night cycle

COGNITIVE

SCIENCE

18,

123-183

(1994)

Mental Models of the Day/Night Cycle STELLAVOSNIADOU University of Athens, Greece and University of Illinois at Urbana-Champaign

WILLIAMF.BREWER University of Illinois at Urbana-Champaign

This article presents the results of an experiment which Investigated elementary school children’s explanations of the day/night cycle. First, third, and fifth grade children were asked to explain certain phenomena, such as the disappearance of the sun during the night, the disappearance of stars during the day, the apparent movement of the moon, and the alteratlon of day and night. The results showed that the ma/orlty of the children In our sample used In a consistent fashlon a small number of relatively well-defined mental models of the earth, the sun, and the maon to explain the day/night cycle. These mental models of the day/night cycle were empirlcaily accurate, logically consistent and revealed some sensltivlty on the part of the children to issues of simpllclty of explanation. The younger children formed initial mental models which provided explanations of the day/night cycle based on everyday experience (e.g., the sun goes down behind mountains, clouds cover up the sun). The older children constructed synthetic mental models (e.g., the sun and the moon revolve around the stationary earth every 24 hours; the earth rotates In an up/down direction and the sun and maon are fixed on opposite sides) which represented attempts to synthesize the culturally accepted view with aspects of their initial models. A few of the older children appeared to have constructed a mental model of the day/night cycle slmllar to the scientific one. A theoretical framework is outlined which explains the formation of inltial, synthetic, and scientific models of the day/night cycle in terms of the reinterpretation of a hierarchy of constraints, some of which are present early in the child’s life, and others which emerge later out of the structure of the acquired knowledge.

The research reported in this article was supported in part by a grant from the National Science Foundation, BNS-85-10254, from the Office of Educational Research and Improvement under Cooperative Agreement No. G&)87-CIOOl-90 with the Reading Research and Education Center and from the Cognitive Science Group, Beckman Institute, University of Illinois. This publication does not necessarily reflect the views of the agencies supporting this research. We wduld like to th&k the principal, teachers and children of Washington School in Urbana, Illinois for their help in canying out this project. We also wish to thank Mar10 Schommer, Marcy Dorfman, and Arm Jolly for their help in testing the children and scoring the data, Clark chinn and Christos Ioannides for their comments, and Delores Plowman for secretarial work above and beyond the call of duty. Correspondence and requests for reprints should be sent to either Stella Vosniadou, Univexshy of Athens, 33 Ippokratus Street, Athens, Greece, or Wiiam F. Brewer, Department of PSYchology, University of Illinois at Urbana-Champaign, 603 B. Daniel Street, Champaign, IL 61820. 123

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The researchreportedin this paperinvestigateselementaryschoolchildren’s mental representationsof the day/night cycle and attemptsto understand how theserepresentations changeduringthe knowledgeacquisitionprocess. The presentwork is a continuationof earlierinvestigationsof the development of children’smentalrepresentations of the earth(Vosniadou& Brewer, 1992),in thecontextof a largerprojectdirectedat understandingthe process of knowledgeacquisitionin the areaof astronomy(Vosniadou& Brewer, 1987). The Process of Acquiring Knowledge about the Physical World

During the last few yearsthere has beena surgeof researchinvestigating how childrenacquireknowledgeaboutthe physicalworld, andmore particularly how theycometo understandthe currentlyacceptedscientificexplanationsof conceptssuchasmatter, weight,density,heat,temperature,force, etc.This researchhasproducedagreementon at leastonefundamentalissue: Children are not blank slateswhenthey are first exposedto the culturally accepted,scientific views, but bring to the acquisition task some initial knowledgeaboutthe physicalworld which appearsto be basedon interpretationsof everydayexperience. Thereis, however,considerabledisagreement abouthow to characterizetheseinitial knowledgestructuresand abouthow to describetheir developmentduring the knowledgeacquisitionprocess. Someresearchers think that initial, intuitive, or naiveknowledgeconsists of a largenumberof looselyorganizedphenomenologicalprincipleswhich representminimal abstractionsof common events(e.g., disessa, 1993). Other researchersbelievethat children start with a few, probably innate, domain-specificprinciples, which are organizedin theory-like structures and which constrain the knowledgeacquisition process(Gehnan, 1990; Spelke, 1990).Researchersalso differ in whether they conceptualizethe knowledgeacquisitionprocessin termsof the enrichmentof initial structures (e.g., Spelke, 1991)or their replacementwith new theories(e.g., Carey, 1991).Our studiesof the developmentof the conceptof the earthhaveled us to the developmentof a theoreticalposition (seeVosniadou,1989,in press-a,in press-b;Vosniadou& Brewer,1992),which will be further elaboratedon in this article. We assumethat the processof acquiringknowledgeabout the physical world is constrainedby a few domain-specificprinciples, such as those describedby Gehnan(1990)andSpelke(1991),whichwe callpresuppositions (e.g., unsupportedobjects fall down). Presuppositionsmay be innate or empirically acquiredconstraintswhich are presentfrom early infancy and whichguidethe waychildreninterprettheir observationsandtheinformation they receivefrom the cultureto constructknowledgestructures.We further believethat in orderto give a full accountof the knowledgeacquisitionprocessit is necessary to posit the existenceof a setof second-orderconstraints,

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whichwecall beliefsandmentalmodels.Beliefsandmentalmodelsareconstraintswhich emergeout of the structureof previouslyacquiredknowledge, andwhich in turn exerttheir influenceon the acquisitionof newknowledge. In the context of this theoreticalframework, we arguethat conceptual changeinvolvesmore than enrichment(e.g., Spelke,1991),and cannotbe fully describedin termsof the directreplacementof onetheorywith another (e.g.,Carey,1991).Conceptualchangeis seenasthe productof thegradual lifting of constraints,as presuppositions,beliefs, and mental models are added,eliminated,suspended,or revisedduring the knowledgeacquisition process. The constructof the mental model is usedhereto describethe kinds of mentalrepresentations wethink individualsconstructwhen.theyreasonabout the physical world (cf. Brewer, 1987).We usethe term mental model to denotea particular kind of mental representationwhich hasthe following characteristics:(a) its structureis an analogto the statesof the world that it represents(Johnson-Laird,1980,p. 90);(b) it canbe manipulatedmentally, or “run in the mind’s eye,” to make predictionsabout the outcomesof causalstatesin the world (Collins, 1985,p. 80);and (c) it providesexplanations of physicalphenomena(Holland, Holyoak, Nisbett, & Thagard,1986, p. 329).We furtherassumethat mentalmodelsaredynamicstructureswhich areusually createdon the spot to meetthe demandsof specific problemsolvingsituations(Johnson-Laird,1983;Vosniadou& Brewer,1992,p. 543). This doesnot excludethe possibility that somemodels, or parts of them, which havebeenprovenusefulin the past, arestoredasseparatestructures andretrievedfrom memorywhenneeded.In additionto actingasconstraints themselves,mental models can provide important information about the underlying knowledgestructure (e.g., presuppositionsand beliefs) from which they aregenerated, Mental Models bf the Earth

In Vosniadouand Brewer(1992),we investigatedelementaryschoolchildren’s mentalrepresentations of the earthby askinga seriesof questionsregarding the shapeof the earthand aboutthe regionson the earthwherepeoplelive. We tried to understandthe mental modelsunderlyingdifferent patternsof responsesto the samequestionsand to determinewhetherthesemodels wereusedin a consistentfashionacrossa largenumber of problems. The resultsof that studyshowedthat most of the childrenwe investigated were consistentIn their use of a relatively small number of well-defined mentalmodelsof the earth.The youngestchildrentendedto form an initial mentalmodel of a flat earth,which could havethe shapeof a rectangleor a disc, and which was supportedby ground. The flat earthmental model is consistentwith everydayexperienceand is not influencedby the culturally accepted,scientificmodel of a sphericalearth.The olderchildrentendedto

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form the culturally acceptedmodel of a sphericalearth, surroundedby space,with peopleliving all aroundit (on the outside). A numberof intermediateor syntheticmentalmodelsof the earthwere also identified, such as the model of a dual earth, the model of a hollow sphere,andthe modelof a flattenedsphere.Childrenwho form the synthetic model of a dual earthbelievethat therearetwo earths-a flat one,on which peoplelive, and a round onewhich is up in the sky. Children who hold the hollow spheremodel believethat peoplelive on flat grounddeepinsidethe sphericalearth,and thosethat hold the model of a flattenedspherebelieve theearthis a sphereflat on the “top” andon the “bottom” wherepeoplelive. Our resultsshowedthat most of the first-gradechildren, about half of the third-gradechildren, and somewhatless than half of the fifth-grade childrenhad formeda syntheticmentalmodelof the earth.The predominance of syntheticmodelsof the earthdemonstrateshow difficult it is for elementary schoolchildrento form the mental representationof a sphericalearth with peopleliving all aroundit, on the outside.This is the casedespitethe fact that the childrenin our culture areconstantlyexposedto the scientific information regardingthe shapeof the earth. In order to explain the formation of thesesyntheticmental modelswe postulatedthat children start by conceptualizingthe earth as a physical object, ratherthan asan astronomicalobject, andthereforeassumethat all the presuppositionswhich apply to physicalobjectsin generalapply to the earthas well (seeVosniadou,in press-b).Two of thesepresuppositionsare particularly important becausethey have the potential for explainingthe syntheticmodelsthat childrenform. They are the presuppositionsthat the groundis flat (asit appearsto be) and that unsupportedthings fall. Syntheticmental modelsof the earth can be explainedby assumingthat childreneitherassimilatethe culturally acceptedview of a sphericalearthto their initial model of a flat earth,or reviseoneof thesepresuppositionsbut not the other (Vosniadou8cBrewer,1992).For example,the syntheticmodel of the dual earthdoesnot requirechangesin anyof the presuppositionsthat give riseto the initial model of a flat earth. Children who form this mental model still believethat the groundis flat and that unsupportedthings fall. Thesechildrensimply addto their existingbeliefstheinformation that there is anotherearthwhich is sphericaland which is up in the sky, like a planet. The syntheticmodel of a hollow sphere,on the other hand, involvesa modification in the child’s presuppositions.The children who form this model havesuspendedthe presuppositionthat the earth needsto be supported,althoughthey still seemto believethat the peopleandobjectslocated on the earthwill fall if they arenot supported.They alsocontinueto believe that the ground is flat. In order to resolvethe conflict betweenthesepresuppositionsandthe culturally acceptedview, theycreatethe mental model of a hollow sphere.By assumingthat the earthis a hollow sphereand that

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peoplelive on flat groundinsidethis sphere,thesechildrensucceed in reconcilingtheir initial presuppositions with the scientificnotion of a sphericalearth. From the above,we concludethat syntheticmodelsarelikely to be formed whenthe knowledgeacquisitionprocessrequiresa revisionof presuppositionsthat arebasedon interpretationsof everydayexperience.In thesecases, syntheticmodelsfunction asintermediatestepsin the changefrom aninitial, intuitive model to the scientific culturally acceptedone. The Present Study

