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Comparison and Categorization in theDevelopment of Relational Similarity

Laura Kotovsky and Dedre GentnerUniversity of Illinois at Urbana-Champaign

KoTOvsKY, LAUHA, and GENTNER, DEDRE. Comparison and Categorization in the Developmentof Relational Similarity. CHILD DEVELOPMENT, 1996, 67, 2797-2822. 4 experiments investigatedthe development of children's ability to recognize perceptual relational commonalities such assymmetry or monotonicity. In Experiment 1, 6- and 8-year-olds were able to recognize higher-order relational similarity across different dimensions (e.g., size/saturation) and across differentpolarities (e.g., increase/decrease), whereas 4-year-olds could recognize higher-order relationalmatches only when they were supported by lower-order commonalities (e.g., size/size but notsize I saturation matches). Further experiments tested how the processes of comparison and cate-gorization affected 4-year-olds' ability to recognize relational similarity. The results of the experi-ments supported the hypothesis that comparison and categorization processes lead to changesin children's representations of relational structure, enabling them to recognize more abstractcommonalities. A computational model lent further support to the claims.

The ability to grasp relational similarity cognitive processing and those who proposeis fundamental to abstract thought. It under- that changes in knowledge representationlies our appreciation of patterns of symmetry are sufficient to cause the relational shift,and mathematical structure and other subtle ^. ^^^ ^^.^ colleagues argued for theand elegant mvariances. It allows us to ^^^^ ^^^ explanation: specifically, thatmakes analogies and apply inferences be- ^^^^^^^ achieve competence in relationaltweensuperficially unlike domains. More .^^^^^^ ^^^^^^ the formal operationsimportant for cognitive development the ^^ ^^^^^ j ^ ^^ J2 years of age (e.g.,ability to perceive relational commonalities p ^^ ̂ j ^g^^^ ^ j ^ . ^ ^ ^^^ ^^^^^IS iundamental to learning beyond the basic i?, l • l. û . r iU • u J r1 I T , j i j 1^. 1 i . unlikely in light of the growing body of re-level. To understand relational categories i j t^. i ^

, J . r . 1 search demonstiating early competence insuch as predator or force—or even tool, -i .. i • -i -^ ^ \ TT lJ. .. Iu U'U i-u Ul relational similarity tasks. For example,weapon, OI contract—the child must be able ^ . nnn-r \ i .i u-u J J U'̂ ' 1 .. 1 1... Gentner (1977a) asked children and adultsto process relational commonalities. . . . u J, J. r -I-^ to carry out a mapping between two ramiliar

Thus the issue of when and how chil- domains, the human body and a tiee. Whendren become able to process relational simi- asked, "If a tiee had a knee where would itlarity commands attention. The research on be?" 4-year-olds were as accurate as adultsthis issue has found considerable evidence at pointing to the correct area of a picture,suggesting a developmental change in chil- They were able to preserve the spatial rela-dren's ability to recognize relational similar- tions among body parts, even when the taskity and use it in analogy and metaphor (e.g., was made difficult by turning the picturesBillow, 1975; Gentner, 1988; Piaget, Mon- upside down or by adding misleading localtangero, & Billeter, 1977; Winner, Rosen- details. Brown (1989) found that 2-year-oldsstiel, & Gardner, 1976). Accounts of this could transfer a solution to a reaching prob-change can be divided into two camps: those lem by choosing a tool based on its function-who postulate a global change in children's ally relevant properties (i.e., possessing a

Laura Kotovsky, Department of Psychology, University of Illinois at Urbana-Champaign;Dedre Gentner, Department of Psychology, University of Illinois at Urbana-Champaign (now atthe Department of Psychology, Northwestern University). This work was supported by NSFgrant no. BNS-9096259. The computational simulation was supported by ONR, contract no.N00014-89-J-1272. The authors would like to thank Mary Jo Rattermann, Judy DeLoache, ReneeBaillargeon, and David Uttal for their insightful comments. We also thank Art Markman for hiscomments and assistance with the computational simulation. Last, we wish to express our grati-tude to the parents and children who participated in the research. Correspondence concerningthis article should be addressed to Dedre Gentner, Department of Psychology, NorthwesternUniversity, 2029 Sheridan Road, Evanston, IL 60208-2710.

[Child Development, 1996,67,2797-2822. © 1996 by the Society for Research in Child Development, Inc.All rights reserved. 0009-3920/96/6706-0042S01.00]

Kotovsky, L., & Gentner, D. (1996). Comparison and categorization in the development of relational similarity. Child Development, 67(6), 2797-2822.

2798 Child Developmenthooked end). Finally, recent research usinglooking-time paradigms has suggested thateven young infants are sensitive to identityrelations (Tyrrell, Stauffer, & Snowman,1991). These kinds of results have led mostresearchers to adopt the knowledge-changeview, that whether children can recognizerelational similarity in a domain dependschiefiy on their knowledge of that domain(Brown, 1989; Brown & DeLoache, 1978;Brown, Kane, & Echols, 1986; Carey, 1985,1991; Chen & Daehler, 1989; Chi, 1981;Chi, Feltovich, & Glaser, 1981; Crisafi &Brown, 1986; Gentiier, 1977a, 1977b, 1988;Gentner & Rattermann, 1991; Goswami,1991, 1992; Goswami & Brown, 1989; Or-tony, Reynolds, & Arter, 1978; Vosniadou,1987, 1989).

However, showing that relational com-petence develops before the formal opera-tions stage does not in itself prove theknowledge-change position. It remains pos-sible that there is a global change in pro-cessing that occurs earlier than Piaget hadproposed. Halford (1987, 1993) and his col-leagues have taken this position, arguingthat the relational shift occurs at around 4years of age as the result of a maturationalincrease in processing capacity. Halford pro-poses that the degree of processing capacityrequired to carry out a match increases fromobjects to binary relations and finally to sys-tems involving ternary relations. As evi-dence that processing capacity sufficient toprocess complex relational comparisons de-velops at around 4 years of age (Halford,1987, 1992, 1993), Halford and his col-leagues have shown gains at around this agein transitivity and class inclusion tasks. Theyhave simulated this progression in the STARmodel, a distributed connectionist systemusing tensor products (Halford et al., 1995).The current studies provide a test of theseclaims.

In this article we test a specific versionof the knowledge-change hypothesis: Gent-

ner's (1988) relational shift hypothesis, lateramplified into what Gentner and Ratter-mann (1991) called the "career of similarity"hypothesis (see also Gentner & Medina,1996). This account posits that within anygiven domain (a) overall similarity is the ear-liest and most naturally responded to (e.g.,Rovee-Collier & Fagen, 1981), and {b) theorder in which partial matches come to benoticed is, first, matching objects, thenmatching relations, and finally matchinghigher-order relations.^ Our assumption isthat this sequence is epistemological, notmaturational: Children come to perceivesimilarity between objects (e.g., the likenessbetween a red apple and a red ball) beforethey perceive similarity among relations{e.g., the similarity between an apple/a/Zingfrom a tiee and a spoon falling from a table);and appreciation of such lower-order rela-tional similarity in turn precedes apprecia-tion of higher-order relational similarity(similarity in relations between relations:e.g., the similarity between a squirrel swish-ing its tail and causing an apple to fall froma tiee, and a toddler waving her arm andcausing a cup to fall off the table).^

Gentner and Rattermann (1991) re-viewed a large body of research that sup-ports the relational shift hypothesis in that(a) the ability to perceive relational similar-ity appears later than the ability to perceiveobject similarity, and {b) this relational in-sight appears at different ages in differentdomains (e.g.. Billow, 1975; Brown et al.,1986; Bryant & Trabasso, 1971; Chipman &Mendelson, 1979; DeLoache, 1989, in press;Gentner, 1977a, 1977b, 1988; Gentner &Toupin, 1986; Goswami, 1989; Pears & Bry-ant, 1989; Rattermann, Gentner, & De-Loache, 1989; Smith, 1984; Uttal & De-Loache, 1995; Uttal, Schreiber, &DeLoache, 1995). In particular, when rela-tional similarity is pitted against object simi-larity, younger children are more infiuencedby object matches, and less able to attend to

1 The relational shift is not a shift away from object similarity; even adults find it easier toprocess overall similarity (that includes object matches as well as relational matches) than toprocess pure analogy, and there is evidence that object matches are processed before relationalmatches (Goldstone & Medin, 1994; Markman & Gentner, 1996).

2 These levels of similarity are more precisely defined using a propositional representation.Attributes are defined as predicates taking one argument (e.g., BIG [a]), and relations as predi-cates taking two or more arguments (e.g., BIGGER [a,b]; Gentner, 1983, 1989; Palmer, 1975).The difference between first-order and higher-order relations is that first-order relations takeobjects or functions as arguments, and higher-order relations take propositions as arguments.That is, a higher-order relation is a relation between relations. Using this representation, objectsimilarity involves a match at the level of attributes, lower-order relational similarity involves amatch at the level of first-order relations, and higher-order relational smilarity involves a matchat the level of higher-order relations.

relational matches, than are older children(Gentner, 1988; Gentiier, Rattermann, Mark-man, & Kotovsky, 1995; Gentner & Toupin,1986). In this research we will test a morespecific hypothesis: Within a domain therecognition of lower-order relational similar-ity precedes the recognition of higher-orderrelational similarity. We also test a secondprediction of the relational shift hypothesisand other knowledge-based theories:namely, that increasing children's knowl-edge of domain relations should lead togreater sensitivity to relational similarity inthe domain. This prediction was partially ad-dressed in an experiment by Goswami andBrown (1989). They examined the effects ofdomain knowledge on analogy in preschoolchildren using a picture-selection task, andfound that children who could correctlycomplete a causal sequence tended to per-form well on an analogy that utilized thesame causal relation. A similar result was ob-tained by Gentner, Rattermann, and Camp-hell (1996).

