Development of Analogical Problem-Solving Skill Author(S): Keith J

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Development of Analogical Problem-Solving Skill Author(s): Keith J. Holyoak, Ellen N. Junn and Dorrit O. Billman Reviewed work(s): Source: Child Development, Vol. 55, No. 6 (Dec., 1984), pp. 2042-2055 Published by: Wiley on behalf of the Society for Research in Child Development Stable URL: http://www.jstor.org/stable/1129778 . Accessed: 30/11/2012 13:48

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This content downloaded by the authorized user from 192.168.82.217 on Fri, 30 Nov 2012 13:48:38 PM All use subject to JSTOR Terms and Conditions Development of Analogical Problem-Solving Skill

Keith J. Holyoak Universityof Michigan

Ellen N. Junn Princeton Unive-sity

Dorrit O. Billman Universityof Pennsylvania

HOLYOAK,KEITH J.; JUNN, ELLEN N.; and BILLMAN, DOR•gT O. Development of Analogical Problem- Solving Skill. CHILD DEVELOPMENT,1984, 55, 2042-2055. 3 experiments were performed to assess children'sability to solve a problem by analogyto a superficiallydissimilar situation. Preschoolers and fifth and sixth graderswere asked to solve a problem that allowed multiple solutions. Some subjects were first read a story that included an analogous problem and its solution. When the mapping between the relationsinvolved in the correspondingsolutions was relatively simple, and the correspondinginstruments were perceptuallyand functionallysimilar, even preschoolerswere able to use the analogy to derive a solution to the transferproblem (Experiment1). Furthermore, salient similarityof the instrumentswas neither sufficient (Experiment2) nor necessary (Experi- ment 3) for success by preschool subjects. When the story analog mapped well onto the transfer problem,4-year-olds were often able to generatea solutionthat required transformation of an object with little perceptualor semantic similarityto the instrumentused in the base analog (Experiment 3). The older children used analogies in a mannerqualitatively similar to that observed in comparable studies with adults (Experiment 1), whereas the younger children exhibited different limitations.

Analogical thinking is widely recognized metaphor is based on salient perceptual as a hallmark of human intelligence, and as similarities (Vosniadou & Ortony, 1983). such the course of its development is a topic of clear importance. The developmental litera- However, some sensitivity to analogical ture in this area has almost exclusively con- relations is apparently within the competence cerned itself with "analogy problems" of the of very young children. The essence of sort used in intelligence tests, most commonly analogical thinking is the transfer of knowl- "proportional" analogies of the form A:B::C:? edge from one situation to another by a pro- (for a brief review, see Sternberg, 1982). The cess of mapping-finding a partial set of corre- consensus of most of this research is that chil- spondences between the elements (objects, dren have great difficulty solving even simple attributes and relations) that form the mental analogy problems prior to at least age 9 representations of the two situations (Hesse, (Levinson & Carpenter, 1974; Lunzer, 1965; 1966). Mapping processes seem to underlie Piaget, Montangero, & Billeter, 1977; Stern- both social modeling (Holyoak & Gordon, berg & Rifkin, 1979). Experimental studies of 1984) and "make-believe" play, which are the development of metaphorical comprehen- clearly exhibited by 3-year-olds (Garvey, sion indicate that performance is generally 1977). For example, when a girl pretends to poor prior to middle childhood (Winner, be the mother of her doll, she modulates her Rosenstiel, & Gardner, 1976), unless the behavior to bring it into correspondence with

This research was supported by NIMH Research Scientist Development Award 1-K02- MH00342-03and NSF grantBNS-8216068, both to K. J. Holyoak.Mary Gick providedboth valuable advice on the experimentaldesign and comments on an earlierdraft. Robert Sternberg and several anonymousreferees also providedhelpful comments.Tsila Evers assisted in testing subjects.We are gratefulfor the cooperationof the students and teachers of Ann ArborAction Child Care, Jackand Jill LearningCenter, Little Lamb Nursery,Perry Nursery School, Pound House Child Care Center (all in Ann Arbor, Michigan), Maplewood Elementary School of Jenison, Michigan, and Chapin School of Princeton, New Jersey. Reprint requests should be sent to K. J. Holyoak, University of Michigan,Human PerformanceCenter, 330 PackardRoad, Ann Arbor,Michigan 48104. Inc. [ChildDevelopment, 1984, 55, 2042-2055. ? 1984by the Societyfor Researchin Child Development, All rightsreserved. 0009-3920/84/5506-0014$01.00]

