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The purpose of this paper is to explore how and when verbal labels facilitate relational reasoning and transfer. We review the research and theory behind two ways words might direct attention to relational information: (1) words generically invite people to compare and thus highlight relations (the Generic Tokens [GT] hypothesis), and/or (2) words carry semantic cues to common structure (the Cues to Specific Meaning [CSM] hypothesis). Four experiments examined whether learning Signal Detection Theory (SDT) with relational words fostered better transfer than learning without relational words in easily alignable and less alignable situations (testing the GT hypothesis) as well as when the relational words matched and mismatched the semantics of the learning situation (testing the CSM hypothesis). The results of the experiments found support for the GT hypothesis because the presence of relational labels produced better transfer when two situations were alignable. Although the CSM hypothesis does not explain how words facilitate transfer, we found that mismatches between words and their labeled referents can produce a situation where words hinder relational learning.
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The Journal of Problem Solving volume 3, no. 1 (Fall 2010)
52
When Do Words Promote Analogical Transfer?
Ji Y. Son1, Leonidas A. A. Doumas2, and Robert L. Goldstone3
Abstract:
The purpose of this paper is to explore how and when verbal labels facilitate relational
reasoning and transfer. We review the research and theory behind two ways words might
direct attention to relational information: (1) words generically invite people to compare
and thus highlight relations (the Generic Tokens [GT] hypothesis), and/or (2) words carry
semantic cues to common structure (the Cues to Specific Meaning [CSM] hypothesis). Four
experiments examined whether learning Signal Detection Theory (SDT) with relational
words fostered better transfer than learning without relational words in easily alignable
and less alignable situations (testing the GT hypothesis) as well as when the relational
words matched and mismatched the semantics of the learning situation (testing the CSM
hypothesis). The results of the experiments found support for the GT hypothesis because
the presence of relational labels produced better transfer when two situations were
alignable. Although the CSM hypothesis does not explain how words facilitate transfer,
we found that mismatches between words and their labeled referents can produce a
situation where words hinder relational learning.
Keywords:
analogical reasoning, transfer, problem solving, relation learning, similarity
The Journal of Problem Solving volume 3, no. 1 (Fall 2010)
52
The authors wish to express thanks to John Hummel, David Landy, and Linda Smith for helpful suggestions
on this work. This research was funded by the Department of Education, Institute of Education Sciences grant
R305H050116, and the National Science Foundation REESE grant 0910218. Correspondence concerning this
article should be addressed to Ji Son, Department of Psychology, California State University, Los Angeles,
5151 State University Drive, Los Angeles, California, or by email at json2@calstatela.edu.
1California State University, Los Angeles; 2University of Hawaii; 3Indiana University
When Do Words Promote Analogical Transfer? 53
volume 3, no. 1 (Fall 2010)
Although there is much debate on the connection between language and thought (e.g.,
Whorf, 1956; Gumperz & Levinson, 1991; see Gentner & Goldin-Meadow, 2003 for a review),
there is general agreement that words are useful for learning new concepts. For example,
even when words and meanings are unknown, as is the case with very young children or
with the use of novel words, linguistic labels facilitate learning (e.g., Lupyan, Rakison, &
McClelland, 2007). Research with young children has shown that words facilitate category
learning more than non-linguistic cues (Balaban & Waxman, 1997; Waxman & Booth, 2003;
Waxman & Markow, 1995). In addition, adults show faster learning and more robust reten-
tion when novel categories are associated with linguistic labels relative to non-linguistic
cues (Lupyan, 2008).
To date, a great deal of work has focused on the general phenomenon of the useful-
ness of words in learning situations, but comparatively little empirical work has focused
on the reason for this usefulness. What makes words so useful in learning contexts?
Relational reasoning—reasoning based on the relations between objects or features
of objects—is a rich domain for looking at potential cognitive benefits of words because
it is a highly demanding cognitive skill and many studies have shown that words make
the task of relational reasoning easier. Relational thinking plays a central role in human
cognition. It underlies our ability to perceive and understand the spatial relations among
an object’s parts (Hummel, 2000; Hummel & Biederman, 1992; Hummel & Stankewicz,
1996), comprehend arrangements of objects in scenes (Green & Hummel, 2006; Markman
& Gentner, 1993; Richland, Morrison, & Holyoak, 2006), and comprehend abstract analo-
gies between otherwise very different situations or systems of knowledge (e.g., between
the structure of the solar system and the structure of the atom; Gentner, 1983; Gick &
Holyoak, 1980, 1983; Holyoak & Thagard, 1995). However, despite its centrality in human
cognition, relational thinking is cognitively demanding. In contrast to simpler reasoning
about object features or single objects, reasoning about relations requires more working
memory and makes greater demands on attention (e.g., Halford, Wilson, & Phillips, 1998;
Hummel & Holyoak, 1997).
There are at least two reasons for the greater cognitive demands of relational think-
ing. First, relations are properties that hold over collections of objects rather than single
objects in isolation (Doumas, Hummel, & Sandhofer, 2008). The relation same-shape (x, y),
for instance, is a property of any two objects with the same shape, but not of any specific
x or y. Two identical shoes are the same-shape in exactly the same way that two triangles
are the same-shape, although same-shape is not a feature of either any single shoe or any
specific triangle. If one of the identical shoes were paired with a cup, the sameness relation
would disappear. By contrast, an object property such as color remains a property of an
object whether it is paired with a green object or another red object. Because relations
are less spatially and temporally stable than the features of single objects, they are easily
overshadowed by more salient object features such as a color. Even highly perceptual
The Journal of Problem Solving
54 Ji Y. Son, Leonidas A. A. Doumas, and Robert L. Goldstone
relations such as spatial relations (e.g., above, in, under; Loewenstein & Gentner, 2005) are
less stable than featural qualities (e.g., has a star on it).
Second, relational reasoning is cognitively demanding because representing struc-
ture is complex (Doumas & Hummel, 2005; Doumas et al., 2008; Gentner, 1983; Hummel &
Holyoak, 1997, 2003). It requires representing (1) the relation and (2) the objects involved
in the relation independently of one another, and (3) the bindings of these objects to
particular relational roles (Doumas & Hummel, 2005). For example, representing the rela-
tion bigger (shoe, cup) requires representing the relation bigger and the two objects, the
shoe and cup, independently of one another. Consequently, we understand that in the
expression bigger (shoe, cup), the shoe is larger and the cup is smaller, and that in the ex-
pression bigger (cup, shoe), the same elements play the opposite roles (the cup is larger
and the shoe is smaller).
The structure inherent in mental representations makes them very powerful for the
purposes of reasoning (e.g., Doumas et al., 2008; Hummel & Holyoak, 2003), but this power
comes at a cost. Considerable empirical evidence indicates that adults process concrete
features and concrete categories faster than relational ones (Gentner & Kurtz, 2005; Kurtz
& Gentner, 2001) and relational categories seem to be acquired later in development as
well (Hall & Waxman, 1993; Keil & Batterman, 1984; Smith, Rattermann, & Sera, 1988).
Studies that show how relational language enables relational reasoning typically
come from developmental research. These studies often teach children relational cat-
egories with or without linguistic labels and then test for generalization. For example,
in a series of studies Kotovsky and Gentner (1996) investigated how labels affected
four-year-old children’s sensitivity to relations such as symmetry and monotonicity. In
Kotovsky and Gentner’s studies, children were taught triads of shapes in a symmetric
(i.e., xXx) or monotonically increasing pattern (i.e., xXX). The symmetric cards were
called “even” and the increasing cards were called “more-and-more.” Then, children
were asked to determine which of two triads was the best match to a target triad,
where the best match involved relations with different dimensions (e.g., a size-based
pattern of xXx matched black-white-black) or different dimension values (e.g., xXx to
OoO). Children who learned the relational labels were able to make relational choices
more frequently than children who did not. Kotovsky and Gentner (1996) suggest that
acquiring a word for the xXx-patterned triads allowed children to notice the relational
similarities among them.
Often experiments regarding words and relational reasoning are designed to dem-
onstrate that words facilitate relational reasoning but they do not allow us to distinguish
between different ways words might help. By one account, favored by Kotovsky and
Gentner (1996), the word even” cues children to compare different triads and to extract the
subtle relational similarity, thus directing their attention. However, there is an alternative
possibility that the labels “even” and “more-and-more” help direct attention by virtue of
When Do Words Promote Analogical Transfer? 55
volume 3, no. 1 (Fall 2010)
their semantics. Perhaps the meanings of these labels, more than the mere act of giving
common labels to situations, helps children attend to relational information over other
sources of similarity. By this account,even” suggests balance or symmetry, which allows
this aspect of “xXx to be emphasized.
The purpose of this paper is to explore how and when verbal labels facilitate relational
reasoning. First, we review the research and theory behind two ways words might direct
attention to relational information: (1) words invite learners to compare, highlight, and
represent relations (the Generic Tokens [GT] hypothesis), and/or (2) words carry semantic
cues to common structure (the Cues to Specific Meaning [CSM] hypothesis). Given these
two (non-mutually exclusive) possibilities, we can make predictions about when words
boost relational learning. Four experiments examine these predictions.
Words as Generic Tokens (GTs) to Represent Difficult Concepts
We have already discussed how relations are difficult to process because they require
more representational capacity and more processing resources than simple objects in
isolation. The crux of the GT theory is that associating a simple symbol (i.e., a word) with
a complex situation (i.e., a relation) might make it easier to access or think about the
situation. Linguistic labels, and other useful symbols, are typically stable across contexts
because they are relatively unchanged by idiosyncratic differences in context (e.g., tokens
of the word “dog” said at different times are highly similar) and are non-iconic to their
referents (e.g., the word dog” does not particularly look like a dog). Because words enjoy
the combination of being relatively context-free and non-iconic, their GT qualities allow
them to stand for potentially subtle relations. When relations are tied to an object-like
word, they might seem more concrete. However, it is important to note that this func-
tion of words does not necessitate that all word and language processing is inherently
symbolic and propositional. In fact, there are theories about the mechanism of language
processing (e.g., Elman, 1995) that suggest that language has the appearance of being
symbolic and context-free even though the underlying mechanism may be dynamic,
continuous, and sensitive to context in real-time (see also Clark, 1998; Dennett, 1991;
Spivey, 2007).
Words as GTs may stabilize highly variable perceptual experiences—a function par-
ticularly useful in learning relational concepts. Having the same label for similar relations
can implicitly induce comparison (Brown, 1958; Gentner & Namy, 2004; Namy, 2001), a
powerful mechanism for structural abstraction (Dixon & Bangert, 2004; Doumas & Hummel,
2005; Doumas et al., 2008; Gentner, 2005; Gentner & Namy, 1999; Gick & Holyoak, 1983).
Symbolic juxtaposition (Gentner & Medina, 1998)—applying the same word to different
instances—is a natural cue to compare instances partly because of our conventional and
ubiquitous practice of labeling categories.
The Journal of Problem Solving
56 Ji Y. Son, Leonidas A. A. Doumas, and Robert L. Goldstone
Although symbolic juxtaposition might suggest that words are only effective when
applied to multiple situations, even having one labeled instance may be effective because
of our general convention of labeling concepts/categories. Some might consider that the
very existence of a word implies the existence of a category/concept (Quine, 1960) and
indeed cross-cultural research has suggested that concepts such as exact numerosity (Pica
et al., 2004) or particular spatial categories (Bowerman & Choi, 2003) are used and acquired
because of the arbitrary labels that stand for these ideas. Even cases of limited “language”
training, such as laboratory-raised nonhuman primates, suggest that understanding nu-
merosity (Boysen & Bernston, 1989) and relational similarity (Thompson & Oden, 1993;
Thompson, Oden, & Boysen, 1997) are mediated by symbolic tokens.
Comparison may drive the discovery of relational similarity but words provide stable
tokens to represent any newly discovered similarities. In other words, once acquired, words
provide a new level of object-like computation over the actual relations (Clark, 1998). Sup-
port for this generic function of words comes from Richard Catrambone’s research on how
words seem to help novices chunk newly learned procedures into meaningful and better
remembered groups (Catrambone, 1996, 1998). Also, separate words applied to subtly dif-
ferent objects help differentiate objects that are difficult to discriminate (Goldstone, 1994).