The purposeof the presentinvestigationwasto seeif the theoreticalframework developedto accountfor the developmentof the conceptof the earth couldexplainthe changesin elementaryschoolchildren’smentalmodelsof the day/night cycle. In addition, we were interestedin finding out if we could identify a small number of mental models of the day/night cycle whichchildrenusedin a consistentmanner,andto seewhetherthesemodels couldbecharacterizedassyntheticin wayssimilar to thosediscoveredin the caseof the shapeof the earth.The presentstudyopensup a setof newissues becausemental modelsof the day/night cycleinvolve not a singleconcept, but a number of interacting concepts(earth, sun, moon, and stars),and thesemodelsrequirethe explanationof the complexinteractionof a number of different phenomena. In the pagesthat follow we presenta brief accountof the explanationsof the day/night cycle found in the history of astronomy.Wecontinuewith a reviewof the empirical literatureon children’sexplanationsof the alternation of day and night. Then we turn to our own study. Explanations

of the Day/Night

Cycle in the History of Astronomy

The earliesttheoriesof the day/night cyclein different culturesfocuson the movementof the sun asthe main causeof the day/night cycle,but differ as to whetherthey conceptualizethe sun as goingbelow the earthat night or not. One early Chinesecosmologypostulatedthat the earth was flat and squareandthat the sunmovedto otherdistantpartsof the earth(Needham, 1975).The earlyGreekphilosopher,Anaximenes,believedthat the earthwas flat like a table.OneearlyGreekcommentatornotesthat Anaximenes“says that the heavenlybodiesdo not move under the earth, as otherssuppose, but round it, as a capturns round our head.The sunis hiddenfrom sight, not becauseit goesunderthe earth,but becauseit is concealedby the higher partsof the earth” (Heath, 1932,p. 10).An early Indian cosmologyalso postulatedthat the sundid not gobelowthe earth,but insteadturneda dark sideto earthand thenretracedits path back to the eastwhereit would rise (Gombrich,1975).The early Greekphilosopher,Xenophanes,believedthe earthwasflat and extendeddown indefinitely. He statedthat the sun was

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madeof fire. Whenthe sunset,the fire wasextinguishedandat eachdawna new sun was ignited (Heath, 1932). Another commonexplanationof the day/night cyclewasthat the setting sungoesunderthe earthandbackto the placewhereit rises.The Sumerians believedthe earth was a flat disc and that when the sun setin the west it wentunderthe earthto risein the east(Lambert, 1975).The earlyEgyptians believedthe earthwasthe shapeof a river valleyand that whenthe sunsetit wentbeneaththe earthto comebackup on the otherside(Plumby, 1975).A contemporarygroupof Quechuaspeakersin Peruhavea somewhatsimilar view. They believethe earthto be a roughlyeast/westorientedriver valley. They believethe sunsetsat the westend, and during thenight travelsunder the river to comeup at the eastend (Urton, 1981). As Greekastronomymatured,the standardview (e.g., that of Aristotle and Ptolemy)wasthat the earthwasa spherewhich wasin the centerof the universe.The sun and moon wereattachedto largersphereswhich rotated aroundthemotionlessearth.The revolutionarymovementof the sunaround the earthgaveriseto the day/night cycle(Heath, 1932).Clearlyin the early stagesof understandingthe day/nightcycle,philosopher-scientists developed a wide rangeof very different modelsto accountfor observeddata. In the nextsectionwewill examinechildren’sexplanationsof thesamephenomena. Prior Research on Students’ Explanations

of the Day/Night

Cycle

Most studiesof knowledgeacquisitionin astronomyhave focusedon an examinationof students’ideasaboutthe shapeof theearthandaboutgravity (e.g., Nussbaum,1979;Nussbaum& Novak, 1976;Sneider8cPulos, 1983). However, two relatively recentstudiesexploredstudents’explanationsof the alternation of day and night. One study, conductedby Sadler(1987), investigatedthe ideasof 25 ninth-gradestudentsabout the day/night cycle, the seasons,and the phasesof the moon. This study revealedthe following five distinct explanationsof the reasonsfor the alternationof day andnight: (1) the earthspins,(2)the sunmovesaroundthe earth, (3)the moon blocks out the sun,(4) the sungoesout at night, and (5)the atmosphereblocksthe sun at night. Sadlerreportsthat overhalf of the studentswho participated in this study werecompletinga one-yearcoursein Earth sciencesbut that thesestudentsdid not provide correctanswersmore often than the others, althoughthey did tend to usescientific termslike “orbit” and “tilt” more often than the studentswho did not take the course. A more detailedstudyof students’ideasaboutastronomicalphenomena, including the alternationof day and night cycle,was conductedby Baxter (1989).In this study, the responsesof 20 studentsrangingin agefrom 9 to 16 yearsof age were obtainedin individual interviews.Theseresponses revealedthe following six explanationsof the day/night cycle: (1) the sun goesbehindhills, (2) cloudscoverthe sun, (3)the moon coversthe sun, (4) the sungoesaroundthe earthoncea day, (5)the earthgoesaroundthe sun

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oncea day, and (6) the earth spins on its axis oncea day. Researchwith additionalsubjectsshoweda preferenceon the part of the youngerstudents for the explanationin which the earthgoesaroundthe sun oncea day and its gradualreplacementwith theexplanationin whichtheearthspins.Despite this change,many of the studentsage 15-16yearsstill believedthat the reasonfor the day/night cycleis that the earthgoesaround the sun or the sun goesaroundthe earth or that the moon coversthe sun. While the studiesdescribedaboveidentify students’explanationsof the day/night cycle, they are limited in their scope.The explanationsare not describedin greatdetail, and the researchersdo not provide explicit information about the criteria usedto derive students’explanationsand about the consistencywith which theseexplanationswere used.Neither do they attemptto provide an accountof how theseexplanationswere formed, or how they changewith development.We will try to answersomeof these questionsin this paper.In the nextsectionwe will elaborateandexpandthe theoreticalframeworkwe havedevelopedto explainthe Baxter (1989)and Sadler(1987)findings and to make further predictions. Constructing

a Mental Model of the Day/Night

Cycle

We assumethat the constructionof a mental model of the day/night cycle dependson individuals’representations of a numberof interactingconcepts (suchasthe conceptsof the earth,the sun,andthe moon), andthat it is constrainedby two kinds of presuppositions:ontologicalpresuppositions, such asthepresuppositionsthat physicalobjectsaresolid, stable,fall downwhen not supported,etc.;andep~temologicalpresuppositions, whicharepresuppositionsaboutthe generalcharacterof explanationsof physicalphenomena, suchasa preferencefor physical/causalexplanations.Thesepresuppositions influencethe way individualsinterprettheir observationsand the information theyreceivefrom the cultureto generatespecificbeliefsaboutthe nature of the physicalworld and constrainthe way thesebeliefsare mappedinto mentalmodels.An outline of this processis givenin Figure 1. Beliefs and mental modelsthemselvescan function as second-order,domain-specific constraintswhich further influencethe acquisitionprocess. In the next sectionwe describethe hypothesizedknowledgeacquisition processwhichunderlieschildren’sinitial explanationsof the day/night cycle anddiscussthe waysin which people’smodelsof the earthand the sun further constraintheir mental modelsof the day/night phenomenon. Hypothesized Knowledge Acquisition

Process

Presuppositions

Weassumethat elementaryschoolchildrenin our cultureoperateunderthe constraintsof certain epistemologicalpresuppositions.For example,they havesomecriteriawhich areusedto decidewhat constitutesa phenomenon,

Figure

Unsupported dew, etc.

(3)

knowledge

fall

are stable

are solid

objects

1. Hypothesized

objects

Physical

(2)

objects

Physical

(1)

Explanations should be given in terms of causal mechanism, etc.

(2)

need to be explained

Phenomena

Presuppositions

(1)

I

acquisition

process

underlying

elementary

school

children’s

beliefs

sky during the day, but not during the

The appearance of the sun and disappearance of the moon and stars a day. The disappearance of the sun and appearance of the moon and stars m night.

1

There is ica sequence of day and night

regarding

(5)

(3) (4)

(2)

(1)

which explain the and disappearance

t s appear and disappear

the alternation

of day

and night

Something moves in front of the objects and hides it The object moves behind something else The object switches off The object moves far away where it cannot be seen The observer turns so they cannot see the object anymore

Mechanisms appearance of objects

in the sky during the night but not during

I

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they know that phenomenarequirean explanation,and arepredisposedto prefercausalexplanationsof physicalphenomena.We further assumethat children are constrainedby a set of ontologicalpresuppositionsregarding the natureof physicalobjects(e.g, that physicalobjectsare solid, stable, requiresupport, etc.). Thesepresuppositionsform the backgroundwithin which children interpret their observationsand constrain the inferential processthat usestheseobservationsto generatespecificbeliefs about the natureof the physicalworld. Wedo not know if thesepresuppositionsareuniversalor arerestrictedto’ childrenraisedin the culturein which thechildrenin our samplewereraised. We havesomecross-culturaldata (Brewer,Herdrich, & Vosniadou,1987; Samarapungavan 8cVosniadou,1988;Vosniadou& Brewer,1990)suggesting that theontologicalpresuppositionswehaveidentifiedarefound acrossdifferentcultures,but the resolutionof this important issueremainsa question for future research(seealso Vosniadou,in press-b). Observations and Related Reliefs

The coreobservationrelatedto the day/night cycleis that the sunis out in the sky during the day, but not during the night. A relatedobservationis that the moon and starsarein the sky during the night, but not during the day. (Most youngchildrenarenot awarethat the moon is sometimespresent in the day sky.) From theseobservations,*and given the presuppositions alreadydiscussed,many childrenderivethe beliefsthat day is causedby the appearanceof the sun and the disappearance of the moon and stars;and that night is causedby the disappearance of the sun and the appearanceof the moon and stars. The appearance anddisappearance of thingsis a verycommonandsalient phenomenonin the everydayexperience of the child. Observationsof infants showpreoccupationwith making things appearor disappear(e.g., Piaget, 1963),and studiesof languageacquisitionshowthat words and utterances expressingthe disappearanceand reappearanceof objects or personsare amongthe very first to appearin the lexicon of the young child (Bloom, 1970;Brown, 1973).By the endof the preschoolyearschildrenseemto have availableto them a numberof possiblemechanismsthat explainthe disappearanceandreappearance of objects,suchas: somethingmovesin front of the objectandhidesit, the objectmovesfar awaywhereit cannotbeseen,etc. Despitethe availability of a rangeof mechanismswe predictthat the particular mechanismswhich areselectedto explainthe day/night cyclearethe mechanismsthat meetthe constraintsimposedby children’smentalmodels of the earthandthe sun,the moon andthe stars.Someof theseconstraints are givenin Figure 2. Constraints on Explanatory

Mechanisms

Explanationsof the day/night cyclemay vary dependingon how an individualconceptualizes theearth,thesun,the moon,andthe stars.Sincemental

Figure

2. Constraints

0) Earthisrsphere, slttmundedbyspremayormaynotmve

Mental Models of Earth

smlsItati0nary

on the

selection

(al Sunmoves

m

Mental Mod& of sun

mechanisms

that

Wa)

explain

the

IbeSungcesbehind a-pin

d&night

Mental Models of the Day/Night

‘Ibe sun goes far ‘WY

cycle.

switchesoff

mb) Thesun

IlAb)

Cycle

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modelsof thesecelestialbodiesare constrainedby ontologicalpresuppositions of the sort discussedby VosniadoudcBrewer(1992),thesepresuppositions alsoact asindirectconstraintson mentalmodelsof the day/nightcycle. In this sectionwe will examinehow children’smental modelsof the earth andthe sunconstraintheir mentalmodelsof the day/night cycle,The question about how the mental modelsof the moon and the starsinfluencethe mentalmodelsof the day/night cyclewill be addressedin the next sections. Initial Models

Basedon our studiesof individuals’ representations of the earth,we assume that childrenstartby forming a mentalmodel of a flat andstationaryearth, supportedby something,usuallydirt and rocks. Giventhe mentalmodel of a flat, supported,stationaryearth,the disappearance of the sun canbe explainedby different mechanismsdependingon whetherthe sun is conceptualizedto be stationaryor moving. If children think that the sun moves they canhypothesizethat at night it goesbehindmountains(Figure2,lAa) or that it goesfar away (Figure2, 1Ab). If the sunis conceptualizedasstationary, childrencan hypothesizethat somethingelse(e.g., clouds,moon, darkness,etc.)comesandcoversit up (Figure2, lBa), or that it switchesoff , (Figure2, 1Bb). Thesemental models of the day/night cycle are called initial models becausethey rely exclusivelyon interpretationsof experiencewhich can be derivedfrom everydayobservations.The syntheticmodelsdiscussedbelow showthe influenceof the’culturally accepted,scientific information about the earth, sun, and the day/night cycle. Synthetic and Scientific Models

The mental model of a flat, stationaryearthrootedin the groundseemsto placestrongconstraintson a child’s understandingof the scientificexplanation of the day/night cycle. For example,it is difficult to conceptualizea flat earththat is rooted in the groundas spinningor revolving aroundthe sun.As childrencometo form a mentalmodelof a sphericalearthsurrounded by space,an additionalclassof day/night mental modelsbecomeavailable to them. Even whenthe sphericalearthis thoughtto be stationaryand the sunasmoving, childrencanthink of the sunasgoingdownto the otherside of the earth, or as revolving around the sphericalearth (Figure 2, 2Aa, 2Ab). On the other hand, childrenwho havebeenexposedto the scientific information that the day/night cycleis dueto the rotational movementof the earthcan conceptualizethe sphericalearth aseitherrevolvingarounda stationarysun (Figure 2Ba), or as rotating around its axis (Figure 2Bb), or both.