However, although this finding is sup-portive of knowledge effects, it is not defini-tive. For example, it could be that high-ahility children performed well on both thecausal task and the analogy task. What isneeded is a demonstiation that providingchildren with knowledge about the domaincan improve their performance on a rela-tional similarity task. The chief goal of thisresearch is to provide such a direct test: Weask whether learning the relations in a do-main improves children's performance on arelational similarity task. A further goal is topropose and test a leaming mechanism bywhich children can learn about domain rela-tions from experience. This mechanism,which we call progressive alignment, is acrucial aspect of our proposal. In the pro-gressive alignment mechanism, experienc-ing concrete similarity prepares children toperceive more abstiact similarity without di-rect instruction. We elaborate on this mecha-nism later in the article. Our final goal is totest the role of relational language in pro-moting relational leaming (Gentner & Me-dina, 1996; Gentiier & Rattermann, 1991;Gentner, Rattermann, Markman, & Kotov-sky, 1995).

In choosing the domain for these studieswe had two criteria in mind: {a) The domainshould be familiar to preschool children, butat the same time, in order to permit a testof the knowledge-change hypothesis, thereshould be higher-order relations that pre-schoolers initially fail to perceive in similar-

Kotovsky and Gentner 2799

ity comparisons; and {b) the domain shouldbe such that the similarity among higher-order relations can be manipulated indepen-dently from the similarity among objects andfirst-order relations. This requirement ofseparable kinds of similarity poses a meth-odological challenge. In natural experience,different levels of similarity are typicallycorrelated (e.g., what looks like a tiger alsohas the causal powers of a tiger), and thiscorrelation is often carried into experimentalmaterials. For example, in Goswami andBrown's (1989) study of causal analogies, thecorrect completion of the a:b::c:?d analogy(i.e., the term "d" such that the c,d causalchain matched the a,b causal chain) oftenshared object-level similarity with the "c"term (e.g., tree: burnt tree stump ..pile ofleaves: ?burnt pile of leaves). A replicationof this study separating object similarity andrelational similarity produced many fewercorrect responses (Gentner et al., 1996). Us-ing materials in which multiple levels ofsimilarity are present may lead to an inflatedview of children's ability.

With these considerations in mind, wechose perceptual patterns as the stimuli forthis research, because (a) they permit inde-pendent manipulation of different aspects ofthe materials to address the problems of cor-related attributional and relational similarityand {b) they are familiar to children whenpresented in simple concrete depictions, butcan prove challenging in more complex in-carnations (e.g., Bryant, 1974; Ghipman &Mendelson, 1979; DeLoache, 1989; Go-swami, 1989; Halford, 1987, 1992; Ratter-mann et al., 1989; Smith, 1984, 1989, 1993).In particular. Smith (1984) showed a rela-tional shift in children's ability to copy sim-ple dimensional relations, and Ghipman andMendelson (1979) showed a developmentalincrease in attention to symmetry in judgingthe complexity of perceptual stimuli. Adultsand older children, but not 5-year-olds,judged patterns as less complex when theywere horizontally symmetiic, consistentwith symmetry's serving as a higher-orderorganizing pattem. Thus, perceptual rela-tions created from geometric forms met bothof our criteria for stimuli design.

We used a triads choice task throughoutthe research. The child was shown three ge-ometiic figures, a standard and two choices,and was asked which of the choices the stan-dard went with best. In each tiiad, the stan-dard and the relational choice shared ahigher-order relation, either symmetry ormonotonicity (e.g., oOo and xXx; see Fig.

2800 Child Development

Same-Polarity Opposite-Polarity

Same-Dimension

Relational Choice Non-relational Choice Relational Choice Non-relational Choice

Cross-Dimension

Reiational Choice Non-reiational Choice Relational Choice Non-relational Choice

FIG. 1.—Samples of Same-polarity, Opposite-polarity, Same-dimension, and Cross-dimensionstimuli types.

1). The elements that made up the standardwere of different shapes and colors from theones that made up the relational choice, sothat its object-level similarity to the standardwas low. The nonrelational choice, or foil,was created simply by rearranging the ele-ments of the relational choice so as to breakthe higher-order relation, for example, oOobecomes ooO (see Fig. 1). This ensured thatthe foil and the relational choice wereequally similar to the standard in their (low)level of object matches. Thus this test is apure test of children's appreciation of rela-tional similarity, since the advantage of therelational choice over the foil lies only in itsrelational commonalities with the standard.

We wanted to gauge children's abilityto appreciate abstiact higher-order relationalsimilarity, as opposed to similarity based onfirst-order relational matches, or on bothfirst-order and higher-order matches. There-fore, we varied the degree of first-order rela-tional similarity that the relational choiceshared with the standard (while keepinghigher-order relational similarity constant).Two aspects of lower-order relational simi-larity were manipulated: dimension and po-larity (see Fig. 1). Dimension concernswhether the dimension of change (over

which the higher-order relation held) wasthe same in the standard and relationalchoice (i.e., whether the match was size-change to size-change or size-change to satu-ration-change). Polarity concerns whetherthe direction of change was the same (xXx/oOo) or different (xXx/OoO) in the standardand relational choice. Varying polarity anddimension orthogonally led to four tiiadtypes varying in degree of match from mostconcrete to most abstiact: for example, forthe higher-order relation of symmetry, theseare (1) Same-dimension, Same-polarity (xXx/oOo), (2) Same-dimension, Different-polarity (xXx/OoO), (3) Different-dimension,Same-polarity (xXx/121), and (4) Different-dimension, Different-polarity—only thehigher-order relation matches (xXx/212). Foradults, the higher-order relation match issufficient. Even for case 4 (the bottom rightcell of Fig. 1), adults virtually always choosethe relational choice. Our first question waswhether young children would perceivecommonality based only on a shared higher-order relation.

The purpose of the first experiment wasto test the predictions of the relational shifthypothesis and to establish a baseline ofchildren's similarity processing against

which to test our further hypotheses con-cerning mechanisms of learning. The pre-dictions were that (a) at all ages (barring ceil-ing effects), children would select therelational choice more reliably the moresupporting commonalities there were (i.e.,the more literally similar the relationalchoice was to the standard); {b) there wouldbe a relational shift, such that older childrenwould be better able to recognize higher-order commonalities in the absence of sup-porting lower-order commonalities.

Experiment 1METHOD

ParticipantsGhiidren were tested in Ghampaign-

Urbana day-care centers, day camps, andpublic schools. There were 24 4-year-olds(mean age 4-7, range = 4-1 to 5-2), 24 6-year-olds (mean age 6-5, range = 6-1 to 7-2), and24 8-year-olds (mean age 8-6, range = 7-11to 9-7). An additional three 4-year-olds weretested but eliminated due to failure to meetthe criterion for tiaining and filler tiials (seeProcedure). All groups had equal numbersof males and females. The majority of thechildren in all of the experiments werewhite and from middle-class families. Sys-tematic data on race and SES were not col-lected in these studies.

Materials and DesignThe design was a completely random-

ized factorial mixed design with four be-tween-subjects factors: age (4, 6, or 8 years),polarity (same or opposite), sex (male or fe-male), and order of presentation of stimuli(A or B); and three within-subject factors:dimension (same or different), higher-orderrelation (symmetiy or monotonic-increase),and dimension of standard (size or satura-tion). Each child received 22 tiiads: 16 testtiiads, 2 training tiiads, and 4 filler tiiads.

Test triads.—The test tiiads consistedof a standard and two choices, a relationalchoice and a nonrelational choice. The stan-dard and the relational choice always em-bodied the same higher-order relation,either symmetry or monotonicity. The non-relational choice was created by permutingthe objects that made up the relationalchoice. Each child received half monotonic-ity and half symmetry trials.

There were two key manipulations ofthe similarity between the standard and therelational choice: polarity (direction ofchange same or opposite) and dimension (di-


mension of change: same dimension orcross-dimension), which were varied orthog-onally to yield four match types, rangingfrom most concrete (Same-dim/Same-pol) toleast concrete (Gross-dim/Opposite-pol)with two intermediate match types (Cross-dim/Same-pol and Same-dim/Opposite-pol)(see Fig. 1).

The stimuli were constructed on 10.2 X15.2 cm index cards. The size-change stimuliwere made up of two shapes, circles andsquares of constant coloring (the squareswere black and the circles had brick pat-terning as shown in Fig. 1). Each shape oc-curred in three sizes. The squares used todepict monotonicity were 1.6 cm, 2.5 cm,and 3.8 cm. The squares used to depict sym-metiy were 1.6 cm and 3.8 cm. The circlesused to depict monotonicity were 1.0 cm, 1.6cm, and 2.8 cm. The circles used to depictsymmetry were 1.0 and 2.8 cm.

