How Do Children Solve Aesop's Fable?

12 Pages·2012·0.77 MB·English

How Do Children Solve Aesop’s Fable?
Lucy G. Cheke, Elsa Loissel, Nicola S. Clayton*
DepartmentofExperimentalPsychology,UniversityofCambridge,Cambridge,UnitedKingdom
Abstract
Studies on members of the crow family using the ‘‘Aesop’s Fable’’ paradigm have revealed remarkable abilities in these
birds, and suggested a mechanism by which associative learning and folk physics may interact when learning new
problems.Inthepresentstudy,childrenbetween4and10yearsofageweretestedonthesametasksasthebirds.Overall
theperformanceofthechildrenbetween5–7-yearswassimilartothatofthebirds,whilechildrenfrom8-yearswereableto
succeedinalltasksfromthefirsttrial.Howeverthepatternofperformanceacrosstaskssuggestedthatdifferentlearning
mechanisms might be being employed by children than by adult birds. Specifically, it is possible that in children, unlike
corvids,performance is notaffectedbycounter-intuitive mechanismcues.
Citation:ChekeLG,LoisselE,ClaytonNS(2012)HowDoChildrenSolveAesop’sFable?PLoSONE7(7):e40574.doi:10.1371/journal.pone.0040574
Editor:ThomasBurne,UniversityofQueensland,Australia
ReceivedMarch7,2012;AcceptedJune8,2012;PublishedJuly25,2012
Copyright: (cid:2) 2012 Cheke et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits
unrestricteduse,distribution,andreproductioninanymedium,providedtheoriginalauthorandsourcearecredited.
Funding:Theauthorshavenosupportorfundingtoreport.
CompetingInterests:Theauthorshavedeclaredthatnocompetinginterestsexist.
*E-mail:[email protected]
Introduction To investigate whether the birds’ performance could be
explained by instrumental learning, Cheke and colleagues
Recent studies with members of the crow family [1,2,3] have conducted a series of control tests that showed that the birds
investigatedthecognitionunderlyingoneofAesop’smostfamiliar were able to learn in a mechanised version of the task in which
fables. In thistale, a thirstycrow comesacross a half-filled jug of stone-dropping resulted in the approach of food. The jays were,
water.Unable toreachthewater todrink,thecrowdropsstones however,unabletolearnwhentherewardprobabilitiesremained
intothepitcheruntilthelevelofthewaterraisesenoughforhimto the same, but the reward did not move. This contrast was
drink.BirdandEmery[1]foundthatRookswerenotonlycapable interpreted to suggest that it was not the causal mechanism of
ofthis,butwouldchoosethemostefficienttool(largeratherthan the Aesop’s Fable task that the birds were able to learn, but the
smallstones)andpreferentiallydropstonesintowaterratherthan relationship between stone-insertions and movement. In a final
sawdust. Subsequent studies with Eurasian Jays [2] sought to control,Chekeandcolleaguespresentedthebirdswitha‘‘U-tube’’
investigatewhetheranotherspeciesofcorvidcouldalsosolvethis apparatus in which insertion of a stone into the correct tube
taskand ifso,whatthese birdsunderstand. apparently caused the level of water in the adjacent tube to rise.
Afterlearningtodropstonesintoatubetoreceiveareward,the This apparatus consisted of a U-tube and a single tube, whose
Jays were presented with a choice between a tube half-filled with bases were hidden beneath an opaque base. Because the U-tube
sawdustandatubehalf-filledwithwater,bothcontaininganout- contained a single body of water, a stone inserted into one arm
of-reach food item. Having had no experience of water in this wouldraisethelevelofwaterinbotharms,whileastoneinserted
form, or discovering the consequences of dropping stones into intothesingletubewouldraisethelevelofonlythattube.Thebait
water,thischoicecouldbeusedtoassessthebirds’abilitytolearn wasplacedwithinonearmoftheU-tube.Thistaskwasdesigned
thenecessaryconditionsforsuccess.Twooutofthefourbirdsthat to offer the same movement cues as the original task (i.e. stone
weretestedlearnedtodropsignificantlymorestonesintothewater insertion into one tube caused the approach of food, stone
thanintothesawdustoverthecourseof15trials(theotherswere insertion into the other tube did not) but with confusing or
uninterested in the task). These two birds also quickly learned to counterintuitivemechanismcues.Chekeandcolleaguesfoundthat
drop significantly more sinking than x floating items into water. thebirdswereunabletolearnthistaskevenwhengiventwiceas
Suchlearning,whileimpressive,cannotbesaidtodifferinnature manytrialsasontheoriginaltask.Theythussuggestedthatwhile
to that characteristic of instrumental learning, namely that instrumental learning involving movement cues was both neces-
performance of a particular action (in this case dropping a sary and sufficient for learning in the Aesop’s fable task, the
sinkable item into water) leads to the increased probability of a presence of cues suggesting a ‘‘possible’’ or ‘‘impossible’’ causal
reward.Forexample,inthesawdustversuswatertask,droppinga mechanism wereable toenhanceor retardlearning respectively.
stoneintowaterwouldleadtothefoodrewardbeingreachableon The Aesop’s Fable paradigm provides a valuable tool with
around a fifth of occasions, while dropping a stone into sawdust whichtoinvestigatetheinteractionbetweeninstrumentallearning
wouldneverresultintherewardbeingaccessible.Thusthebirds (theabilitytolearntoperformanactionifthatactionisrewarded),
may simply have learned which tube was more likely to be causalreasoning(understandingthatoneeventcausesanother)and
rewarded.Droppingastoneintowaterwouldalsoleadtothefood mechanistic inference (understanding why one event causes
moving slightly closer, which may also be rewarding, while another,i.e.theabilitytoexplainthecausalrelationshipbetween
dropping a stone into sawdust leads to no movement of the two things interms of theunderlying mechanism). An advantage
reward. of this particular paradigm is that the mechanism is natural (i.e.