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Criteria for the Evaluation of Explanations: Accuracy, Consistency, and Simplicity

Kuhn (1977)discusses five criteria (or values)which scientistsuseto evaluate the adequacyof a theory. Three of these,accuracy, consistency, and simplicity, seemto us to be good criteria by which to judgechildren’sexplanations of the day/night cycle. A theory shouldbe accuratewithin its domain in the sensethat the consequences deduciblefrom the theoryshouldagreewith the resultsof existing observationsand experiments.In our casethis meansthat children’sexplanationsof the day/night cycleshouldbe consistentwith the empiricalobservationswhich arerelatedto the phenomenonof the alternationof day and night (seeFigure 1). On the basisof the existingresearchfindings (Baxter, 1989;Sadler,1987),we would expectthat children’sexplanationswill indeed demonstratesuchempirical accuracy. Kuhn’s (1977)secondcriterion is the criterion of logical consistency.A theoryshouldbeinternallyconsistentwith itself aswell aswith otheraccepted theoriesabout relatedphenomena.Notice that researchers who claim that children’sexplanationsof phenomenaare fragmentedor looselyorganized areassertingthat childrendo not adopt a principle of logical consistencyin theorizingabout the physicalworld (see,e.g., disessa,1988,1993;Reif & Allen, 1992;Solomon, 1983). In our discussionof the constraintsthat the mental modelsof the earth and the sun imposeon the mental modelsof the day/night cycle,we have assumedthat children will show logical consistency.We assume,in other words,that childrenwith thementalmodelof a stationarysunwill not choose to explainthealternationof dayandnighton thebasisof thesun’smovement, asin (Figure2) models1Aa and 1Ab or models2Aa and 2Ab. Similarly, we expectchildrenwith mental modelsof a flat and stationaryearth will not provideexplanationsaccordingto which the earthrotatesaroundits axis or revolvesaroundthesun. Childrenwho saythat the sunor the earthis stationary in responseto questionsregardingthe movementof the sunandtheearth and then go on to explainthe day/night cyclein terms of the movementof the sun or the movementof the earth, are logically inconsistent. It is logically possible,however,to’think that the sun movesbut not to usethe movementof the sun as the mechanismto explain the day/night cycle.This would meanthat the mentalmodels1Baor 1Bbin Figure2 would still belogicallyconsistentmodelsfor a child who hadthe modelof a moving sun. The interdependencies betweenchildren’s mental models of the sun, moon, starsand eartharerathercomplexandaredescribedin detail laterin this article,whenwediscussthe criteriausedfor the derivationof children’s mental modelsof the day/night cycle.What shouldbe stressedhereis that our hypothesisthat childrenwill showlogicalconsistencymakesstrongpredictions about the relationshipsbetweenindividuals’ mental modelsof the

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earth and the sun and their mental modelsof the day/night cycle, which allow us to test this hypothesis. A third criterion by whichto judgea theoryis, accordingto Kuhn (1977), the criterion of simplicity-“ a theory should be simple, bringing order to phenomenathat in its absencewould be individually isolatedand, as a set confused”(Kuhn, 1977,p. 322).Wethink that it is possibleto decidewhether childrenare sensitiveto the criterion of simplicity in their explanationsof the day/night cycleby looking at the similarity of the mechanismsusedto explainthe disappearance of the sunduring the night and the moon during the day. If childrenthink that the moon and starsare causallyimplicatedin the day/night cyclethen their mentalmodelsshouldincludean explanationfor the appearanceof the moon and the starsduring the night and their disappearanceduring the day. If, in addition to empirical accuracy,children strive for logical consistency,then they should usemechanismsto explain the appearance andthe disappearance of the moon and starswhich obeythe sameconstraintsasthosethat governthe appearanceand disappearance of the sun. Logicalconsistencydoesnot require,however,that the samemechanism is usedto explainthe appearanceand disappearance of all celestialobjects. Childrenwho think that the sungoesbehindthe cloudsat night, but that the moon and starsswitch on and off are‘asinternally consistentas children who usethe samemechanismto accountfor the disappearance of the sun, moon, and stars.Using the same mechanismto explainthe disappearance of thesun,themoon andstarsduringthe alternationfrom dayto night, shows sensitivitynot only to logicalconsistency but alsoto simplicityof explanation. To conclude,wehypothesizethat elementaryschoolchildrenwill be able to provideaccurateandlogically consistentmechanisticexplanationsof the day/night cycle.Wepredictthat theyoungerchildren’sexplanationswill be in termsof the occlusionof the sunby clouds,the sunswitchingoff, thesun movingbehindsomething,or the sunmovingfar away,dependingon whether the sun is conceptualizedas stationaryor moving. We further predict that theolderchildrenwill generatesyntheticandscientificmodels-accordingto which the earthrevolvesaroundthe sun, the sunrevolvesaroundthe earth, or the earthrotatesaroundits axis. In addition, our theoreticalframework predictscertaininterrelationshipsbetweenchildren’smental modelsof the earth,the sun, the moon and the starsand their mentalmodelsof the day/ night cyclewhich can provide important information aboutchildren’ssensitivity to issuesof simplicity of explanation. Methodological

Issues

The methodologyusedin this studyis similar to themethodologydescribed in Vosniadouand Brewer(1992).It consistedof askingchildrenquestions,

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someof which requireda verbalresponse,andotherswhichrequiredmaking a drawing. Someof the questionsusedcould be answeredon the basisof information derivedeitherfrom experienceor from instruction(e.g.,Where is the sun during the day?Doesthe earthmove?).Other questionsrequired explanationsof phenomenawhich cannotbe directly observed,and about which children do not usually receivedirect instruction (e.g., Whereis the sun at night? Whereare the starsduring the day?).Theselatter types of questionshavethe potential of revealingthe kinds of mental modelsindividuals usegenerativelyto answernovel questionsand to solveunfamiliar problems. . Different setsof questionswereaskedabout the sun,the moon, and the stars,and children’sresponsesto thesequestionswereusedas the basisfor deriving information about their mental modelsof thesecelestialobjects. The children werealsoaskedto explainthe phenomenonof the day/night cyclein a separatesetof questions.Children’soverallmental modelsof the day/night cycle.werederivedat the end by comparingeachchild’s mental modelsof thesun,the moon, andthestarswith his or her explanationsof the alternationof day andnight. Only thechildrenwho exhibitedlogical consistencyin their modelsand explanationswereconsideredto havean internally consistentoverall mental model of the day/night cycle. The others were placedin a mixed category. METHOD Subjects

The subjectsfor this study were60children:20 first graders,rangingin age from 6 yearsand4 monthsto 7 yearsand5 months(meanage,6 yearsand9 months);20 third gradersrangingin agefrom 9 yearsand 3 monthsto 10 yearsand 3 months (meanage9 yearsand 9 months);and 20 fifth graders rangingin agefrom 10yearsand 3 months to 11yearsto 9 months (mean age11years).The childrenattendedan elementaryschoolin Urbana,Illinois and came from predominantlymiddle-classbackgrounds.Approximately half of the childrenweregirls and half wereboys. Thesesubjectswerethe samesubjectsas thosein Vosniadouand Brewer(1992). Materials

The materialsconsistedof a 48-item questionnaire.The questionnairewas developedthroughextensivepilot work and wasdesignedto provideinformation aboutchildren’sknowledgeof certaincritical conceptsin astronomy, including their ideasabout the earth’sshapeandgravity. Only the 13questions investigatingchildren’s ideasabout the disappearanceof the sun at night, the movementof the moon, the explanationof the day/night cycle, and the disappearance of the starsduring the day will be discussedin this paper. These questionswere selectedfor their potential to differentiate

DAY/NIGHT

Questions

Used

to Investigate

CYCLE

TABLE 1 Children’s Mental

137

Models

of the Day/Night

Cycle

The Disoppeoronce of the Sun ot Night Where is the sun at night? 422: Q23: HOW does this happen? Q240: Does the earth move? Q24b: Does the sun move? Explortoflons of the Doy/Nlght Cycle [The experimenter drew o circle to depict left side of the circle.] 425: Q26o:

the earth

and placed

a flgure

on the upper

Now make It so It Is day for that person. Good1 Now make It so It Is night for thot person. Tell me once more how thls happens.

The Movement of Q30: Does the Q31: Does the Q32: Does the Why does Q33:

the Moon moon move? moon move along moon move when the moon move?

wlth you when you are asleep

you go for a walk? In your bed?

The Dlsappeoronce of the Stars During the Day Q36o: Where are the stars at nlght? Q36b: Where are they during the day? Do the stars move? Q37:

,

amongthe different mental modelsof the day/night cyclepreviouslydiscussed.The 13 questionsare given in Table 1. Questions22 and 23 (Whereis the sun at night, How doesthis happen?) provideinformation about children’sexplanationof the disappearance of the sunat night. Questions24aand24b(Doesthe earthmove?andDoesthe sun move?)revealedchildren’sknowledgeregardingthe movementof the earthand the sun. This information was necessaryto allow us to test our predictionthat children’sbeliefsabout the movementof the earth and the sufiwould constraintheir choiceof mechanismto explainthe disappearance of the sun at night. The next set of questions(425, Q26a)requiredan explanationof the alternationof day and night. Weexpectedthat theseexplanationswould be basedon the belief that the day/night cycleis causedby the appearance and disappearance of the sun.If the childrensawthe appearance and disappearanceof the moon and the starsas causallyrelatedto the day/night cycle, theyshouldprovidean explanationof the disappearance and appearanceof the moon and the starsas well. The questionsabout the movementof the moon (430, 431,432, 433) andaboutthe disappearance of the starsduringthe day (Q36a,Q36b,437) weredesignedto provide further information about the relationshipthat childrensawbetweenthe sun,the moon andthe stars.This information was

138

VOSNIADOU

AND

BREWER

intendedto enableus to understandchildren’smental modelsof the day/ night cycleandto judgewhetherthesemodelswereempiricallyandlogically consistentand showedsensitivityto issuesof simplicity of explanation. Procedure

The childrenwereseenindividually in an interviewwhich lastedbetween30 and45minutes.Theexperimenter madedetailednotesof children’sresponses. The interviewwasalsorecordedusinga tape-recorder.The scoringwasdone later on the basisof both the transcribeddata andthe experimenter’snotes.