This content downloaded by the authorized user from 192.168.82.217 on Fri, 30 Nov 2012 13:48:38 PM All use subject to JSTOR Terms and Conditions Holyoak, Junn, and Billman 2043 that of an appropriateadult, while makingthe to investigate the development of analogical doll "behave" like an infant. Gentner (1977) problem-solving skill. Our aims in the three demonstratedthat 4-year-olds could respond experiments reported below were twofold. appropriatelywhen they were shown a pic- First, we wished to determine at what age ture of a mountain and asked such questions children are first able to apply simple as, "If the mountainhad a knee, where would analogies to performa goal-directedproblem- it be?" (i.e., the children preserved relative solving task. The earlier the age of success, spatial positions when mapping human body the more likely it is that analogy provides a parts onto the picture). Gentner's task seems potential mechanism for early cognitive de- very similarto pretend play. Youngchildren's velopment. Second, we sought to answer success in her study may reflect the simplicity more analyticquestions concerningthe condi- of the higher-order relation between the tions under which young children succeed or mapped relations, which was typically iden- fail in using analogies and the components of tity on such perceptual dimensions as relative analogyuse that pose particulardifficulty. The height. latteraspect of the study was guided by Holy- oak's (1984) analysis of the components re- thinking re- Understanding analogical quired to solve a problem by analogy. These quires more naturalistic experimental para- are mental of than the format that has (1) constructing representations digms proportional a known analog (the base) and of the novel typically been employed. While a great deal of work has been done on the of anal- analogous problem (the target), (2) noticing solving the potential analogy between the base and ogy problems, relatively little has been done an initial in target, (3) constructing partial map- on the use of analogy solving problems, by between the elements of the base and or in life a ping children adults. Yet everyday pri- the and the to function of is not to target, (4) extending mapping mary analogical thinking constructa solution procedureappropriate for "solve (unless one is taking an in- analogies" the target problem. telligence test) but ratherto help solve novel problems by relating them to known situations, which may sometimes be drawn from Experiment 1 differentsemantic domains.Analogies in very was to assess the science the analogy between the motion Experiment 1 designed (e.g., abilities of children at two different levels of billiard balls and of gas particles) involve age the use of one situation as a frameworkfor to use analogies to solve problems. of constructinga causal model another (Op- Method penheimer, 1956). Transfer problem.-The transfer prob- Recent studies have begun to investigate lem used in this study, the "ball problem," the processes by which adults solve problems was adapted from the "pea problem" dis- by analogy. A paradigmthat has been used to cussed by Raaheim (1974). Two bowls were study analogical problem solving by college set on a table, one within the child's reach and students involves having subjects solve a one fartheraway. One bowl contained a num- problem after reading a story describing an ber of small gumballs, and the other was analogous problem and its solution (Gick & empty. Also on the table were an aluminum Holyoak, 1980, 1983). For example, Gick and walking cane, a large rectangular sheet of Holyoak (1980) had subjects attempt to solve heavy paper (posterboard), a hollow card- Duncker's (1945) "radiation problem" after board tube long enough to reach the farther reading about an analogous militaryproblem. bowl, child-safe scissors, string, tape, paper The radiationproblem allows a variety of po- clips, and rubber bands. The subjects' task tential solution plans. By varyingthe solution was to devise as many ways as possible, using to the militaryproblem provided in the story the materials provided, of transferring the analog, Gick and Holyoak were able selec- balls from the filled to the empty bowl with- tively to facilitatediscovery of particularsolu- out leaving their seat. Like the radiationprob- tions to the radiation problem. While most lem used with adults by Gick and Holyoak subjects were clearly able to solve the radia- (1980), the ball problem allows multiple solution problemby analogy,many failed to notice tions, making it possible to facilitate alterna- the relevance of the story until given a hint to tive solutions selectively by varyingthe prior use it. In addition,lessening the degree of cor- analog. However, the ball problem is less respondence between the two problem situa- complex and requires motoricrather than ver- tions reduced the frequency with which sub- bal solutions, making it more suitable for use jects produced the analogous solution. with young children. The present study adapted the paradigm Story analogs.-Two stories were used developed by Gick and Holyoak (1980, 1983) as base analogs. Each was a picture-bookfairy

This content downloaded by the authorized user from 192.168.82.217 on Fri, 30 Nov 2012 13:48:38 PM All use subject to JSTOR Terms and Conditions 2044 Child Development

tale, written and illustrated by the second au- the cane or else the magic carpet with the thor. The text of the two stories is provided in sheet of paper. The relations involving the the Appendix. The beginning of each story above objects (e.g., transferring) can also be was the same and concerned a genie who mapped. These correspondences can be used wished to move his home from one bottle to to construct a solution to the ball problem. another. The genie faced the problem of The solution suggested by the magic staff safely transferring a number of precious story is to use the cane to draw one bowl jewels to the new bottle. The two stories de- closer to the other; that suggested by the scribed different solutions used by the genie. magic carpet story is to roll the sheet of paper In the "magic staff" story the genie used his to form a tube, position the tube between the magic staff to pull the new bottle over to th6 two bowls, and then roll the balls through the side of the old one. In the "magic carpet" tube. Accordingly, successful use of a story story he commanded his magic carpet to roll analog should be evidenced by an increase in itself into a tube, placed it so as to form a "hol- the frequency with which the analogous solu- low bridge" between the two bottles, and tion to the transfer problem is generated by then rolled his jewels through it. Each story subjects. was by a series of colored pic- accompanied The materials provided with the ball tures illustrating the story. Each step in the problem afford a second solution that is par- solution was clearly depicted. tially analogous to the magic carpet story; the Analogical correspondences.-Table 1 balls can simply be rolled down the cardboard presents a schematic outline of the major tube. This tube solution is a somewhat less analogical correspondences between the two complete analogy than is the rolled paper so- stories and the ball problem, including the lution, since it does not involve construction main analogous solutions to the latter. Each of a tube. But for this very reason the tube problem and solution is organized in terms of solution requires a less detailed mapping; it an abstract "problem schema," consisting of can be viewed as a "shortcut" procedure an initial state, solution plan, and outcome. based on a mapping with the later stages of The representation in Table 1 is an abstrac- the genie's solution. In addition, the card- tiofi that omits the various noncorrespon- board tube probably appears more similar to dences between the story analogs and the ball the carpet rolled into a tube than does the problem (e.g., the genie has magical powers sheet of paper to the flat carpet. The tube solu- whereas the child does not; the child has tion should therefore be easier to produce available items such as scissors that do not than the rolled paper solution, given the map onto objects in the story). magic carpet analog. To use these analogies the genie can be Procedure.-Each child was tested indi- mapped with the child, the jewels with balls, vidually in a session lasting 10-20 min. In the the bottles with bowls, and (depending on magic staff and magic carpet conditions, the which story is provided) the magic staff with experimenter first read the appropriate story

TABLE 1

SCHEMATICOUTLINE OF BALL PROBLEM SHOWING CORRESPONDENCESWITH ANALOGOUSSTORIES

Story Analogs Ball Problem Initial state: Goal ...... Genie wishes to transferjewels Child wishes to transferballs from from one bottle to another. one bowl to another. Resources ...... Magic staff/magiccarpet. Walking cane/sheet of paper. Constraint ...... Must not drop or lose jewels. Must not drop or lose any balls. Solution plan 1 ... Genie (a) uses magic staff to pull Child (a) uses cane to pull goal bowl goal bottle closer to initial bottle; closer to initial bowl; (b) drops jewels into goal bottle. (b) drops balls into goal bowl. Solution plan 2 .... Genie (a) rolls magic carpet to Child (a) rolls sheet of paper to form form a long hollow tube; long hollow tube; (b) places tube so it extends from (b) places tube so it extends from initial bottle to goal bottle; initial bowl to goal bowl; (c) rolls jewels through tube to goal (c) rolls balls through tube to goal bottle. bowl. Outcome ...... Jewels are transferredsafely. Balls are transferredsafely.