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HowDoChildrenSolveAesop’sFable?
notman-made)andperceivable(inthatitdoesn’tinvolveinvisible items in particular locations and an approaching reward. This is
forces such as electricity or magnetism), and the action (stone based on literature suggesting that children of this age can learn
dropping) is physically simple. This means that the ability to andactoncause-effectrelationships[5,6,7,8,9,12].Thesechildren
understandtheaffordancesofthetaskcanbeeasilyseparatedfrom will not, however, have a concept of the causal mechanism and
exposuretotechnologyandfinemotorcapacityandthusmakesit consequently they would perform equally well on all three tasks.
appropriate for investigating physical cognition in both young We predicted that older children (7-/8-/9-year-olds) would have
children andanimals. formed a (potentially simplified) concept of the mechanism
Much research on causal reasoning in children has employed underlying displacement (as predicted by previous studies on
paradigms in which the to-be-inferred mechanism is explicitly causal mechanism [13,16,17,18]). These children should have a
explainedandprimed[4]orisopaque[5,6,7,8,9].Assuchitdoes pre-formed idea about what is and is not possible given this
not allow investigation into the interaction between causal and mechanism. Consequently, these children should perform com-
mechanistic reasoning. Such studies reveal that children of 3– parably on the first two tasks, but perform badly on the U-tube
4 yearsareabletoinfercausationfromco-variationandcontiguity since this task presents an apparently impossible causal relation-
(andmanyotherfactorssuchastemporalorderandreasoningby ship.Finally,theoldestchildren(10-years)maybeabletoflexibly
exclusion).Eveninfantsarecapableofformingexpectationsfrom adapttheirinferredmechanismandpotentiallyinferthepresence
complex statistical regularities [10,11,12], although they are of the U-tube so as to allow them to marry the perceptual
unable to act upon them. However, these studies cannot assess contingency with their understanding of mechanism. These
the extent to which children are making inferences about the children were thus expected to perform with a very high success
mechanism. Our aim is to investigate the interaction between rateonallthreetasks.Finally,weconjecturedthatperformanceon
causal understanding based on instrumental learning (that is, tasks 1 and 2 should be predicted by performance on the
based on contingency and contiguity) and understanding of conservation of volumetask [14,15,16].
mechanisminthelearningofphysicalproblems.Further,wewish
to explore whether cognitive systems as structurally divergent as Methods
those of corvids and humans can be said to be functionally
Subjects
convergent in terms of not only their performance on physical
cognition tasks, but also in the manner in which these tasks are Children aged 4–10 (N=80: 4-year-olds: n=20; 5-year-olds:
learned. n=16;6-year-olds:n=4;7-year-olds:n=14;8-year-olds:n=11;
9-year-olds: n=8; 10-year-olds: n=5) were recruited from a
Ithasbeenarguedthatcausalreasoningbasedonstatisticaland
CambridgeshirePrimarySchool.Thesampleconsistedof40boys
perception-based analysis may develop separately to mechanism-
and 42 girls. Two subjects (both boys: one 4-year-old and one 5-
based analysis. These two systems interact to allow children to
year-old) were removed from the analysis because they were
flexiblyadapttheircausalmodelsoftheworldbyneitherbeingled
unwilling totake part intheexperiment.
toooftendownblindalleysbycoincidentalcontingency,orbeing
prevented from identifying causation in situations involving
unfamiliar mechanisms [13]. Thus one might expect children to Ethics Statement
passthroughseveralstagesofunderstandingastheydevelop;from This study was approved by the University of Cambridge
being unabletolearnabout therelationship betweenactionsand ResearchEthicsCommittee.Informedwrittenconsentwasgained
consequences, through having a concept of causality based on fromparents before anychildtook part.
perceptual andstatistical regularities only,tohaving a conceptof
mechanismsthatcanbeadaptedandfinessedbyperceivedcausal Procedure
relationships(forexample,understandingthatunsupportedthings Subjectsweretestedindividuallyinaroomintheschool.Each
usuallyfallbutbeingabletolearnthatthisisnottrueifthosethings subjectwaspresentedwithaseriesoftasksthatwereequivalentto
have wings). those used by Cheke and colleague’s recent experiments with
Inthecurrentexperiment,childrenbetweentheagesof4-and Eurasian Jays[2].
10-yearsweretrainedtodropstonesintotubesinasimilarmanner
as the Eurasian Jays [2]. They were presented with three of the Training
same tasks as the birds: Water versus Sawdust [1,2,3], Sinking The children were presented with the ‘‘platform’’ apparatus
versusFloating[2,3],andtheU-tube[2].Inalltasksthechildren originally used by Bird and Emery [19] and subsequently by
were given five 2-minute trials in which to attempt to retrieve a Cheke and colleagues [2] consisting of a Perspex box in which a
floatingtokenthatcouldbeexchangedforasticker.Finally,these platform is held in place by a magnet. When a heavy object is
results were compared to performance on the classic Piagetian droppeddownatubeinthetopofthebox,theplatformisreleased
conservation of volume task, which has been classically used to andanythingrestingonitisreleasedfromthebox[seefig1].The
differentiate between pre-operational and concrete operational children were shown a small red token and informed that these
thought in children. The former is associated with ‘‘phenomen- could beexchanged forstickers.Thetoken wasthenplaced onto
istic’’reasoning(inferringcausationfromco-occurrence)whilethe theplatformandthechildrenwereshownabowlofbluestones.If
latter is associated with reasoning about seen or inferred thechildrendidnotspontaneouslydropthestonedownthetube,
mechanisms. This transition is thought to occur around the age theywereencouragedtodosobytheexperimenterdemonstrating
of 7-years[14,15,16]. this action to them. Training was completed when the children
We hypothesised that the children would pass through several had dropped a stone into the apparatus, retrieved the token and
stages of performance during development (see Table 1). Specif- swapped itfor asticker twice.
ically, we predicted that many 4-year-olds would be unable to The following experiments were conducted as near as possible
learn any of the tasks and would perform at chance (due to the to the way that the corvids were tested so as to maintain the
complex cause-effect relationships involved), whereas the slightly possibility for direct comparisons between the studies. For this
older children (older 4-year-olds, 5-year-olds and 6-year-olds) reason, tasks were presented in a specific order which was not
wouldbeabletolearntheassociationbetweendroppingparticular counterbalanced between subjects. In all tasks, the children were
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HowDoChildrenSolveAesop’sFable?