scoring The datawerescoredby two independentjudgeswho examinedthe four sets of questions(the disappearance of the sun at night, the alternationof day and night, the movementof the moon, and the disappearance of the stars duringthe day)separately,assigningchildrento variouscategoriesof explanations.All disagreements werediscusseduntil consensus wasachieved.Our previouswork (Vosniadou& Brewer,1992,pp. 54%547,554-555)hasshown high reliability for classifyingchildren’sresponses to thesetypesof questions. In assigningchildren to mental modelswe followed a proceduresimilar to that describedin Vosniadouand Brewer(1992).First, we identified, on the basisof our dataandpreviousresearchin this area,a seta possibleexplanations for the disappearance of the sun or the stars,of the movementof the moon, etc. Then, we generatedthe pattern of responsesto our questions which would be expectedassumingthat the childrenusedeachexplanation consistentlyto answerall relevantquestions.Wethen checkedthe expected patternof responses againstthe patternof obtainedresponses to the relevant questions,and assignedchildren to various categoriesof explanations.If the children were not logically consistent,they wereplaced in the mixed category. After we classifiedeachchild’s responses to the four setsof questions,we examinedthe four setsof responsescombinedand assignedchildrento an overallmental model of the day/night cycle.At the end, we checkedto see whetherthe derivedmental modelsof the day/night cycle wereconsistent with children’smental modelsof the earth which had beenderivedin our earlierpaper. The derivationof the mental modelsof the day/night cycle wasdoneindependentlyfrom and without knowledgeof children’smental modelsof the earth. The detailedcriteria usedfor assigningchildrento a categoryof explanation for the four setsof questionsaredescribedin Table2 andarediscussed in the next section. RESUT.iTS

In this sectionwepresentthe criteriausedto assignthe childrento the various categories of explanationsof thedisappearance of thesunat night,thealtema-

DAY/NIGHT

CYCLE

139

tion of the day andnight, the movementof themoon, andthe disappearance of thestarsduringthe day.Thenwepresentthe criteriafor assigningchildren to overallmental modelsof the day/night cycleand discussthe consistency betweenmentalmodelsof the day/nightcycleandmentalmodelsof the earth. Logical consistencyin children’sresponses to thevariousquestionswasa necessary requirementfor beingassigned to an explanationtype.The response patternsjudgedaslogicallyconsistentfor eachsetof questionsaredescribed below. The Disappearance of the Sun at Night

Four questionswereaskedto determinechildren’sexplanationsof the disappearance of the sunat night. Thesequestionscanbe found in thetop row of Table 2. Children’s answersto thesequestionswere classifiedinto 11 explanationtypeswhich areshownin the first column of Table2. The first explanationtype attributesthe day/night cycleto the occlusionof the sun by cloudsor darkness.Explanations2 to 6 focus on the movement of the sun asthe primary reasonfor its disappearance, while,explanations7 and 8 usethe movement of the earth asthe primary reasonfor the disappearance of the sun at night. The body of the table contains,for eachquestion,the typesof responsesthat wereclassifiedasinstancesof eachexplanationtype. Responses to Question24b, “Does the sun move?“, werecritical in differentiatingthe childrenwho attributedthe disappearance of the sunto the movement of the sun from thosewho attributed it to the movement of the earth. Children assignedto explanationtypes 2 to 6 were expectedto say that thesun movesup/down or east/west.Childrenassignedto explanation types7 and 8 wereexpectedto say that the sun is stationaryor to mention movementsthat could not be usedto explainthe day/night cycle(e.g.,that thesunrotatesaroundits axisor movesdueto theexpansionof the universe). Responsesto Question24a, “Does the earth move?” were critical for assigningchildrento explanations7 and 8. For explanation7 the children wereexpectedto say that the earthturns, spins,goesaround in circles,or movesand for explanation8 that the earthgoesaroundthe sun.Affirmative responsesto question24a “Does the earth move?” were not considered inconsistentwith explanations1 to 6 becauseit is possibleto havea model of the earthmoving which doesnot explainthe disappearance of the sunat night. Ideallywe expectedthat thechildrenwho attributedthe disappearance of the sunat night to the sun’smovementwould saythat the earthis stationary. However,many childrenwho areexposedto the information that the earthmovesdo not understandexactlyhow the earthmovesor do not realize that this movementhasany explanatorypowerwith respectto the alternation Ofdayandnight. It is possibleto constructvariousmentalmodelswherethe movementof the earthis not logically inconsistentwith the explanationof the disappearance of the sunbasedon the sun’smovement(e.g.,the earth moves/shakesasin an earthquake,or that the earthmovesrotationally but very slowly-once during a year, and so on).

of Explanation

by

Down

5. The sun goes unspecified 12. 0. 0=2)

down,

Below the earth; under the earth; down to the other side of the earth

4. The sun goes down to other side of the earth (2, 0, 1=3)

In space

Behinds clouds In darkness In the sky

is the sun at night?

far the Disappearance

The sun moves down on/in the ground; moves down behind hills, mountains, in the water

in and

b

Where Q22

Types

3. The sun goes down on/in the ground (6, 1, 1=8)

2. The sun moves out of space (1, 1,0=2)

1. The sun is occluded clouds or darkness (2,2, 1=5)

Type

Explanation does

this

out into

down

way

The sun goes down; it goes to another country

The sun moves down to the other side of the eorth

The sun moves

The sun goes space

cover

happen?

Clouds or darkness the sun up

How Q23

TABLE 2 of the Sun at Night Questions the earth

Frequency

No or Yes

No or Yes

No or Yes

No or Yes

No or Yes

Does Q24a

and Their move?

as a Function

Yes,

Yes.

Yes,

Yes,

it moves

it moves

it moves

it goes

space

up/down

up/down

up/down

into

the sun move?

Yes or No

Does Q24b

of Gradea

a n=60

Undetermined (3, 4, 027)

(1, 2, 3=6)

and

of the

TABLE

made

earth

way

around

inconsistent

it that

goes

the

for each grade. across grades.

No response, do not know, irrelevant or ambiguous response

Logically resuonses

God

The sun

around,

rotates, goes in circles, or moves

turns

turns,

the

spins, around

around

2 (Continued) goes

Earth

The sun earth

of explanation type gives the frequency

where it is or on the side of the earth

give the frequency 5. The last number

Anything

Anything

b The numbers in parentheses Grade 3, and the third for Grade

11.

10. Mixed

day

Anything

2=3)

9. God made night (0, 1, O=l)

(0.1,

Stays other

(3, 7, 12=22)

8. The earth revolves around the sun

side

where it is or on the side of the earth

Stays other

7. The earth turns the sun is fixed

and

At the other earth

6. The sun revolves around the earth (0, 1, O=l)

The first

number

No or Yes

Inconsistent

No

Yes it goes sun

moves the

is the frequency

responses

around

Yes; earth turns, spins, goes around in circles or

No or Yes

around

the

above

far

Grade

Yes or No

Inconsistent

No

As

1, the second

responses

for

No or if Yes only axis rotation or movement due to expansion of universe

Yes, it goes earth

142

VOSNIADOU

AND

BREWER

Information abouthow children’sresponsesto Questions22and 23were usedto assignthem to the specificexplanationtypesis presentedin Table2, which alsoshowsthe frequencyof theseexplanationsasa function of grade. Table3 givesa protocolexamplefrom eachexplanationtype.A moredetailed discussionof certain aspectsof the classificationsis given below. The critical information for placinga child in explanationtype4 (sungoes down to the other side of the earth) was the useof phrasessuchas below, under, or down to the othersideof the earthto Question22, “Where is the sunat night?Thesephraseswereusedto distinguishexplanationtype4 from explanationtype 3 (the sun goes down on/in the ground). Two childrendid not give enoughinformation in their responsesto Questions22 and 23 to determinewhetherthey believedthe sun stayson the groundor whetherit goesdown,to the othersideof theearth.For example,Jeff (protocolnumber 5, Table3) saidthat the sun goesdown “to a city or something.”This city could be on the sameside or on the “other” side of the earth. Thesetwo childrenwereplacedin explanationtype 5 (the sun goes down, unspecified). In explanationtype 6 (the sun revolves around the earth), the earth is consideredfixed and the sun revolvesaround it. The one child who was placedin this categorythoughtthat the sunandthe moon “trade places” as they revolvearoundthe earthevery24 hours.This child statedthat the sun is “on the other side of the earth” to Question22, “Where is the sun at night?“, because“the sun goesaroundthe earth” (Question23). Seeprotocol number 6, Table 3 for more details.Note the interestingcontrastof explanationtype 6 with explanationtype 8 (the earth revolves around the sun) in which the sun is consideredfixed and the earth revolvesaround it. Thereweresomechildrenwho could not be classifiedinto oneof the nine explanationtypes.A patternof responses wasscoredasexplanationtype 10 (mixed)whenmore than onemechanismwasusedto explainthe disappearanceof the sun at night, thus resultingin an internally inconsistentmodel, For example,Sandra(protocolnumber 10,Table 3) startsby explainingthe disappearanceof the sun in terms of the up/down movementof the sun, continueswith an occlusionexplanation,and whenaskedwhetherthe earth moveschangesto an earthaxis rotation explanation.A numberof children wereclassifiedas explanationtype 11 (undetermined). The childrenplaced in this categoryeithersaid that they did not know how to explainthe phenomenonin questionor gavean explanationwhichwe couldnot understand. An exampleof one of the undeterminedresponsesis givenin Table 3 (protocol number 11).Many of the mixed andundeterminedresponsesrevealed children’sattemptsto keepelementsof their initial explanations(usuallyin termsof an occlusionor sunmoving up/down mechanism)astheyreplaced them with the culturally acceptedexplanationof a rotating earth. Examination of Table 2 showsthat, as was expected,most of the firstgradechildrenprovidedexplanationsin termsof the initial mentalmodelof

by clouds

down,

unspecified.

(No. 45, Grade 1) Where is the sun at night? Down there. Where’s there? It goes down. Down where? It goes to a city or something. Does the earth move? No. Does the sun move? Yes.

goes

The sun

5.

Jeff E: C: E: C: E: C: E: c: E: C:

Tomara (No. 3, Grade 5) E: Where is the sun at night? c: It’s hiding. Where’s it hiding? E: It’s hiding? c: I don’t know. . .cause it won’t shine. E: How does this happen? c: The clouds block it. E: Does the earth move? c: It goes around. It goes east, west, north. E: Does the sun move? c: Yes.

1. The sun is occluded or darkness

in and

out of

of Explanations

sun

revolves

around

the

earth.

goes

of the down

the

7.

Sun at Night on/in

Betsy (No. 53, Grade 1) E: Where is the sun at night? C: Down. E: Down where? C: Below the hills E: How does this happen? C: I don’t know. E: Does the earth move? C: No. E: Does the sun move? C: It goes up and down.

3. The sun ground

TABLE 3 of the Disappearance

Koren (No. 37, Grade 3) E: Where is the sun at night? C: Well, it goes under the earth to Chino. See, while we have day, China has night and while China hos night, we have day. . E: How does this happen? C: Well, the moon and the sun trade places every. . . I guess it’s. . . E: Do you mean 24 hours? C: OK, every half of 24 hours they will change, they trode. Like they . . . in the a.m. the sun is here.. .for 12 hours and the moon is in China for 12 hours. And when China has sun for 12 hours, we have the moon for 12 hours. E: Well, does the sun move then? C: Oh yes, it moves every hour. Well, every yeor, yoa. It moves very slow. Every year it moves a little bit, but it moves slowly and uhmm, every year it’s gone around once. E: It’s gone around what? C: The sun has gone around the earth once.. .every year. Well, not once. . . it goes around every year, the sun does. But the earth moves around in a circle every year. E: Does it move oround anything? C: To me, everything moves oround the earth, and it doesn’t move around anything.

6. The

Kristie (No. 52, Grade 1) Ez Where is the sun at night? c: Gone in space. E: How does this haooen? goes way C: When it get dark’it into space. E: Does the earth move? c: Yes, the earth just floats. E: Does the sun move? c: Yes

moves

Examples

2. The sun space

Protocol

turns

ond

the

sun

is fixed.

(continued)

Cindy (No. 29, Grade 3) E: Where is the sun at night? C: On the other side of the earth. Because when night comes over here the sun goes onto the other side of the earth and it’s day on there. E: How does this happen? C: The earth turns around. E: Does the earth move? C: Yeah. E: Does the sun move? C: No.