These results suggest that words have generic properties, apart from their meanings, that
may foster more efficient encoding and categorization.
Words as Cues with Specific Meanings (CSM)
Thinking about words as generic tokens places the emphasis on the ability of words to
efficiently capture complex ideas and make manipulation of these ideas easier. However,
language probably derives much of its power from connections to real experiences. When
known words are used, children also seem to show consistent benefits in detecting rela-
tional similarities. An experiment reported by Rattermann and Gentner (1998) showed
that brief training with known words significantly increased relational responding in
children compared to children who did not receive word training. In their task where tod-
dlers could make matches by relative size similarity or object similarity, children typically
made object matches. However, when objects were named with labels that children of
this age spontaneously use to mark monotonic size changes (e.g., daddy, mommy, baby),
children were able to make relational matches. However, this benefit was not found when
objects were labeled with arbitrary words (jiggy, gimli, fantan). This result indicates that
associations between words and past experiences significantly influence whether words
can highlight relations. Likewise, Loewenstein and Gentner (2005) found that some sets
of words promote relational responding more effectively than others. Labeling locations
in a three-tiered box as {top, middle, bottom} promoted children’s ability to use spatial
information more effectively than the labels {on, in, under}. Both studies suggest that the
When Do Words Promote Analogical Transfer? 57
volume 3, no. 1 (Fall 2010)
specific content of the words, or the relational framework they invoke, matters for provid-
ing cognitive benefits.
As GTs, mommy and jiggy are essentially equivalent (both are equally good symbolic
tokens). However, if words are thought of as CSMs, not all words are predicted to be equally
beneficial. The fact that mommy works well as a relational label may be the consequence
of mommy having rich associations to experiences that suggest medium size (especially in
the context of daddy and baby). However, the acquisition of relational meanings is not at
all straightforward. Hall and Waxman (1993) have attempted to teach children a relational
word by providing a definition. They taught children an arbitrary word, murvil (with the
equivalent meaning as the word “passenger”), and even defined it for them (i.e. This is
a murvil because it is riding in a car”). Despite the provision of a relational word and an
explicitly relational definition, children were not able to learn that murvils are any and all
dolls that sit in cars. Instead, children interpret the label murvil as the name of dolls that
look like the doll that was named. This suggests that it is not only difficult to learn the murvil
category (how to generalize the label) but also to learn the explicitly provided relational
concept. Because of the label’s lack of rich associations to other words and experiences,
there is no relational benefit from using an arbitrarily defined word.
There might be a continuum of words (and their meanings) from semantically empty
(i.e., jiggy, murvil) to semantically rich and matching the referent (e.g., daddy to refer to
something large) and some in between (e.g., semantically rich but not matching, such as
using the word daddy to refer to something small). We focus our research (with adults)
on the semantically meaningful end of the spectrum, looking at semantically meaningful
words that can either match or mismatch their referents. Semantically mismatching words
may be a better control for matching words since they control for the meaningfulness, but
not the appropriateness, of the label. Also, it is possible that there are additional memory
demands from having to learn a nonsense term like jiggy.
Rationale of Experiments
The majority of the experiments reviewed above illustrate difficulties that children have
with relational similarity, but even for adult learners, novel abstract relations are difficult to
acquire (e.g., Goldstone & Sakamoto, 2003). This paper examines the dual role of words, as
GTs and CSMs, in adult relational reasoning in order to test how linguistic labels can affect
relational reasoning. Our central question concerns how and when words confer benefits
in relational reasoning. Is it because labels act as GTs that are easier to manipulate and
remember than entire relational systems? Or, is it because the specific semantic content
of the words provides clues to a situation’s underlying relational structure? We conducted
four experiments to investigate how words confer benefits in relational reasoning. In each
experiment, participants were presented with a tutorial, a corresponding tutorial quiz
The Journal of Problem Solving
58 Ji Y. Son, Leonidas A. A. Doumas, and Robert L. Goldstone
followed by a structurally similar transfer situation and a corresponding transfer quiz. Each
experiment tested two conditions: a Word condition with relational labels included in the
tutorial situation, and a Control condition without those labels.
The behavior of interest was the ability of learners to utilize relational knowledge
from the tutorial situation in a new transfer context. The underlying system of relations
that participants learned and transferred was Signal Detection Theory (SDT). SDT is a way
of understanding decision making that involves uncertainty. Typically an SDT situation
involves some sort of evidence upon which a categorical decision is made, the decision
itself (e.g., “yes/no,” “in/out, “healthy/sick,” “signal/noise”), and the actual status of the
decided entity (whether it was actually signal or noise). Although the evidence is informa-
tive as to whether something is signal or noise, it is often imperfect so the decision has
some uncertainty. Under these conditions, there are ways to maximize the likelihood of
making hits (deciding “signal” when the signal is actually present) and minimizing false
alarms (deciding “signal” when the signal is not present). A parallel expression of the same
idea is to maximize correct rejections (deciding “noise” when signal is not present) and
minimizing misses (deciding “noise” when the signal is actually present). SDT provides an
informative framework for understanding a variety of decision-making situations under
uncertainty. The relational words that we used were: evidence, target (signal), distracter
(noise), hit, miss, correct rejection, and false alarm. We did not use the traditional SDT terms
signal and noise because those are grounded in the historical development of SDT that is
probably not intuitive to our participants.
We crossed two aspects of similarity in order to test the effects of GTs and CSMs as
well as their interactions. If words are GTs that represent relations efficiently, then regard-
less of the semantics of the relational labels, they should provide a benefit. Especially when
working together with comparison (Doumas et al., 2008; Markman & Gentner, 1993) to
drive the discovery of relational similarity, the presence of GTs that can represent these
extracted relations may be beneficial. More alignable (relationally comparable) SDT
stories will benefit from GTs more than less alignable SDT stories. To test this prediction,
Experiments 1 and 2 used tutorial and transfer situations that were more alignable and
Experiments 3 and 4 contained situations that were less alignable (see the columns of
Table 1). If the generic properties of words work together with useful comparisons, then
alignable and thus more comparable stories should show an advantage to learning with
relational words (Experiments 1 and 2).
However, if the CSM aspect of words is critical for directing attention to relations, the
similarity of words’ meanings to the referents in the story should also modulate relational
learning. To test this prediction, Experiments 1 and 3 had greater similarity and Experi-
ments 2 and 4 had less similarity between the relational words and the story elements
they referenced (see the rows of Table 1). Given that the relational label target (especially
in contrast to distracter) is a positive term, Experiments 1 and 3 paired it with a positive
When Do Words Promote Analogical Transfer? 59
volume 3, no. 1 (Fall 2010)
element in the tutorial situation (healthy athletes) while distracter was paired with the
corresponding negative element (unhealthy athletes) so that the relational labels were
semantically aligned with the story elements. Even though positivity could be construed
as a superficial feature, it may provide a semantic clue toward the relational structure. By
contrast, in Experiments 2 and 4 the positive label target referenced a negative story ele-
ment (sick patient) while the negative label distracter referenced a positive story element
(healthy patient). Table 2 shows the complete set of relational labels aligned with their
intended referents in the tutorial and transfer stories. If the semantic overlap between
relational words and their referents during learning is important, we should see greater
benefits of relational words in Experiments 1 and 3. A semantic mismatch between re-
lational labels and their referents might also lead to a deleterious influence of relational
words in Experiment 2 and 4.
We used three different measures: a learning quiz to test whether words have any
impact on initial learning, a transfer quiz to test appreciation of the implicit relational
similarities between tutorial and transfer stories, and an analogy quiz (matching corre-
spondences between story contexts) to see if subjects can explicitly make connections
between the simulations.
Experiment 1
The conditions of Experiment 1 provide the best chances of producing a benefit for learn-
ing with relational words because this experiment provides both semantic alignment
between tutorial and transfer elements as well as semantic overlap between the relational
labels and their tutorial referents.
Table 1
The overall design of the four experiments was created by manipulating whether the
relational words semantically align with the tutorial (rows) and whether the tutorial story
semantically aligns with the transfer story (columns). Positive target means that the SDT
target in the story is semantically positive, such as healthy athlete or sweet melon. Nega-
tive target means that the referred element is negative, such as sick patient or infected
melon.
Stories align Stories do not align
Relational words semantically
overlap with tutorial elements
Experiment 1
Positive target tutorial
Positive target transfer
Experiment 3
Positive target tutorial
Negative target transfer
Relational words do not
semantically overlap
Experiment 2
Negative target tutorial
Negative target transfer
Experiment 4
Negative target tutorial
Positive target transfer
The Journal of Problem Solving
60 Ji Y. Son, Leonidas A. A. Doumas, and Robert L. Goldstone
Method
Participants and Design
Eighty-seven undergraduates from Indiana University participated in this experiment for
credit. A computer program randomly assigned half of these participants to be in the Word
condition (N = 44) and the other half were assigned to the Control condition (N = 43). Three
additional participants who took less than 15 minutes to complete the experiment were
excluded from analysis. When participants were debriefed at the end of the experiment,
Table 2
Table 2 presents the relational labels with their story referents from all four experiments.
Participants in the Word conditions were presented with a tutorial that included both the
relational labels and story referents while corresponding Control tutorials only presented
the story referents. There were no relational labels in any of the transfer contexts.
Relational Labels
(Explicitly presented in the
Word condition tutorial)
Positive Target Tutorial
(Exp. 1 & 3)
Negative Target Tutorial
(Exp. 2 & 4)
Target Healthy athlete Sick patient
Distracter Unhealthy athlete Healthy patient
Evidence Cell strength Cell distortion
Hit Healthy diagnosed “healthy” Sick diagnosed “sick”
Miss Healthy diagnosed “unhealthy” Sick diagnosed “healthy”
False alarm Unhealthy diagnosed “healthy” Healthy diagnosed “sick”
Correct rejection Unhealthy diagnosed
“unhealthy”
Healthy diagnosed “healthy”
(None of these labels were
presented in transfer)
Positive Target Transfer
(Exp. 1 & 4)
Negative Target Transfer
(Exp. 2 & 3)
Target Sweet melon Infected melon
Distracter Bitter melon Normal melon
Evidence Melon weight Melon weight
Hit Sweet melon exported Infected melon sent to analysis
center
Miss Sweet melon rejected Infected melon sold
False alarm Bitter melon exported Normal melon sent to analysis
center
Correct rejection Bitter melon rejected Normal melon sold
When Do Words Promote Analogical Transfer? 61
volume 3, no. 1 (Fall 2010)
they reported how much they previously knew about SDT. All of our participants did not
know it at all or had heard of it but did not know what it was about.
Materials and Procedure
All undergraduates read through a computer-based SDT tutorial made up of pictures and
explanatory text (screenshots are provided in Figure 1; full tutorials and corresponding
quizzes from all four experiments are available online, http://www.calstatela.edu/cen-
ters/learnlab/sdt). The tutorial was a 47-screen self-paced slide show covering basic SDT
concepts such as the difference between evidence for a decision, the decision, and the
actual status of the decided entity (either signal or noise). Students were shown how a
decision boundary could lead to two ways of making the right decision (hits and correct
rejections) and two ways of being incorrect (misses and false alarms). This was followed by
two examples where the decision boundary was moved in order to show the relationship
between these categories. Additionally, participants were shown what would happen if
the signal distribution shifted along the evidence continuum.
The principles of SDT were embedded in the context of a doctor trying to pick out
healthy athletes to play for the university by examining blood cell strength. In the tutorial
story, athletes with strong cell samples were more likely to be healthy than those with
weak cell samples. Although cell strength was an imperfect indicator of health, the doc-
tor tried to optimize his decisions based on this imperfect evidence. The Word condition
differed from the Control condition in only one respect: interspersed into the tutorial
were relational labels presented alongside contextual elements. Healthy athletes were
labeled targets and the unhealthy athletes were distracters. Those that the doctor deemed
“healthy” were labeled “target” with quotation marks around both the story element and
the relational term indicating that this is only the doctor’s decision rather than the actual
status of the athlete. Hit, miss, correct rejection, and false alarm were also included in the
Word condition’s tutorial. Other than the addition of the labels, the tutorials for the Word
and Control conditions were identical.