Table1. Predictedperformance ofchildren ofdifferentage groups.
Typeofrulethatcan
Age LearningAbility belearned Predictedperformance
(aspredictedby Task1Water/ Task2Sinking/ Task3U-
literature) Sawdust Floating tube
Abletoadjust 8months Babiesasyoungas8 Normally,whenIseeX, 7 7 7
expectationsfrom –4years monthsaresurprisedwhen thenIseeY.
statisticalregularities, statisticalregularitiesare
butunabletoacton violated,butarenot
thisinformation capableofactingonthis
information.[10,11,12]
Abletouse 4–6 4Year-Oldsabletoinfer IfIdoX,thenYhappens. 3 3 3
covariationtoinfer causalrelationshipsusing
causalrelationships CovariationandContiguity
andactuponthem.
[5,6,7,8,9,12](butexamples
usedwereeasiercause-
effectrelationsthatthose
presentedhere)
Abletoinfer 7–9 7–9Year-Oldsableto IfIdoX,thenYhappens, 3 3 7
underlying comeupwithintuitive because…
mechanism novelssolutionsand
reasonintermsof
mechanisms.[14,16,17,18]
Abletoflexibly 10 NormallyifIdoX,thenY 3 3 3
understand happens,butnotwhen
underlyingmechanism Zbecause
doi:10.1371/journal.pone.0040574.t001
informed that if they could retrieve the/one of the tokens they paintedtodisguisetheirmaterial.Thechildrenweregiven5trials.
could swap it for a sticker. To prevent them from reaching their Iftheydidnotspontaneouslyinsertanyitemstheywereprompted
entire arm into the tube/tubes, the children were also told that with‘‘Youareallowedtotryanythingyoulike’’or‘‘whynotjust
they were not allowed to put their thumb in the tube. To ensure trythings’’or‘‘trytogetthe/oneofthetokens’’.Approximately7
that the objects used were ‘‘novel’’ and that previous knowledge items were needed to retrieve the token, although this varied
about the specific properties could not affect performance and depending on children’s token-retrieval technique. Trials were
reduce the need for task-specific learning, all objects used were ended after two minutes or if the children inserted all available
Figure1.Schematicoftheapparatusesused.1a.TrainingApparatus.Whenastoneisdroppedintothetube,theplatformdropsandthe
tokenisreleased.1b.Tokens.Whenatokenisretrieved,itcanbeswappedforastickerofthechild’schoice.1c.Task1:WaterversusSawdust.Whena
marbleisdroppedintothewater,thelevelofthefloatingtokenrises.Whenastoneisdroppedintothesawdust,thelevelofthetokendoesnot
change.1d.Task2:SinkingversusFloating.Whenamarbleisdroppedintothewater,itsinksandthelevelofthefloatingtokenrises.Whenacork
ballisdroppedintothewateritfloatsandthelevelofthetokendoesnotchange.1e.Task3:U-tube.WhenastoneisdroppedintotheU-tube,the
levelofthefloatingtokenrises.Whenastoneisdroppedintotheseparatetube,thelevelofthetokendoesnotchange.
doi:10.1371/journal.pone.0040574.g001
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HowDoChildrenSolveAesop’sFable?
items. If children had an error-free performance, including methods to prevent possible confounds resulting from repeated
successfully retrieving the token, on three consecutive trials they questions [20].
were deemed to fully understand the task and were not tested
further (so as to prevent them from losing interest). Number and Analysis
location of item insertions were recorded, as well as success in Becausethemajorityofthedatatobeanalysedisintheformof
retrieving the token. Number of item insertions was used as the proportions (number of correct actions out of total actions)
dependant variable, token retrieval is reported in Supporting statistical analysis was mostly nonparametric. Performance was
Information S1. comparedtochanceusingone-sampleWilcoxonsignedranktests.
The average age of different groups was compared using
Task 1: Water versus Sawdust independent samples t-tests. Performance was correlated with
The children were presented with two Perspex tubes (inner other metrics using Kendall’s Tau. Performance across tasks was
diameter 5 cm, outer diameter 6 cm, height 18cm), one that modelledusingGeneralizedEstimatingEquationswithabinomial
contained water and the other containing sawdust. A token was logistic response type and generalized Chi statistic. Post-hoc tests
placed into both tubes such that it rested on the surface of the were conducted usingMann-WhitneyU andWilcoxontestswith
water/sawdust and was approximately 2cm from the children’s Sˇida´kalpha correction formultiple comparisons.
reach. Between the tubes was placed a bowl containing ten red
marblesof2 cmdiameter.Betweentrials,thepositionsofthetwo Results
tubes were exchanged pseudo-randomly.