This content downloaded by the authorized user from 192.168.82.217 on Fri, 30 Nov 2012 13:48:38 PM All use subject to JSTOR Terms and Conditions Holyoak, Junn, and Billman 2045 to the child, pointing to the accompanying ger subjects in that condition was near the pictures. To ensure that the children under- ceiling. stood the story, they were asked to retell it to the experimenter, who questioned them The procedure was also piloted with sev- about any major aspects that they omitted. eral children still younger in age (3-2 to 4-4). Some of the younger children required an ex- Since it proved difficult to ensure that these planation of what a "genie" was, but all sub- subjects understood the stories and transfer jects appeared to understand the story by the problem, the attempt to use such young chil- end of the initial part of the session. dren was terminated. Results and Discussion Subjects in the two story conditions then were with the ball those Frequencies of analogous solutions.- presented problem; The results concern the in the control condition were the ball major frequencies given with which the three critical solutions-use of without The child problem any prior story. the rolled and the cardboard was seated next to the filled bowl and asked to cane, paper, tube-were produced in the vari- remain in the chair, so as not to be able to by subjects ous conditions. These frequencies are pre- simply reach to the empty bowl. The problem sented in Table 2, broken down by solutions was introduced as a game involving moving given before and after the first hint to consider the balls from the nearer to the farther bowl, the story. All the solutions reported in Table 2 using any of the materials on the table. The were executed Since to each of the successfully. subjects experimenter pointed objects were asked to some but did not name them. give multiple solutions, individually, Subjects more than one of the were to the available subjects produced target encouraged manipulate solutions. All levels in and to as significance reported objects freely produce many possible this for in solution solutions as could. To children's paper differences frequen- they separate are based on exact to notice the from their cies Fisher's probability ability analogy ability test. to apply it, those in the story conditions were not immediately told that the story was related The preschoolers were clearly able to de- to the problem. However, if they appeared to rive the cane solution to the ball problem by run out of ideas without producing the analo- applying the magic staff analog. All 10 of the gous solution, the experimenter gave two pro- subjects who were given the magic staff story gressively more specific hints: "Does any- produced the cane solution, as opposed to thing in the story help?" and "What did the only one subject in each of the other two con- genie do and could you do anything like ditions, p < .001 for each comparison. Five of that?" If the child produced an analogous so- the magic staff subjects gave the cane solution lution, the experimenter asked how the child without any hints to use the story. There was arrived at it. The experimenter recorded all also evidence that the magic staff analog solution attempts in order of occurrence, created a "set" effect, in that the frequency of noted the timing of hints, and recorded perti- the nonanalogous tube solution was reduced nent comments by the subject. The session relative to the control condition, p < .05. Gick lasted until the child appeared to be unable to and Holyoak (1980) found similar evidence in- come up with any further possible solutions. dicating that story analogs can decrease the frequency with which adult subjects produce Subjects.-Forty-eight subjects were nonanalogous solutions. tested, divided into two age groups, with approximately equal proportions of boys and The magic carpet story, on the other girls within each age level and experimental hand, had a much less clear effect on solution condition. The younger group consisted of frequencies for the preschool subjects. Three preschool children in nursery schools and a subjects produced the analogous rolled paper kindergarten, ranging in age from 4-7 to 6-0, solution when given the story (all without with a median age of 5-6. The older subjects hints), as opposed to just one subject in the were fifth and sixth graders, ranging in age control condition and none in the magic staff from 10-0 to 12-0, with a median of 11-0. The condition. This difference, while suggestive, 30 preschool subjects were divided equally involved frequencies too small to merit statis- among the two story conditions and the con- tical comparisons. Nine of the 10 magic carpet trol condition. Of the 18 older subjects, 10 subjects generated the partially analogous so- served in the magic carpet condition and eight lution, use of the tube; however, this may not in the control condition. The magic staff story have reflected use of the analogy, since eight was not used with the older subjects after it of the 10 control subjects produced the same became apparent that performance by youn- solution without any prior analog.