The tutorial teaches some basic concepts of SDT without using the traditional nor-
mal distributions typically used in SDT classes or textbooks because of the limited time
constraints of the experiment. Pilot experiments teaching students SDT with traditional
normal distributions contrasted with other attempts using frequency bar graphs sup-
ported the claim that frequency information is far easier to understand than probability
information (in both general cognition, Gigerenzer & Hoffrage, 1995, and pedagogy, Bak-
ker & Gravemeijer, 2004). We speculated that the overlapping region of the traditional
distributions (i.e., where the evidence could be indicative of either targets or distracters;
see Figure 1) was particularly crucial for understanding SDT but also particularly confus-
ing for students. Because we were not interested in teaching graph reasoning per se, we
developed bar graphs that utilized non-overlapping spaces and color codes tailored to
The Journal of Problem Solving
62 Ji Y. Son, Leonidas A. A. Doumas, and Robert L. Goldstone
represent critical concepts of SDT (see Figure 1). Non-overlapping regions of the screen
(i.e., top and bottom of Figure 1c) were used to represent two different distributions (i.e.,
actually healthy and actually unhealthy people). Colored labels (“H” and “U”) provided a
perceptual indicator for the categorization the detector has made (i.e., diagnosed “healthy”
versus “unhealthy”). The tutorial implemented the combination of these features because
SDT requires an understanding of two distinctions: (1) which cases are in which categories
and (2) what categorizations have been made by the detector.
Each case is represented by an idealized cell in a box outline. The evidence is the
strength of the cell and this is indicated by how dark and how large each cell is. The cases
are spatially ordered, from left to right, by increasing cell strength. The columns of cases
(see Figure 1b) indicate how frequent a particular level of cell strength is. If a particular
level of strength indicates a higher likelihood of predicting actual health, there are more
actually healthy cases (green boxes) in the column than actually unhealthy (red boxes).
If a particular level of strength indicates a lower likelihood of predicting actual health,
there are more actually unhealthy cases (red boxes) in the column than actually healthy
(green boxes). Columns that include both red and green boxes can be seen as analogous
to the overlapping regions of traditional SDT distributions because the same level of
strength could belong to either category. Although in a typical SDT distribution there is
an actual physical overlap to signify that both categories can occur with the same cell
strength level, in our diagrams, we illustrate this with instances from both categories
stacked in the same column. The cases are then separated by category into two different
bar graphs (see Figure 1c) to clearly show the actual status of these athletes. This reflects
the SDT distinction between actual target and distracter distributions, as contrasted with
the doctor’s decision.
After reading through the tutorial, participants answered eight multiple-choice ques-
tions about the tutorial’s doctor situation that could be answered correctly by applying
SDT principles. Difficult quiz questions were purposefully used to ensure that participants
needed to use SDT principles rather than relying on common sense. (Tutorial quiz ques-
tions have been included in the Appendix and are available online.)
Then, participants received an opportunity to transfer what they had learned to a
different context. Participants read a few paragraphs (included in the Appendix) presented
on three slides describing a small town that wants to export sweet melons and avoid send-
ing out bitter melons. Sweet melons, laden with nectar, tend to be heavier, so this town
decides to sort the melons by weight (even though weight is not a perfect indicator of
sweetness). Heavy melons are exported and sold while light melons are rejected. However,
all of the melons were subject to consumer reports that allow the town to find out which
melons are actually sweet/bitter. An eight-question transfer quiz was administered. At the
end of the experiment participants were told that these two stories were analogous and
asked to explicitly place elements of the two stories in correspondence with each other
in a six-question multiple-choice mapping quiz.
When Do Words Promote Analogical Transfer? 63
volume 3, no. 1 (Fall 2010)
Figure 1. These are screenshots of the tutorial in the Word condition, showing relational
labels such as “targets” and “distracters” alongside elements of the story, “healthy” and “un-
healthy” people. Each patient’s blood test (the evidence for the diagnosis) is represented by
what is in each rectangle, the diagnosis is represented by the letter, and the actual status
of the patient is represented by the color of the outline.
Figure 1. These are screenshots of the tutorial in the Word condition, showing
relational labels such as “targets” and “distracters” alongside elements of the
story, “healthy” and “unhealthy” people. Each patient’s blood test (the evidence
for the diagnosis) is represented by what is in each rectangle, the diagnosis is
represented by the letter, and the actual status of the patient is represented by the
color of the outline.
The Journal of Problem Solving
64 Ji Y. Son, Leonidas A. A. Doumas, and Robert L. Goldstone
Results
Because this study examines the impact of learning relational words not only in immedi-
ate learning situations but also performance on other relationally similar examples, there
are two dependent measures of interest here, the scores on the tutorial quiz and the
transfer quiz. The relationship between the quizzes and the experimental manipulation
were analyzed with a mixed-design 2 x 2 ANOVA (quiz type x condition). There were no
main effects for quiz type, F(1, 85) = 0.04, nor word manipulation, F(1, 85) = 0.08, but this
analysis confirmed that there was a significant interaction, F(1, 85) = 8.63, p < 0.01 (see
Table 3). Participants in the Word condition had showed an improvement (a positive dif-
ference) from transfer and tutorial scores (M = 0.07, SD = 0.25) while the Control condition
participants showed a decline (M = -0.08, SD = 0.23). A paired t-test confirmed that this
change in performance (transfer score - tutorial score) was significantly different between
Word and Control conditions, t(86) = 8.63, p < 0.01.
Figure 2. Overlapping normal curves are typically used to represent the structure of SDT.
This figure shows the SDT structure of both tutorial and transfer stories used in Experi-
ment 1.
Figure 2. Overlapping normal curves are typically used to represent the structure
of SDT. This figure shows the SDT structure of both tutorial and transfer stories
used in Experiment 1.
After reading through the tutorial, participants answered eight multiple-
choice questions about the tutorial’s doctor situation that could be answered
correctly by applying SDT principles. Difficult quiz questions were purposefully
used to ensure that participants needed to use SDT principles rather than relying
on common sense (tutorial quiz questions have been included in the Appendix and
are available online).
Then, participants received an opportunity to transfer what they had
learned to a different context. Participants read a few paragraphs (included in the
Appendix) presented on three slides describing a small town that wants to export
sweet melons and avoid sending out bitter melons. Sweet melons, laden with
nectar, tend to be heavier, so this town decides to sort the melons by weight (even
though weight is not a perfect indicator of sweetness). Heavy melons are
exported and sold while light melons are rejected. However, all of the melons
were subject to consumer reports which allow the town to find out which melons
were actually sweet/bitter. An eight-question transfer quiz was administered. At
the end of the experiment participants were told that these two stories were
When Do Words Promote Analogical Transfer? 65
volume 3, no. 1 (Fall 2010)
Students who learned more from the tutorial should be predicted to do better on the
transfer quiz regardless of condition. But we also wanted to know whether learning SDT
with relational labels helped make SDT concepts more flexible and transferable to new
contexts. An ANCOVA first revealed that the tutorial score is a significant covariate, F(1, 84)
= 32.17, p < 0.001, on transfer performance. More surprisingly, this analysis also revealed
that the word manipulation is still a significant factor influencing transfer performance,
F(1, 84) = 5.62, p < 0.05, with words predicting better transfer performance than no words.
This was a small effect size (calculated using Cohen’s d, d = -0.25) but the experimental
manipulation was also subtle. Even though the Control participants look better than those
in the Word condition on the tutorial quiz (not significantly different though, t(86) = 3.03, d
= 0.37), these Word participants seemed to have transferred more of what they learned.
If words direct attention to structure or provide comparison opportunities that high-
light structure, one might expect the Word condition to outperform the Control condition
even in the mapping quiz. The mapping results are shown in Table 4. However, we found
that there were no differences in performance on the mapping quiz, t(83) = 0.78, with
Control and Word participants both scoring well, averaging 0.74 (SD = 0.17) and 0.71 (SD
= 0.16), respectively. A second look at our mapping questions indicates that the questions
might have been too well constrained to show differences. A question typically asked about
one element of either the tutorial or the transfer story (e.g., “heavy melon”—evidence of
being a target) and presented four possible answers. Two of the answers would be jus-
tifiable SDT answers, “patient with strong cells (evidence of being a target) and “patient
with weak cells” (evidence of being a distracter) while the other two would be incorrect
according to SDT structure (i.e., healthy person or sick person, targets and distracters). If
a participant could narrow down his or her choice to the two SDT answers, then a loose
similarity between the dimensions of heaviness and strength could lead to a correct match:
“heavy melon” with “strong cells.”
Discussion
The results of Experiment 1 suggest that even when the Control participants exhibited
learning on the tutorial quiz, they did not transfer their learning to the new situation as
well as those in the Word condition. There were no differences between conditions on the
tutorial quiz, but those in the Word condition may have performed better if quiz questions
also included the relational words. The exclusion of these relational words from the tuto-
rial quiz may have limited their performance on the assessment. However, even with this
disadvantage, the Word participants were able to show better transfer of their learning
to the second quiz. The interaction between quiz (initial or transfer) and condition (Word
or Control) underscores the importance of separating variables that affect immediate
learning versus those that make knowledge readily transferable (Bransford & Schwartz,
1999; Goldstone & Sakamoto, 2003; Chi, Feltovich, & Glaser, 1981). Relational words may
The Journal of Problem Solving
66 Ji Y. Son, Leonidas A. A. Doumas, and Robert L. Goldstone
be generally difficult for learners to acquire (Keil & Batterman, 1984; Gentner, 1975; Hall
& Waxman, 1993), but it seems that their real benefit shows up later on. The interaction
between learning relational words and the quizzes could be interpreted as evidence for
words making relations more salient when seen again in a new context, thereby allowing
the transfer situation to seem more similar to the tutorial situation.
Table 3. Tutorial and transfer quiz results from all four experiments are shown here. Positive
target contexts (i.e., healthy athletes, sweet melons) have been colored green and negative
target contexts (i.e., sick patients, fungus-infected melons) have been colored red.
Relational Words Tutorial Transfer
Experiment 1
target Healthy athlete Sweet melon
distracter Unhealthy athlete Bitter melon
Control 0.55 (SD = .25) 0.47 (SD = .27)
Word 0.46 (SD = .23) 0.53 (SD = .24)
Experiment 2
target Sick patient Fungus-infected melon
distracter Healthy patient Normal melon
Control .56 (SD = .22) .37 (SD = .26)
Word .52 (SD = .22) .43 (SD = .19)
Experiment 3
target Healthy athlete Fungus-infected melon
distracter Unhealthy athlete Normal melon
Control .50 (SD = .18) .48 (SD = .25)
Word .52 (SD = .23) .55 (SD = .28)
Experiment 4
target Sick patient Sweet melon
distracter Healthy patient Bitter melon
Control .57 (SD = .23) .47 (SD = .22)
Word .51 (SD = .22) .36 (SD = .23)
When Do Words Promote Analogical Transfer? 67
volume 3, no. 1 (Fall 2010)
Table 4. Mapping results from all four experiments are shown here. In Experiments 1
and 2, the tutorial and transfer stories were designed to align semantically. However, in
Experiments 3 and 4, the two stories preserved the structural alignment without the same
semantic overlap. Thus, the latter experiments had two different mapping possibilities,
favoring structure or semantic alignment.