Task 1: Water versus Sawdust
Task 2: Sinking versus Floating All80childrentookpartinthistask.Eightchildrencompleted3
consecutiveerror-freetrials(inwhichtheyonlyinsertedstonesinto
The procedure was identical to Task 1 except that a single
thetubecontainingwater).Fourofthesechildren(one7-year-old,
water-filledtube(innerdiameter5cm,outerdiameter6cm,height
two8-year-oldsandoneone10-year-old:meanage8.48)showed
18cm) was presented beside a bowl containing 10 yellow cork
mistake-free performance from the first trial. A further four
balls (1.5g) and 10 yellow marbles (15g). These were visually
children (one 5-year-old, one 7-year-old, one 8-year-old and one
indistinguishable in size (2cm diameter) and colour (yellow), but
10-yearold:meanage8.41)showedperfectperformancefromthe
differed indensity andweight.
secondtrialonwards.Whilethesechildrenwerenottestedforthe
subsequent trials, their performance was extrapolated for the
Task 3: U-tube
purposes of analysis.
The children were presented with an apparatus consisting of
Overall,performanceimprovedgraduallywithageandreached
oneU-shapedtubewithonewidearm(3cminnerdiameter)and
a plateau at 8years (Fig. 2a). Children aged 4–7 years gradually
one narrow arm (1.3cm inner diameter), and a single wide tube
learnedover5trialswhichwasthecorrecttubeinwhichtoinsert
(3 cm inner diameter). These were embedded in an opaque base
marbles. The proportion of stones inserted into the correct tube
such that the join of the U-tube was hidden and the apparatus
wascomparedtoachancelevelof0.5foreachagegroupforeach
appearedtoconsistoftwoidenticalwidetubeswithanarrowtube
trialusingone-sampleWilcoxonsignedranktests(seefigure2for
between them (as shown in Fig. 1). Both tubes were filled with
statistics). Due to sample size constraints, performance against
watersuchthatthelevelwasequalbetweenthemandatleast1cm
chancewas not calculated forthe6-year-olds and the9/10-year-
from the aperture of the narrow arm of the U-tube. The base of
old groups were combined. 4-year-olds performed better than
each wide tubewas markedwith a different coloured shape.
chance on their 5th trial only. 5-year-olds performed better than
Thechildrenwerepresentedwithtenbluestones.Thesecould
chance on their 4th and 5th trials. 7-year-olds performed better
be inserted into the wide arm of the U-tube or the single wide
thanchanceontheir3rdand5thtrials.Bycontrast,8-and9/10-
tube,butweretoolargetofitintothenarrowarmoftheU-tube.A
year-oldsallperformedbetterthanchanceonthe1sttrialandall
tokenwasplacedintothenarrowtube(i.e.thenarrowarmofthe
subsequent trials.
U-tube).Afterthefinaltrial,thechildrenwereasked‘‘howdoyou
Age correlated positively with the proportion of marbles
think this works?’’ Children’s answers were coded into four
inserted into the correct tube on all trials (Kendall’s tau: trial 1:
categories:‘‘NoExplanation’’consistedofsilence,‘‘Idon’tknow’’
R(61)=0.302, p,0.005; trial 2: R(71)=0.204, p,0.05; trial 3:
orirrelevantresponses,‘‘DescriptiveExplanation’’consistedofan
R(77)=0.260, p,0.005; trial 4: R(78)=0.182, p,0.05; trial 5:
accurate description of the relationship between the children’s
R(76)=0.244,p,0.01).Therewasasignificanteffectofage-group
actionsandthemovementofthetoken,‘‘InferenceExplanation’’
on proportion of marbles dropped into water in the first trial
consistedofaninferenceaboutahiddenconnectionbetweentwo
(Kruskal Wallis test: p,0.05) but not in any subsequent trials.
ofthetubes,and‘‘MechanisticExplanation’’consistedofanswers
Post-hocpair-wisecomparisons(Mann-WhitneyUtestwithSˇida´k
mentioning that the water was displaced by the dropping of the
correction) indicated no significant differences between any
stone.
specific age-groups. Taken together, these results suggest that by
the age of 8 years, children know that dropping a marble into
Piagetian Conservation Task
waterwillcausetheleveltorisewhilethoseagedbetween4-and
Torelatetheresultsofthisexperimenttoclassictasks,children
7-yearsare abletolearn thisoverthecourseof 5 trials.
werealsotestedonthePiagetianconservationofvolumetask(e.g.
[15]). Children were presented with a tall thin container and a
Task 2: Sinking versus Floating
shortwidecontainerandwitnessedwaterbeingpouredfromone
All80childrentookpartinthistask.Thirteenchildren(one5-
totheother.Theywerethenaskedwhethertheamountofwater
year-old,two7-year-olds,seven8-year-oldsandthree9-year-olds,
was now the same, more or less than it had been. The order in
meanage8.23)solvedthetaskwithoutmistakes(i.e.insertedonly
whichtheseoptionswerepresentedwascounterbalancedbetween
sinkableitemsintothetube)on3consecutivetrials,althoughnone
children. This methodology was chosen over more common
of them did so from the first trial. While these children were not
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HowDoChildrenSolveAesop’sFable?
Figure2.PerformanceofChildrenonTask1.2a.showsthemedianproportionofchildrenofdifferentagegroupsacrossthefivetrialsofTask1.