The saturation-change stimuli were con-structed using Chromarama colored paper.They were made of squares and circles ofconstant size (the squares were 3.8 cm andthe circles were 2.5 cm). There were twocolors, red and blue. Each color occurred inthree saturations (produced by the additionof white). The reds used to depict monoto-nicity were numbers 6141, 6145, and 6149.The reds used to depict symmetiy werenumbers 6141 and 6149. The blues used todepict monotonicity were numbers 6321,6325, and 6329. The blues used to depictsymmetiy were numbers 6321 and 6329.

Training triads.—Children receivedtwo tiaining tiiads designed to demonstiateeasily the matching game; the child matchedidentical animals. For example, in one of thetiaining tiiads the child had to indicate thatan elephant "goes with" an identical ele-phant and not with a butterfly.

Filler triads.—There were four filler tii-ads depicting simple geometiic figures thatshared object-level as well as Iower-order-relational and higher-order-relational simi-larity. These were designed to be very easy,both to boost the child's confidence and tocheck whether the child was on task. Forexample, in one filler tiiad the child had toindicate that three large ovals "go with"three small ovals and not with two ovals anda square.

ProcedureAfter the two tiaining triads, the 16 test

tiiads were presented in one of the twosemirandom orders (random except for the


stipulation that there be no more than twoof the same triad type consecutively). Eachfigure in a triad was presented on a separateindex card. The cards were presented on agame board with four slots for index cards(see Fig. 2). The experimenter placed thetwo choice cards in the two top slots and putthe standard card in front of the child, ask-ing, "Do you know where that one [the stan-dard] goes best?" Children could indicatetheir choice either by poinbng to one of thetwo alternatives or by putbng the standardcard in the slot under their choice. No feed-back was given on the test trials.

The four filler trials were spaced evenlythrough the study. During these trials thechildren were given general encourage-ment, such as "I like how you are playingthis game. You look at all the pictures care-fully and choose the best match." To be surethat children were on task we eliminatedchildren who made more than one incorrectresponse on the training and filler trials.

Prelim-inary AnalysesPreliminary analyses including the fac-

tors of sex and order of presentation of thesbmuli revealed no significant main effectsand no significant interactions involvingthese factors. The data were therefore col-lapsed across these factors in subsequentanalyses.

RESULTS

The results are shown in Table 1. Aspredicted, there was a relabonal shift: 4-year-olds responded relabonally on 53% ofthe test triads, 6-year-olds on 78%, and 8-year-olds on 90%. Also as predicted, chil-dren chose more relationally when first-order as well as higher-order relationsmatched. A 3 x 2 x 2 (age x polarity x

dimension) ANOVA with dimension as awithin-subject factor revealed a main effectof age, F(2, 66) = 55.08, p < .0005, and maineffects of polarity, F(l, 66) = 7.67, p < .01,and dimension, F(l, 66) = 16.01, p < .0005.Children chose the relational choice moreoften on Same-polarity triads, M = 78%,than on Opposite-polarity triads, M = 70%(see Fig. 3), and more often on Same-dimension triads, M = 79%, than on Cross-dimension triads, M = 69% (see Fig. 4). Thiswas true at all ages. There were no reliableinteractions involving age. As predicted,even the 8-year-olds were more likely tochoose relationally when the higher-ordermatch was supported by common first-orderrelations.

Consistent with the prediction thathigher-order similarity emerges later thanfirst-order similarity, the 4-year-olds showedabove-chance levels of relational respondingonly when there was maximum lower-orderrelational support for the higher-order com-monality: that is, in the Same-dim/Same-polcondibon: M = 68%, chance = 50%; t{ll)= 3.4, p < .01; all other ts < 0.82, all ps >.20. (This failure to choose relationally wasnot due to lack of understanding of the task,as most of the 4-year-olds chose the similaritem on all four filler triads.) In contrast, the6- and 8-year-olds responded reliably abovechance in all conditions, all ts > 3.92, allps < .01 (see Table 1).

Further analyses including the factors ofhigher-order relation (symmetry or monoto-nicity) and dimension of standard (size orsaturation) revealed a significant interactionbetween the dimension of the standard andage, F(2, 69) = 3.09, p = .05. Bonferronicomparisons using a family alpha of p < .01revealed that the 6-year-olds performed

FIG. 2.—Stimulus presentation


TABLE 1

MEAN PROPORTION OF RELATIONAL RESPONSES BY AGE ANDCONDITION IN EXPERIMENT 1

Age

4-year-oIds:Same-dimensionCross-dimension

6-year-olds:Same-dimensionCross-dimension

8-year-olds:Same-dimensionCross-dimension

Same-Polarity

.68

.49

.90

.75

.96

.90

Opposite-polarity

.49

.48

.77

.72

.93

.80

more relabonally when the standard de-picted a change in saturabon (M = 81%)than when the standard depicted a changein size (M = 76%). The opposite pattern wasobtained with the 8-year-olds (saturation,M = 86%; size, M = 93%). There was nodifference in the 4-year-olds responses tosaturabon (M = 53%) versus size (M =54%). No other main effects or interactionswere significant.

DISCUSSION

The data from the triads task are consis-tent with the relational shift hypothesis: (a)at all ages, children were better able to rec-ognize higher-order commonalibes when

they were supported by lower-order com-monalibes, and {b) only the older children(6- and 8-year-olds) were able to recognizehigher-order commonalities in the absenceof supporting lower-order commonalities.Four-year-olds required lower-order rela-bonal support to see the match.

Children's acbve processing of the simi-larity matches was revealed in their sponta-neous comments during the task. Even onthe Same-dimensional triads, 6-year-oldssometimes articulated their choices, as inthese remarks on symmetry: "Big little big,that's the pattern." and "I figured it out, thisis one different color in the middle." OnCross-dimensional matches, children some-

S 0.8-O

on 0.6-o

Pro

po

rtio

n R

o

toI

.I

.

Same

'"'^^^^--''^ Opposite• —

chance

4yrs 6yrs

Age

8yrs

FIG. 3.—Performance of children in Experiment 1 on Same- and Opposite-polarity trials


1.0

chance

4yrs. 8yrs.6yrs.

AgeFIG. 4.—Performance of children in Experiment 1 on Same- and Cross-dimension trials

bmes named the correspondences, as in this6-year-old's comment on symmetry: "This isa big one, this is pink. This is a small one,this is red." Another strategy was to mapacross a relational system from a more famil-iar domain: "A dark one and a big one makedaddies. The other one [the rejected alterna-tive] has two twins and a daddy on the side"(see Gentner & Rabermann, 1991). Theemerging appreciabon of relational com-monality can be seen in this comment by an8-year-old, who after struggling with her firstseveral Cross-dimension matches, then ex-citedly arbculated a startlingly apt descrip-bon of relational similarity: "It's exactly thesame, but different!" She proceeded tochoose relationally for all the remainingtriads.

These results extend and refine thefindings on the relational shift. It appearsthat the perception of pure higher-order re-lational commonality indeed emerges laterthan the perception of matches supported byboth higher-order and lower-order relations.With this foundation, we now move to oursecond goal, namely, to determine whetherthis gain in relabonal sensitivity is dueto changes in knowledge representabon(Brown, 1989; Gentner & Rattermann, 1991;Vosniadou, 1989) or to changes in generalprocessing ability (Case, 1987; Halford,1987, 1993). In the remainder of this arbcle.

we test the core predicbon of the knowl-edge-change hypothesis: that providing chil-dren with insight into the domain relationsshould increase their ability to perceivehigher-order similarity. This experiencecould take the form of direct instruction inrelational categories (as investigated in Ex-periment 3), but we also wished to explorethe possibility of experiential learning of do-main relations. Specifically, we wished to in-vestigate a particular experiential learningmechanism, that of progressive alignment.According to this hypothesis, repeated com-parisons involving overall concrete similar-ity can facilitate noticing higher-order rela-tional commonalities, and thus promote thesubsequent recognition of pure higher-orderrelational similarity.

The first assumption of the ProgressiveAlignment hypothesis is that the similaritycomparison process is one of alignment andmapping between representational struc-tures, as in the structure-mapping processfor analogy (Gentner, 1983, 1989). We fur-ther assume that structural alignment is eas-ier the more commonalities are present, pro-vided that they form a structurally consistentsystem (Gentner, 1989; Gentner, Ratter-mann, & Forbus, 1993; Gentner & Toupin,1986; Goldstone & Medin, 1994; Markman& Gentner, 1993). Further, we assume thatone result of carrying out a similarity com-


parison is to highlight the relational struc-ture, making it more salient (Forbus & Gent-ner, 1986; Gentner & Wolff, in press). Asecond innovative aspect of the ProgressiveAlignment hypothesis is the assumption thatthe process of carrying out a similarity com-parison may lead to a change in the repre-sentation, and that this change will tend toincrease the uniformity of the two represen-tabons (Gentner et al., in press; Gentner &Markman, 1995; Gentner & Rattermann,1991; Gentner & Wolff, in press). Tbus theprocess of comparison and alignment actsboth to make relabonal commonalibes moresalient and to make the representationsslightly more uniform. Thus, experiencecomparing literally similar pairs that share agiven higher-order relation (e.g., symmetry)promotes the ability to recognize thishigher-order commonality in more abstract(e.g., cross-dimensional) comparisons. Thisclaim that experience with concrete similar-ity promotes the development of abstractsimilarity differs sharply from the standardview of category learning, dating back to be-haviorist research, which assumes that thelearning process ends when learners findcategories that are sufficiently abstract tosubsume the training stimuli.