The earth

Brian (No. 43, Grode 1) Ez Where is the sun at night? C: Under the earth. E: How does this happen? C: Because the moon comes out and the sun comes down. E: Does the eorth move? c: No. E: Does the sun move? C: Yes, it goes down.

4. The sun goes down to the other side of the earth.

E

8.

The

around

3)

the

sun.

9.

God

E: c: E: c: E: c: E: c: E: c:

day 3)

night.

3 (Continued) and

21, Grade

made (No.

TABLE

Where is the sun at night? h’s in another land, or mwbe another How does this happen? . It’s the way the earth is made. Can you explain this move? It’s just the way God created it. Does the earth move? No. Does the sun move? No.

’ Jamie

Charles (No. 36, Grade 3) E: Where is the sun at night? C: Behlnd the moon. E: How does this happen? C: The earth is rotating. The earth is going around in circles on its axis. And it’s making the sun move toward the moon. It looks like it because the earth is rotating. E: Does the earth move? c: Y&s. E. Does the sun move? C: Some, maybe, yes.

11. Undetermined

c: E: c: E: c:

E:

E: c:

revolves

39, Grade

earth

(No.

Where is the sun during night? On the other side of the earth. How does this happen? The earth moves around and it has a line and the sun keeps going around that, around the earth.. . l mean around the sun. Now wait, I just got a little confused. How does the earth move again? It moves around the sun.. . does the sun move? No. Now, what’s that thing about the line? Well, the line is like a path that it just keeps going around, it doesn’t go back and forth.

Isaac

_,

planet.

lO.Mixed (No,

27, Grade

3)

E: Where is the sun during the night? C: It went down to the moon. E: How does this happen? C: Because at 5 o’clock the sun sets and it rises in the morning and sets at night. It goes down when it has to. E: Why does it have to? C: Because it sun, it’s night and day and it’s supposed to be night around 5 or 6 o’clock and day around 1 or 2 or 3 o’clock. E: So is the sun moving? C: Yes. E: Can you tell me how it moves? C: l don’t think it really moves, but I think the clouds just cover it all up. E: Does the earth move? C: No.. .the earth do move I mean. E: How does the earth move? C: Because it rotates around, and that’s how the sun goes down, because the earth is turning to one half and the other half be day and it wait for 24 hours and it turn to the other half. And this half be night and this half be day.

Sandra

DAY/NIGHT

CYCLE

145

a sunmoving down on the ground,whereasmost of the older childrenprovidedexplanationsin terms of the rotational movementof the earth. The Alternation

of Day and Night

Children’sexplanationsof the alternationof dayandnight weredetermined on the basisof their responsesto Questions25 and 26a,which areshownin Figure3. For Questions25,the experimenterdrewa circleto depictthe earth andplaceda figure on the upperleft sideof the circle. Shethensaid, “Make it soit is day for thisperson”andthen“Make it soit is nightfor this person.” In Question26aa verbalexplanationof the day/night cyclewas requested (“Tell me oncemore how this happens.“)When assigningchildrento categoriesof explanationswe looked at the consistencybetweentheir drawings andtheir verbalexplanations.Childrenwereplacedin an explanationcategorywhenthe drawingandtheir verbalexplanationindicatedthat the same mechanismwasusedto explainthe day/night cycle.Neutraldrawings(e.g., thechild simply crossesout the sun,asshownin Figure3, ExplanationType 6) were acceptedif the verbal explanationwas unambiguous.Similarly, neutralverbal explanationswereacceptableif the drawingwas unambiguous. If the drawing and the verbal explanationwereboth ambiguous,the child’s responsewas placedin an undeterminedcategory.If they wereinconsistentwith eachother (in that they implied the useof different mechanisms),the child was scoredas mixed. Whenthe decisionwasmadeto usethe drawing of a circle to depict the earthwith a figureplacedon theupperleft sideto depictthe peoplewho live on the earth we had not yet understoodchildren’s mental models of the earth.This drawingturned out to be somewhatproblematicbecausesome of the childrenwho participatedin this studydid not think of the earthasa sphere,or did not believethat it is possiblefor peopleto live on the surface of this sphere.Some children in our samplebelievedthat the earthis flat like a rectangleor like a disc, or a hollow spherewith peopleliving on flat grounddeepinside it (seeVosniadou8cBrewer, 1992). As will becomeclearin the protocolexamplespresentedin Table4 andthe drawingspresentedin Figure3 and Figure4, someof.the childrenexplicitly rejectedour drawingandput their figureinsidethe circle,on a flat line inside thecircle,or on a flat line underneaththecircle. Othersdid not sayanything but ignoredthe drawing and madetheir own. In somecases,however,the drawingand the placementof the figure may haveresultedin pictorial representationsof the day/night cyclewhich wereinconsistentwith the verbal explanationsor which did not reflect them accurately.We tried to take the child’spoint of viewinto considerationasmuch aspossiblewheninterpreting the drawings,but in a few caseswe may haveplacedchildrenin the mixed categorywhenthey did not actually belongthere. We could have decided not to usethe drawingdata,but had wedoneso, muchinterestingandvaluable information would have beenlost in order to eliminate a relatively small numberof problematiccases.

= 1)

3. Explanations

lllcslmgaudmmfotbcorsidc ofthcca&(andtbcmamwmaup)

(4.0,0=4)

lltcsungocsdmvnwinlhcgmund (drht-g=~P)

(1.1.0-2)

ThcSWlObOVUiolOspacc

(1.0.0

llwsunbacckkdbycbDdsor

Figure

day/night

cycle.

mskcitsoitbdayforlbslpcrxm

of the

and

their

frequencies

of grade.

Iolbcc4K?si&ofIbce(sndlbe

TtlCSUlgOUdOWllUldCXIbCeanhor

-fb.smlgoudown~nIhcgmmKt (ovcrlhchill,intiwsw)andtbc mm coma up

llh?slmgouinlospaccaodcomu

CbUd3or&anigb1covcruplbc

OS a function

Thesongocsdown-tmspccif~~wiih

-rhecmhmvolvusmlmdlhcslm

mlcurlhfJmsup/dovmandrheslm is fd (moon mtqlccified)

9

rtspmlOlXUlhSid0

8

6

T)pz of Explanation

soilisdayforlhalp make it so it is night for

1tgoesloanolhu

The sun slays in one place

llu.eanhtumsamuwJ(spinsormfau9)

lllcc.mhgoes(mrm)aIolmdIhcsml

mslmgocsdown

moon

3 (Continued)

is the frequency

for grade 1, the

No response. irrelevant or ambiguous

The earth turns around (spins or rotate)

When lhe earLh pf3 around its orbit, this side becomes day and hii side becomes

‘Ihe earth turns away from the sun

When il is daylime tbe cailh turns (spins ormtatcs)amuodtbestm. Whmitis nighttime. it turns to where the moon is

type for each grade. The first number gives the frequency across gradn.

nse, irrelevant or ambiguous

bThc numbers in parentheses give the frequency of explanation second for grade 3, and the third for gade 5. Thc last number

an=60

(2,2,2=6)

12 Tbecanhtumssi&waysandtks andmomlamfmYJatoppositesidcs

11 lkcanbtumssi&ways lwpccirvd

(0.3.5-8)

aodmoonarcfiicdatoppositesides

Figure

DAY/NIGHT

CYCLE

149

Finally, it shouldalsobementionedthat children’sresponses wereplaced in themixed categoryif at any otherplacein the interviewtheyprovidedan explanationof the day/night cyclewhich was different from the one they gavein responseto Questions25and 26a.Suchopportunitiesexistedat differentpartsin the interview, for example,whenchildrenwereaskedabout theapparentmovementof themoon, or the disappearance of thestarsduring theday.The strict criteriafor internalconsistencyweemployedmay explain the relativelarge number of mixed casesfor this set of questions(11/60). The exact criteria for assigningchildren to eachexplanationtype are givenin Figure 3 and will be further discussed.Figure 3 alsoshowsthe frequencyof children’sexplanationsasa function of grade.Protocol examples for eachexplanationtype canbe found in Table4 (pp. 150-151).The drawings of the children whose protocols were usedin Table 4 are shown in’ Figure4 (p. 152). In explanationtype 1 the sunis occludedby clouds,while in explanation type2, daygoesawayandnight takesits place.Explanationtype2 doesnot useocclusionasthe mechanismfor the disappearance of the sunbut rather the movementof thesun (aswell aseverythingelsethat constitutesday)to anotherplace. In orderto be placedin explanationtype4 (thesungoesdown on/in the ground)a child had to provide someevidence,either in a drawing or in a verbalstatementor in both, that the sungoesdown on or in theground(not down to the other sideof the earth). Statementssuchas “on” or “in the ground” “behind hills, 3’ “in the water,” etc. were used by the children togetherwith drawingswhich depictthe sungoingdownbut not to theother sideof the earth. Children’sdepictionsof the sun going down on the ground variedconsiderably.As shownin Figure3, somechildrenplacedthesuninsidethe circle depictingthe earth (Figure3, explanationtype 4, drawingsa and b). There werea variety of other options.In drawingb the child drewanothersunto indicatethe downwardmovement.In drawing c the child showedwith an arrow how the sun goesdown to the ground. In drawingd we havea child with a two-earthmodel who showedthe sun going down towardsthe flat groundwhich is supposedto be below the sphericalearth.Thesedrawings showthat the way children conceptualizethe movementof the sun varies greatlydependingon their mentalmodel of the earth,but theexactrelationship betweenmentalmodelsof the earthand mentalmodelsof the day/night cyclewill be discussedlater in this article. Finally, it is important to note that all but oneof the childrenplacedin this categoryimplicatedthe moon in the day/night cycle by sayingthat when the sun goesdown, the moon goesup. The crucial differencebetweenexplanationtype 5 (thesun goesdown to theotherside of the earth)and explanationtype 4 is that the childrenprovided evidenceeither in their drawing or in their verbal statementsor in

Allison (No. 52, Grads 1)

Autumn (No. 51, Grade 1)

E: Now make it d-q for that pman. c: Sun and clouds in the sky. Ralnbaw, mlndrop (see drawing 2 in Figure 4). E: Now make it so It is night for that pwsa”. c: Everything goes away. E: Can you make II night? c: How? E: Go ahead and draw It in. How *ould it be? c: The stuff would go away E: Da you know we,. It would go? C: Into another place. E: Da you know bow that happens? C: Yes. Urn the night takes aver the *un.

Tamam (No. 9, Grade 5)

E: Now can you make It so it Is day for that person? c: He’s outside the earth. E: Where should he be? c: In hero (see Figure 4, drawing 1). E: . . .OK now. make It daylime for him. c: The .un is out here. but It looks like it’s In the earth, when It shines.. . E: OK. What happens at night? c: The clouds covered it up. E: Tell me once more hw, it haPP-C: Cause ol 12 o’clock It’s dark.

E: Now make it so It is day for that perwn. C: (child makes drewlng 3 shown in Figure 4) Right here? E: Whatever you think. Now make It nigh. c: It gaea in space. E: Show me. Tell me how It happens. OThesuncamolbackdawn.It goes into space and when it gets dark the moan comes back out.

3. The run mover auf into space.

1. The sun Is occluded by clouds or darkn~.

2. Day Is replaced by night.

TABLE 4 Protocol Examples for Explanations of the Dcy/Nlght

E: Can you make it day for this pe-? c: (see drawing 4 In Figure 4) E: Now make it night for that person. c: To make It night, erase the sun and r+ca It with the moan. E: Can you tell me once mare how It bappelr? C:The.ungaesdawnondthemaon comes up, and then the moan goes davm and the sun coma up. E: Where Is the moan when the sun Is up? c: The maanir where the run rests.

Harmony (No. 41, Grads 1)

4. The sun gaea dawn on/in the ground (and the moan comes up).

Cycle

shown

E: Tell me once mere how it hOppll% c: When the moan tamer up and the sun goes dawn. E: W-tare war the moan before? c: Under the earth. E: who, time was It when It goes under the earth? c:Day.