Errorbarsrepresent95%confidenceintervals.2bshowstheindividualmarbleinsertionsof3childrenchosenatrandomfromeachagecohort.Each
column represents the order in which items were inserted within a single trial. Grey columns indicate trials not performed due to error-free
performanceinthethreeprevioustrials.Starsrepresenttrialsinwhichthatagegroupperformedabovechanceaccordingtoone-samplewilcoxen(4-
year-olds:(1st:W=1,n=9,p.0.05;2nd:W=36,n=12,p.0.1;3rd:W=38,n=12,p.0.1;4th:W=29,n=10,p.0.1;5th:W=71,n=13,p,0.05;5-year-
olds:1st:W=12,n=8,p=.0.05,2nd:W=7,n=10,p.0.5,3rd:W=29,n=12,p.0.1,4th:W=63,n=14,p=0.05;5th:W=82,n=15,p,0.05;7-year-
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HowDoChildrenSolveAesop’sFable?
olds:1st:W=28,n=9,p.0.05;2nd:W=11,n=9,p.0.05,3rd:W=41,n=9,p,0.02;4th:W=59,n=14,p.0.05;5th:W=100,n=14,p,0.001;8-year-
olds:1st:W=52,n=11,p,0.05;2nd:W=45,n=11,p,0.05;3rd:W=66,n=11,p,0.005;4th:W=52,n=11,p,0.05;5th:W=66,n=11,p,0.005;9/
10-year-olds:1st:W=75,n=12,p,0.005;2nd:W=45,n=11,p,0.002;3rd:W=78,n=12,p,0.005;4th:W=82,n=13,p,0.005;5th:W=78,n=12,
p,0.005).
doi:10.1371/journal.pone.0040574.g002
tested for the subsequent trials, their performance was extrapo- not calculated for the 6-year-olds and the 9/10 year-old groups
lated forthepurposes of analysis. werecombined.Chancewasalsonotcalculatedforthe4-year-olds
As in the first task, performance improved gradually with age, andthefirsttrialofthe5-year-oldsbecausethemajorityofscores
although it seemed to drop in the oldest children (Fig. 3a). The were exactly 0.5. Wilcoxon analyses discount ‘‘matching’’ pairs
proportion of stones inserted into the correct tube was compared fromthedatasetandthusthesamplesizewasreducedtounder5.
toachancelevelof0.5foreachagegroupforeachtrialusingone- The5-year-oldsdidnotperformabovechanceinanytrial,the7-
sample Wilcoxon signed rank tests (exact statistics reported in year-oldsperformedabovechanceinalltrialsexceptthe2ndand
figure 3). Due to sample size constraints, performance against 4th,the8-yearoldsperformedabovechanceinallexceptthe2nd
chance was not calculated for the 6-year-olds and the 9/10 year trialandthe9-/10-year-oldsperformedabovechanceinalltrials.
old groups were combined. 4-year-olds did not perform above Agecorrelated withperformanceonlyinthe4thand5thtrials
chance in any trial, 5-year-olds performed above chance in the (Kendall’s Tau: Trial 4: R(63)=0.291, p,0.005; trial 5:
2ndand5thtrials,7-year-oldsperformedabovechanceinthe2nd R(62)=0.266, p,0.01). There was an effect of age on perfor-
trial and all subsequent trials and 8- and 9-/10-year-olds mance in only the 4th trial (p,0.05). Post-hoc pairwise
performed above chanceinall trials. comparisons revealed a significant difference between 4- and 8-
Age correlated significantly with performance in all trials year-olds(Mann-WhitneyUtestwithSˇida´kcorrection:p,0.001)
(Kendall’s Tau: 1st: R(78)=0.422, p,0.001; 2nd: R(77)=0.458, andbetween4-and9-year-olds(Mann-WhitneyUtestwithSˇida´k
p,0.001; 3rd: R(78)=0.344, p,0.001; 4th: R(77)=0.416, correction: p,0.001)on the4th trial only.
p,0.001; 5th: R(78)=0.372, p,0.001). There was a significant In answer to the question ‘‘how do you think this works?’’, no
effectofageinalltrials(Kruskal-Wallistests:trial1:p,0.001;trial children offered ‘‘Mechanistic Explanations’’, 25 children offered
2:p,0.001;trial3:p,0.001;trial4:p,0.001;trial5:p,0.001). ‘‘Inference Explanations’’, 16 children offered a ‘‘Descriptive
Post-hoc pairwise comparisons revealed a significant difference Explanation’’ and 19 children offered no explanation at all (see
between 4- and 8-year-olds on all trials (Mann-Whitney U test Table2forexamples).Childrenwhooffereddescriptiveexplana-
with Sˇida´k correction, trial 1: p,0.001; trial 2: p,0.001; trial 3: tions were significantly older than children who offered no
p,0.001; trial 4: p,0.001; trial 5: p,0.001) between 4- and 9- explanation (independent samples t-tests t(33)=3.528, p,0.001;
year-olds on all trials (Mann-Whitney U test, Sˇida´k correction, means7.89and5.83respectively;seeFig.5).However,therewas
trial 1: p,0.003; trial 2: p,0.001; trial 3: p,0.001; trial 4: no difference in the age of children who offered an inference
p,0.001;trial5:p,0.003),between5-and8-year-oldsontrials1, explanation and those who offered a descriptive explanation
3, 4 and 5 (Mann-Whitney U test with Sˇida´k correction, trial 1: (independent samples t-tests t(37)=0.21, p.0.8; means 8.02 and
p,0.001;trial3:p,0.001;trial4:p,0.001;trial5:p,0.003)and 7.89 respectively). Obviously verbal and general cognitive
between 5- and 9-year-olds on trials 2 and 4 (Mann-Whitney U development will account for much of the difference between
test with Sˇida´k correction, trial 2: p,0.001; trial 4: p,0.001). individuals in their reports; children may be able to understand a
Taken together these results suggest a similar developmental concept,butnotverballyabletoreportit.Nonetheless,suchverbal
trajectorytothatfoundforthefirsttask,namelythatbytheageof reports areinformative as tochildren’s thoughtprocesses.