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It is possible that discovery of the tube control group (eight out of 10 vs. zero out of solution may have tended to block generation eight subjects). We have no firm explanation of the rolled paper solution by subjects in the for this trend. It may be that the younger chil- magic carpet condition; for this reason, the dren had had more recent experiences manip- tube was not presented to subjects in Experi- ulating similar tubes in art classes or that the ments 2 and 3. In addition, there are several older children had developed competing asso- reasons to view the analogy with the magic ciations that led to increased functional staff story as simpler than that with the magic fixedness. Also, the older control subjects pro- carpet story. The staff and cane share more duced more total solution attempts (see be- perceptual and functional attributes than do low), some of which may have blocked gener- the magic carpet and sheet of paper, which ation of the tube solution. The older subjects should facilitate the mapping process in the did not simply ignore the tube, however, as former case. In addition, the latter solution in- four of the eight used it in some other way volves the construction of a more elaborate (three used it as a scoop and one as a blow- sequence of mappings between relations (first pipe). the then then forming tube, positioning it, Other solution attempts.-As would be rolling the balls through). The difficulty of ar- expected given the variety of materials avail- riving at the rolled paper solution may also be able, subjects made numerous types of solu- increased by the fact that the solution proce- tion attempts other than those related to the dure in the story analog allows a less than story analogs. Some of these were crude, such complete mapping (the genie forms a tube by as throwing the balls; some were more cre- a simple command, whereas the child must ative, such as using the tape dispenser as a actually roll the paper and decide how to keep scoop; many were unduly optimistic, such as it rolled, perhaps by using a rubber band). using a paper clip as a catapult. Total number of solution In contrast to the younger subjects, those attempts (not counting repetitions of the same did not differ in the older age group were clearly able to solution) signifi- across conditions within either generate solutions on the basis of the analogy cantly age level. The number increased between the magic carpet story and the ball substantially of 2.95 vs. from the to problem. All 10 of the subjects given the story (means 5.00) younger the older = for produced both the rolled paper and tube solu- age level, F(1,36) 12.4, p < .01, the two conditions and tions, whereas none of the control subjects comparable (control A different produced either, p < .001 for both compari- magic carpet). pattern emerged when solutions were scored. sons. Eight subjects in the story condition only successful These included the solution gave the tube solution immediately as their types presented in Table 2 several such as first solution, and nine gave it prior to a hint to plus others, rolling the ball across the unfolded to the bowl. use the story. The rolled paper solution ap- paper For the the mean number of peared more difficult, as all but three children younger subjects, successful solutions was 1.70 for both required a hint before they generated it. The story conditions and 1.30 for the control condition. frequency of the latter solution for the magic These differences were not carpet condition increased significantly across statistically significant. For the older the means the two age groups, p < .001. In addition, four subjects, were 2.20 for the condition and of the story subjects at the older age level also magic carpet tried to turn the hollow aluminum cane into a .38 for the control condition, F(1,18) = 43.3, p < .001. The older control thus tended tube by removing the stoppers from its ends, a subjects to a number of different solu- solution none of the control subjects at- produce large tion but few that were suc- tempted. These subjects thus gave evidence attempts, actually in than the con- of having used the story analog and transfer cessful-fewer, fact, younger trol = < .05. This problem to induce a general "schema" for subjects, F(1,16) 5.08, p difference reflects the fact that the older con- various types of tube solutions. (See Gick & trol did not the tube solu- Holyoak [1983] for discussion of the relation- subjects produce as noted above. In for the ship between analogical thinking and schema tion, contrast, magic condition the older induction.) In general, the older age group carpet age group produced more successful solutions had difficulty in noticing a potentially useful significantly than did the younger group, F(1,18) = 6.08, p analogy, but not ii applying it, as has been observed in comparable experiments with < .05, largely because of the greater success adults (Gick & Holyoak, 1980, 1983). of the older group in generating the analogous rolled paper solution. One surprising feature of the results was the apparent decrease in the frequency of the Process of applying analogies.-Subjects' tube solution from the younger to the older spontaneous comments and responses to

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questions were scrutinized for evidence re- superficially dissimilar problems to derive a garding the process of analogical problem solution to a transfer problem in a manner solving. All subjects in the magic carpet con- qualitatively similar to adult performance. dition at the older age level were clearly This skill is less developed in preschoolers. aware that their analogous solutions had been Experiments 2 and 3 were designed to pro- suggested by the story; most seemed sur- vide a more detailed assessment of the fac- prised that the experimenter needed to ask. tors that influence the success or failure of Seven of the 10 magic staff subjects in the younger children in using analogies. younger group indicated in some that way The evidence from they noticed a relation between the story and strongest Experiment 1 that have some of skill the target problem, as did two of the three preschoolers degree in came from the successful magic carpet subjects. sub- solving problems by analogy Many staff in which all jects at both age levels exhibited behavioral magic condition, subjects produced the cane solution. It signs of excitement and triumph after generat- analogous may be that this result ing an analogous solution. objected, however, positive was critically dependent on the salient per- A few of the younger subjects made spon- ceptual and functional similarity between the taneous comments that revealed details of the staff illustrated in the story analog and the mapping process. Several children referred to cane available to solve the target problem. the bowls on the table as "bottles," suggesting Perhaps the young children did not attend to a mapping with the prior story. One child in the detailed correspondences between the the magic carpet condition said he produced base analog and the target but rather followed the tube solution " 'Cause I saw the genie roll a simple strategy of using an object with sa- his towel." Two subjects in the magic staff lient similarities to the instrument in the story. condition referred to the cane as a "magical Experiment 2 tested this possibility by com- cane"; and another exclaimed, "Just like the paring the effectiveness of the magic staff genie!" after producing the cane solution. story used in Experiment 1 with that of other versions in which the Perhaps the most revealing protocol was analogical correspondences with the ball were less com- obtained from one of the very young pilot sub- problem even the staff was used in ex- jects, a girl aged 4-4 who was given the magic plete, though the same If children follow a carpet story. After being introduced to the actly way. young of an transfer problem, she immediately picked up simple strategy using object functionally and/or similar to the instrument the cardboard tube and rolled the balls down, perceptually in the should saying, "Let's pretend they're real jewels." depicted prior story, they generate the cane solution with Later in the session she said, "That will be a equal frequency across all conditions. if the magic carpet," and then laughed as she picked story However, children are in fact relations be- up the paper, rolled it, and asked the experi- mapping tween the base and the stories with re- menter to help tape it. "That's the way the target, duced will lead to fewer genie did it," she cried as she rolled the ball correspondences cane solutions. Gick and through the newly constructed tube. "I did it Holyoak (1980) found that adult are sensitive to varia- just like the genie." Here the process of subjects tions in the of analogical mapping is transparently revealed. degree analogical correspondence between a story analog and target prob- Two instances of control subjects drawing lem. analogies to extraexperimental situations were noted. One preschooler began the problem by Method exclaiming, "I know!" and then giving the Story analogs.-Three illustrated stories tube solution and no others. When asked why were used as base analogs: the original magic she solved the problem this way, the girl re- staff story used in Experiment 1 and two new plied, " 'Cause I always do that. I use marbles versions (see Appendix). All of the stories in- at home." A sixth grader, the only subject to volved a genie who used his magic staff to use the tube as a blowpipe, said she got the pull a new bottle up next to his old one and idea because "It's sort of . . . like a pea- then dropped jewels from the old bottle into shooter." These observations are consistent the new one. Thus all the stories contained with the possibility that children also use elements that can be mapped onto the cane analogies to solve problems outside of the lab- solution to the ball problem. However, the oratory situation. two new versions differed from the original story in that they introduced changes that less- 2 ened the degree of analogical correspondence Experiment with the transfer problem. In the extra- The results of Experiment 1 indicate that character version, a friend of the genie is in- 11-year-olds can use an analogy between troduced into the story. Although the basic