Relational Words
Experimental
Example Control condition Word condition
Experiment 1
Target = Target mapping
(Structure + Semantic)
healthy person =
sweet melon
.74 (SD = .19) .70 (SD = .16)
Target = Distracter mapping healthy person =
bitter melon
.10 (SD = .10) .09 (SD = .14)
Experiment 2
Target = Target mapping
(Structure + Semantic)
sick person =
infected melon
.71 (SD = .21) .72 (SD = .25)
Target = Distracter mapping sick person =
normal melon
.09 (SD = .10) .07 (SD = .12)
Experiment 3
Target = Target mapping
(Structure)
healthy person =
infected melon
.24 (SD = .17) .22 (SD = .10)
Target = Distracter mapping
(Semantic)
healthy person =
normal melon
.66 (SD = .17) .64 (SD = .20)
Experiment 4
Target = Target mapping
(Structure)
sick person = sweet
melon
.20 (SD = .22) .31 (SD = .22)
Target = Distracter mapping
(Semantic)
sick person = bitter
melon
.61 (SD = .31) .37 (SD = .25)
Experiment 2
The advantage of learning labels seen in Experiment 1 may have been due to one of two
factors: (1) because labels provided a generic cue to compare the doctor and melon story
or (2) because the content of the labels (i.e., target—a positive label) were consistent
with the corresponding elements of the tutorial (i.e., healthy athlete—a positive story
element). If labels function as a comparison cue, then it is critical that the doctor and
melon stories are alignable. In Experiment 1, they were alignable in that the doctor was
looking for positive targets (e.g., healthy athletes) and the melon farmers were looking for
The Journal of Problem Solving
68 Ji Y. Son, Leonidas A. A. Doumas, and Robert L. Goldstone
positive targets (e.g., sweet melons). In Experiment 2, the stories were alignable because
the doctor looks for negative targets (e.g., sick patients) and the melon farmers also look
for negative targets (e.g., infected melons). Preserving the alignability in this way forfeited
the consistency between the label (i.e., target—positive label) and the tutorial element
(i.e., sick patient—negative story element).
If the Word condition in this experiment promotes transfer like Experiment 1, this
would provide support for the hypothesis that labels help by promoting comparison be-
tween stories, allowing participants to see common relational structure. However, if the
Word condition does not promote transfer, this provides further support for the hypothesis
that it is the semantic overlap between relational labels and their contextual objects that
determines whether words facilitate transfer.
Method
Participants
Seventy-five undergraduates (34 in the Control condition, 41 in the Word condition) from
Indiana University participated in this experiment for credit. Seven additional participants
were excluded from analysis because they took less than 15 minutes to read through the
tutorial. All participants reported that they had not previously learned SDT.
Materials
Tutorials similar to those used in Experiment 1, with and without relational words, were
used in this experiment. The main changes were to the tutorial and transfer story contexts
to convert them into situations where the detector searches for a negative target. In the
new tutorial story the doctor is trying to diagnose leukemia patients by examining blood
samples. People with distorted cell samples are more likely to have leukemia than those
with pure cell samples. Although cell distortion is an imperfect indicator of leukemia, the
doctor must try to optimize his decisions. The new melon transfer story is semantically
aligned to this tutorial story. The melon farming town is now trying to detect fungus-
infected melons in order to send them to an analysis center. Heavier melons tend to be
infected because they are carrying spores, but melon weight is not a perfect indicator
of fungus. Reports from the analysis center as well as consumers allow the town to find
out which melons are actually infected/normal. The alignment between the two stories
is demonstrated in Table 2.
The relational labels are the same as those in Experiment 1, only applied to the ele-
ments of the new story. The positive label, targets, refers to actually sick people and the
negative label, distracters, refers to actually healthy people. Those that the doctor has
diagnosed are marked as “sick” and, in the Word condition, they are accompanied by the
label “target. Those that have been diagnosed as “healthy” are labeled “distracters.” The
departure from Experiment 1 removes the consistency between relational words and the
When Do Words Promote Analogical Transfer? 69
volume 3, no. 1 (Fall 2010)
story elements that may have aided Word participants. Note that the relational words
preserve the structure of SDT and are correctly applied to the doctor context. We will
sometimes refer to Experiment 2’s tutorial as a negative target tutorial to draw attention
to the reduced semantic overlap between the positive relational word “target” and the
negative targets in the story (Table 2 shows the mappings between the relational words
and story elements more fully). Similarly, Experiment 2’s transfer context is a negative
target transfer situation.
Once again, other than the addition of relational words, the tutorials for the Word
and Control conditions were made up of the same pictures and explanatory text. Note
that unlike Experiment 1, there is no mention of rejection in the transfer situation here.
The relational role of the correct rejection in the new melon scenario is filled by normal
melons that get sold to consumers instead of getting sent to the fungus analysis center.
Any transfer that might be found from the relational word tutorial cannot be explained
by an explicit connection between the words and the transfer context.
Other materials included an eight-question multiple-choice tutorial quiz, a transfer
quiz, and a six-question mapping quiz. The wording of the quizzes was changed to re-
flect the new stories. One of the transfer questions was also changed from Experiment 1
(Question #1).
Procedure
The procedure was the same as before. First participants were presented with a tutorial
involving patients, then a quiz based on the tutorial, then a transfer situation based on
melons, and finally a transfer quiz. At the very end of the experiment, there was a mapping
quiz between the leukemia-detecting doctor and the fungus-detecting town.
Results and Discussion
If words foster relational transfer by capturing the alignment across story contexts, then
more similar situations should show the benefits of labeling. By this account, despite the
dissimilarity between the labels and the tutorial context, the relational labels could serve
as a representation of the similarity between stories to encourage transfer. A mixed-design
2 x 2 ANOVA (quiz type x condition) showed that there was a main effect of quiz type,
F(1, 73) = 34.80, p < 0.001, and a significant interaction, F(1, 73) = 4.27, p < 0.05. There was
no main effect of Word condition, F(1, 73) = 0.19. These results are shown in Table 3.
The interaction is consistent with the pattern found in Experiment 1 because even
though participants in the two conditions seem to have performed similarly in the initial
tutorial context, t(74) = 0.29, d = 0.18, those who also learned relational words were bet-
ter able to transfer their learning to a new situation. An ANCOVA showed that the Word
condition significantly outperformed the Control condition in transfer, F(1, 72) = 4.08, p
< 0.05, d = -0.70, and the tutorial quiz score is also a significant covariate, F(1, 72) = 41.28,
The Journal of Problem Solving
70 Ji Y. Son, Leonidas A. A. Doumas, and Robert L. Goldstone
p < 0.001. An initially mismatching set of relational words, when supported by alignable
similarities, aids in transfer of previously learned material to a new situation. Especially
because the difference between conditions arises in transfer, we can speculate that the
Word participants may have used the relational words to capture the abstract similari-
ties that arose between the two stories. The relational words in Experiment 2 may have
provided cognitively easy handles for difficult relational concepts.
Unlike Experiment 1, there was a main effect of quiz type where performance on the
tutorial quiz was generally better than transfer (d = 0.61). A paired t-test showed that across
both conditions, there was a significant decline (M = 0.13, SD = 0.20) between tutorial and
transfer quizzes, t(74) = 5.61, p < 0.001. It may be that the negative target transfer quiz was
harder or that learning from the negative target tutorial was not as transferable.
In the mapping quiz, participants had to match the analogous elements, such as sick
patient (target) to infected melon (also target), and correct matches were both structurally
and semantically aligned. In this way, the difficulty of Experiment 2’s mapping quiz was
similar to that of Experiment 1. The resulting patterns of results were also similar. There
was no difference in mapping scores between the Control and Word conditions, t(74) =
0.12 (means and standard deviations shown in Table 4).
The similarity between the results of Experiments 1 and 2 suggests relational
words allow students to exploit alignable similarities between the tutorial and transfer
contexts. The labels used in Experiment 1 had little in common with their corresponding
tutorial elements, but the labels in Experiment 2 had even less in common with their
corresponding tutorial elements. Even despite the introduction of dissimilarity, words
still had a beneficial effect for transfer. However, this set of results does not rule out the
possibility that the inclusion of relational words could help learners to think about the
scenarios more relationally in general. If the semantics of target and distracter can guide
learning of SDT, even without alignable stories, we should see benefits of tutorials with
relational words.
Experiment 3
So far we have shown that there is a beneficial effect of relational words when there are
alignable similarities, which have been implicated in creating structural representations
(Markman & Gentner, 2000). Experiment 3 examines whether the meanings of the relational
words alone (even without alignable stories) could also encourage learning relational
concepts. To illustrate this point, recall the Rattermann and Gentner results (1998), where
daddy-mommy-baby were helpful lexical terms but jiggy-fantan-gimli were not helpful
for children learning about monotonic decrease (large-medium-small). Presumably the
meaning of daddy helps children focus on the large size. Under this explanation, part of
the success of Experiment 1’s Word condition may have been due to the semantic overlap
When Do Words Promote Analogical Transfer? 71
volume 3, no. 1 (Fall 2010)
between target, a positively valenced relational word, and healthy athlete, a positively
valenced story element.
Experiment 3 used the tutorial from Experiment 1 but did not use the well-aligned
transfer story of Experiment 1 to take away the influence of easily comparable situations.
Instead, the positive target tutorial was followed by the negative target transfer situa-
tion (infected melon story from Experiment 2). If relational words require the support of
alignable similarities to be beneficial, we should see no benefit in the Word condition.
However, if the initial semantic overlap of the relational words to the tutorial context is
also effective, we should see benefits in transfer even without the analogous elements of
the two scenarios being semantically aligned.
Additionally, this experiment may shed light on why Experiment 2’s transfer scores
were overall lower than the tutorial scores. If the negative target transfer quiz (infected
melon) is simply more difficult than the positive target transfer quiz (sweet melon), then
Experiment 3 should show a similar pattern of decrease in transfer performance. However,
if seeking positive targets in the tutorial (healthy athletes) is a better tutorial than seeking
negative targets (sick patients), then Experiment 3 should be more similar to Experiment
1 and show no overall decreases in transfer.
Method
Participants
Sixty-one undergraduates (32 in the Control condition, 29 in the Word condition) from
Indiana University participated in this experiment for credit. Eight additional participants
were excluded from analysis because they took less than 15 minutes to read through the
tutorial. One other participant was excluded because of previous SDT knowledge. All other
participants reported not knowing SDT.
Materials
The tutorials, with and without relational words, used here were the same as Experiment
1. The transfer materials were the ones used in Experiment 2. This design, positive target
tutorial with negative target transfer, is shown in Table 2. Importantly, there is a match
in the semantics between the relational words and the tutorial elements (i.e., target and
healthy athlete are both positive; distracter and unhealthy athlete are both negative)
but a misalignment between the tutorial and transfer elements (i.e., healthy athlete and
infected melon; unhealthy athlete and normal melon).
Because the tutorial and transfer stories were not closely aligned, the grading of
the mapping quiz in this experiment was different than in the previous experiments. For
a mapping question such as What in the melon story is most analogous to the healthy
athlete in the doctor scenario?” students could pick the other target-like element (infected
melon). However, if we assume that targets can legally map to distracters (because in
The Journal of Problem Solving
72 Ji Y. Son, Leonidas A. A. Doumas, and Robert L. Goldstone
some contexts, which element is signal and which is noise is an arbitrary decision), map-
ping healthy athlete to normal melon still preserves the structure of SDT. In fact, in an
impoverished setting like a multiple-choice quiz, this is more appealing because of the
semantic similarity.
Given the experimenters familiarity with SDT, the tutorial and transfer situations
were designed with the healthy athlete-infected melon match (the target-target match)
in mind. One reflection of that intention is found in the spatial organization of the tuto-
rial and transfer figures, with cell strength and melon weight increasing from left to right
(for a schematic illustration see Procedure). Because of this spatial alignment, the targets
were both on the right side (the higher end of the evidence dimension) and the distracters
were on the left side (the lower end). We will call this mapping the structural answer. The
mapping quiz was graded in three ways: a structural score (mapping healthy athletes to
infected melons), a semantic score (mapping healthy athletes to normal melons), and a
total mapping score (both answers counted as correct).
Procedure
The procedure was the same as before. The tutorial and the tutorial quiz were followed
by the transfer situation and the transfer quiz. A mapping quiz was administered at the
end of the experiment.
Results and Discussion
A mixed-design 2 x 2 ANOVA (quiz type x condition) showed important similarities and
differences from previous experiments. First, there was no main effect of quiz type, F(1,
59) = 0.019, like Experiment 1 and unlike Experiment 2. This suggests that there is noth-
ing inherently difficult about the negative target transfer situation in which the farmers
look for infected melons. However, transfer seems less difficult overall with positive target
tutorials (Experiments 1 and 3). The ANOVA also revealed no significant effect of condition,
F(1, 59) = 0.654, nor any interaction, F(1, 59) = 0.411. Although these are null effects, these
results are important to consider in the context of the other two experiments. The results
are presented in Table 4 for ease of comparison.