8 years, children know that dropping a sinking, rather than a Theproportionofstonesdroppedintothecorrecttube(theU-
floating, object into water will cause its level to rise. In common tube) by children who offered different types of explanation was
withthefirsttask,wealsofoundthatyoungerchildren,specifically compared to a chance level of 0.5 using one-sample Wilcoxon
thoseagedbetween5-and7-years,areabletolearnthisoverthe signed rank tests. Children who offered no explanation did not
course of 5 trials. Unlike the first task, however, the 4-year-old perform above chance in any trials (1st: W=20, n=8, p.0.05;
children appear unable to learn the sinking versus floating task 3rd:219,n=10,p.0.1;4th:W=6,n=9,p.0.05;5th:W=27,
within5 trials. n=10, p.0.5). Children who offered a descriptive explanation
performed above chance in all trials (1st: W=28, n=7, p,0.02;
Task 3: U-tube 2nd: W=45, n=9, p,0.01; 3rd: W=58, n=12, p,0.05; 4th:
Some children took part in another experiment (not reported) W=103,n=14,p,0.002;4th:W=74,n=15,p,0.05).Children
insteadoftheU-tubetask,whichiswhysamplesizewasreduced whoofferedaninferenceexplanationperformedabovechancein
to Sixty-four children for this task. Of these, four children solved all trials (1st: W=78, n=12, p,0.005; 2nd: W=77, n=14,
the task without mistakes (inserted no stones into the single tube) p,0.02; 3rd: W=231, n=21, p,0.001; 4th: W=231, n(/r)=21,
on 3 consecutive trials. One child (age 9.37) performed mistake- p,0.001;5th:W=247,n=22,p,0.0001).Therewasasignificant
freefromthefirsttrial.Threechildren(one5-year-old,one8-year- effect of level of explanation on performance in all 5 trials
old and one 10-year-old: mean age 8.2) performed mistake-free (independent samples Kruskal-Wallis Test: trial 1; p,0.001, trial
fromthesecondtrial.Whilethesechildrenwerenottestedforthe 2:p,0.05,trial 3:p,0.001,trial 4:p,0.001, trial 5:p,0.001).
subsequent trials, their performance was extrapolated for the Taken together, the data on performance on the U-tube task
purposes of analysis. suggeststhat,asinthepreviousexperiments,childrenfrom8years
Performance on this task was similar to Tasks 1 and 2. Again, wereabletolearnwithinasingletrialwhichtubetheyshoulddrop
performanceimprovedwithageandtrials(Fig 4).Theproportion stone into to cause the token to rise, even when the mechanism
ofstonesinsertedintothecorrecttubewascomparedtoachance washidden(andpotentially‘‘counter-intuitive’’).Youngerchildren
level of 0.5 for each age group for each trial using one-sample struggled with the task, but 7-year-olds could learn over 5 trials.
Wilcoxen signed ranks tests (exact statistics reported in figure 4). The children’s ability to pass this task appears to depend not on
Due to sample size constraints, performance against chance was their capacity to infer the presence of a hidden U-tube, but on
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HowDoChildrenSolveAesop’sFable?
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HowDoChildrenSolveAesop’sFable?
Figure3.PerformanceofChildrenonTask2.3a.showsthemedianperformanceofchildrenofdifferentagegroupsacrossthefivetrialsofTask
2.Errorbarsrepresent95%confidenceintervals.3bshowstheindividualitemsinsertedby3childrenchosenatrandomfromeachagecohort.Each
column represents the order in which items were inserted within a single trial. Grey columns indicate trials not performed due to error-free
performanceinthethreeprevioustrials.Starsrepresenttrialsinwhichthatagegroupperformedabovechanceaccordingtoone-samplewilcoxen(4-
year-olds:1st:W=215,n=9,p.0.05;2nd:W=23,n=6,p.0.05;3rd:W=7,n=8,p.0.05;4th:W=29,n=9,p.0.05;5th:W=14,n=9,p.0.05;5-year-
olds:1st:W=28,n=5,p.0.05;2nd:W=32,n=8,p=0.05;3rd:W=37,n=10,p.0.05;4th:W=6,n=8,p.0.05;5th:W=35,n=9,p=0.05;7-year-
olds:1st:W=17,n=8,p.0.05;2nd:W=36,n=9,p=0.05;3rd:W=49,n=10,p,0.02;4th:W=62,n=11,p,0.01;5th:W=64,n=11,p,0.005;8-year-
olds:1st:W=55,n=10,p,0.01;2nd:W=53,n=10,p,0.01;3rd:W=45,n=9,p,0.005;4th:W=55,n=10,p,0.01;5th:W=55,n=10,p,0.01.9-/10-
year-olds:1st:W=45,n=9,p,0.005;2nd:W=66,n=11,p,0.005;3rd:W=55,n=10,p,0.01;4th:W=66,n=11,p,0.005;5th:W=60,n=12,p,0.02).
doi:10.1371/journal.pone.0040574.g003
Figure4.PerformanceofChildrenonTask3.4a.showsthemedianperformanceofchildrenofdifferentagegroupsacrossthefivetrialsofTask
3.Errorbarsrepresent95%confidenceintervals.4bshowstheindividualstoneinsertionsof3childrenchosenatrandomfromeachagecohort.Each
columnrepresentstheorderinwhichitemswereinsertedwithinasingletrial.Starsrepresenttrialsinwhichthatagegroupperformedabovechance
accordingtoone-samplewilcoxen(5-year-olds:2nd:W=11,n=10,p.0.5;3rd:W=27,n=10,p.0.1;4th:W=7,n=9,p.0.05;5th:W=14,n=10,
p.0.1;7-year-olds:1st:W=45,n=9,p,0.05;2nd:W=37,n=10,p.0.05;3rd:W=56,n=11,p,0.02;4th:W=38,n=10,p.0.1;5th:W=91,n=13,
p,0.002;8-year-olds:1st:W=21,n=6,p=0.05;2nd:W=43,n=11,p.0.05;3rd:W=55,n=10,p,0.01;4th:W=62,n=11,p,0.01;5th:W=55,n=10,
p,0.01:9/10-year-olds:1st:W=36,n=9,p,0.05;2nd:W=45,n=9,p,0.005;3rd:W=76,n=12,p,0.005;4th:W=60,n=12,p,0.02;5th:W=78,
n=12,p,0.005)
doi:10.1371/journal.pone.0040574.g004
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HowDoChildrenSolveAesop’sFable?