This content downloaded by the authorized user from 192.168.82.217 on Fri, 30 Nov 2012 13:48:38 PM All use subject to JSTOR Terms and Conditions Holyoak, Junn, and Billman 2049 plot is identical to that of the original version, subjects who received one of the two new ver- the friend is an element of the base analog that sions mentioned the genie's friend in retelling does not map onto the subsequent transfer the story, indicating that they attended to that problem. The altered-goal version also in- aspect of the story. troduces the friend as an additional character, The result of central interest but in addition the primary goal of the genie is involves the of the cane changed. The genie is now trying to move into frequency solution across the three conditions. As a new bottle big enough to share with his the data in Table 3 indicate, all friend; the transfer of jewels is treated in a eight children in the original condition the cane relatively incidental manner. Accordingly, the generated solution, compared with one of five in each of altered-goal version is less analogous to the only subjects the other ball problem than either of the other stories. conditions. The difference in solution frequencies between the original condition and Design and procedure.--Subjects served the other two combined (100% vs. 20%) was in one of three conditions, receiving either the highly significant, p = .001. version of the staff the original magic story, The decrement in extra-character version, or the striking performance altered-goal associated with the two new versions version. The transfer problem was identical to (espe- the ball as it was in cially the extra-character version, which in- problem presented Exper- volved a iment that the tube was not only relatively small change in the 1, except among of the the available to the whereas a completeness mapping) clearly indi- objects child, cates that the coffee and a dowel with a slit at cane solution does not result scoop long from task demands or one end were included. The was simply leading prompts procedure from the identical to that of the conditions in Ex- experimenter. Protocols for these story conditions indicated that that a more hint subjects often failed periment 1, except prolonged to was used if the child failed to generate the cane solution despite a great sequence pro- deal of effort and extensive duce the cane solution in response to even the problem-solving hints from the experimenter. With to second hint (i.e., "What did the genie do?"). respect effort, the mean number of total solution at- The second hint was repeated several times different "Could tempts (including repetitions) was almost using slightly wordings (e.g., twice as for who received the do what the did?") before the ses- large subjects you genie new versions than for those who received the sion was terminated. No control group was original (5.13 for the original version, 10.40 for run because the opposing hypotheses being the extra-character version, and 11.40 for the tested depend solely on differences in solu- altered-goal version). The difference between tion frequencies among the story conditions. the original condition and the other two was Subjects.--Eighteen kindergartners and significant, F(1,16) = 7.81, p < .02, indicating first graders, with approximately equal pro- that subjects in the latter conditions expended portions of boys and girls across conditions, more overall effort. The same pattern was ap- served as subjects. They ranged in age from 5- parent when mean number of nonredundant 4 to 7-2, with a median age of 6-4, and thus attempts was compared (means of 5.13, 7.40, were approximately 1 year older than the pre- and 9.00 for the original, extra-character, and schoolers used in Experiment 1. Eight sub- altered-goal conditions, respectively). No subjects received the original version, and five jects in Experiment 2 produced successful so- received each of the other two versions. lutions other than the cane solution (e.g., none produced the rolled paper solution). Results and Discussion All children were able to repeat the gist In an attempt to determine just how of the story to the experimenter and men- difficult it might be to elicit the cane solution tioned the use of the cane to move the bottle with a weak analogy, the session for one sub- and transfer the jewels. Comprehension ap- ject in the altered-goal condition was ex- peared equally good for all three versions. All tended. This subject failed to generate the

TABLE 3

NUMBER OF SUBJECTS PRODUCING CANE SOLUTION, EXPERIMENT2

Story Version Pre-hint Post-hint Total Original (N = 8) ...... 1 7 8 Extra-character(N = 5) ...... 0 1 1 Altered-goal (N = 5) ...... 0 1 1