Comparing the means between the Control and Word conditions, there seems to
be a trend toward better transfer performance with relational words than without them.
However, this is not borne out statistically, t(60) = 0.86. This suggests that relational words
did not consistently provide advantages when the two stories were not alignable.
Mapping results showed that all participants preferred making semantic matches,
0.65 (SD = 0.19), over structural ones, 0.23 (SD = .14), F(1, 59) = 114.14, p < 0.001. Word and
Control conditions showed no difference in the number of semantic mappings made,
t(60) = 0.18, nor in the number of structural matches made, t(60) = 0.14. The semantically
similar elements (i.e., an infected melon and an unhealthy athlete) were more influential
When Do Words Promote Analogical Transfer? 73
volume 3, no. 1 (Fall 2010)
than the structural aspects of the stories (targets corresponding to targets). The sparse
multiple-choice format of the mapping quiz may have biased participants toward form-
ing local mappings.
Experiment 4
So far we have learned that labels facilitate relational reasoning best in the context of stories
with semantically matching elements, and matching the meanings of the relational words
to the training scenario alone does not result in the same benefits. However, from these
results we do not know what the effect of relational words are when there is no overlap-
ping meaning between the word and the contextual element and no alignment between
stories. We will use the Rattermann and Gentner (1998) study to illustrate a plausible, but
untested, conjecture: relational responding may have suffered if they had labeled the
small object daddy and the large object was called baby. Even though semantic associa-
tions alone do not significantly improve quiz performance, without them, performance
might actually suffer. To test this, participants learned relational words in the context of a
negative target tutorial but transferred to a positive target situation.
Figure 3. The structure of the stories used in Experiment 3 shown with examples
of the counterintuitive structural mapping (green arrows).
Results and Discussion
A mixed-design 2x2 ANOVA (quiz type x condition) showed important
similarities and differences from previous experiments. First, there was no main
effect of quiz type, F(1, 59) = .019, like Experiment 1 and unlike Experiments 2.
This suggests that there is nothing inherently difficult about the negative target
transfer situation in which the farmers look for infected melons. However,
transfer seems less difficult overall with positive target tutorials (Experiments 1
and 3). The ANOVA also revealed no significant effect of condition, F(1, 59) =
.654, nor any interaction, F(1, 59) = .411. Although these are null effects, these
results are important to consider in the context of the other two experiments. The
results are presented in
Figure 3. The structure of the stories used in Experiment 3 are shown with examples of
the counterintuitive structural mapping (green arrows).
The Journal of Problem Solving
74 Ji Y. Son, Leonidas A. A. Doumas, and Robert L. Goldstone
If there is no effect of learning relational words in this experiment, it provides further
support for the hypothesis that labels interact with comparison of well-aligned stories.
Also, if there is a decline between tutorial and transfer quiz performance, like in Experi-
ment 2, this suggests that the negative target tutorial is not as effective for transfer as the
positive target tutorial (Experiments 1 and 3).
Method
Participants
Sixty-five undergraduates from Indiana University participated in this experiment for
credit. They were randomly assigned to the Word (N = 33) or Control (N = 32) condition.
Five additional participants who took less than 15 minutes to complete the experiment
were excluded from analysis. At the end of the experiment, all participants reported that
they had not previously learned SDT.
Materials and Procedure
The tutorials, with and without relational words, used here were the same as Experiment
2. The transfer materials were the ones used in Experiment 1. This design, negative target
tutorial with positive target transfer, is shown in Table 2. There is less overlap between the
semantics of the relational words and the tutorial elements (i.e., target is positive but sick
patient is negative; distracter is negative but healthy patient is positive). Also, there is no
alignment between the tutorial and transfer elements (i.e., sick patient and sweet melon
play the same role, as do healthy patient and bitter melon).
Because of this lack of alignment, the mapping quiz was scored like Experiment 3.
For a mapping question that inquired about sick patients, participants could pick the
transfer’s target (sweet melon) or the distracter (bitter melon). Although matching sick
patients to bitter melons is probably more appealing because of the semantic similarity,
the sick patient-sweet melon match is the structural mapping by both being the target-
target match and being the spatial match. The mapping quiz was graded in three ways: a
structural score (mapping sick patients to sweet melons, see Figure 3), a semantic score
(mapping healthy patients to sweet melons), and a total mapping score (both answers
counted as correct).
Results and Discussion
Table 3 shows the results of the tutorial and transfer quiz broken up by condition. A mixed-
design 2 x 2 ANOVA (quiz type x condition) showed no reliable interaction, F(1, 63) = 1.70,
but showed a significant main effect of quiz, F(1, 63) = 26.41, p < 0.001, d = 0.59. Similar
to Experiment 2, the other experiment that used a negative target tutorial, participants
had significantly higher scores on the tutorial quiz, 0.54 (SD = 0.23), than the transfer quiz,
When Do Words Promote Analogical Transfer? 75
volume 3, no. 1 (Fall 2010)
0.41 (SD = 0.23). Experiment 4 was the only experiment where the ANOVA showed even
a marginal effect of condition, F(1, 63) = 3.38, p < 0.08.
Although words typically show benefits for fostering appreciation of relational struc-
ture in the literature, our results show a trend in the opposite direction in which the Control
condition has generally better quiz scores than the Word condition (see Table 3). However,
quiz-specific analysis revealed that this advantage is primarily driven by differences on
the transfer quiz, t(64) = 6.09, p < 0.05, d = 0.49, and there was no significant difference in
tutorial quiz performance, t(64) = 0.98, d = 0.27. Control participants showed significantly
better transfer performance than those trained with relational words. An ANCOVA further
revealed that even though the tutorial scores were found to be a significant covariate, F(1,
62) = 27.11, p < 0.001, condition was still a significant influence on transfer performance,
F(1, 62) = 4.07, p < 0.05. In this case, learning with relational words actually was disadvanta-
geous rather than being neutral (Experiment 3) or beneficial (Experiments 1 and 2). These
results underscore the importance of alignment between scenario elements as removing
alignment also removes the benefit of learning relational words. These results go further
to suggest that there are hazards of teaching relational words when there is little semantic
overlap between the relational word and the learning context.
The harmful effects of learning relational words, particularly for transfer, might lead
one to expect participants in the Word condition to have low mapping quiz scores as well.
Total mapping scores, both structural and semantic answers together, did differ, with the
Control condition scoring significantly better (M = 0.87, SD = 0.16) than the Word condition
(M = 0.79, SD = 0.18), t(64) = 4.49, p < 0.05. When the composite score was broken down into
structural and semantic mappings and analyzed with a mixed-design 2 x 2 (mapping type
x condition) ANOVA, there was a main effect of mapping type, with participants generally
making more semantic matches, 0.49 (SD = 0.30), than structural ones, 0.26 (SD = 0.22), F(1,
63) = 15.34, p < 0.001. This result supports the notion that superficial semantic similarity
strongly influences mapping (Gentner & Toupin, 1986; Ross, 1989), but we should note
that these explicit mappings were made after the transfer quiz, so they may or may not
have been used during transfer (Ross, 1987).
There was also a main effect of condition, F(1, 63) = 10.52, p < 0.01, as well as a
significant interaction between these variables, F(1, 63) = 8.68, p < 0.01. These results
are shown in Table 4. Control participants made significantly more semantic mappings
than the Word condition, t(64) = 11.75, p < 0.01. The poorly transferring Word condition
showed significantly more structural choices than the Control condition, matching the
explicit target in the tutorial context (sick patient) with the implicit target in the transfer
context (sweet melons), t(64) = 4.22, p < 0.05. This is surprising since the structural choice
is both counterintuitive and a more relationally sophisticated choice. As counterintuitive
as the structural mapping of the two contexts may be to all of our novice participants, this
alignment might be obviously seen as the “right answer” if the words introduced in the
The Journal of Problem Solving
76 Ji Y. Son, Leonidas A. A. Doumas, and Robert L. Goldstone
experimental condition were used to explicitly connect scenario elements. An example
of an explicit connection would be if participants were asked, “Which is the target of the
patient story? Which is the target of the melon story?” The Word condition participants
were perhaps more likely to make the implicit connection between the targets of the
two scenarios.
Even so, participants in the Word condition still made more semantic than structural
mappings, suggesting one of two possibilities: (1) half of the participants in the Word
condition made structural alignments and the other half made semantic ones; or (2) the
individual participants in the Word condition do not have a consistently aligned view of
the analogy and flip-flopped between structural and semantic mappings. To examine
these two possibilities, we categorized students by how many structural and semantic
mappings they made out of a possible six. Then for each participant, we registered the
mapping type in which the participant showed the majority of correct answers (i.e., if a
participant made two structural and four semantic mappings, we tallied the four semantic
mappings) and created Figure 4 out of these majority mapping scores. If the participants
in the Word condition showed high majority mapping scores (5 or 6 out of 6), this supports
the first possibility, that participants are split into consistently structural and consistently
semantic mappers. If participants in the Word condition tend to make only some semantic
and some structural mappings (2-4 out of 6), this supports the second possibility, that each
participant only makes a few of each type of mapping. Figure 4 shows that only 10 (out of
32) Word participants were consistently structural or semantic. More than half of the Word
condition (22 out of 32) had a majority mapping score between 2 and 4 mappings. It seems
that participants in the Word condition are influenced by both semantic and structural
construals, and these construals yield a hodgepodge of inconsistent mappings. Words may
cause some pull toward a structural perspective but cannot completely overcome the
attractive semantic mapping. There is enough uncertainty to prevent Word participants
from settling on one coherent perspective. This instability may have contributed to their
poor performance on the transfer task.
General Discussion
Taken together, these four experiments reveal a system of effects that connects to im-
portant themes of research in language and analogical reasoning. We have explored how
learning and applying deep principles (such as SDT) are sensitive to interactions between
similarity and language. When relational words about SDT structure were introduced with
two readily alignable stories, participants in the Word condition showed better transfer
than Control participants (Experiments 1 and 2). This benefit of relational words was
shown even when the valence-based semantics of the relational words did not match
the semantics of the elements of either tutorial or transfer contexts (Experiment 2). When
When Do Words Promote Analogical Transfer? 77
volume 3, no. 1 (Fall 2010)
the corresponding elements of the tutorial and transfer stories did not semantically align,
there was either no effect (Experiment 3) or a slight disadvantage (Experiment 4) of learn-
ing relational words. Less semantic overlap between the relational labels and the learning
context is more harmful than better semantic overlap, as revealed by the difference in
results between Experiments 3 and 4.
The notion that words help us interpret a situation immediately before us may be
generally accepted, but our experiments show that words actually continue to influence
learners even in new situations presented without those relational words. Our experiments
did not find any significant differences between conditions on tutorial performance; the
main differences were found during transfer. Furthermore, this influence actually relies
on the alignability of new transfer situations to old ones. When story similarities support
structural alignments, then learning relational words fosters transfer. This suggests that
words foster relational transfer best when they function as GTs—convenient, easily ma-
nipulated representations—that stand for relational structure.
Without alignment between tutorial and transfer stories, words may have either no
influence (Experiment 3) or even a negative influence (Experiment 4). Note that the transfer
Figure 4. The Word participants in Experiment 4 are shown with their majority mapping
score, which is the greater of their correct semantic or structural mapping scores. Note
that most of these participants tend to make two to four correct mappings as opposed
to five to six mappings.
Figure 4. The Word participants in Experiment 4 are shown with their majority
mapping score, which is the greater of their correct semantic or structural
mapping scores. Note that most of these participants tend to make 2-4 correct
mappings as opposed to 5-6 mappings.
GENERAL DISCUSSION
Taken together, these four experiments reveal a system of effects that
connects to important themes of research in language and analogical reasoning.
We have explored how learning and applying deep principles (such as SDT) are
sensitive to interactions between similarity and language. When relational words
about SDT structure were introduced with two readily alignable stories,
participants in the Word condition showed better transfer than Control
participants (Experiments 1 and 2). This benefit of relational words was shown
even when the valence-based semantics of the relational words did not match the
semantics of the elements of either tutorial or transfer contexts (Experiment 2).