Some aspects of this proposal are al-ready well attested. Many researchers havesuggested that one result of a comparison isto highlight common elements and thus pro-mote common abstractions (Brown et al.,1986; Elio & Anderson, 1981; Forbus &Gentner, 1986; Gick & Holyoak, 1980,1983;Hayes-Roth & McDermott, 1978; Medin &Ross, 1989; Ross, 1989; Thorndike, 1903).For example, when Gick and Holyoak (1983)asked parbcipants to write out the common-alities between two analogous passages, thecommon schema became more accessible ina subsequent memory task. However, the ex-tant psychological research has concentratedchiefiy on directed schema extraction fromexplicit comparisons. Our proposal goes fur-ther in suggesbng that the mere process ofcarrying out a similarity comparison, evenwithout explicating the resulbng commonframe, can increase the salience of the com-mon structure. For example, Markman andGentner (1993) gave adult parbcipants a dif-ficult mapping task in which there werecompeting mappings between two scenes.Parbcipants were more likely to choose astructurally consistent relational mappingover a competing mapping that was basedon a superficial but striking object match ifthey had previously rated the similarity of

the two scenes. This is evidence that theprocess of carrying out a similarity compari-son involves an alignment of relabonal struc-ture. Our goal in this research was to test thestrong claim that experience with concretesimilarity promotes recognition of abstractrelabonal similarity.

A follow-up study to Experiment 1 pro-vided some encouragement for this possibil-ity. We asked whether children would showpositive transfer effects if they experiencedconcrete similarity comparisons followed byabstract relational similarity (when both in-volve the same relabonal structure). To testthis, we brought back (within 1 week, meandelay = 2 days) the children who had parbc-ipated in Experiment 1 and gave them thetask again, but in the alternate polarity con-dibon. Thus, one-half of the children werepresented with the more abstract Opposite-polarity triads after experiencing the moreconcrete Same-polarity triads. The predic-bon was that these children would performmore relationally on the Opposite-polaritytriads than those who had received the Op-posite-polarity triads wth no prior concreteexperience.

We focused on the 4-year-olds, who inExperiment 1 had shown no ability to rec-ognize abstract higher-order relabonal simi-larity in the absence of supporting lower-order relational similarity. In the follow-upexperiment, on the Same-dimension trialsthe 4-year-olds showed the predicted im-provement: M = 49% for Opposite-polsurity-first and M = 60% for Opposite-polarity-second, t{22) = 1.84, p < .05, one-tailed.This did not appear to be a general pracbceeffect in that there was no such improve-ment on the Same-polarity trials: M = 68%for Same-polarity-first and M = 53% forSame-polarity-second. This pattern is con-sistent with the possibility that preschoolers'ability to extract pure higher-order relationalsimilarity was improved by prior experiencewith similarity matches in which the samehigher-order commonality was supportedby concrete lower-order commonalities. Al-though the improvement was slight, itoccurred without feedback and with arelabvely small number of concrete trialspresented some days before the abstracttrials.

Our goal in Experiment 2 was to testthe Progressive Alignment hypothesis moresystemabcally. We focused on 4-year-olds,since they seemed to show little or no inibal


recognition of pure higher-order relations.We reasoned that if experience with con-crete similarity promotes recognition of ab-stract relational similarity, then experiencewith Same-dimensional triads should facili-tate performance on Cross-dimensional tri-ads. To test this predicbon, we gave childrenthe same triads as in Experiment 1, butblocked them so that the eight Same-dimension triads preceded the eight Cross-dimension triads, instead of mixing thetriads as in Experiment 1. According tothe Progressive Alignment hypothesis, thisshould lead to improved perfonnance on theCross-dimensional triads. However, a fur-ther control is necessary here, for there is apossible alternate explanation of the pre-dicted result (of improved performance onthe abstract triads). Such an improvementcould simply come about through some gen-eral benefit of practice on easy triads, ratherthan specifically through the alignment andhighlighbng of common relabonal structure.

To rule out this explanabon, a controlgroup was run. Like the experimental group,the control group received eight Same-dimension triads followed by eight Cross-dimension triads. However, the make-up ofthe Same-dimension triads was varied be-tween the groups. Whereas the experimentalgroup received four size-change and foursaturation-change triads, the control groupreceived eight size-change triads. Thus thecontrol group should experience any bene-fits deriving from easy practice triads,but only the experimental group is giventhe opportunity to align concrete similaritymatches along both dimensions. If, asclaimed by the Progressive Alignment hy-pothesis, alignment of concrete matcheshelps highlight relabonal structure andpaves the way for abstract matches, then theexperimental group should outperform thecontrol group (as well as the children in Ex-periment 1) on the Cross-dimension triads.More specifically, we predicted that those4-year-olds who successfully align the rela-

tional structures in a block of Same-dimension trials involving size and a blockof Same-dimension trials involving satura-tion should be best able to respond to therelational similarity on a subsequent blockof Cross-dimension trials. Thus, we pre-dicted a positive relation between perfor-mance on Same-dimension trials and perfor-mance on Cross-dimension trials in theexperimental condition of Experiment 2 andno such relation in the control condition orin Experiment 1.

Experiment 2METHOD

ParticipantsThe participants were 24 4-year-olds, 13

boys and 11 girls, mean age 4-6 (range = 4-2to 5-0). Six boys and six girls were assignedto the experimental condition (mean age 4-6,range = 4-2 to 4-9) and seven boys and fivegirls were assigned to the control condition(mean age 4-6, range = 4-2 to 5-0). Parbci-pants in this and the remaining experimentswere recruited from the Champaign-Urbanacommunity and tested individually in a labo-ratory at the Beckman Insbtute at the Uni-versity of Illinois.

MaterialsThe stimuli in the experimental condi-

tion were the Same-polarity sbmuli from Ex-periment 1:̂ eight Same-dimension triads,eight Cross-dimension triads, and six train-ing and filler triads. The sbmuli in the con-trol condition were the same as those usedin the experimental condition, except that inthe Same-dimension trial block, instead offour Same-dimension size triads and fourSame-dimension saturation triads, childrenreceived eight Same-dimension size triads.The new size triads were created by re-versing the polarity in the original Same-dimension size triads.*

ProcedureThe procedure was idenbcal to that of

Experiment 1, except that in the experimen-

^ The dimension manipulation has certain advantages over the polarity manipulation. In themonotonicity triads, the same and different polarities are mirror images (e.g., 1-2-3, 3-2-1), so achild could conceivably follow a rule such as "read hoth directions when looking for a match."This is not the case for dimension. There is no simple transformation hetween size and color,so in order to perform relationally on the Cross-dimension match the child must rely on abstractrelational structure. The remaining experiments all utilize dimension as the varying aspect,holding to Sfime-polarity.

^ Polarity was not manipulated as an experimental factor. All of the triads in the experimentwere Same-polarity. That is, the polarity was the same In the standard and the relational choice.However, children received monotonicity from left to right in some triads and monotonicity fromright to left in others.


tal condition the triads were presented inthe fixed order shown in Table 2, and in thesize-only control condition the triads werepresented in the same fixed order except thatthe Same-dimension-color triads were re-placed with Same-dimension-size triads.These fixed orders were created by firstblocking by dimension so that the Same-dimension trials came before the Cross-dimension trials and then choosing an orderthat seemed to facilitate alignment of struc-ture. The idea was to maintain the samehigher-order relabonal match between suc-cessive trials, along with other commonali-ties where possible. For example, a sampleSame-dimension sequence might be sym-metry in size, then symmetry in color, thenmonotonicity in color, then monotonicity insize, and so on. The Cross-dimension triadswere also sequenced by higher-order rela-bons. As in Experiment 1, no feedback wasgiven in either condition.

RESULTS

As predicted, children in the experi-mental condition who performed well onthe Same-dimension trials also performedwell on the Cross-dimension trials. The chil-dren who scored above the median score(62%, range = 38%-100%) on the Same-dimension trials responded relabonally to80% of the Cross-dimension trials, as com-pared to 46% for the children who scored ator below the median on the Same-dimensiontrials.

A chi-square analysis using a mediansplit on both the Same-dimension and theCross-dimension (Mdn = 62%, range =25%—88%) trials supported the associationbetween these two variables, x^W ~ 12.03,p < .005. As Table 3 shows, the relation is

TABLE 3

NUMBER OF CHILDREN PERFORMING ABOVE ANDBELOW THE MEDIANS ON THE SAME-DIMENSION

AND CROSS-DIMENSION TRIALS INEXPERIMENTS 2 AND 1

SAME-DIMENSION

Experiment 2:Experimental condition:

BelowAbove

Control condition:BelowAhove

Experiment 1:BelowAhove

CROSS-DIMENSION

Below

70

23

54

Ahove

05

34

12

quite strong. All 12 of the children in theexperimental condition fell into the two pre-dicted cells (above-above and below-below).That is, children who were above the me-dian on the Same-dimension triads wereabove the median on Cross-dimension tri-ads, and those below the median on Same-dimension triads were below the median onCross-dimension triads.