This content downloaded by the authorized user from 192.168.82.217 on Fri, 30 Nov 2012 13:48:38 PM All use subject to JSTOR Terms and Conditions 2050 Child Development cane solution by the conclusion of the stan- the table. The standard functions of carpet and dard procedure. Further prompts were then blanket are clearly different from a piece of given in an extended session lasting a total of paper. Of course, in an analogy between two 35 min. The subject eventually generated the tasks involving the manipulation of concrete cane solution, but only after it was virtually objects, there must be some similarity among "given away" by the experimenter. The sub- objects, such as "rollability," for the solution ject noticed the cane at the very beginning of in one to be relevant to the other. the problem-solving session, mapped ele- were used in with elements of the Slightly younger subjects ments of the story target 3 than in but sev- was led to consider the idea Experiment Experiment 1, problem, general eral additional were introduced to of a and even the idea of a changes moving bowl, using facilitate of the solution. New still did not the cane solu- discovery target hook, yet generate were written involving charac- tion. The solution was after story analogs finally given only ters more familiar to the subjects than genies. extensive and a total of 18 prompting prior In addition, some subjects received two story solution attempts. analogs rather than just one, a manipulation The results of Experiment 2 clearly indi- that facilitates transfer for adult subjects (Gick cate that perceptual and functional similarity and Holyoak, 1983). The tube was not in- between objects in the base and target analogs cluded among the objects the child could use, is not by itself sufficient to elicit the analogous to ensure that its availability did not block solution reliably. Rather, young children are generation of the rolled paper solution. sensitive to the degree of correspondence of multiple components. Preschoolers' skills are Method were fragile and easily disrupted. Mismatch of Story analogs.-Two new stories based goals or protagonists impairs performance de- written and illustrated (see Appendix), spite perceptual and functional similarity of on characters from the Peanuts cartoon strip In objects. Furthermore, children typically re- and the Muppets television program. a blan- quire hints to consider the prior problem. "Woodstock's Eggs," Snoopy rolls up ket and uses it to transfer eggs to a nest. In Experiment 3 "Miss Piggy's Jewels," Miss Piggy rolls up a carpet and uses it to transfer jewels to a safe. 3 tested whether children Experiment Neither story contains elements with salient could use a to derive the more story analog perceptual or functional similarities to those rolled solution. The results of complex paper required for the analogous solution to the ball 2 indicate that and Experiment perceptual problem (i.e., rolling a piece of paper into a of elements is not a functional similarity tube to transfer gumballs). sufficient condition for analogical transfer, but served they do not exclude its necessity. Whereas Ex- Design and procedure.-Subjects Those in the one- periment 2 was designed to find conditions in one of three conditions. under which it is relatively difficult to gener- analog condition received one of the two story ate the cane solution by analogy, Experiment analogs prior to the transfer problem; those both 3 was designed to find conditions in which it in the two-analog condition received in the control condition at- is possible for young children to generate the stories; and those without rolled paper solution. Several aspects of the tempted to solve the ball problem any Within the condition procedure were altered to investigate this prior story. one-analog used more complex solution, which involves less each of the two stories was equally often; condition each or- similarity between story and solution. and within the two-analog der of the two stories was used equally often. In Experiment 1 the magic carpet story did not clearly elicit a significant number of The story or stories were read to subjects rolled paper solutions among the preschool in the same manner as in the previous experi- were asked subjects. At most, subjects mapped from the ments. After each story, subjects constructed tube in the story to the con- to retell it. Children in the two-analog condi- structed tube on the table. In Experiment 3 a tion were not told that the two stories were constructed tube was not presented. New ver- related to each other. The transfer problem sions of the story were written, one involving was then administered. No constructed tube rolling a carpet and the other a blanket. The was provided, but a new "obvious" solution used perceptual similarities between magic staff was added. The coffee scoop and dowel and cane and between constructed tube in the in Experiment 2 were hooked together to story and tube in the task (Experiment 1) make a long-handled scoop that could be used seem much greater than between a blanket or to transfer the gumballs. This "obvious" po- to ensure that a carpet on the floor and the sheet of paper on tential solution was intended

This content downloaded by the authorized user from 192.168.82.217 on Fri, 30 Nov 2012 13:48:38 PM All use subject to JSTOR Terms and Conditions Holyoak, Junn, and Billman 2051 subjects did not become discouraged by fail- Another responded to prompts by saying he ure to find any successful solution. could roll a blanket up, but that there was no blanket on the table. Such protocols suggest Subjects.-Twenty-four subjects, ranging that the preschoolerssometimes had difficulty in age from 4-1 to 5-0, served as subjects. the to the control performing mappings required to use a Twelve subjects were assigned when the ele- condition,and six were to each of the story analog corresponding assigned ments lacked obvious perceptual and func- other two conditions. tional similarities. Results and Discussion The total number of successful in all sub- solutions, As the previous experiments, which consisted of use of the to the stories mainly long- jects appeared comprehend handled in addition to of the Table 4 the number of sub- scoop rolling pa- readily. presents also tended to be for the in each of the conditions who per, higher analog jects generated than for the control of the rolled solution either before or after groups group (means paper 1.42 and .75 solutions per subject, respec- a hint to use the story.The results clearly indi- tively), although the difference fell short of cate that the preschoolers used the story significance, F(1,22) = 3.06, = .09. analogsto constructthe criticalsolution. Over- p all, seven of the 12 subjects who received analogs (either one or two) produced the General Discussion rolled paper solution, as contrastedwith zero This study has implicationsfor the devel- of the 12 control subjects. Fisher's exact prob- opment of analogical reasoning skills and for ability test showed the numberof criticalsolu- the potential contribution of analogical rea- tions to be significantlyhigher for the analog to other of The = soning aspects development. conditions than the control condition, p study demonstrates that even preschoolers .002 for total solutions, p < .05 for solutions can use analogies to solve problems. It also priorto any hint. The fact that the advantage begins to diagnose when children are likely of the analog conditions was significanteven to succeed or fail in using analogies and how for pre-hint solutions is evidence against the the factors limiting successful performance possibility that the result simply resulted from change with age. more extensive prompting of subjects in the analog conditions than those in the control For 11-year-olds,the factor limiting per- condition. The frequencies involved in the formanceon our simple problem seems to be one-analog and two-analog conditions were the same as for adults solving more complex too small to yield statistically significant dif- problems (Gick & Holyoak, 1980, 1983). Like ferences between them. adults, our subjects frequently failed to notice that two situations might be analogous. Once Although the story analogs were clearly the analogy was pointed out, the 11-year-old effective in eliciting the rolled paper solution, subjects were uniformlyable to carryout the sub- performancewas less than perfect. The necessary mapping much as adults do. jects who failed to produce the critical solution did so despite promptingto use the story The situationis not so simple with young- and to "do the same thing as Snoopy/Miss er children. The 4-6-year-olds did demon- Piggy." One child responded to the sugges- strateconsiderable ability in analogical prob- tion, "Could the story help?" by retrieving lem solving. However, their ability is more two pictures that had been used to illustrate fragile, varies more from child to child, and is the story and using them to push the balls limited by differentfactors. The results of Ex- around. Another child repeated that Miss periment 1 suggest that preschoolersare able Piggy rolled up the carpetto make a tube, but to solve a problem by analogy if the mapping denied that he could do anything like that. between the relations involved in the corre-

TABLE 4 NUMBEROF SUBJECTSPRODUCING ROLLED PAPER SOLUTION, EXPERIMENT 3 Condition Pre-hint Post-hint Total

Control (N = 12) ...... 0 One analog (N = 6) ...... 1 2 3 Two analogs (N = 6) ...... 3 1 4 NOTE.-Hints to use stories were only given in the story conditions, not in control condition.