When the corresponding elements of the tutorial and transfer stories did not
semantically align, there was either no effect (Experiment 3) or a slight
disadvantage (Experiment 4) of learning relational words. Less semantic overlap
between the relational labels and the learning context is more harmful than better
semantic overlap, as revealed by the difference in results between Experiments 3
and 4.
The Journal of Problem Solving
78 Ji Y. Son, Leonidas A. A. Doumas, and Robert L. Goldstone
disadvantage in Experiment 4 was not simply due to poorer performance on the tutorial
itself. This suggests that words function as CSMs as well since relational words with less
effective meanings result in poorer transfer than relational words that meaningfully point
to contextual elements. This finding fits with research that indicates that although words
generally foster relational reasoning, not all words are equal in that ability (Rattermann &
Gentner, 1998; Son et al., under review). This also supports indications that the mere pres-
ence of a relational word does not always mean that a relational category or mapping will
be formed (Hall & Waxman, 1993; Keil & Batterman, 1984).
Altogether, these results further suggest that the two functions of words (as GTs and
CSMs) may be considered additive. If they are additive, we have an explanation for why
Experiment 1’s Word condition benefited even more than the Word condition in Experi-
ment 2 and Experiment 3. In Experiment 1, the words were effective CSMs that matched
the story elements but also acted as GTs that took advantage of alignable situations to
promote transfer. Experiment 2 only had words that functioned as GTs and Experiment 3
only had words that functioned as CSMs. All words, novel and meaningful, function as GTs
but only some words are CSMs. So perhaps the meaningful aspect of relational labels like
daddy/mommy/baby (Rattermann & Gentner, 1998) and target/distracter builds upon the
way that novel labels such as grecious/leebish (Lupyan, 2008) function.
Beyond our manipulation of relational words, positive target tutorials (used in Ex-
periments 1 and 3) seemed to transfer more readily than negative target tutorials (used
in Experiments 2 and 4). Evidence for this comes from the decreases in quiz score from
tutorial to transfer that was found in Experiments 2 and 4, even though they used different
transfer tests (2 used a negative target transfer and 4 used a positive target transfer). The
story about a doctor detecting leukemia may be a poorer tutorial situation than a doctor
looking for healthy athletes for several reasons. Perhaps SDT inherently has something
more in common with detecting positive things, because in many situations we look for
things that we desire. Another speculative reason for the disadvantage of the leukemia
story may be because of participants’ general familiarity with that kind of situation. It may
have been difficult to reconceptualize a familiar situation as an example of SDT rather than
a more novel medical example. Research in other domains has found that learning with
concrete, familiar situations can hinder transfer (Goldstone & Sakamoto, 2003; Kaminski,
Sloutsky, & Heckler, 2008). We have explored the impact of different levels of contextu-
alization, personalization, and familiarity in learning SDT in another line of experiments
(Son & Goldstone, 2009). This work has confirmed that more familiar, personally relevant
scenarios produce less robust transfer than more distant, generic scenarios.
Similarity plays a major role in analogical mapping and usually mappings that can
be made on the basis of object similarity are the least effortful (Gentner & Toupin, 1986).
In Experiments 1 and 2, the correct mappings were both superficially and relationally
similar, but in Experiments 3 and 4 semantic and structural information did not foster the
When Do Words Promote Analogical Transfer? 79
volume 3, no. 1 (Fall 2010)
same alignment. When the mappings are in conflict, regardless of condition, participants
generally preferred semantic mappings to structural ones. When there are answer options
with a high degree of superficial similarity to the target (i.e., unhealthy athletes correspond-
ing to infected melons; Experiment 3), semantic mappings are virtually unavoidable, with or
without relational language. A lesser degree of similarity (i.e., sick patients and bitter melons;
Experiment 4) may have allowed mappings to be more affected by relational words.
Typically models of relational reasoning assume that mapping comes before trans-
fer. If this were the case, then better mappings should always be accompanied by better
transfer. In our experiments, structural mappings could be considered the most reflective
of SDT. However, when we compare Experiments 3 and 4, the participants who made the
most structural mappings, the Word condition in Experiment 4, also had one of the worst
transfer scores. This suggests several possibilities. Perhaps when a system of mappings
is inconsistent or incomplete, transfer suffers. Another possibility is that the ecology of
a mapping task is different from transfer (the mechanisms may differ as well; see Leech,
Marschal, & Cooper, 2008). Particularly in our paradigm, mapping questions were presented
as separate comparisons between individual elements. This seems to reflect a very differ-
ent environmental context than our transfer task, where participants must consider a full
situation and the contingencies within that system. Understanding the structure within
one context may be a different problem than connecting elements across two contexts.
The former case requires a more global understanding of the structure, but only in one
context, but the latter may be more affected by more local relations and features between
contexts. However, it is important to note that mappings were probed at the end of the
experiment so the participants may or may not have used these correspondences for the
transfer test.
Language and Abstraction
As flexible and useful as a formalized understanding of SDT might be, conveying these
schemas in highly stripped down forms, such as equations and sparse graphs, may lead
to representations that are too stripped down to foster learning, much less transfer, in
novices. In the experiments described here, the participants Control conditions always
learned the abstractions completely embedded in the doctor context whereas those in
the Word conditions also had exposure to decontextualizing descriptors. In general, the
Control participants may have relied more heavily on the tutorial context, perhaps result-
ing in scaffolded performance on the tutorial quiz. However, the payoff (and the detriment
in Experiment 4) for the extra work of learning decontextualized relational words was
seen rather late, in transfer performance. In fact, because the alignability of the transfer
contexts played such a large role in whether words were effective or not, the processes
of comparison may be fundamental to fostering abstract understandings.
The Journal of Problem Solving
80 Ji Y. Son, Leonidas A. A. Doumas, and Robert L. Goldstone
These findings shed light on the first of two ways (as GTs and as CSMs) in which rela-
tional words could exert their influence. Decontextualized relational words seem to interact
with commonalities between two alignable contexts. This suggests that words function
like GTs that represent abstractions more concretely such that they can be utilized more
effectively in transfer. When contexts do not have transparent structural alignments, the
availability of GTs does not facilitate transfer. Any benefit of relational words on transfer
between well-aligned situations would fit with other research on words, comparison, and
abstraction of relations (Kotovsky & Gentner, 1996; Gentner & Rattermann, 1991). This
influence of language adds to analogy research that implicates contextual similarities in
application of abstractions (Barnett & Ceci, 2002; Bassok, 1998; Ross, 1987, 1989).
Because structure is often learned in situ with no immediate need for decontextual-
ization, the GT aspect of words may facilitate transfer by encouraging decontextualization
and abstraction. If the very act of labeling serves as an invitation to form abstract, relational
concepts (as suggested by Gentner & Namy, 1999; Gentner & Rattermann, 1991), then we
may have seen all labels fostering better relational responding. Instead, the beneficial ef-
fects of labeling were mediated by how easy it was to actually form relational concepts,
assuming that alignment makes it easier to compare and abstract relations. Although
previous explanations of this “invitation to abstract suggests that comparison occurs
when two items share the same label, our experiments show that the presence of labels
in even one entity plays an important role in relational extraction. This begs the question,
how do words—that we have learned in the past—impact our ability to notice difficult
relations in a scenario?
Our GT hypothesis suggests that the presence of relational words might encourage
students to represent the relations and downplay contextual features. This differentiation
between relations and concrete features would allow relational similarities to be selec-
tively attended and also further encapsulated by the words. For example, the features
that are in common between healthy athlete and targets could be used to redefine target
in a manner consistent with SDT. Thus, learners would be primed with a notion of target
that could be useful for understanding sweet melons in the transfer situation. If the word
target is applied to a sick person, the meaning of the word might be adjusted to reflect
a target that is bad and must be spotted and weeded out. In this case, learners would be
primed with a notion of target useful for looking for infected melons.
Also, the relations represented by target, by being anchored by a word, can be more
concretely understood, exerting a larger influence on how scenarios are interpreted. The
label target may come to mean lots of things, including “goal (SDT signal) and “good thing”
(in the case of two overlapping good things in Experiment 1, and perhaps “thing that are
important to detect” in Experiment 2), and even though the label was used with only the
former meaning in mind, the latter is also acquired. Local features such as “good thing”
may be important in aligning the stories, which in turn helps participants become sensi-
When Do Words Promote Analogical Transfer? 81
volume 3, no. 1 (Fall 2010)
tive to deeper SDT structure. These local, and often superficial, similarities are critical in
theories of relational reasoning, such as the Structure-Mapping theory (Gentner, 1983), as
well as computational models (e.g., MAC/FAC with SME, Forbus, Gentner, & Law, 1995; LISA,
Hummel & Holyoak, 1997; DORA, Doumas & Hummel, 2005). When relational and featural
similarities both support a particular alignment (SME) or binding (LISA and DORA), there
is a greater likelihood for success in relational responding in these models.
This theory of words as priming future relations is best captured by this metaphor:
language is a filter for our perceptual experiences. This perspective would suggest that
words simplify our experiences (Clark, 1997) by helping us ignore and/or highlight certain
aspects. In learning new words, we may also acquire tools (Clark, 1997; Gentner, 2003; Vy-
gotsky, 1962) that aid our capability to selectively attend. And because language has such
a primary role in communication, language may also reshape the perceptions of others
as well as our own experiences. In this way, the jargon used in a particular community (i.e.
scientific, cultural, geographical) goes beyond communicating about ideas.
If we accept that language can act as a filter, this should also help us understand how
it facilitates the processes of abstraction. One way of defining abstraction is to define it as a
process of simplification through stripping away irrelevant information and retaining only
critical information. Having language with words that label ideas might help us reduce
the complex world, allowing us to abstract key information. This process of simplification
and reduction may be at the foundation of what makes human reasoning so flexible and
sophisticated. Whether our reasoning abilities are augmented through words and labels
or some other cognitive tool, these boosts may be at the heart of what makes us smart.
Appendix
Tutorial Quiz (Experiment 1)
1. The numbers of actually healthy and unhealthy people are the same two months
in a row. However, in the second month, the doctor is diagnosing more patients as
healthy when they are actually healthy and more people as healthy when they are
actually unhealthy. What must have changed in the second month?
a. The doctor must be diagnosing people with weaker cells as healthy.
b. The doctor must be diagnosing people with stronger cells as healthy.
c. The doctor must be diagnosing more people who are actually healthy as
unhealthy.
d. The doctor must have become better at diagnosing healthy people.
2. For a particular kind of cell, the doctor knows from his experience this month that
there is a 50% chance that this level of cell strength indicates anemia. What does
this mean?
The Journal of Problem Solving
82 Ji Y. Son, Leonidas A. A. Doumas, and Robert L. Goldstone
a. 50% of people with anemia have this level of cell strength.
b. 50% of all the patients the doctor has seen this month have anemia.
c. The doctor has seen equal numbers of people with anemia and people with
strong cells this month.
d. The doctor has seen equal numbers of healthy people with this level of
strength and unhealthy people with this level of strength.
3. The doctor is looking into a new blood test for finding weakened cells. How can he
find out whether this new test is better than the old one?
a. The doctor changes his decision boundary and diagnoses more healthy peo-
ple as healthy.
b. The doctor changes his decision boundary and diagnoses more strong-celled
samples as healthy.
c. The doctor does not change his decision boundary and diagnoses more
healthy people as healthy.
d. The doctor does not change his decision boundary and diagnoses more weak
samples as unhealthy.
4. If the doctor moves his decision boundary all the way to include even extremely
strong as evidence for anemia, it means:
a. he is generally more accurate because he is able to make less errors.
b. he never mistakenly diagnoses healthy people as unhealthy.
c. he always diagnoses people as unhealthy when they are actually healthy.
d. he always diagnoses people as healthy when they are actually healthy.