The child makes the dmwlngr in Flgun 4.

Tlmathy (No. 47. Grade 1)

5. Thewngaesdawltotheothw IIda of tha earth (and tha moan gon UP).

and the sun Is fixed

Eddie (No. 20. Grade 5) C: (Child makes dmwlng 11 shown In Fl&tre 4) E: Tell ms how It happnr. c: Catle when the earth turns away from the sun, it gets dark.

11. The earth rotates Ieft/rfght (moon unspecified).

Karen (No. 37, Grads 3) The child makes drawing 7 shown Figure 4.

Quinten (No. 44, Grade 1) E: Now make it day. Now make It night. c: (see dmwing 6 in Figure 4) E: Tell me onca more how this happwts. c: Because he’s on top of the earth and the sun’s going to ba coming out of the whole *pace. The sun’s supposed to be in the mkidle of the whole part.. .rmd It coma out. Then he’ll ba rtandlng on the earth so he’ll ga to sea the sun. And when the moon comes, he con see the moon too. E: Does the sun move? c: Only up and down. E: Does the moon mow up and dwm too7 c:Ye,

Venlka (No. 33. Grade 3) C: (Child makes dmwlng 12, Flgure 4) E: Can you tell me how this hoppens? c: when the earth turns around Its orbit, this rl& and the other ride comes night.

and

comes day

Robert (No. 5. Grade 5) E: Now make it sa it is day for tflat person. c: (child makes drawing 10 sbovm In flgura 4) E: Now can you make it nighttime? C: Can I draw him somewhere else? (draws figure at the bottom of the earth) E: sure. c: (Child dmvn arrows to show how earth spins) E: Tell me bow it hoppens. C: when It was dayiime. the earth spinnd around to the sun. Wlwn it was nighttime. the earth turned around to where the moon Is.

10. The earth rotates up/down and the *un and moon ore fixed at opposite rida.

Joshua (No. 1. Grade 5) c: (Child produces drawing 13. Figure 4) E: How does this happen? c: Cause Lo world rotates.

13. The earth rotates in unspecified direction, moon unrpecifled.

E: Tell me how It happens. c: The sun stays In one place mid the earth turns. E: How? C: It turns around.

Chd (No. 19. Gr& 5) Child makes dmwlng 9 shown in Agur.4.

9. The earth rotates up/down the run is fixed (moon unspectfied).

and the sun and moon ore

Mike (No. 11, Grade 5) E: Make it so It’s day time for this pemn c: (roe drawing 8. Ffgure 4) E Make it so It’s nIgftt. c: Moon (child draw moon) c: Tell me once more how It happens. c: The earth turns around the sun. and the sun gives heat.

8. The earth revohres around the sun.

12. Tb. earth rotates left/right fixed at opposite alder.

E Now make it so it Is night. t: We hove to cross out the sun and put it over here. E: Tell me once mom how it haPpen,. c: Well. the sun vibrates around the earth every 12 hours. And then the moon goes the other dlrectlon and vibrates wound the earth every 12 hours. 50 both us and Chlna have the moon and the sun.

7. The run and the moon revolve around the earth.

6. The run goa down, unspacified as to whkh ride of the earth bd the moo” wea UP).

TABLE 4 (continued)

Drawing

Drawing

No. 4

No. 1

Figure

4. Drawings

od

of children

ore

9

Drawing

No. 2.

protocols

Drawing

whose

as examples

No. 5

given

of explanations

of the

No. 3

No. 6

Drawing

cycle.

Drawing

day/night

L

d

153

154

VOSNIADOU

AND

BREWER

both, that the sun wentdown to the other side of the earth. The three children placedin this categorymade drawingssuchas the one shownin Figure 3, depictingthe sun going down to the other side of the earth, and also said that the sungoesdown,under,or to the othersideof theearth.Two of these childrenalso saidthat the moon goesup whenthe sungoesto the otherside of the earth.An exampleof this typeof responseis protocolnumber5, Table 4 and drawing number5, Figure 4. In explanationtype 7 (the sun and the moon revolve around the earth), the alternation of day and night is causedbecausethe sun and the moon revolvearoundthe earth every24 hours. Sincethe sunand moon are conceptualizedasbeinglocatedat two diametricallyopposedsidesin their orbital path, this explanationnicely accountsfor the alternationof day and night for the different parts of the earth. The criteria for explanationtype 8 (the earth revolves around the sun) wereeither an unambiguousdrawing showingthe earth revolving around the sun or a verbal explanationindicating revolutionarymovementof the earth,or both. Note that the model accordingto which a nonrotatingearth revolvesaround the sun in 24 hours generatesthe appropriateday/night cycle. Children who gavea revolution explanationbut a rotation drawing wereplacedin the mixed category.The four childrenplacedin this category saidexplicitly that the earthgoesaroundthe sunin their verbalexplanations and madea drawingwhich was not inconsistentwith this explanation.An exampleof this type of responseis protocol number8, Table4 and drawing number 8, Figure 4. Explanationtype 9 (the earth rotates up/down and the sun isfixed) is one of a classof rotation explanationswhich is characterizedby the up/down rotationof theearth(Le.,rotationaroundan axisthroughthe equatorinstead of through the poles).The childrenplacedin this categoryail said that the earth turns around and the sun staysin one place.Information about the directionof the rotation wasobtainedfrom their drawings.Up/down rotation wasindicatedeitherwith an arrow or by placingthe figureat the bottom of the earth to make it night time (seedrawingsa and b respectivelyfor explanationtype 9, Figure 3). An exampleof this type of responseis given in Table4, protocol 9 and Figure4, drawing 9. Childrenwho saidthat the earthturns, spins,or rotatesbut madea neutraldrawingwith respectto the direction of rotation wereplacedin explanationtype 13. Examination of explanationtype 9, Figure 3, showsthat thereis another possibleinterpretationof the up/down arrow. One could imaginethat one is viewingthe earthfrom abovethe north poleandthat the figureis standing on the equator. If one adoptsthis perspectivethen the arrow that we are interpretingas “up/down” would actuallybe west/east(i.e., rotationaround a polar axis).Weunderstandthat this is a logically consistentinterpretation of the drawingby an adult. However,our experiencewith childrencarrying out the drawingtask suggeststhat theyinterpretthe figure in our drawingas

DAY/NIGHT

CYCLE

155

standingon the “top” of the earth(Le.,at the north pole). It is possiblethat this preferenceis relatedto problemschildrenhavewith gravity.In addition, wehaveunpublisheddatain whichchildrenaregivena spherewith a person on it andareaskedto makeit dayor night for the figure.Whenmanipulating themodelsthe childrentendto carry out an up/down rotation, not a west/ eastrotation of the earth. On the basisof these‘observations,we haveconcludedthat the bestinterpretationof the type of drawingsgivenin Figure3, explanationtype 9, is up/down rotation. Explanationtype 10 (the earth rotates up/down and the sun and moon are fixed at opposite sides) is similar to explanationtype9 with the additional constraintthat the sunandmoon arefixed at two oppositesidesof theearth, The information that the sun and moon are fixed at oppositesidescould comeeitherfrom an unambiguousverbalexplanationor from an unambiguousdrawing or from both. The drawingsexpectedfor this explanation typeareshownin Figure3 and areof two kinds: (1) they depictthe sunand themoon fixed at the top andbottom of the earth at least90” apart, or (2) theydepictthe sunand themoon to be fixed at the left andright sidesof the earthat least 90’ apart and indicateup/down rotation of the earthby the useof an arrow or by the placementof figureson the bottom parts of the earth.This additional information is requiredwhen the sun and the moon arefixedat the left and right sidesof the earthbecausein this casetheir position alonedoesnot provideinformation aboutthe directionof the rotation. An exampleof oneof theseresponsesis protocol 10,Table4, and drawing 10,Figure4. Thereweresomechildrenwho could not be classifiedinto oneof the 13 explanationtypespreviouslydescribed.Thesechildrenwereplacedeitherin explanationtype 14 (mixed)or in explanationtype 15(undetermined).The childrenplacedin explanationtype 14 (mixed) providedevidencefor two conflictinginterpretationsof the day/night cyclein their responses.Sometimesthe conflict existedin the inconsistencybetweenthe drawingand the verbalexplanation,suchasin subjectnumber15,who drewan arrow showing theearthto rotateup/down but saidthat the earthturns aroundthesun. At othertimes the conflict existedin the inconsistencybetweenchildren’s responses to Questions25 and26a,andwhat wassaidlaterin the interview. For example,subjectnumber46 startedwith a perfectlyclearearthup/down rotationexplanationand changedto a sun up/down explanationat the end of the interview. Another type of inconsistentexplanationwasa combination of occlusionof the sun versussun up/down movement.The children who wereplacedin explanationtype 15 (undetermined)did not provide a mechanismfor the day/night cyclein their responses. Examinationof Figure3 showsthat, aspredicted,most of the first grade childrenexplainthe day/night cyclein termsof the up/down movementof the sun and moon, while most of the fifth gradechildrenusea rotation of the earthexplanation.

156

VOSNIADOU

AND

BREWER

The Movement of the Moon Children’sideasaboutthemovementof the moon weredeterminedby looking at the patternof their responsesto the four moon movementquestions which appearin the top row of Table5 Op.157).Eight categoriesof explanation typesfor moon movementresponseswereobtainedand thesearealso shownin Table 5. Protocol examplesfor someof thesecategoriesappearin Table 6 (p. 158). Childrenwho saidthat the moon doesnot moveto all the relevantquestions (430, 43 1, and 432) wereplacedin explanationtype 1. In Question 30 somechildren said that the moon appearsto move becausethe earth movesbut that it doesnot really move.Similarly, somechildrenmentioned, in responseto Question31, that the moon appearsto movealong with you when you go for a walk but that it doesnot really move. One child said spontaneouslythat the moon stayswhereit is andthe reasonwhy you don’t seeit during the day is becausecloudscoverit up. Question33, “Why does the moon move?“, wasnot askedfor thesechildrenbecausethey said that the moon doesnot move.Seeprotocol 1, Table6 for anexampleof this type of response. The childrenclassifiedin explanationtype 2 all saidthat the moon moves in an up/down fashion,in responseto Questions30and 32. Someof these children claimed that the moon movesin a “hydraulic” relation with the movementof the sun,that is, the moon goesdownin themorning whenthe sun goesup, and later, when the sun goesdown the moon goesup. Most childrensaidthat the moon doesnot movealongwith you whenyou go for a walk (431) althoughsome acknowledgedthat it may appearto do so. Finally, all the childrenexplainedthe movementof the moon (433) in relation to the day/night cycle. Seeprotocol 2, Table 6 for an exampleof this type of responsepattern. A number of children said that the moon revolvesaround the earth in responseto Questions30and 32, and that it doesnot movealongwith you, althoughit may seemso, in responseto Question31. Thesechildrenwere placedin explanationtype 4. Most of the explanationsof the revolution of the moon in Question33, “Why doesthe moon move?” weregivenin terms of the day/night cycle--” to makeit night.” An exampleprotocolis givenin Table6 (protocol4). No gravity explanationsweregivenin this categoryas they weregivenin the previousone. The absenceof the scientifictypesof explanationsin this categorysuggests that therevolutionof themoon around the earthwasnot understoodin termsof the scientificmodelbut wasseenas causallyimplicated in the day/night cycle. Table 5 showsthe frequencyof moon movementresponsesasa function of grade.Thereis a clearshift from seeingthe moon asmoving at first grade to seeingit as stationaryat grades3 and 5. Thus, the movementquestion givesa very interestingU-shapedfunction. The young childrentend to say the moon doesmove, the ,olderchildren tend to saythat it doesnot move,

5

Yes Up and

Yes, Up/down (3, 0, 2=5)

Yes, movement unspecified (11, 3,4=18)

Yes, revolution around earth (0, 4, 2=6)

Yes, mixed (0, 0, l=l)

2.