This content downloaded by the authorized user from 192.168.82.217 on Fri, 30 Nov 2012 13:48:38 PM All use subject to JSTOR Terms and Conditions 2052 Child Development sponding solutions is relatively simple and mentioning the important elements. How- the corresponding instruments are perceptu- ever, some rejected the idea that the story ally and functionally similar (the magic staff could be related to the problem. Others made condition). Experiment 2 demonstrated that a partial mapping (from jewels to balls, for ex- such similarity of instruments is not a suffi- ample), but were unable to progress further. cient condition for success; rather, young chil- Such failures might be based on memory limi- dren are extremely sensitive to the com- tations that prevented children from simulta- pleteness of the overall mapping between the neously attending to and coordinating the base and target analogs. The difficulties young components of the analogs. Alternatively, the children encounter in using analogies are differences between the contexts of the story- therefore not attributable to their use of a sim- reading task and the ball-transfer game may ple strategy of using an object with salient have made the mapping seem implausible. similarities to the instrument depicted in the With age the limitations on successful prior story. analogical problem solving seem to shift from Experiment 3 demonstrated that a high the mapping processes to the decision pro- degree of perceptual and functional similarity cesses involved in initiating an attempt at is not a necessary condition for analogical mapping. This represents a change from de- transfer, even for children as young as 4 years velopment of "tactical" context-dependent old. When the story analogs mapped well onto skills (e.g., the ability to perform a mapping) to the target problem, these young subjects were development of "strategic" skills related to often able to generate the rolled paper solu- the circumstances for appropriate application. tion. This solution requires a relatively com- Similar shifts from learning local skills to plex mapping involving the transformation of learning appropriate contexts of use are found an object (paper) that has relatively little per- in many other aspects of cognitive develop- ceptual or semantic similarity to the in- ment, such as number skills (Gelman & Gal- struments used in the base analog (either a listel, 1978) and communication skills (Shatz, blanket or a carpet). Taken together, the 1978). demonstrate that children as experiments The use of somewhat open-ended tasks as 4 old can solve a young years problem by and interview procedures provides a sensitive to a dissimilar analogy superficially problem method for discovering children's abilities. and that a of and func- high degree perceptual However, when using a procedure responsive tional of the instru- similarity corresponding to a complex set of the child's activities rather ments is neither a nor a sufficient necessary than a simple criterion, the effects of variation condition for success it well be (although may in procedure are hard to assess. One concern helpful). is whether experimenter bias might have pref- The performance of the young children, erentially guided children to the "desired" so- unlike the 11-year-old subjects, was highly lution, via unintentional cues. The magnitude variable. Some 4-year-olds spontaneously of any such effect cannot be assessed from our noticed and elaborated the set of mappings in data, but one finding argues against its impor- the most difficult problem. At the other ex- tance. In Experiment 2, more solutions were treme was the child who responded to re- attempted in the two altered conditions than peated prompts to "see if the story could in the original conditions, even though more help" by fetching the cards that had been analogous solutions were produced in the lat- used to illustrate the story and using them to ter condition. The greater number of solutions push the balls. There are many possible elicited in the altered conditions might have sources for such variability in performance. reflected a bias of the experimenter to keep Children differ in their familiarity with meet- trying to evoke solutions when the target solu- ing the task demands of arbitrary adult-set tion was not achieved, but argues against any goals. They differ in their experience with the simple account of experimenter attention story characters used in the base analogs and evoking the "desired" response. with the object-oriented "engineering" play Our results indicate that under optimal required by the transfer problem. More re- circumstances children as young as 4 years old search is required to determine which of the can make substantial use of analogies to solve various possible factors are most critical. problems. Analogical problem solving may in Although young children did not always fact provide a basic mechanism for cognitive notice the analogy spontaneously, this did not development. Analogy use allows the goal- seem to be the component that most severely directed transfer of information from a domain restricted their performance. When prompted that is well understood to a novel domain that to use the story, many children could retell it, is not yet understood. Furthermore, there is