5. This month, each sick person’s cells get weaker while healthy people’s cells do not
get better or worse. The doctor does not know this information. If the doctor does
not change his decision boundary, how does this change in the population help
him?
a. he increases the number of actually healthy people he diagnoses as healthy.
b. he decreases the number of actually sick people he diagnoses as healthy.
c. he increases the number of actually healthy people he diagnoses as sick.
d. sick people become more common so he gets more experience diagnosing
them.
6. Which of the following decision strategies will ensure that the doctor maximizes
the number of actually healthy people he diagnoses as healthy?
a. diagnose everyone as healthy.
b. look more carefully at the cell distortion levels before his diagnosis.
c. examine the previous months ratio of healthy patients to unhealthy patients
before his diagnosis.
d. examine the previous months ratio of patients with strong cells to patients
with weak cells before his diagnosis.
When Do Words Promote Analogical Transfer? 83
volume 3, no. 1 (Fall 2010)
7. Which is most likely to lead to inaccuracy in the doctors diagnoses?
a. Unhealthy people develop extremely weak cells.
b. Unhealthy people and healthy people have similar cell strength levels.
c. The people diagnosed as healthy all have similar distortion levels.
d. Weak cells are more common among unhealthy people.
8. Very strong cells are often enriched with protein bundles. Knowing this, the doc-
tor’s accuracy can:
a. improve at detecting who is actually healthy and unhealthy.
b. improve at detecting who is actually unhealthy.
c. improve at detecting who is actually healthy.
d. not improve based on this information.
Transfer Quiz (Experiments 1 and 2)
1. (Use graph above.) Approximately what percentage of all 1000 gram melons (1 kg)
are sweet?
a. 10%
b. 25%
c. 33%
d. 50%
e. 66%
TRANSFER QUIZ (EXPERIMENTS 1 AND 2)
1. (Use graph above.) Approximately what percentage of all 1000 gram melons
(1 kg) are sweet?
a. 10%
b. 25%
c. 33%
d. 50%
e. 66%
TRANSFER QUIZ (EXPERIMENTS 1 AND 2)
1. (Use graph above.) Approximately what percentage of all 1000 gram melons
(1 kg) are sweet?
a. 10%
b. 25%
c. 33%
d. 50%
e. 66%
The Journal of Problem Solving
84 Ji Y. Son, Leonidas A. A. Doumas, and Robert L. Goldstone
2. (Use graph above.) There was a very bitter shipment of melons last year so the
townspeople wanted to be extremely careful this year. They set a 1750 gram mini-
mum weight but they do not know which melons are sweet or which melons are
bitter. How many melons that weighed 1500 grams were rejected?
a. 300
b. 450
c. 500
d. 750
e. 950
3. (Use provided graph—question 2’s graph) With the minimum weight for the plu-
ma melon set at 1750 grams, how many of bitter pluma melons are rejected?
a. 400
b. 950
c. 1550
d. 2000
e. 2600
4. Some of the people in Chanterais debate over using a high-tech digital scale in
place of their old-fashioned analog scale. What would be evidence that the high-
tech scale is a better diagnostic?
a. Chanterais changes their required weight and exports more sweet fruit.
b. Chanterais changes their required weight and rejects more bitter fruit.
c. Chanterais does not change their required weight and rejects more bitter
fruit.
2. (Use graph above.) There was a very bitter shipment of melons last year so the
townspeople wanted to be extremely careful this year. They set a 1750
gram minimum weight but they do not know which are sweet or bitter.
How many melons that weighed 1500 grams were rejected?
a. 300
b. 450
c. 500
d. 750
e. 950
3. (Use provided graph – question 2’s graph) With the minimum weight for the
pluma melon set at 1750 grams, how many of bitter pluma melons are
rejected?
a. 400
b. 950
c. 1550
d. 2000
e. 2600
4. Some of the people in Chanterais debate over using a high-tech digital scale in
place of their old-fashioned analog scale. What would be evidence that
the high-tech scale is a better diagnostic?
a. Chanterais changes their required weight and exports more sweet fruit.
b. Chanterais changes their required weight and rejects more bitter fruit.
c. Chanterais does not change their required weight and rejects
more bitter fruit.
2. (Use graph above.) There was a very bitter shipment of melons last year so the
townspeople wanted to be extremely careful this year. They set a 1750
gram minimum weight but they do not know which are sweet or bitter.
How many melons that weighed 1500 grams were rejected?
a. 300
b. 450
c. 500
d. 750
e. 950
3. (Use provided graph – question 2’s graph) With the minimum weight for the
pluma melon set at 1750 grams, how many of bitter pluma melons are
rejected?
a. 400
b. 950
c. 1550
d. 2000
e. 2600
4. Some of the people in Chanterais debate over using a high-tech digital scale in
place of their old-fashioned analog scale. What would be evidence that
the high-tech scale is a better diagnostic?
a. Chanterais changes their required weight and exports more sweet fruit.
b. Chanterais changes their required weight and rejects more bitter fruit.
c. Chanterais does not change their required weight and rejects
more bitter fruit.
When Do Words Promote Analogical Transfer? 85
volume 3, no. 1 (Fall 2010)
d. Chanterais does not change their required weight and rejects more light-
weight fruit.
5. For 1750 gram melons, Chanterais knows from last month that there is a 25%
chance that these melons are sweet. What does this mean?
a. 25% of sweet melons will weigh 1750 grams.
b. 25% of the melons will be sweet.
c. 75% of the melons will be bitter.
d. 25% of 1750 gram melons will be sweet.
6. If Chanterais lowers their minimum weight, which of the following would happen?
a. They will export more sweet fruit and less bitter fruit.
b. They will never export sweet fruit.
c. They will export less sweet fruit and more bitter fruit.
d. They will export more sweet fruit.
7. In a particular year, there is plenty of rainfall and all the melons get about 250
grams heavier. The prior year Chanterais exported melons that weighed 1500
grams or more. If they do not change their policy:
a. Chanterais will only accept more heavy melons that are sweet.
b. Chanterais will only reject more light melons that are sweet.
c. Chanterais will accept more melons that are sweet.
d. Chanterais will reject more melons that are lightweight.
8. How does this graph support the idea that melon weight is a good predictor of
sweet melons?
d. Chanterais does not change their required weight and rejects more
light-weight fruit.
5. For 1750 gram melons, Chanterais knows from last month that there is a 25%
chance that these melons are sweet. What does this mean?
a. 25% of sweet melons will weigh 1750 grams.
b. 25% of the melons will be sweet.
c. 75% of the melons will be bitter.
d. 25% of 1750 gram melons will be sweet.
6. If Chanterais lowers their minimum weight, which of the following would
happen?
a. They will export more sweet fruit and less bitter fruit.
b. They will never export sweet fruit.
c. They will export less sweet fruit and more bitter fruit.
d. They will export more sweet fruit.
7. In a particular year, there is plenty of rainfall and all the melons get about 250
grams heavier. The prior year Chanterais exported melons that weighed
1500 grams or more. If they do not change their policy:
a. Chanterais will only accept more heavy melons that are sweet.
b. Chanterais will only reject more light melons that are sweet.
c. Chanterais will accept more melons that are sweet.
d. Chanterais will reject more melons that are lightweight.
8. How does this graph support the idea that melon weight is a good predictor of
sweet melons?
a. There are fewer heavy melons that are bitter than are sweet.
d. Chanterais does not change their required weight and rejects more
light-weight fruit.
5. For 1750 gram melons, Chanterais knows from last month that there is a 25%
chance that these melons are sweet. What does this mean?
a. 25% of sweet melons will weigh 1750 grams.
b. 25% of the melons will be sweet.
c. 75% of the melons will be bitter.
d. 25% of 1750 gram melons will be sweet.
6. If Chanterais lowers their minimum weight, which of the following would
happen?
a. They will export more sweet fruit and less bitter fruit.
b. They will never export sweet fruit.
c. They will export less sweet fruit and more bitter fruit.
d. They will export more sweet fruit.
7. In a particular year, there is plenty of rainfall and all the melons get about 250
grams heavier. The prior year Chanterais exported melons that weighed
1500 grams or more. If they do not change their policy:
a. Chanterais will only accept more heavy melons that are sweet.
b. Chanterais will only reject more light melons that are sweet.
c. Chanterais will accept more melons that are sweet.
d. Chanterais will reject more melons that are lightweight.
8. How does this graph support the idea that melon weight is a good predictor of
sweet melons?
a. There are fewer heavy melons that are bitter than are sweet.
The Journal of Problem Solving
86 Ji Y. Son, Leonidas A. A. Doumas, and Robert L. Goldstone
a. There are fewer heavy melons that are bitter than are sweet.
b. There are fewer light melons that are bitter than are sweet.
c. There are fewer light melons than heavy melons.
d. There are more sweet melons than bitter melons.
e. There are more heavy melons than light melons.
Analogy questions for Experiment 1
1. A patient diagnosed as sick but is actually healthy is like what?
a. A bitter melon that is rejected.
b. A bitter melon that is exported. (target-to-distracter)
c. A sweet melon that is rejected. (target-to-target)
d. A sweet melon that is exported.
2. What in the doctor story is most analogous to a heavy melon?
a. A patient with strong cells. (target-to-target)
b. A patient with weak cells. (target-to-distracter)
c. A patient who is sick.
d. A patient who is healthy.
3. A melon that is sweet but was rejected is analogous to:
a. A sick patient who had been diagnosed as sick.
b. A sick patient who had been diagnosed as healthy. (target-to-distracter)
c. A healthy patient who had been diagnosed as healthy.
d. A healthy patient who had been diagnosed as sick. (target-to-target)
4. What in the melon export story is most analogous to the sick patient in the doctor
scenario?
a. A sweet melon. (target-to-distracter)
b. A bitter melon. (target-to-target)
c. An exported melon.
d. A rejected melon.
5. The patient with anemia who has been diagnosed as sick is most like:
a. A melon that is rejected and sweet.
b. A melon that is rejected and bitter. (target-to-target)
c. A melon that is exported and bitter.
d. A melon that is exported and sweet. (target-to-distracter)
6. An exported melon is like:
a. A patient who has been given weak cell results.
b. A patient who has been given strong cell results.
c. A patient who has been given a sick diagnosis. (target-to-distracter)
d. A patient who has been given a healthy diagnosis. (target-to-target)
When Do Words Promote Analogical Transfer? 87
volume 3, no. 1 (Fall 2010)
Analogy questions for Experiment 2
1. A patient diagnosed as sick but is actually healthy is like what?
a. A bitter melon that is rejected.
b. A bitter melon that is accepted. (target-to-target)
c. A sweet melon that is rejected. (target-to-distracter)
d. A sweet melon that is accepted.
2. What in the doctor story is most analogous to a heavy melon?
a. A patient with distorted cells. (target-to-target)
b. A patient with pure cells. (target-to-distracter)
c. A patient who is sick.
d. A patient who is healthy.
3. A melon that is sweet but was rejected is analogous to:
a. A sick patient who had been diagnosed as sick.
b. A sick patient who had been diagnosed as healthy. (target-to-target)
c. A healthy patient who had been diagnosed as healthy.
d. A healthy patient who had been diagnosed as sick. (target-to-distracter)
4. What in the melon export story is most analogous to the sick patient in the doctor
scenario?
a. A sweet melon. (target-to-target)
b. A bitter melon. (target-to-distracter)
c. An exported melon.
d. A rejected melon.
5. The patient with leukemia who has been diagnosed as sick is most like:
a. A melon that is rejected and sweet.
b. A melon that is rejected and bitter. (target-to-distracter)
c. A melon that is exported and bitter.
d. A melon that is exported and sweet. (target-to-target)
6. An exported melon is like:
a. A patient who has been given low distortion test results.
b. A patient who has been given high distortion test results.
c. A patient who has been given a sick diagnosis. (target-to-target)
d. A patient who has been given a healthy diagnosis. (target-to-distracter)
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... même système relationnel à travers des situations de différents domaines, alors que les labels de domaine n'ont pas d'effet sur l'évocation superficielle puisque les objets seraient encodés de façon stable quels que soient les contextes.Deux explications possibles à l'influence bénéfique de la présence de labels sur le transfert analogique spontané ont été évaluées empiriquement(Son, Doumas & Goldstone, 2010). La première possibilité envisagée est que les labels disposent de propriétés génériques indépendantes de leur signification facilitant l'extraction de structure et invitant à comparer les analogues. ...