Figure 5. Number of children in each age group that offered
eachlevelofexplanation.
doi:10.1371/journal.pone.0040574.g005
Figure6.Patternofperformanceofchildrenofeachagegroup
theirabilitytonoticeanddescribethecausalrelationshipbetween
oneachtask.ErrorBarsrepresent95%confidenceintervals.
a particular actionandtheapproach of thetoken. doi:10.1371/journal.pone.0040574.g006
Analysis across Tasks differenttasks(levelofexplanation6taskinteraction:x2(4)=15.0,
Data from all children in all three tasks was entered into a p,0.01). However, children of different ages did not perform
Generalised Estimating Equations model with a binary logistic differently on different tasks (no age 6 task interaction
response. The model included age (in years) and level of (x2(12)=13.932, p.0.3, see Fig. 6) and children did not to
explanation as between subjects factors, and trial and task as improve over trials at different rates in different tasks (no trial6
within subjects factors. The model also included the following task interaction: x2(8)=8.644, p.0.3). Given that there was an
interactions: age 6 trial, age 6 task, explanation 6 age, interaction between age and level of explanation, and between
explanation 6 trial, explanation 6 task, trial 6 task. The boththesefactorsandtrial,itwouldhavebeenidealtoinvestigate
dependant variable was proportion of correct actions (i.e. the interaction between these three factors. However, there were
marbles/stones dropped into the correct tube, or correct item not sufficient degrees of freedom tosplitthedata anyfurther.
dropped into the water tube) out of total actions performed (i.e. These effects were further explored with a series of post-hoc
total number of itemsdropped). investigations.Performancedidnotdifferbetweenthetasks.There
The model found a main effect of Age (in years) was no significant difference between performance on any of the
(x2(6)=120.752, p,0.001), task (x2(2)=14.152, p,0.001), trial tasks (Wilcoxon signed ranks tests: task 1–2: p.0.2, task 1–3:
(x2(4)=25.269,p,0.001)andlevelofexplanation(x2(2)=13.061, p,0.9,task2–3:p.0.5).Thisremainedthecaseevenifonlydata
p,0.001).Childrenof differentages werealsoshowntoimprove fromchildrenwhodidnotinferthepresenceoftheU-tubeinTask
over trials at different rates (age 6 trial interaction: 3wereincluded(FriedmanANOVA:p.0.3).Lookingatthetasks
x2(24)=93.214,p,0.001)andofferdifferentlevelsofexplanation together, performance improved significantly over trials: perfor-
(level of explanation6age interaction (x2(8)=48.136, p,0.001). mance on trial 1 differed from performance on trials 4 and 5
Children with different levels of explanation were shown to (Mann Whitney Utests: p,0.001andp,0.005respectively) and
improve over trials at different rates (explanation 6 trial performance on trial 2 also differed from performance on trial 5
interaction: x2(8)=28.669, p,0.001) and perform differently on (MannWhitney U test:p,0.005).
Table2. Examplesofanswers givento the question‘‘How doyouthinkit works?’’
TypeofExplanation AgeofChild ExplanationOffered
NoExplanation 4-Years- ‘‘GreenandPurple’’-
Childrendonotdescribeanyassociation 4-Years ‘‘Dunno’’
betweenactionandoutcome.
DescriptionExplanation 5-Years ‘‘Greenmakeswatergodown.Purplemakeswatergoup.’’
Childrendescribetherelationship,butoffer -7-Years ‘‘Onetubemakesitgohigher,theotherdoesn’t,dunnowhy.’’
noexplanation. -7-Years ‘‘Thisonemakesthemiddlerise,thisonedoesn’tdoanything.’’
InferenceExplanation 8-Years- ‘‘Thepurpleonehasaconnectingpipe–pushesitdown,makesitrise.Thegreenone
Childrenofferanexplanationthatinvolves 8-Years hasnoconnectingpipe.’’
aconnectionbetweenthetubes. ‘‘Purpleworks,notGreenone.There’swaterunderneath–stopsthepebbles,makes
waterriseinthemiddletube.’’
Answerswerecodedbytwoobservers,whohadan89%concordancerate.Childrenwhosaidnothingwerenotincluded,childrenwhospokebutdidnotdescribewere
codedas‘‘noexplanation’’,childrenwhodescribedsomeconnectionbetweentheiractionandtheoutcome,butofferednoexplanationwerecodedas‘‘description
explanation’’andthosethatmentionedconnectivityor‘‘pushing’’werecodedas‘‘inferenceexplanation’’.
doi:10.1371/journal.pone.0040574.t002
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HowDoChildrenSolveAesop’sFable?