This content downloaded by the authorized user from 192.168.82.217 on Fri, 30 Nov 2012 13:48:38 PM All use subject to JSTOR Terms and Conditions Holyoak, Junn, and Billman 2053 evidence that analogical mapping between it to roll itself up into a long hollow tube. Next the two concrete problems fosters the construc- genie commandedhis flying carpetto place one end tion of a more abstract knowledge structure at his old home and the other end at his new home that describes the commonalities between the so thatit formeda sortof hollow bridge between the two bottles. the took one two domains & This Then, genie very carefully (Gick Holyoak, 1983). from inside his old home and placed it into new structure subse- jewel knowledge facilitates the opening of his carpet.At once, the jewel began quent transfer of knowledge to additional tumblingand rollingthrough the carpettube until it novel domains. The overall process of detect- reached his new home and plopped safely inside. ing analogies, finding mappings, and con- The genie grinnedhappily and began rolling all his structing new knowledge structures would jewels through the carpet into his new home. In yield "skill hierarchies" similar to those pos- fact, I'm sure you can still find him sitting in his tulated in Fischer's (1980) theory of cognitive new, bigger and better bottle with all his jewels and even development. Our results generally support smiling contentedly today! the that transfer is a possibility analogical po- Two Additional Versions of the "Staff" tential mechanism for developmental change Story Used in Experiment 2 for preschoolers. The results have important Extra-characterversion.-Once upon a time implications for educational practice, suggest- there lived a magical genie. He was a very old, ing that children are ready to benefit poten- wise, and rich genie indeed. One day while he was tially from the use of analogy as an instruc- polishing his home, which was actuallya bottle, an tional device by the time they enter school. old friend came up. The genie told his friend, "I'm a and better home to live in. However, teachers need to be aware of the going to look for bigger kinds of and difficulties that Will you help me look?" So they began searching noticing mapping far and wide for another bottle. the children are to en- Finally genie young especially likely found the perfect home. It was larger,prettier, and counter. not too far away from his old bottle. The genie was very excited and wanted to begin moving his be- Appendix longings right away. But now the genie had a problem. He had a great many beautiful and very pre- Story Analogs cious jewels in his old home. He had to somehow all the from his old bottle to the new Two to the Ball Problem get jewels Story Analogs bottle without droppingor losing a single jewel. Used in Experiment 1 Beginning-both stories.-Once upon a time After thinking a bit, the genie came up with a there lived a magical genie. He was a very old, wonderful idea. He began searching for his magic wise, and rich genie indeed. One day while he was staff, or wand. He then commanded his staff to polishing his home, which was actuallya bottle, he stretch itself from his old home to his new home. decided he would like to find an even bigger and Next, the genie tugged and pulled on his magical better home to live in. So he began searching far staff until at last he pulled the new bottle right up and wide for another bottle. Finally he found the next to his old bottle. At once, the genie began perfect home. It was larger,prettier, and not too far gatheringhis jewels together in his old home and away from his old bottle. The genie was very simply dropped them carefully into his new home excited and began moving his belongings right right next to him. When all his jewels were safely away. But now the genie had a problem. He had a tucked away in his new home, the genie settled in in greatmany beautiful and very preciousjewels in his happily. He invited his friend to come and ad- old home. He had to somehow get all the jewels mire his new home. His friend came in and said, from his old bottle to the new bottle without "Whata good house for you!" I'm sure you can still droppingor losing a single jewel. After thinking a find the genie sitting in his new bigger and better bit, the genie came up with a wonderful idea. bottle with all his jewels and smiling contentedly even today! Continuation-magic staff story.-He began searching for his magic staff, or wand. He then Altered-goal version.-Once upon a time commanded his staff to stretch itself from his old there lived a magical genie. He was a very old, home to his new home. Next, the genie tugged and wise, and rich genie indeed. One day while he was pulled on his magicalstaff until at last he pulled the polishing his home, which was actuallya bottle, an new bottle right up next to his old bottle. At once, old friend came up. The genie and his friend had how the genie began gatheringhis jewels togetherin his lived together long ago. They talked about old home and simply dropped them carefully into much fun it had been to play and do magic together. his new home rightnext to him. When all his jewels The genie's friend said, "I'm looking for a new were safely tucked away in his new home, the genie home right now." The genie said, "Let's find a bot- settled in happily. In fact, I'm sure you can still find tle big enough for both of us. Then we can live him sitting in his new, bigger, and better bottle togetherand have fun again."They began searching with all his jewels and smiling contentedly even farand wide for a bigger bottle. They searchedand today! they searched.Finally they found the perfecthome, a bottle that was big enough for both of them. The Continuation-magic carpet story.-He genie was very excited. He wanted to move all his searchedfor his magic carpet.Then he commanded belongings right away so he and his friend could

This content downloaded by the authorized user from 192.168.82.217 on Fri, 30 Nov 2012 13:48:38 PM All use subject to JSTOR Terms and Conditions 2054 Child Development settle in. But the bottle was very far away and the had so many jewels-how could she get them all genie had many beautifuljewels to move. It would over to the safe quickly and safely? be a lot easier forthe to move if his new home genie Miss had a idea. She was closer to his old one. Now the had a Suddenly Piggy great genie prob- rolled her off the floor and "lem.How could he get his new bottle up close to his up carpet picked it up. old bottle? The carpetjust reached from her jewel box to the safe. Then Miss Piggy quickly rolled her jewels After thinking a bit the genie came up with a throughthe rolled carpetand into the safe. She was wonderful idea. He began searching for his magic finished in a jiffy, before Fozzy Bear and Gonzo staff, or wand. He then commanded his staff to came back. The jewels were safe, and Miss Piggy stretchitself fromhis old home to their new home. was very happy. Next, the genie tugged and pulled on his magical staff until at last he the new bottle pulled right up References next to his old bottle. Then the genie was happy.He could move in no time at all. He gathered up his Duncker, K. On problem solving. Psychological in his old home and them jewels dropped carefully Monographs,1945, 58(5, Whole No. 270). into their new home right next to him. Fischer, K. W. A theory of cognitive development: Then the genie said to his friend,"What a won- The control and constructionof hierarchiesof derful home! Now we can play and do magic to- skills. Psychological Review, 1980, 87, 477- gether every day." The genie's friend just smiled 531. and smiled. I'm sure can still find the two of you Garvey, C. Play. Cambridge,Mass.: HarvardUni- them sitting in their bigger bottle playingand doing Press, 1980. magic even today! versity Gelman, R., & Gallistel, C. R. The child's under- number. Cambridge, Mass.: Har- Two Used in 3 standing of Story Analogs Experiment vard University Press, 1978. Woodstock's eggs.-Woodstock had built a D. Children's on a nest on of She had her Gentner, performance spatial top Snoopy'sdoghouse. put task. Child eggs in it and was waiting for them to hatch and the analogies Development, 1977, 48, baby birds to come out. But Snoopy was unhappy 1034-1039. about all this. The nest was in the way when he Gick, M. L., & Holyoak, K. J. Analogicalproblem tried to lie down. And Snoopy was afraidthat when solving. Cognitive Psychology, 1980, 12, 306- the baby birds arrived,they would make so much 355. noise with their chirpingthat he wouldn'tbe able to Gick, M. L., & Holyoak,K. J. Schemainduction and sleep at all! analogical transfer. Cognitive Psychology, Woodstockdidn't want to get Snoopy upset, 1983, 15, 1-38. and so she agreed that the eggs would have to be Hesse, M. B. Models and analogies in science. moved. 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