... La seconde est que les propriétés sémantiques associées aux labels (leur signification) servent d'indices pour inférer la structure des exemplaires. Dans l'étude menée parSon et al. (2010), un exemple source de situation faisant intervenir la théorie du signal était présenté avant l'introduction d'un exemple analogue cible superficiellement différent.L'exemple source décrit un médecin qui tente de trier des personnes saines ou en mauvaise santé en fonction de l'état plus ou moins bon de leurs cellules sanguines. Bien que cet indicateur ne soit pas parfaitement fiable, le médecin fixe un seuil de qualité des cellules pour décider si une personne est saine ou en mauvaise santé. ...
Thesis
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L’analogie est un mécanisme fondamental permettant d’interpréter une nouvelle situation à travers des expériences passées. La présente thèse vise à redonner toute sa force à ce postulat en mettant en avant la capacité à percevoir comme essentiellement similaires des expériences d’apparence pourtant différentes. Partant du principe que les analogies constituent un mécanisme naturel par lequel le système cognitif traite l’information nouvelle, un intérêt particulier est attribué à leur manifestation spontanée (i.e. sans incitation par un tiers à effectuer la comparaison), telles qu’elles apparaissent à travers l’assimilation de nouvelles expériences à des conceptions familières stockées en Mémoire à Long Terme (MLT). Ce mécanisme est envisagé comme un moteur du développement conceptuel chez le jeune enfant.Les trois premières études empiriques ont pour objectif de tester l’hypothèse selon laquelle des concepts abstraits familiers sont utilisées pour comprendre la structure profonde des situations rencontrées quotidiennement et évoquer des expériences passées en se basant sur des similitudes structurelles plutôt que superficielles. Les résultats issus de paradigmes expérimentaux de rappel d’histoires écrites, de rappel de situations filmées et d’évocation libre d’expériences personnelles valident notre hypothèse, dévoilant que les situations structurellement similaires sont plus fréquemment évoquées que les situations superficiellement similaires. Compte tenu du rôle des concepts abstraits dans la compréhension, la quatrième étude aborde la question de leur développement chez le jeune enfant. Nous faisons l’hypothèse que les processus cognitifs et neuronaux impliqués lors du traitement d’approximations sémantiques verbales (ex : « elle déshabille l’orange ») par le jeune enfant de 4 ans reflètent le mécanisme par lequel des catégories lexicales aux frontières immatures sont appliquées par analogie à de nouvelles situations. Conformément à notre prédiction, les Potentiels Évoqués (PE) indiquent que les jeunes enfants détectent l’incongruence (effet N400) de verbes inappropriés, mais pas celles des approximations sémantiques.Les implications et les perspectives émergeant de nos résultats sont discutées dans le cadre d’une approche plaçant la capacité à établir spontanément des rapprochements profonds au centre des mécanismes de compréhension de développement des catégories.
... For example, given a number of examples of instances where one object is larger than another object, DORA can extract and learn a structured representation of the invariant properties of all those larger things (e.g., it learns a predicate for larger from the properties that are invariant across instances of one larger and one smaller object). The resulting representations support successful reasoning in a wide range of relational tasks (see, e.g., Doumas & Hummel, 2010;Doumas et al., 2008;Hamer & Doumas, 2013;Martin & Doumas, 2017;Morrison et al., 2012;Son et al, 2010; a more detailed description of the model is also given below). ...
Preprint
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How a system represents information tightly constrains the kinds of problems it can solve. Humans routinely solve problems that appear to require structured representations of stimulus properties and relations. Answering the question of how we acquire these representations has central importance in an account of human cognition. We propose a theory of how a system can learn invariant responses to instances of similarity and relative magnitude, and how structured relational representations can be learned from initially unstructured inputs. We instantiate that theory in the DORA ( Discovery of Relations by Analogy ) computational framework. The result is a system that learns structured representations of relations from unstructured flat feature vector representations of objects with absolute properties. The resulting representations meet the requirements of human structured relational representations, and the model captures several specific phenomena from the literature on cognitive development. In doing so, we address a major limitation of current accounts of cognition, and provide an existence proof for how structured representations might be learned from experience.
... Previous work has demonstrated that these principles-and the models we have developed to instantiate them-account for over 100 major findings in human cognition, spanning at least seven domains: (a) shape perception and object recognition (16,29,30); (b) relational thinking (17,23,(31)(32)(33)(34)(35)(36)(37), (c) learning structured representations (19,38,39), (d) cognitive development (19,(41)(42)(43), (e) language processing (24,44), (f) normal cognitive aging (45), and (g) decline due to dementia, stress, and brain damage (46). As such, we take these principles to be on firm ground as a starting point for a computational account of cross-domain transfer. ...
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People readily generalise prior knowledge to novel situations and stimuli. Advances in machine learning and artificial intelligence have begun to approximate and even surpass human performance in specific domains, but machine learning systems struggle to generalise information to untrained situations. We present and model that demonstrates human-like extrapolatory generalisation by learning and explicitly representing an open-ended set of relations characterising regularities within the domains it is exposed to. First, when trained to play one video game (e.g., Breakout). the model generalises to a new game (e.g., Pong) with different rules, dimensions, and characteristics in a single shot. Second, the model can learn representations from a different domain (e.g., 3D shape images) that support learning a video game and generalising to a new game in one shot. By exploiting well-established principles from cognitive psychology and neuroscience, the model learns structured representations without feedback, and without requiring knowledge of the relevant relations to be given a priori. We present additional simulations showing that the representations that the model learns support cross-domain generalisation. The model's ability to generalise between different games demonstrates the flexible generalisation afforded by a capacity to learn not only statistical relations, but also other relations that are useful for characterising the domain to be learned. In turn, this kind of flexible, relational generalisation is only possible because the model is capable of representing relations explicitly, a capacity that is notably absent in extant statistical machine learning algorithms.
... Según Santibáñez (2010), aunque muchos estudios han indagado conceptos y figuras retóricas y argumentativas, el fenómeno del razonamiento analógico/metafórico no ha recibido suficiente atención desde las ciencias cognitivas, especialmente en lingüística. Algunos estudios de orden cognitivo han sostenido que el uso continuo de analogías permite evidenciar el enriquecimiento semántico (Son, Doumas & Goldstone, 2010); sería uno de los mecanismos cognitivos-lingüísticos responsables del razonamiento moral y de sus respectivos enunciados morales (Dwyer, Huebner & Hauser, 2010); y el uso de analogías junto con un despliegue del razonamiento científico se convierte en un buen predictor para la construcción de conceptos científicos (Chuang & She, 2013). ...
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Resumen El presente artículo tiene como objetivos analizar el uso de la analogía como forma argumentativa para justificar la aprobación o el rechazo a la implementación de proyectos agro-mineros en territorios de una comunidad indígena colombiana y estudiar el sustrato emocional de dicho esquema argumentativo desde la teoría de la emoción denotada de Christian Plantin. Desde una perspectiva cualitativa e interaccional, 18 participantes (11 mujeres y 7 hombres con edades entre los 17,3 años hasta los 23,8 años), discutieron sobre un proyecto de extracción de petróleo. El corpus utilizado en este reporte, estuvo conformado por 8 registros con 1163 turnos de palabra con una duración conjunta de 121 minutos y 15 segundos del cual se escogieron dos secuencias específicas. Los análisis dan cuenta de la forma cómo la analogía ha sido utilizada unánimemente por los estudiantes para justificar el rechazo de la minería sobre los territorios indígenas. Este recurso permitió un análisis de las consecuencias plausibles de la explotación minera tanto financieras como ambientales y culturales. El esquema propuesto por Plantin se muestra pertinente para estudiar el uso de las emociones como coadyuvantes al rechazo del dilema presentado como objeto de discusión. Palabras Clave: Analogía, razonamiento analógico, emoción, problemática socio-científica, análisis interaccional.
... Según Santibáñez (2010), aunque muchos estudios han indagado conceptos y figuras retóricas y argumentativas, el fenómeno del razonamiento analógico/metafórico no ha recibido suficiente atención desde las ciencias cognitivas, especialmente en lingüística. Algunos estudios de orden cognitivo han sostenido que el uso continuo de analogías permite evidenciar el enriquecimiento semántico (Son, Doumas & Goldstone, 2010); sería uno de los mecanismos cognitivos-lingüísticos responsables del razonamiento moral y de sus respectivos enunciados morales (Dwyer, Huebner & Hauser, 2010); y el uso de analogías junto con un despliegue del razonamiento científico se convierte en un buen predictor para la construcción de conceptos científicos (Chuang & She, 2013). ...
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How a system represents information tightly constrains the kinds of problems it can solve. Humans routinely solve problems that appear to require abstract representations of stimulus properties and relations. How we acquire such representations has central importance in an account of human cognition. We briefly describe a theory of how a system can learn invariant responses to instances of similarity and relative magnitude, and how structured, relational representations can be learned from initially unstructured inputs. Two operations, comparing distributed representations and learning from the concomitant network dynamics in time, underpin the ability to learn these representations and to respond to invariance in the environment. Comparing analog representations of absolute magnitude produces invariant signals that carry information about similarity and relative magnitude. We describe how a system can then use this information to bootstrap learning structured (i.e., symbolic) concepts of relative magnitude from experience without assuming such representations a priori.
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Humans excel among species in abstract representation and reasoning. We argue that the ability to learn through analogical comparison, augmented by symbolic systems, underlies our cognitive advantage. The relations same and different are an ideal testbed for these ideas: they are fundamental, essential to abstract combinatorial thought, perceptually available, and studied extensively across species. The evidence suggests that whereas a sense of similarity is widely shared across species, abstract representations of same and different are not. We make three key claims, First, analogical comparison is critical in enabling relational learning among humans. Second, relational symbols support forming and retaining same and different relations in both humans and chimpanzees. Third, despite differences in degree of relational ability, humans and chimpanzees show significant parallels in the development of relational insight.
Chapter
Humans have an astounding ability to acquire new information. Like many other animals, we can learn by association and by perceptual generalization. However, unlike most other species, we also acquire new information by means of relational generalization and transfer. In this chapter, we explore the origins of a uniquely developed human capacity—our ability to learn relational abstractions through analogical comparison. We focus on whether and how infants can use analogical comparison to derive relational abstractions from examples. We frame our work in terms of structure-mapping theory, which has been fruitfully applied to analogical processing in children and adults. We find that young infants show two key signatures of structure mapping: first, relational abstraction is fostered by comparing alignable examples, and second, relational abstraction is hampered by the presence of highly salient objects. The studies we review make it clear that structure-mapping processes are evident in the first months of life, prior to much influence of language and culture. This finding suggests that infants are born with analogical processing mechanisms that allow them to learn relations through comparing examples.
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Infants begin acquiring object labels as early as 12 months of age. Recent research has indicated that the ability to acquire object names extends beyond verbal labels to other symbolic forms, such as gestures. This experiment examines the latitude of infants' early naming abilities. We tested 17-month-olds' ability to map gestures, nonverbal sounds, and pictograms to object categories using a forced-choice triad task. Results indicated that infants accept a wide range of symbolic forms as object names when they are embedded in familiar referential naming routines. These data suggest that infants may initially have no priority for words over other symbolic forms as object names, although the relative status of words appears to change with development. The implications of these findings for the development of criteria for determining whether a symbol constitutes an object name early in development are considered.
Article
A major feature that sets language apart from other communication systems is the use of categorylabels—words. In addition to providing a means of communication, there is growing evidence that category labels play a role in the formation and shaping of concepts. If verbal labels help humans acquire or use category information, one can ask whether it is easier to learn labeled categories compared to unlabeled ones. Normal English-speaking adults participated in a category-learning task in which categories were labeled or unlabeled. The presence of labels facilitated the learning of unfamiliar categories and resulted in more robust category representations. The advantage for acquiring named categories was observed even though the category labels did not convey any additional information and all participants had equivalent experience categorizing the stimuli. This work provides empirical support for the idea of labels as conceptual anchor points (Clark, 1997).