concrete activities when students finally enter into the symbolic/abstract phase. This is indeed helpful for students for understanding abstract concepts through interpreting unambiguous objects [22,23]. In this phase, it is also important to foster students in engaging in mental activities with symbolic representations by generating alternative symbolic forms and comparing these representations and forms [24]. ...
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Conceptual understanding has been emphasized in the national curriculum and principles and standards across nations as it is the key in mathematical learning. However, mathematics instruction in classrooms often relies on rote memorization of mathematical rules and formulae without conceptual connections. This study considers the concreteness fading instruction strategy—starting with physical activities with manipulatives and gradually fading concreteness to access abstract concepts and representations—as a promising and sustainable instructional model for supporting students in accessing conceptual understanding in mathematics classrooms. The results from the case study support the validity of the concreteness fading framework in providing specific instructional strategies in each phase of concept development. This study implies the development of sustainable teacher education and professional development by providing specific instructional strategies for conceptual understanding.
... Previous research suggests that language may be one such factor. Providing the same label to multiple examples can help children think of those examples as similar and detect commonalities (e.g., Gelman & Markman, 1986;Gentner et al., 2011;Kotovsky & Gentner, 1996;Posid, Clark, Bonawitz, & Sloutsky, 2018;Son, Smith, Goldstone, & Leslie, 2012). For example, 4-year-olds sometimes struggle on relational matching tasks (e.g., match light, dark, light with little, big, little). ...
Emerging research demonstrates a central role of early patterning skills in supporting cognitive development. This study focused on the labels used to describe patterns. Children (N = 90; M age = 5.4 years) solved and explained 10 pattern abstraction tasks (i.e., recreated a model pattern using novel materials). Using a between-participants design, children were taught using one of four labels: letters (AAB, AAB), numbers (112, 112), quantitative grouping labels (two one, two one), or no labels (this part, this part). All three forms of abstract language were beneficial relative to no labels. Grouping labels, which conveyed information about quantity, also aided performance on posttest items. Children's speech and gesture provided further insights into how abstract language may support early patterning skills and attention to structure.
Analogies are fundamental to our minds as they allow us to interpret incoming experiences, which are always, strictly speaking, new, in light of more familiar situations. This chapter explores the processes involved in building an initial representation, as well as their link with the type of analogies that can be implemented. It proposes that prior knowledge, through its influence on encoding, constrains the implementation of analogies. The chapter reviews the studies documenting the influence of familiar knowledge on encoding, and as a consequence, on analogical retrieval and mapping. The link between encoding and analogical retrieval has been highlighted by many researchers. The chapter introduces the proposal according to which cognitive flexibility is a key process allowing participants to go beyond their initial encoding and adopt a new perspective to appreciate analogies that initially went unnoticed. Revealing the role of flexibility in analogy‐making opens up promising educational avenues aimed at promoting the generalization of academic concepts.
Recent studies have found that infants show relational learning in the first year. Like older children, they can abstract relations such as same or different across a series of exemplars. For older children, language has a major impact on relational learning: labeling a shared relation facilitates learning, while labeling component objects can disrupt learning. Here we ask: Does language influence relational learning at 12 months? Experiment 1 (n = 64) examined the influence of a relational label on learning. Prior to the study, the infants saw three pairs of objects, all labeled “These are same” or “These are different”. Experiment 2 (n = 48) examined the influence of object labels prior to the study, with three objects labeled (e.g., “This is a cup, this is a tower.”). We compared the present results with those of Ferry et al. (2015), where infants abstracted same and different relations after undergoing a similar paradigm without prior labels. If the effects of language mirror those in older children, we would expect that infants given relational labels (Experiment 1) will be helped in abstracting same and different compared to infants not given labels and that infants given object labels (Experiment 2) will be hindered relative to those not given labels. We found no evidence for either prediction. In Experiment 1, infants who had heard relational labels did not benefit compared to infants who had received no labels (Ferry et al., 2015). In Experiment 2, infants who had heard object labels showed the same patterns as those in Ferry et al. (2015), suggesting that object labels had no effect. This finding is important because it highlights a key difference between the relational learning abilities of infants and those seen in older children, pointing to a protracted process by which language and relational learning become entwined.