3.

4.

5.

No

8. No, undetermined (2, 2, 1=5)

in parentheses third for Grade

No

No, mixed (1, 2, 0=3)

7.

a n=68 b The numbers Grade 3, and the

Yes

6. Yes, undetermined (1, 2, 2=5)

Yes

moon

for

move?

Movement

give the frequency 5. The last number

5

and

it seems

to

it seems

to

for each grade. across grades.

Ambiguous response (e.g., the sun was following us when my mom and I were going to see my grandpa)

No

No

No

No or Yes, move

No or Yes, it seems to move but does not really

No or Yes, move

No or Yes No, it seems to move; it it does not really move

move along you go for

Questions

TABLE

Does the moon with you when a walk? Q31

of the Moon

of explanation type gives the frequency

moves and as if it moves

the

or without revolution

Down

eorth it seem

Yes, with mentioning

Yes

No No-the makes

1. No, with or without explanation (2, 7, 8=17)b

the

Q30

Does

Types

of Movement

Type

Explanation

goes

around

the

it time

so

number

is the frequency

Ambiguous response (e.g., the moon is on another planet during the daytime)

Yes

No

No

Yes-it earth

Yes or No-because moves some other

Yes-it moves up/down or No-it moves at dawn the sun can get up to make day

No

Q32

the

moon

for

know

know

not

move.

for

move?

1, the second

does does.

night

know

Grade

I don’t

I don’t

I don’t

The moon The earth

To make

I don’t know To make day/night Because of the earth’s aravitv

day/night

relevant

does

To make

Not

Q33

Why

of Grade”

move when in your bed?

as a Function

Does the moon you are asleep

Frequency

The first

Their

No,

(No.

with

1, Grade

or without

5)

explanation.

Examples

(No.

Yes,

you

with

earth.

are

you

in your bed? C: Yes. It moves around the earth. E: Why does the moon move? C: So that when the sun comes up here _ be night on the other half.

when

the

along

move?

3)

around

move

moon

the moon

the

32, Grade

revolution

you go for a walk? C: No. E: Does the moon move

E: Does c: Yes. E: Does

Josh

4.

it will

asleep

when

E: Does the moon move? C: Yes. No cross that out. It doesn’t move. It’s you that’s moving. And it looks like the moon is moving. It’s still while you’re moving. E: Does the moon move along with you when you go for a walk? c: No. E: Does the moon move when you are asleep in your bed? C: No. It stays in the same place. The earth moves.

Joshuo

1.

Protocol Yes,

Questions

(No.

1)

TABLE 6 Investigating

44, Grade

up/down.

the

the

Movement

E: Does the moon move? C: Only up and down. E: Does the moon move along with you when you go for a walk? c: No. E: Does the moon move when you’re asleep in your bed? C: No. E: Why does the moon move? C: Cause when the sun’s gonna come up it gotta go down, when the sun goes down it gotto come up.

Quinten

2.

from Yes, (No.

5)

unspecified

13, Grade

movement

Moon

E: Does the moon move? C: Yes. E: Does the moon move along with you when you go for a walk? c: No. E: Does the moon move when you are osleep in your bed? C: Yes. E: Why does the moon move? C: Because it’s attracted to the earth’s gravity. And it moves with the earth.

Luther

3.

of the

DAY/NIGHT

CYCLE

159

andadultssayit doesmove(unpublisheddatafrom undergraduate subjects). Cur detailedcategorizationof the different typesof moon movementprovidesa very goodexplanationfor the progressionof thesedifferent answers to thesameverbalquestionwith age.Whenthe youngsubjectssaythemoon movesthey tend to meanthat it movesin an up/down fashionwith respect to the earth’ssurface. When the older subjectssay that it doesnot move theyaretypically operatingwith a rotating earthmodelwith themoon fixed in oneposition.Whenadult subjectssaythe moon movestheyarereflecting thescientificmodel in which themoon revolvesaroundthe earth,This analysisof responsesto questionsabout the movementof the moon showsthe powerof the mental model approachin providing an explanationof data that, at first glance,appearquite puzzling. The Disappearance of the Stars During the Day

Children’sexplanationsof the disappearanceof the stars during the day wereexploredby askingthe threequestionswhich appearin the top row of Table7 (p. 160).The various explanationtypesand their frequenciesare shownin Table7. Protocol examplesfrom eachcategoryareshownin Table 8 (p. 161).The data presentedin Table 7 showthat the first-gradechildren givea wide rangeof explanationsof the disappearance of the starsduring theday-they are occludedby cloudsduring,theday, they move down on theground,they move to the other sideof the earth. Theseare similar to their explanationsof the disappearanceof the sun at night. However,the largestgroup of children (24 out of 60) said that the starsstay wherethey areduringthe day andthat the reasonwe cannotseethem is becauseof the brightnessof the sky dueto the light comingfrom the sun.This explanation is particularlycommon among the fifth-grade children(12 out of 20). Overall Mental Models of the Day/Night

Cycle

Childrenwereplacedin the variousexplanationtypesalreadydiscussedif theymet the criteria for logical consistencywhich we developedon a priori basisand which werepreviouslydescribed.In this sectionwe describethe criteriausedto assignchildrento an “overall mentalmodel of the day/night cycle.” In orderto be assignedto an overallmodel of the day/night cyclea givenchild had to havebeenplacedin explanationcategoriesin the four sets of questionspreviouslydiscussedwhich werenot logically inconsistentwith eachother. Thecriteriafor assigningchildrento mentalmodelsaredescribedin Table 9 (PP.162-163)and arediscussedin detail in the following sectionaccording to model numbers.The frequencyof occurrenceof eachmodel type by gradeis also givenin Table 9. Model I: The Sun is Occluded. The four childrenplacedin this category all saidthat something(usuallycloudsor darkness)blocksthesun,in response

The stars the earth

move down, (3, 1, 1=5)

ore

a n=tJl b The numbers Grade 3. and the

9. Undetermined (4, 3, 2=9)

in parentheses third for Grade

sky

sky

sky

sky

sky

sky

sky

sky

sky

ore

During

of explanation type aives the freauencv

at night?

of the Stars the stars

give the frequency 5. The lost number

In the

In the

where

they

In the

In the

8. The stars stay (3, 9, 12=24)

somewhere

of

In the

In the

The stars move else (l,O,O=l)

side

under

In the

In the

In the

Where Q36a

the Disappearance

7. The stars dtsoppear (l,O, O=l)

6.

5. The stars move down, unspecified as to which earth (2, 0, 0=2)

4.

the

3. The stars go down on/in ground (behind hills) (1, 0, 1=2)

for

space

out

2. The stars move (2, 2, 1=5)

by

Types

into

occluded

of Explanation

1. The stars are clouds (3, 5,3=ll)b

Type

Explanation

7

hills

Behind

for each grade. across arades.

The first

No response, I do not irrelevant or ambiguous

number

stars

they

for

Grade

1, the second

move

move?

of Grade”

don’t

know

Yes or No

No,

I don’t

Yes

Yes

Yes

Yes

Yes

Yes or No

Do the Q37

as a Function

is the frequency

know, response

are still up on the sky. You see them because of the light f.

They can’t sun’s

gone-disappeor

country

side

are

city,

go down

or the

space

Frequency the day?

other

Their

during

and

They

Another

They

They go under of the earth

owoy,

into

they

Clouds

are

Questions

Move

Behind

.Where Q36b

the Day

TABLE

for

Autumn (No. 51, Grade 1) E: Where are the sto” at night? c: In the sky. E: In the day? c: Into another city. E: Do the stars move? c: Yes.

else.

Rusrel (No. 59. Grade 1) E: Where are the stars at night? c: They an In the sky. E: During the day? c: In the day they are gone. Disappear E: Do the rtws move? c: I don’t know.

7. The stars dInappear.

h? c: wuy in space and when it gets daytime they go down. E: Do the .ten move? c Yes

d4 c: Behind the clouds. E: Do the stars move? t: Yes.

6. The stars move somewhere

Margaret (No. 60, Grade 1) E: Where ore the stars ot night? C: Up In the sky. E: Where ora the stars during the

Sandy (No. 57. Grade 1) E: Where ore the stars at night? c: In the sky. E: Where ore they during the

move Od into space.

2. The ,tan

1. The stws are occluded by clouds.

E: Where are the ston during the day? c: Thy am still in space. E: Can we roe them? c: No. E:why? c: Seause we’re facing the sun and the sun gives us too much light and we can’t we them. E: Do the stars move? c: No.

c: They 010 In q&a.

Donlelle (No. 4, Grade 5) E: Where ore the $an ot night?

8. The stat-a stw where thev ore

Betsy (No. 53. Grade 1) E: Where 0” the stoe at night? c: .ln tfw sky. E: Where ore the stars during the day? c: Down behind the hills. E: Do the stars move? c: Only when it is doytlme.

of the Stan

c: E: C. E: c: E: c:

day? They are not there. When are they? I don’t know. Do the stars move? Yes. How. Once In D while they move with you when you walk or ride a bike or when riding a car

hvln (No. 55. Grade 1) E: Where are the stars ot night’? c: In space. E: Where are the stars during the

9. Undetermined.

Brian (No. 43. Grade 3) E Where are the stars ot night? .c: Up in the sky. E: Where ore the stoo during the day? c: Under the earth. E: How did this hopp+n? c: When the sun comer out the stars go down and the moon goes dam. E: Do the stoo move? c: Ya¶

4. The stars move down under the earth.

TABLE 8 Investigating the Dlsappearonce

3. The stars move dawn on/in the ground.

Protocol Examples from the Questions

Donald (No. 49, Grade 1) E: Where are the stars ot night? c. up In the sky. E: Where am the stars during the day? c: Down hers. They went down. E: Down where? c: Down some place. E Do the stars move? c:Ye,

-Ills stms move down, unspecified as as to which side of the earth.

Sun revolves earth

Earth revolves the sun

Earth fixed

6. Sun and moon revolve around earth every day (0, 1, O=l)

7. Earth and moon revolve around the sun every day (0, 1, O= 1)

8. Earth rotates up/down; sun and moon fixed at opposite sides (1,3,7=11)

turns

Sun moves space

5. Sun moves out into space (1, 1,0=2)

sun

around

around

and

out

into

Sun moves unspecified

4. Sun and moon move up/down unspecified (3, 0, 0=3)

down

Sun moves down to the other side of the earth

on

is

of

9 and

Their

Frequency

around

Earth turns in up/down direection

Earth revolves sun and moon

into

moon

around

out

down and

Sun revolves earth

Sun moves space

Sun goes unspecified goes up

Sun goes down to the other side of the earth and moon goes up

Sun goes down on the ground and moon goes up

Sun is occluded by clouds or darkness

of the Cycle

TABLE Cycle

Explanations Day/Night

of the Day/Night

3. Sun and moon move up/down to the other side of the earth (2, 0, 0=2)

down

Sun is occluded clouds or darkness

The Disappearance the Sun &restions

Models

Sun moves the ground

Sun is occluded by clouds or darkness (2. ..- 1. 1=4P .

of Model

Mental

2. Sun and Moon move up/down on the ground (7, 0, 0=7)

I.

Type

Overall

Moon

Moon

Moon earth

Moon

does

moves

revolves

moves

Moon moves unspecified

Moon moves unspecified

Moon moves unspecified

not

move

unspecified

around

unspecified

up/down

up/down

up/down

or

or

or

of Grade”

Moon moves unspecified or does not move

The Movement of the Moon

as a Function

of

are occluded or behind clouds

the

move

stay

stay

where

where

Stars stay where move into space, occluded

Stars

Stars

out

are

are

Day

(continued)

they ore, or are

they

they

into

unspecified

go down to the side of the earth

Stars move space

Stars

Stars other

Stars disappear-occluded by clouds or hills--move into space

Stars move

The Disappearance the Stars During

Mixed: Earth rotates sun moves up/down fl. 0.4=51

13.