In contrast to the experimental condi-tion, the size-only control condition showedno reliable relation between performance onthe Same- and Cross-dimension trials, x^(l)= 0.01, p > .50 (see Table 3). Children whoscored above the median on the Same-dimension trials (Mdn = 100%, range =25%-100%) responded relabonally to 52%of the Cross-dimension trials, as comparedto 50% relabonal responding for childrenwho scored at or below the median. Thus it

TABLE 2

ORDER OF TRIADS IN THE EXPERIMENTAL CONDITIONOF EXPERIMENT 2

Dimension

samesamesamesamecrosscrosscrosscross

Dimensionof Standard

sizesizecolorcolorsizecolorsizecolor

High-OrderRelation

monotonic-increasesymmetrysymmetrymonotonic-increasesymmetrysymmetrymonotonic-increasemonotonic-increase

NOTE.—The children received two of each of the eight triad types.


does not appear that the improvement in theexperimental group is due simply to pracbcewith easy triads.

A further test of the Progressive Align-ment predictions is to compare the experi-mental group, which received the eight con-crete Same-dimensional matches before theeight Cross-dimensional matches, with thesubjects in Experiment 1, who received thesame 16 triads in mixed order. An analysisof the results of Experiment 1 revealed thatperformance on the Same-dimension trialsdid not predict performance on the Cross-dimension trials. The children who scoredabove the median (62%, range = 38%-88%)on the Same-dimension trials respondedrelationally to only 48% of the Cross-dimension trials. This was no better thanthe 50% relational responses on Cross-dimensional trials produced by the childrenwho scored at or below the median on theSame-dimension trials (see Table 3). A chi-square analysis failed to indicate any rela-tion between Same-dimension and Cross-dimension performance, x^W ~ 0.44, p >.15.

To compare all three of these groups,we performed a 3 x 2 ANOVA includingcondition (experimental, control, or Experi-ment 1) and Same-dimension-performance(above or below median) as between-subjects factors, and percentage correct onthe Cross-dimension trials as the dependentvariable. The analysis revealed reliablemain effects of both condition, F(2, 30) =3.34, p < .05, and Same-dimension-perfor-mance, F(l, 30) = 5.17, p < .04, and a reli-able interaction between condition andSame-dimension-performance, F(2, 30) =5.35, p < .02. Inspection of the means (re-ported again here for convenience) revealeda marked contrast. The children in the ex-perimental condition in Experiment 2 whoperformed above the median on the Same-dimension trials responded most relabonallyto the Cross-dimension trials {M = 80%).The other five groups showed uniformlylow relabonal responding on the Cross-dimension trials (Ms ranged from 46% to52%). Three pairwise Bonferroni contrastscompared the above- and below-mediangroups in each condibon. As predicted, onlyin the experimental condition in Experiment2, where Same- and Cross-dimension wereblocked and both size and saturation trialswere presented in the Same-dimensionblock, did Same-dimension performancepredict Cross-dimension performance. A fi-nal contrast found a reliable difference be-

tween the above-median group in the exper-imental condition in Experiment 2 and theother five groups. The family alpha for thecontrasts was p < .01.

DISCUSSION

The results of the experimental condi-bon in Experiment 2 are consistent with theclaim that repeated experience with con-crete triads led to an increase in the chil-dren's ability to recognize higher-order rela-tional similarity. This pattern of results is notlikely to have been produced by simple taskpracbce effects, as discussed above. It alsoseems unlikely that the pattem could haveresulted from individual differences. If theassociation between Seime-dimension andCross-dimension trials in the experimentalcondition were due to the fact that certaintalented children simply performed wellacross the board (perhaps because they en-tered the task already attuned to relationalsimilarity), then we should have been suchan associabon in the control condition andin Experiment 1, but as described above,this was not the case: In neither case didperformance on concrete trials predict per-formance on abstract trials. A further argu-ment against the individual differencesexplanation comes from examining perfor-mance on the Same-dimension trials. Themedian score for the experimental condi-bon of Experiment 2 was no higher thanthat for Experiment 1 (62% in both), and wasconsiderably lower than that for the size-only control condition (100%). Thus, it is notthe case that the children in the experimen-tal condibon were simply "smarter" fromthe start. Individual differences do not ap-pear to account for the pattern of results.

Together these results suggest that onlythe children who successfully aligned andextracted the relabonal structure of both di-mensions prior to the Cross-dimension trialswere able to perform relationally on thesetrials. Children who received Same- andCross-dimension trials mixed together, or re-ceived only size/size trials prior to tlieCross-dimension trials, were unable to rec-ognize the higher-order match on the Cross-dimension trials. The results are not consis-tent with explanabons based on individualdifferences and/or pracbce effects. Althoughthe number of participants in this experi-ment was not large {N = 24), the pattern ofresults is intriguing. It suggests that the pro-cess of carrying out concrete similarity com-parisons on both dimensions—the processof aligning, highlighting, and re-repre-

senting the relational structure—pro-duced a felicitous condition for the exper-ienbal detecbon of higher-order common-alities.

A key claim of the knowledge-changeview is that learning about domain relabonsfacilitates the recognition of relational simi-larity. If this is true, then we should sbll seethis facilitabon if children are taught the do-main relations by another means. One par-ticularly interesting route is the use of rela-bonal language. We conjected that providinglabels for the higher-order relations mightincrease the salience of the common rela-bonal structure of the stimuli. Giving chil-dren labels has proven effective in improv-ing performance of children in a variety oftasks. There is a vast amount of researchdemonstrabng that noun labels can call at-tenbon to object categories, overriding com-peting associabons (e.g., Gelman & Mark-man, 1987; Markman, 1989; Markman &Hutchinson, 1984; Waxman & Gelman,1986; Waxman & Hall, 1993; Waxman &Markow, 1995). Gentner (1982, in press) hasspeculated that such effects may be strongerfor relabonal terms than for nominal terms.There is evidence that naming relational cat-egories can make them more salient. For ex-ample, Rattermann and Gentner (1996) haveshown that labeling three objects of increas-ing size "baby," "mommy," and "daddy"improves children's perfonnance in an ana-logical mapping task where the relation theymust attend to is "monotonic increase" (seeGentner & Rattermann, 1991; Gentner et al.,1995; Rattermann & Gentner, 1996).

In Experiment 3, we invesbgatedwhether leaming labels for higher-order re-lational categories would improve children'sability to perceive relabonal similarity. Wetaught a group of 4-year-olds to label andcategorize the higher-order relations of sym-metry and monotonicity and then testedthem in the triads task. To maximize thechance of children learning the correct map-ping of the relational label, we used a richtraining technique. First, we introduced thechildren to a "picky penguin" (Waxman &Gelman, 1986) and labeled the relabonalstructure. For example, for symmetry wesaid, "This is a very picky penguin and heonly likes things that are even." We thenpresented the children with figures thatwere either symmetrical or nonsymmetrical(e.g., the relabonal and the nonrelabonalchoices from Experiment 1; see Fig. 1). Weasked the children what the picture was


called (labeling) and whether the penguinthat only likes even things would like thepicture (categorization). Then we gave thechildren feedback as to whether they hadcategorized correctly. If the children werecorrect we continued with the next trial. Ifthey were wrong we gave them an explana-bon (e.g., we pointed out the symmetricalpattern and explained why the figure waseven).

Because we wanted to separate the pos-sible benefits of gaining relational knowl-edge from those of comparison and align-ment, one training technique we did notutilize was to invite comparison of the fig-ures; instead we presented the items one ata time. After this training, children were pre-sented with the eight Cross-dimension tri-ads from Experiment 2. The question waswhether training on the higher-order rela-tions would lead to increased relabonal per-formance on the Gross-dimension compari-sons. The plan was to compare performanceon the categorizing and labeling training toperfonnance on the Gross-dimension triadstask.

Experiment 3METHOD

Participants and MaterialsThe participants were 12 4-year-oIds, six

boys and six girls (mean age 4-6, range =4-1 to 5-0). The sbmuli were the 16 triadsused in Experiment 2. Each figure from theeight Same-dimension triads was presentedone at a time, creating 24 training items, 12for symmetry and 12 for monotonicity. Be-cause the stimuli were formed from the tri-ads, each of the two sets of 12 containedeight examples of the higher-order relabon(e.g., xXx) and four distractor patterns (e.g.,xxX). We also used a toy penguin and walrusand two plasbc baskets as part of the trainingtask.

ProcedureTraining: Labeling and categoriz-

ing.—The child was seated at a table infront of the toy penguin and the two baskets,one near the penguin and one on the otherside of the table. The experimenter told thechild that the penguin was very picky andonly liked things that were "even." Thechild was told to put the even things in thepicky penguin's basket and the things thatwere not even in the other basket. Then chil-dren were given the 12 symmetry trainingcards one at a bme and asked, "Do you know


what this is?" The experimenter remindedthe child that the picky penguin only likedthings that were even and asked whether thepicky penguin would like the card on thetable. The child then put the card in one ofthe baskets. If the choice was correct, theexperimenter said, "That's right, that onewas even"; if incorrect, the experimenter re-trieved the card and explained in detail whythe answer was wrong (e.g., "No, that one isnot even. See, that one has two little onestogether and to be even, it would have tohave two the same on the outside and a dif-ferent one in the middle. In this one, thedifferent one is on the side. This is some-thing else, so let's put it in the otherbasket").

This procedure was repeated for each ofthe figures from the Same-dimension-sym-metry triads. Then the penguin was takenaway and the child was introduced to a pickywalrus who only liked things that were"more and more." The same procedure wasthen repeated for the 12 monotonicity cards,using the label "more and more."