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Very few questions have cast such an enduring effect in cognitive science as the question of “symbol-grounding”: Do human-invented symbol systems have to be grounded to physical objects to gain meanings? This question has strongly influenced research and practice in education involving the use of physical models and manipulatives. However, the evidence on the effectiveness of physical models is mixed. We suggest that rethinking physical models in terms of analogies, rather than groundings, offers useful insights. Three experiments with 4- to 6-year-old children showed that they can learn about how written multi-digit numbers are named and how they are used to represent relative magnitudes based on exposure to either a few pairs of written multi-digit numbers and their corresponding names, or exposure to multi-digit number names and their corresponding physical models made up by simple shapes (e.g., big-medium-small discs); but they failed to learn with traditional mathematical manipulatives (i.e., base-10 blocks, abacus) that provide a more complete grounding of the base-10 principles. These findings have implications for place value instruction in schools and for the determination of principles to guide the use of physical models.
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Participants in 2 experiments interacted with computer simulations designed to foster understanding of scientific principles governing complex adaptive systems. The quality of participants' transportable understanding was measured by the amount of transfer between 2 simulations governed by the same principle. The perceptual con- creteness of the elements within the first simulation was manipulated. The elements either remained concrete throughout the simulation, remained idealized, or switched midway into the simulation from concrete to idealized or vice versa. Transfer was better when the appearance of the elements switched, consistent with theories pre- dicting more general schemas when the schemas are multiply instantiated. The best transfer was observed when originally concrete elements became idealized. These results are interpreted in terms of tradeoffs between grounded, concrete construals of simulations and more abstract, transportable construals. Progressive idealization ("concreteness fading") allows originally grounded and interpretable principles to become less tied to specific contexts and hence more transferable. Cognitive psychologists and educators have often debated the merits of concrete versus idealized materials for fostering scientific understanding. Should chemical molecules be represented by detailed, shaded, and realistically illuminated balls or by simple ball-and-stick figures? Should a medical illustration of a pancreas in- clude a meticulous rendering of the islets of Langerhans or convey in a more styl- ized manner the organ's general form? Our informal interviews with mycologists at the Royal Kew Gardens (personal communication, Brian Spooner and David Pegler, May 1998) indicate a schism between authors of mushroom field guides.
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La signification des relations spatiales est exprimee en anglais, et dans d'autres langues apprentees, par le systeme des particules locatives. Mais, meme entre des langues etroitement liees comme le danois et l'anglais, il existe des differences substantielles dans la semantique et la morphologie des particules locatives. Le japonais, meme s'il utilise les particules locatives dans l'expression des relations spatiales, repartit la signification des relations spatiales de maniere totalement differente entre plusieurs classes formelles. L'A. analyse les consequences de ces differences pour l'acquisition de l'expression des relations spatiales en anglais, en danois et en japonais
Five studies examined how interacting with the physical environment can support the development of fraction concepts. Nine- and 10-year-old children worked on fraction problems they could not complete mentally. Experiments 1 and 2 showed that manipulating physical pieces facilitated children's ability to develop an interpretation of fractions. Experiment 3 demonstrated that when children understood a content area well, they used their interpretations to repurpose many environments to support problem solving, whereas when they needed to learn, they were prone to the structure of the environment. Experiments 4 and 5 examined transfer after children had learned by manipulating physical pieces. Children who learned by adapting relatively unstructured environments transferred to new materials better than children who learned with "well-structured" environments that did not require equivalent adaptation. Together, the findings reveal that during physically distributed learning, the opportunity to adapt an environment permits the development of new interpretations that can advance learning.