Children’s overall performance improved with age, but there extenttowhichtheexperienceoftasks1and2helped,hindered,
was not an increase in learning over trials (as measured by the or was necessary for performance in task 3 was thus not
differenceinproportionofcorrectactionsbetweentrials1and5) investigated, although this would make an interesting topic of
withage.Therewasastrongpositivecorrelationbetweenageand future study.
the proportion of correct actions (Kendell’s tau: R(41)=0.750, The performance of children on the first two tasks is
p,0.001)butnocorrelationbetweenageandlearning(Kendall’s comparable to that of the three corvid species studied. Rooks,
tau:R=20.068,p.0.4).Theseresultssuggestthatwhilethemain EurasianJaysandNewCaledonianCrowswereallabletolearnto
effect of age was due to a relatively linear improvement in dropstonesintowaterratherthansawdustwithinabout5trials,a
performance,thiswasnotthecasewiththelearningeffect.Given performance that equates roughly with the 4–7-year-old children
the poor performance of the youngest children and the almost testedhere.EurasianJaysandNewCaledonianCrowswereable
perfectperformanceoftheoldestchildren,thismightsuggestthat tolearntodropsinkingitemsintowaterratherthanfloatingitems
the younger children were less able to learn across the five trials, within 5 trials, a performance that equates roughly with the 5–7
whiletheolderchildrendidnotneedtobecausetheirperformance year-old children.
was goodfromthefirst trial. Suchcomparisonsareusefulonlytotheextenttowhichweare
The children who offered ‘‘Inference Explanations’’ scored able to investigate the possible presence of some common
better overall than those that offered ‘‘No Explanations’’ (Mann mechanism by which the children and corvids may be solving
Whitney U test with Sˇida´k correction: p,0.001). No other such tasks. As such, an interesting difference between the
comparisons regarding the levels of explanation were significant. performance of the corvids and the children emerges in Task 3
Children who offered ‘‘Descriptive Explanations’’ improved over (The U-tube Task). The Eurasian Jays tested performed substan-
trialstoadifferentdegreetochildrenwhoofferednoexplanation tiallyworseonTask3thanonTasks1and2.Thiswastakenby
(Mann Whitney U with Sˇida´k correction: p,0.017) Children’s Cheke and colleagues [2] to suggest that the birds had a
levelofexplanationhadanimpactonscoresonlyintasks2and3 rudimentary concept of the causal mechanism underlying the
(Mann Whitney U test with Sˇida´k correction; p,0.001 and relationship between their stone dropping and the movement of
p,0.001 respectively). This pattern of results suggests that while thereward,andthecausalrelationshipintheU-tubetaskviolated
performance on Task 1 did not depend on the ability to infer theassumptionsofwhatwaspossibleaccordingtothismechanism.
unobservable events, or even describe causal relationships, The children’s performance was equivalent on this task to the
performance on Tasks 2 and3 did relate tothese factors. other tasks, even in those individuals that did not infer the
presenceof theU-tube.Thechildrenwhowere successfulonthe
Comparison with Piagetian Measure U-tube task were those that were able to notice and describe the
Therewasnosignificantdifferencebetweenchildrenthatdidor causal relationships between putting a stone in a particular place
did not pass the conservation test in any of the tasks, although andtheapproachofthefood.Thesechildrencouldbesaidtobe
there was a trend suggesting conservers performed better than learning using a model of instrumental learning suggested by
non-conserversontheU-tubetask(task1:t(63)=0.709,p=0.481; ChekeandcolleaguesintheEurasianJaypaper[2]:ModelD:Do
task2: t(63)=0.018,p=0.985;task 3:t(52)=21.802,p=0.077). theactionthatcausesthemovementofthereward.Incontrast,the
Jays’performancewasmoreinlinewithModelE:Dotheaction
that causes the movement of the reward, where the choice of
Discussion
action is affected by, but not reliant on, some concept of
Our data indicate that children have, by the age of 8 years, mechanism.
developed a sophisticated understanding of the relationship The fact that children were not impaired on the U-tube task
between sinking objects and the resulting change in the level of relative to the other tasks may indicate that the they did not
liquid. Thesechildren performed above chancefromthe 1st trial interpret the event as ‘‘impossible’’ because they did not
in all tasks. Children between 4 and 7 years were able to learn understand that insertion of an item into one body of water
within5trialstodropmarblesintowater,ratherthansawdust,to cannot raise the level of another body of water. More likely, the
raise its level, and children between 5 and 7 years were able to children simply ignored the ‘‘impossible’’ causal cues. Indeed, it
learnwithin5trialstodropsinking,ratherthanfloating,itemsinto has been found that children as old as 11-year-old prioritise
water to raise its level. There was a suggestion that the younger contingency and contiguity as evidence of causality above
children(ages4–5-years)learnedmoreslowlythanolderchildren informationaboutmechanismandmayignoreinformationabout
(7-years), while children of 8-years and older were able to learn mechanism altogether if this conflicts with apparent contingency
within the first trial. This may suggest that instrumental information [13,21,22]. When applied to the current results this
conditioning ability improves gradually across these age groups, findingmightsuggestthat,duetotherobustcovariation,children’s
and is, by 8-years, an extremely fast and effective learning willingness to believe their actions to be causal was not impacted
mechanism. There was no significant difference between perfor- by the presence of cues indicating that the token was not in the
mance on these tasks and performance on a task designed to same body of water as the stones. On the other hand, it may be
present‘‘confusing’’physicalcues.Thiswasthesameacrossallage that children with no comprehension of the mechanism did not
groups(asindicatedbythelackofage6taskinteraction)andwas explicitly attribute causation, but simply allowed covaration
nottheresultofchildreninferringthepresenceoftheU-tube.This information toguidetheiractions.
is counter to the hypotheses outlined in the introduction, which That a bias to prioritise co-variation above mechanism
predicted that children of between 7 and 9 years would have a informationexistsinchildrenisextremelyinteresting andworthy
rudimentaryunderstandingofthemechanismsunderlyingraising offurtherinvestigation.Itmaybethatitisausefuldevelopmental
the water level, and therefore be less able to perform on tasks in stage which exists to allow children to learn about causation
whichdroppingastoneintoonebodyofwaterapparentlycauses unfetteredbyideasofwhatisandisnot‘‘possible’’.Ontheother
thelevelofanadjacentbodyofwatertorise(Task3).Itshouldbe hand, such a bias could conceivably come about as a product of
notedatthispointthatthetaskswereconductedinafixedorder extensive technological enculturation: children have considerable
by all subjects to maintain comparability with the corvids. The experience of devices with hidden mechanisms that make
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