Test: Cross-dimension triads.—After thecategorization training, the child was toldthat it was time to play a different game. Thetriads task was conducted in the same man-ner as in Experiment 1. Afrer the two train-ing triads and one filler triad, the child re-ceived the eight Gross-dimension triadswith one filler triad after the first four triads.The triads were presented in a fixed orderdesigned to facilitate transfer as determinedby pilot testing: first, the four symmetry tri-ads and then the four monotonicity triads(see the cross-dimension portion of Table 2for exact order of presentation). As before,no feedback was given.

RESULTS

Categorization TaskAs predicted, children who did well on

the categorizabon task tended to do w êll onthe Gross-dimension triads task. Ghiidrenwho scored above the median (67%, range= 42%—81%) on the categorization task re-sponded relationally to 67% of the Gross-dimension triads, whereas children whoscored at or below the median on the catego-rizabon task responded relationally to 52%of the Cross-dimension trials (chance =50%). As in Experiment 2, a median-splitanalysis was performed. Ten of the 12 chil-dren fell into the predicted cells (below-below and above-above, see Table 4). Achi-square analysis confirmed the noninde-

TABLE 4

NUMBER OF CHILDREN PERFORMING ABOVE ANDBELOW THE MEDIANS OF THE CATEGORIZATION

TASK AND THE TRIAD TASK IN EXPERIMENT 3

CATEGORIZATION

Below . ....Ahove

TASK

TRIAD

Below

62

TASK

Ahove

04

pendence of performance on these two tasks,X^(l) = 6.00, p < .025.

Production of LabelsOverall, there were very few produc-

tions of the labels. Of the 12 children in theexperiment, five did not correctly label anyof the 24 items, four produced two or threecorrect labels, and only three children pro-duced more than eight correct labels. Al-though this limited amount of productiondata does not permit firm conclusions, therewas an interesting qualitative relation be-tween propensity to label and performanceon the Cross-dimension triads task. Themean proportions correct were 55%, 56%,and 71% for the children producing 0, 2—3,and 8 or more labels, respectively.

DISCUSSION

Learning to label and categorize higher-order relations enhanced 4-year-olds' recog-nition of those higher-order commonalities.Again, the number of participants was small(N = 12), and the gain in Cross-dimensionalperformance was not large, but in view ofthe relabvely modest amount of experiencethe children had with the relational labels,the results are encouraging. These resultsbuttress the knowledge-based account of therelational shifl and the claim that children'sincreasing ability to notice relational simi-larity is due at least in part to their learningof higher-level relabonal categories. Theseresults also raise the intriguing possibilitythat language learning—specifically, learn-ing the names of relational categories—maybe a factor in the development of relabonalsimilarity (see Gentner & Rattermann,1991).

Experiment 4In Experiment 4, we returned to the

Progressive Alignment hypothesis with theintent of creabng a more definibve test. Weshowed in Experiment 2 that a relabvelymodest amount of experience with Same-


dimensional comparisons can facilitate cbil-dren's perfonnance on Gross-dimensionalsimilarity. However, these benefits werelimited to those children who did well onthe Same-dimension trials, raising the con-cern that the apparent training effects mightresult from certain children being advancedon both tasks. Against this possibility is thefact that, as discussed above, this positiverelation between performance on tbe Same-dimension and Gross-dimension tasks wasfound only when the former preceded thelatter (in Experiment 2), and not when thetwo kinds of trials were mixed together (inExperiment 1). However, a more convincingdemonstrabon of the hypothesis would be toshow that, across the board, giving childrenmore insight into the Same-dimension taskwill improve their performance on theCross-dimensional task. Therefore, in Ex-periment 4 we trained children to a criterionon the Same-dimension triads and used apretest-posttest comparison to see if thistraining led to the predicted gain in Gross-dimension performance.

A second goal of Experiment 4 was tocheck for a possible problem with the sbm-uli in the prior studies. The children's taskwas to choose whether the relabonal choiceor the nonrelabonal choice was a bettermatch for tbe standard. However, becausethe matching relational items were alwaysexamples of either symmetry or monotonic-ity, children might simply have learned tochoose the "good" pattern (either symmetryor monotonicity) over the other altemabve(the nonrelabonal choice, which was alwaysa permuted pattem of the same componentobjects). It is even conceivable that children

sometimes remembered and chose the sameitems on the Cross-dimension task as theyhad chosen on the Same-dimension task.That is, children might simply be learningto select certain response alternatives orclasses of alternatives (the "good" relations),rather than carrying out a cross-dimensionalcomparison with the standard. In eithercase, children's responding would havemimicked successful Cross-dimensionalcomparison without such comparisons actu-ally occurring.

To eliminate these possibilities, in Ex-periment 4, the response alternatives for theCross-dimension triads were altered. In-stead of choosing between a relational alter-native and a nonrelational alternative, chil-dren were given a monotonicity alternativeand a symmetry alternative. Thus they hadto choose between two good relational alter-nabves, only one of which matched the stan-dard (see Fig. 5). Since children had experi-enced both these pattems as the best matchequally often in the Same-dimension train-ing, the strategy of picking a known patternwould not work. There was no way to choosethe correct relational pattem without com-paring the alternatives to the standard.

To establish a baseline, we first gave the4-year-olds a pretest using the new kind ofCross-dimension triads. This was followedby a training procedure on the Same-dimension triads in both dimensions, afterwhich we again tested children on the newCross-dimension triads. In the Same-dimension braining, we were careful to useonly terms specific to the particular dimen-

Standard

Matching Relational Choice Non-matching Relational Choice

FIG. 5.—Sample of Cross-dimension triads used in Experiment 4


sion. We know from Experiment 3 thatCross-dimensional performance can be facil-itated by giving children common abstractlabels (such as "even" or "more and more")that invite them to perceive the cross-dimensional relational abstraction. Here weare interested in a pure test of the Progres-sive Alignment hypothesis that experiencealigning within dimensions promotes align-ment of the same relational structure acrossdimensions. We therefore avoided givingchildren domain-general abstractions in or-der to see whether they could arrive at theabstracbon for themselves. Thus, the experi-menter took care to use dimension-specificterms such as "darker" or "bigger" ratherthan terms that could apply to both size andsaturation, such as "more" for monotonicity.The hypothesis was that insight into theSame-dimension triads would make chil-dren better able to recognize the purehigher-order commonalities in the Cross-dimension triads.

METHOD

ParticipantsThe participants were 11 4-year-oIds,

five boys and six girls (mean age 4-6, range= 4-0 to 5-0). Three additional childrenwere tested and replaced. One child waseliminated due to failure to meet criterion(see Training), one due to experimenter er-ror, and one due to poor performance on thefiller trials (more than one incorrect).

Design and MaterialsThe dependent measure was posttest

Cross-dimension performance compared topretest Cross-dimension perfonnance. Theeight Same-dimension triads were the sameas those used in Experiments 1 and 2. Theeight Gross-dimension triads were like thoseused in Experiments 1 and 2 except that thenonrelational choice was replaced by a non-matching relational choice (see Fig. 5). Thisnew figure depicted either symmetry ormonotonicity (whichever was not depictedin the standard and the matching relationalchoice). In order to control object-level simi-larity, the foil (i.e., the nonmatching rela-tional choice) ublized the same objects asthe matching relational choice, insofar aspossible. For example, if the matching rela-bonal choice was a symmetrical pattem ofblue circles (light dark light), the foil wasa monotonically increasing pattem of bluecircles (light medium dark). The trainingand filler triads were identical to those usedin the previous experiments, except that twofiller triads were added.

ProcedurePretest.—Children were given two

fraining trials, a filler trial, and then fourCross-dimension trials with a filler trial be-tween the first and last two. There was nofeedback.

Training.—After the pretest, childrenwere trained to a criterion on the eightSame-dimension triads. Afrer each trial thechild was given feedback and a "same-dimension explanation" if needed. If thechild chose the relational choice, the experi-menter said, "That's right! Let's try anotherone." If the child chose the nonrelationalchoice, the experimenter said, "That is notquite right. I think it would go better here.Let me show you how to figure it out." Thenthe experimenter would explain the correctchoice using terms specific to the dimensionthat was involved in the comparison (size orcolor saturabon). The experimenter used di-mension-specific terms such as "dark" or"bigger" and avoided domain-general termsthat apply to both size and saturabon, suchas "more" for monotonicity or "even" forsymmetry. For example, in a same-dimension explanabon, the Experimentermight point to a symmetrical standard andsay, "See, this one has two little ones on thesides and a big one in the middle. And see[pointing to the relational choice], this onehas two little ones on the sides and a big onein the middle. That is why this one goes withthis one. This one [pointing to the nonrela-tional choice] is not right because it has twolittle ones here and a big one on the side.Let's try another one!"

The criterion for the training trials wasseven out of the eight Same-dimension trialscorrect. If a child got more than one trialwrong, the entire set of eight trials was re-peated. This was continued until the childmet the criterion (nine children) or until theexperimenter judged the child to be gettingfrustrated with the task. In this case, the ex-perimenter repeated only the incorrect tri-ads until the child got them all correct.Three children fell into this category. Fi-nally, one child was unable to meet this cri-terion and was dropped from the analyses.The 11 children included in the analysesreached the criterion in an average of 15.4training trials (range = 8—24 trials).

Test.—After completing the trainingtask, the children were presented with theeight Cross-dimension triads. All of these tri-ads had two "good" relational choices. Fourof these triads were identical to the Cross-dimension triads in the Pretest and four

were new. The triads were presented in thesame manner as in previous experiments. Nofeedback was given.

RESULTS AND DISCUSSION

PretestThe first question was how the children

would initially perform on the new kind ofCross-dimension trial (with two "good" rela-tion choices). As in the prior studies, the 4-year-olds initially showed no ability tochoose the matching higher-order pattern.They chose the matching relational responseon 41% of the Cross-dimension trials:chance = 50%; t{10) = 1.07, p > .15, one-tailed.

TestAs predicted, relational selectivity was

elevated on the Cross-dimension trials fol-lowing the Same-dimension training trials.Ten of the 11 children performed more rela-tionally in the posttest than in the pretest.Overall, the children chose the matching re-lational response on a mean of 74% of theCross-dimension trials. This was reliablyabove the pretest performance, f (10) = 5.39,p < .0005, one-tailed, and also reliablyabove chance, t{10) = 4.01, p < .003, one-tailed. Consistent with the ProgressiveAlignment hypothesis, leaming to align theSame-dimension triads improved children'srecognition of the higher-order relationalcommonality in the Cross-dimension trials.

General DiscnssionThe present research suggests four con-

clusions. First, there is support for the claimof a relational shift from early reliance onconcrete similarity to later ability to per-ceive purely relational commonalities. Sec-ond, our findings support the claim that thisdevelopment is driven by changes in do-main knowledge, rather than changes inglobal competence or processing capacity.Third, we found evidence that languagelearning—specifically, the acquisition of re-lational terms—can promote the develop-ment of relational comparisons. Finally, wefound evidence that the process of similaritycomparison itself is instrumental in this de-velopment. Although the number of partici-pants in each of the experiments was notlarge, the consistency in the overall pattemof the results across the four experimentsprovides converging support for these con-clusions. Based on these results, we conjec-ture that the acquisition of relational lan-guage and the process of relationalcomparison provide mutual bootstrappingthat drives representational change.

Kotovsky and Centner 2813

Knowledge and the Relational ShiftAccording to the "career of similarity"

framework put forward by Centner and Rat-termann (1991), children's very early simi-larity matches rely on massive overlap be-tween the items; with experience theybecome able to appreciate partial similarity,with object matches preceding relationalmatches and in turn higher-order relationalmatches (see also Centner & Medina, 1996).Our current findings support this account ofthe relational shift. For example, in Experi-ment 1, we found that children could recog-nize relatively concrete similarity involvingfirst-order as well as higher-order matchesbefore they could take advantage of purelyhigher-order relational commonalities. Rec-ognition of higher-order relational similaritygradually emerged between the ages of 4and 8 years.

Further, we found that children's per-formance in the relational task could be im-proved by their gaining more knowledge ofthe domain relations. We found that even4-year-oIds, who were unable to recognizepure higher-order matches in Experiment 1,could perceive pure higher-order matchesafter training in the domain relations (Exper-iment 3) or repeated experience with theconcrete pairs (Experiments 2 and 4). Theserapid changes provide strong evidence for achange of knowledge view of the develop-ment of relational ability (Brown, 1989;Centner & Rattermann, 1991; Goswami,1992; Vosniadou, 1989), as opposed to matu-rational changes in global competence (Pia-get et al., 1977) or processing capacity (Half-ord, 1987, 1992).

Progressive AlignmentAccording to the Progressive Alignment

hypothesis, the process of carrying out acomparison, even a concrete comparison,leads to an alignment of representations(Centner & Markman, 1993, in press; Cold-stone, 1994; Goldstone & Medin, 1994;Markman & Gentner, 1993; Medin, Gold-stone, & Gentner, 1993; Novick, 1988; Ross,1984, 1989; Schumacher, 1988). Throughthis alignment the common relational struc-ture becomes more salient. Further, becauseindividuals prefer to see similarity ratherthan dissimilarity (e.g., Kmmhansl, 1978),the process of comparison invites adjust-ments to promote better alignments, leadingto an increase in the uniformity of the repre-sentations (Gentner & Rattermann, 1991;Gentner et al., 1995; Gentner & Wolff, inpress). Progressive alignment acts as a kindof bootstrapping mechanism. As childrenmake similarity comparisons in a domain.


the representations of the relational struc-ture in the domain become highlighted andpossibly more uniform (see below). This inturn makes possible even more abstract, oranalogical, comparisons. This cycle can beseen as a kind of disembedding or decontex-tualizing of relations from initially situatedrepresentations to representations that canbe matched across domains.

We found three lines of support for theProgressive Alignment hypothesis. First, inExperiment 2, we found that giving 4-year-olds a very small amount of concentrated ex-perience comparing figures that were similarenough for them to align (the four same-dimension-size comparisons and the foursame-dimension-saturation comparisons) al-lowed these children to recognize subse-quently abstract relational similarity that 4-year-olds without the experience could notrecognize. This occurred without feedback.Further, the gain could not be attributed toa general practice efFect, for no such benefitoccurred for children who received eightsize-size comparisons. In order for 4-year-olds to recognize abstract higher-order com-monalities, general practice in making com-parisons was not enough; the results suggestthat the relational structure in both of theparticipating dimensions needed to bealigned and highlighted. Finally, in the fol-low-up study to Experiment 1, we found thatthis pattern of concrete alignment promotingabstract alignment held for polarity as wellas for dimensional alignment. These resultssupport progressive alignment as a mecha-nism of experiential learning.

There is additional evidence that com-parison experiences can lead to recognitionof further similarity. Namy, Smith, andCershkofF-Stowe (in press) found that 2-year-oids more readily learned how to cate-gorize two sets of like objects if they weregiven opportunities to compare the objects.Uttal, Schreiber, and DeLoache (1995)found that 4-year-oIds were able to solve adifficult delayed version of the DeLoache(1987) room-to-model mapping task (inwhich children search for a hidden toy byfinding the object in one room that corre-sponds to a designated object in another,smaller room) if they had first experienced aversion in which they were allov '̂ed tosearch immediately. Children in the imme-diate search task had perhaps achieved analignment of the two spaces which theycould then preserve under more difficult cir-cumstances. In a study by Marzolf and De-Loache (1994), children were better able tomake the correspondence between a room

and a rather dissimilar model after experi-ence with a room and a highly similar model.

Re-representationHow might concentrated experience

in alignment within each of the two di-mensions potentiate subsequent cross-dimensional alignment? We conjecture thatthe relations here are initially representedin a domain-specific manner (e.g., darkerthan and bigger than). That is, for youngchildren, the representation of a differencein magnitude is bound up with the dimen-sion of difference. Some kind of decomposi-tion is required in order to see these patternsas alike: for example, re-representing thedifferences in a manner that separates thecomparison and die dimension (i.e., great-eridarkness{a), darkness{b)]). The idea isthat such a re-representation makes it easierto notice the commonality between changein size and change in darkness, thus permit-ting cross-dimensional alignment. This ideais related to work within lexical semanticsthat seeks lexical entries capturing the en-tailments of a word (e.g., LakofF, 1987;McCawley, 1968, 1972; Norman & Rumel-hart, 1975; Sehank & Abelson, 1977).

Our claims about re-representation arerelated to Karmiloff-Smith's (1991, 1992)theory that representational redescriptionallows initially implicit procedural knowl-edge to become available explicitly. How-ever, there are some differences. First, thescale of the changes discussed here is morelocal than in Karmiloff-Smith's discussion.Whereas Karmiloff-Smith emphasized meta-level insights into one's own processes, wesee a role for re-representation even at thesimple content level. We suggest also thatthe accumulation of many small, content-level adjustments may potentiate larger in-sights. Second, our research focuses onmechanisms of re-representation, usingcomputational models from analogy andcase-based reasoning (Burstein, 1983; Fal-kenhainer, 1988, 1990; Falkenhainer, For-bus, & Gentner, 1989; Forbus & Oblinger,1990; Holyoak & Thagard, 1989; Kass, 1989;JCass & Leake, 1987; Kolodner & Simpson,1989; Novick, 1988; Novick & Holyoak,1991; Sehank & Leake, 1989). Third,whereas Karmiloff-Smith proposes that rede-scription processes begin only after behav-ioral mastery is attained in a given domain,we assume that alignment and re-representation happen from the start. Thereason that re-representation does not seemto be occurring in very young children is thattheir earliest representations are so richlyembedded in concrete detail, and so lacking


in higher-order abstracdons, that only themost conservadve similarity matches can bemade. Hence these early matches and theirresulting inferences are often so mundaneas to escape adult notice. Nonetheless, wesuggest that they pave the way for the moredramadc comparisons to come.

Computational ModelingWe have hypothesized that an articula-

don or decomposition of the representationcould lead to better recognition of abstracthigher-order commonalides. Is this hypothe-sis reasonable? It is difficult to assess theexact form of a human subject's representa-don. Moreover, since both representationsand processing modes can change over thecourse of children's development, it is diffi-cult to assign causality. Therefore, we useda computational model to keep the processof comparison fixed while varying theknowledge representation on which it oper-ates. If the postulated changes in knowledgerepresentation produce the observedchanges in children's similarity perfor-mance, this is evidence that change-of-knowledge could provide a sufficient expla-nadon for the ohserved effects.

We used the Structure-Mapping Engine(SME) developed by Falkenhainer, Forbus,and Gentner (1986, 1989), a computadonalmodel that simulates the similarity compari-son process specified by structure-mappingtheory (Gentner, 1983). SME is given propo-sitional representadons of two situadons andproduces a favored mapping (a maximalstructural alignment). (SME also has infer-ential and incremental mapping capabilidesnot germane to the present simuladon; seeFalkenhainer et al., 1989; Forbus, Gentner,& Law, 1995.) In the present case, we gaveSME representadons of the standard and therelational choice in all four of the mono-tonic-increase triad types (Same-dim/Same-pol, Same-dim/Opposite-pol, Cross-dim/Same-pol, and Gross-dim/Opposite-pol; seeGentner et al., 1995) and it produced map-pings indicating its preferred correspon-dences between the three objects in thestandard (e.g., the small, medium, and largesquares) and the three objects in tbe rela-tional choice (e.g., the light, medium, anddark circles).

The critical manipuladon was the kindof representadons given to SME. We specu-lated that the younger children representedmagnitude difference in a dimension-specific way (e.g., A is taller than B). Incontrast, we assumed that the older chil-dren—and the younger children after

training—could represent magnitude in a di-mension-general manner that separates thespecific dimension out of the magnitudecomparison (e.g., A's size is greater than B'ssize; see Fig. 6). Although the same informa-don is encoded, dimension-general repre-sentadons more readily permit the recogni-don of abstract change-of-magnitude (i.e.,that one value is somehow "more" than an-other along their respective dimensions)than do specific dimensional relations like"A is bigger than B" or "G is darker thanD." Such representadons should permit thelearner to see the common dimensionalstructure even in the more abstract cases,such as in cross-dimensional pairs.

SME's mappings showed this to be thecase. The dimension-general representa-dons received relational mappings for allfour pairs. SME aligned the pairs on the ba-sis of common relational structure evenwhen both the dimensions and polarides dif-fered. This parallels the performance of the8-year-olds in Experiment 1, who were suc-cessful at making Gross-dim/Opposite-polmatches. In contrast, when SME was givendomain-specific representations, it generallyfailed to produce a relational alignment.Since the representadons did not make man-ifest the potentially common reladonalstructure across the dimensions, SME wasreduced to object matches or to positionalalignments. Only in the most concrete case,the Same-dim/Same-pol comparison, didSME align dimensional magnitude reladonsin its mapping (e.g., TALLER to TALLER).This parallels the performance of the 4-year-olds in Experiment 1, who were at chancein their responding to all but the Same-dim/Same-pol comparisons.

By their nature, these results cannotserve as proof that these changes occur inchildren. However, they do consdtute an ex-istence proof that change of representa-tion—more specifically, re-representadon ofdmension-specific magnitude relations as ar-ticulated dimension-general magnitude re-lations—could account for the relationalshift in our results. The results of the com-putational simulation show that re-representadon can lead to substantial im-provement in reladonal insight whilemaintaining the same basic comparisonprocess.

One arena in which we speculate thatre-representadon is important is in dimen-sionfJ leaming. There is evidence that theacquisidon of adult dimensional structures


) ( ) ( c )

DMENSION X ) (DMBMSION X ) (DMBJSION X ) (DMBgSION X

FIG. 6.—The top portion of the figure depicts a dimension-specific representation of height in-crease in which the dimension of height and the direction of cfiange are embedded. The bottom portionof the figure depicts a dimension-general representation of monotonic increase in which the dimensionand the direction of change are disembedded. See text for additional details.

involves a shift from overall global similarityto more differentiated similarity (Foard &Kemler-Nelson, 1984; Garner, 1978; Shepp,1978; Smith, 1989; Smith & Kemler, 1977;Tighe & Tighe, 1968) characterized by con-sistent polar alignments across dimen-sions—for example, loud big, big more(Smith & Sera, 1992). We conjecture thatover development children must not onlylearn separate perceptual knowledge into di-mensions but also come to see them as di-mensions, as possessing a coherent (often atleast ordinal) structure (see Zwislocki &Goodman, 1980). Once dimensions are ex-tracted, it becomes possible to grasp struc-tural parallels across different dimensions:for example, cross-domain metaphoric sys-tems such as up/down good/bad and theothers discussed by Lakoff and his col-leagues (Gibbs & O'Brien, 1990; Lakoff &Johnson, 1980; Turner, 1987, 1991).

The Role of LanguageThere is a considerable literature show-

ing that labeling sets of objects can facilitate

children's forming categories around thoseobjects (e.g., Gelman & Markman, 1987;Imai & Gentner, 1993; Markman, 1989;Markman & Hutchinson, 1984; Waxman,1991; Waxman & Gelman, 1986; Waxman &Markow, 1995). However, this research hasfocused almost exclusively on names for ob-jects. Based on Gentner's (1981, 1982) rela-donal relativity argument that verbs andother reladonal terms are more linguisticallyshaped than are concrete noun categories,we speculate that the influence of languageand labels may be much greater for rela-donal concepts than for common object cate-gories.

Our investigations support the claimthat learning reladonal category names canserve to highlight reladonal structure. Expe-rience labeling and categorizing the figuresused in the study helped children to recog-nize the higher-order commonalities sharedby the figures. It is worth nodng that theamount of language training was rather mod-est: Ghiidren sorted eight instances and four

noninstances of each pattern, and the experi-menter provided the label if the child couldnot. Nonetheless, the evidence from Experi-ment 3 suggests that language can facilitateattention to common relational structure.

Addidonal research likewise suggeststhat language may be an important pathwayto leaming to think reladonally. Smith andSera (1992) gave children aged 2 dirough 5a cross-dimensional triads task in which theyhad to decide, for example, whether a darkmouse matched with a big mouse or witha small mouse. They found that children'smapping preferences changed developmen-tally, and further that their preferences on averbal version of the task, using the namesof the dimensions, appeared to lead theirpreferences on a nonverbal perceptualmatching task by 1 or 2 years. This suggestedan infiuence of dimensional language on thedevelopment of dimensional structure andcross-dimensional mapping. Rattermann etal. (1989) gave 3-year-olds a mapping taskbetween two triads of objects monotonicallydecreasing in size (see also Gentner & Rat-temiann, 1991; Gentner et al., 1995). Thechildren had to say which object in their setcorresponded to a designated object in theexperimenter's set, using a "same-relative-size" mle (e.g., choose the largest objectin the set). The task was quite difficult,due to extraneous object similarities (cross-mappings) that competed with the relationalmapping. For example, the experimenter'ssmall, medium, and large objects might be acar, cup, and house, and the child's small,medium, and large objects an identical cup,an idendcal house, and a Hower pot. Thus,when the largest object was designated inthe experimenter's set (the house), the childhad to pass over the house in his or her setand choose the fiower pot. Even with correc-dve feedback, 3-year-olds were at chance onthis task. However, when they were taughtto use reladonal labels for the three objects(e.g., "Daddy, Mommy, Baby" or "big, litde,dny") they were able to learn the correctmapping, and even to transfer to new sets ofobjects.

These results suggest that the acquisi-tion of reladonal language may promote therecognidon of abstract relational similarityand the development of relational categories(Gentner & Medina, 1966; Gentner & Rat-termann, 1991; Premack, 1983; Vygotsky,1962). Addidonal research might investigatethe effect of more intensive training on thereladonal labels (e.g., training to a criterion),the longevity of such effects, and the gener-


alizahility of such relational language toother situations.

Concluding CommentsOur goal in this research was to study

the leaming processes by which childrencome to appreciate relational categories.Therefore we must ask whether this leamingpersists beyond the immediate session andwhether these processes bear any resem-blance to processes occurring in the realworld. On the first point we have some evi-dence from the follow-up study to Experi-ment 1 that the gains made from aligning themore concrete triads can endure for at leasta few days. In this study, 4-year-olds showeda transfer effect from the Same-polarity tothe Opposite-polarity trials in spite of thefact that the Opposite-polarity dials werepresented roughly 2 days after the Same-polarity trials. Further, Radermann andGentner (1996) have found retendon overseveral weeks of the relational leaming intheir "Daddy, Mommy, Baby" mapping taskdescrihed above.

A second issue is whether these kindsof comparison processes occur in children'snatural processing. There is anecdotal evi-dence that they do. Dan Slobin (personalcommunication, April 1986) reports a spon-taneous example from his daughter, Heida,then a well-traveled 3-year-old. One day inTurkey she heard a dog barking and re-marked, "Dogs in Turkey make the samesound as dogs in America. . . . Maybe alldogs do. Do dogs in India sound the same?"For Heida to arrive at this quesdon, she hadto have compared dogs from different coun-tries and noted that they sound the same.But the comparison goes further, for Slobinnoted in his joumal, "She apparendy no-ticed that while the people sounded differ-ent from country to country, the dogs didnot." Thus Heida must also have comparedpeople from different countries and notedthat they typically sound different (speakdifferent languages); and, finally, she musthave aligned these two comparisons to drawthe contrast, "As you go from country tocountry, people sound different but dogssound the same." Thus her own experientialcomparisons led her to a deep questionahout the difference between human lan-guage and animal sounds.

Our findings support progressive align-ment and re-representation as mechanismsby which children may come to recognizeabstract relational similarity and form rela-donal categories. We further suggest that


progressive alignment takes place naturallyand spontaneously as children make similar-ity comparisons. It can be promoted by con-certed experience and by the use of commonlabels to call attention to the relational com-monalities. The process of making simplecompairisons may be a path toward findingricher and deeper commonalities.

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