Undetermined (1, 2, 0=3)

16.

rotates (1, 2, 2=5)

turns

and

sun

turns

unspecified

rotates

Undetermined or God made it that wav

Mixed: sun occluded moves up/down and earth rotates

Mixed: earth and revolves

Mixed: earth rototes sun moves up/down

Earth

Earth turns around axis and sun is fixed

Earth turns around axis or unspecified

Earth fixed

and

and

is

turns

turns

turns

unspecified

around

around

in up/down

rototes

and

The first

Undetermined or God made it that wav

Mixed

Mixed: earth and revolves

Mixed: earth rotates sun moves up/down .

Earth

Earth axis

Earth axis

Earth turns direction

9 (Continued)

b The numbers in parentheses give frequency of explanation type for each grade. 3, and the third for Grade 5. The last number gives the frequency across grades.

Mixed: generol (0, 5, 1=6)

15.

14. Mixed: earth ond revolves

Earth rotates in unspecified direction (1, 1, 1=3)

12.

and

Earth rotates around axis; sun is fixed but moon moves (0, 1, O= 1)

11.

rotates around sun and moon at opposite sides 1=2)

Earth axis: fixes (0, 1,

10.

9. Earth rotates up/down; sun is fixed but moon moves (0. 1, 3=4)

TABLE

does

not

move

number

Moon move

Moon move

Moon move

The

Move move

or does

or does

or does

is the frequency

moves

moves

not

where

where

occluded

where

1, the second

Anything

Anything

Anything

Anything

stoy

stay

Stars

Stars

are

stay

Stars

Stars

for Grade

not

not

not

or mixed

or does

moves

moves

moon

moves

Moon moves unspecified or revolves around earth

Moon

Moon moves unspecified or revolves around earth

for

are

are

ore

Grade

they

they

they

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to the questionsregardingthe disappearance of the sunduringthe night and in the questionsrequiring an explanationof the day/night cycle. Two of thesechildrensaidthat somethingalsoblocksthe moon andthe starsduring the day, but the remainingtwo said that the moon and the starsmove in an unspecifiedway or move in order to go behindthe clouds which then coverthem. Wedistinguisheda classof mentalmodels(Models2 to 6) which arebased on the assumptionthat the alternationof day andnight happensbecausethe sun and the moon move up/down and exchangepositions. Thesemodels were further differentiatedwith respectto exactly wherethe sun and the moon move:Model 2: on the ground; Model 3: to the other side of the earth; Model 4: unspecified; Model 5: out in space; and Model 6: revolve around the earth.

Model 2: The Sun and the Moon Move Up/Down on the Ground. The sevenchildrenplacedin Mental Model 2 all said that the sun movesdown on the ground,in responseto the questionsregardingthe disappearance of the sun; that the moon movesup/down or unspecified,in responseto the questionsregardingthe movementof the moon; that the day/night alternation occursbecausethe sungoesdown with additionalpossiblereferenceto the moon goingup, in responseto the questionsregardingthe explanation of theday/nightcycle;andthat thestarsdisappearin variousways-undetermined, occludedby cloudsor hills, or move into space,in responseto the questionsregardingthe disappearanceof the starsduring the day. Model 3: The Sun and the Moon Move Up/Down to the Other Side of the Earth. Two childrenwereplacedin this mental model. They both said that the sun movesup/down to the other sideof the earth, that the moon movesup/down or unspecified,that the day/night cyclehappensbecause the sun movesdown to the other sideof the earthand the moon movesup, and that the starsalso moveto the other sideof the earth during the day. Model 4: The Sk and the Moon Move Up/Down But Unspecifiedwith Respectto EarthZide. The threechildrenplacedin this categoryall saidthat the sun and moon move up/down but differed from the childrenplacedin the previouscategoryin that they did not giveinformation asto whetherthe sun movesdown on the ground or to the other sideof the earth. Model 5: TheSun Moves Out in Space.Two childrenwereplacedin this category.They both saidthat the sunmovesout into spaceduring the night and that the samehappensto the starsduring the day. Thesechildrenalso explainedthe day/night cyclein termsof the sun’smovementinto spaceand said that the moon movesin responseto the moon,movementquestions.

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Model 6: The Sun and the Moon Revolve Around the Earth Every Day.

Only onechild wasplacedin this interestingmodelin which the sunandthe moon (at oppositesides)revolvearoundthe eartheveryday: Whenthe sun is on our sideof the earth,the moon is on the other side.Accordingto this modelthe starsremainwherethey areduringthe dayandthereasonwe cannot seethem is becauseof the brightnessof the sun’slight. We identified six different mental models (Models7 to 12),which used the movementof the earth as the basisfor forming an explanationof the day/night cycle. Thesemental modelswere differentiatedwith respectto thetypeof movementof the earth(e.g.,Table9, revolution- Model 7; rotation - Models8, 9, 10, 11and 12).The rotation modelswerefurther differentiatedwith respectto the type of rotation (up/down or west/east)aswell as with respectto the movementof the moon (moon fixed or revolving aroundthe earth). Model 7: The Earth and the Moon Revolve Around the Sun Every Day.

Only onesubjectwasfound to haveformed Model 7 accordingto whichthe earthand the moon revolvearound the sun every24 hours, and the stars staywherethey are. Model 8: The Earth Rotates Up/Down; the Suri and the Moon are Fixed at Opposite Sides. The 11childrenwho wereplacedin this classificationall

explainedthe disappearanceof the sun at night by sayingthat the earth turnsandthat the sunis fixed. Thesechildrenalso saidthat the moon does not movein responseto the questionsregardingthe movementof the moon. The day/night cyclewasexplainedin terms of the up/down rotation of the earth.They gavea variety of explanationsof the stars(e.g., the starsstay wherethey areand we cannotseethem becauseof the sun’slight, they are occludedby cloudsor move out in spaceduring the day). Model 9: Earth Rotates Up/Down;

the Sun 13Mxed But the Moon Moves.

This mental model is similar to the previousone with only one exception. Themoon is not fixed at the oppositesideof the earthfrom wherethe sunis locatedbut moveseitherin an unspecifiedway or revolvesaroundthe earth. Four childrenwereplacedin this category. Model 10: Earth Rotates Around Axis; the Sun and the Moon are FLved at Opposite Sides. Two children wereplacedin this category.They both

saidor indicatedin their drawingsthat the earth turns aroundits (north/ south)axisin responseto the questionsregardingthe disappearance of the sunat night and/or the questionsrequiringan explanationof the day/night cycle.In addition,they saidthat the moon doesnot moveandthat the stars, which also do not move, are occludedby cloudsduring the day.

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Model II: Earth Turns Around Axis; the Sun 2s Fiked, But the Moon Moves. Only one child wasidentified as havingthis model. This child said

that the earth turns around its axis, the sun is fixed, the moon revolves around the earth, and the starsstay wherethey are. Model 12: Earth Turns in Unspecified Direction; Sun is Fked But Moon May or May Not Move. The childrenplacedin this categorydid not specify

how the earthmoves.Someof thesechildrensaidthat the moon movesand othersthought it is stationary.Threechildren wereplacedin this model. A numberof mixedmentalmodelsof the day/night cyclewereidentified. Wedifferentiatedthemodelswhichpresenteda combinationof earthrotation and sunmovesup/down explanations(Model 13)from thosewhichconfused rotation andrevolution(Model 14).All otherswereplacedin a generalmixed model. The childrenwho did not provide enoughinformation to be placed in a mental model wereput in the undeterminedcategory. Model 13: Mixed. Earth Rotates and Sun Moves Up/Down. The five children placedin this model thought that the earth rotates and the sun movesup/down at the sametime. Most of thesechildrenthought that the moon also movesand provided different kinds of explanationsregarding the disappearance of the starsat night (e.g.,staywheretheyare,movedown, are occluded). Model 14: Mixed. Earth Rotates and Revolves. Another five children explainedthe day/night cyclesometimesin termsof the earth’srotation and sometimesin terms of its revolutionarymovement. Model 15: Mixed General. This categoryincludedvariousmixed explanations of the day/night cycle. Somechildrenattributed the day/night cycle both to the occlusionof the sun by cloudsand its movementdown to the ground.Somechildrenmentionedin additionto thesetwo explanationsthat the earthrotatesor revolves.Onechild first gavean explanationof the day/ night cyclein termsof the up/down movementof thesunandthe moon and lateran explanationin termsof therevolutionof thesunandthemoon around the earth. Six children wereplacedin this category. Model 16: Undetermined. The threechildrenin this categorygaveundetermined responsesto the questionsregardingthe disappearanceof the sun during the day and the questionsrequiringan explanationof the day/night cycle, or said that “God madeit that way” in one of them. The frequencyof the mental modelsof the day/night cycleasa function of gradeis shownin Table 9. We againseea shift from an initial model of an up/down moving sun and moon to earth rotation explanationswith increasinggrade.

DAY/NIGHT

of the Subiect

TABLE 10 Relationship Between Children’s Day/Night Cycle and their Models Model

NO.

No.

167

Overall Models of the Shape of the

Eartha

& Description

Earth

RecfoflgulOr

4. Sun and

49 Duo1 Earth 42, 51 53, 57, 59

moon

move

up/down

unspecified

1. Sun is occluded by clouds or darkness 2. Sun and Moon move up/down on the ground 5. Sun moves out into space

31, 52 Hollow 9 2

CYCLE

Sphere 1. Sun is occluded by clouds or dorkness 8. Earth rotates up/down: sun ond moon fixed at opposite sides 9. Earth rotates up/down; sun is fixed but moon moves 10. Earth rotates around axis: sun and moon fixed at opposite

13 20, 33 Flattened 43

Sphere 3. Sun and moon move 11. Earth rotates around

11 Sphere 24

1. Sun is occluded

39

7. Earth B. Earth sides 9. Earth

1, 3, 4, 7, 18, 19, 26, 20, 29, 50 5, 6, 36 a Only

sides.

subjects

who

hove

well

up/down to the other side of the axis: sun fixed but moon moves

by clouds

or darkness

and moon revolve rotates up/down;

around the sun every doy sun and moon fixed at opposite

rotates

sun

up/down:

specified

models

earth

is fixed

of both

earth

but

moon shape

moves and day/night.

Relationship Between Children’s Overall Mental Models of the Day/Night Cycle and Mental Models of the Earth

In theintroductionwe describedsomeof the constraintsthat mentalmodels of the earthimposeon mentalmodelsof the day/night cycle(seeFigure2). Sincewe had independentlyassignedthe children who participatedin this studyto mentalmodelsof the earth(seeVosniadou8cBrewer,1992),wehad theinformation requiredto examinethe relationshipbetweentheir mental modelsof the day/night cycleand their modelsof the earth. As Table 10 shows,this comparisonindicatedthat the childrenwith rectangle,disc,and dual earthmodelsprovidedexplanationsof the day/night cyclein termsof the up/down movementor occlusionof the sun (Models 1, 2, 4, or 5), or hadmixed or undeterminedmodels. We did not observeany caseswherea fundamentallyflat model of the earthwasassociatedwith an explanationof the day/night cyclein termsof therevolutionor rotation of the earth,or eventhe explanationaccordingto whichthe sun goesdown to the other sideof the earth(Table9, Model 3).

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On the other hand, childrenwith sphericalor syntheticmodelsof the earth typically gaverotational explanationsand only occasionallygaveexplanations of the day/night cyclein termsof occlusionor of the up/down movement of the sun and the moon. We carried out an analysisof the data presentedin Table 10.The childrenwho held flat modelsof the earthwere comparedwith the overall sampleof children with specifiedearth models with respectto the numberwho held “no rotation” models(Models1,2,4, & 5) versusother models of the day/night. The children with flat earth modelswerereliablydifferentfrom the overallsample,x2(1, N = 8)= 16.00, pc .OOl.Theseresultsare consistentwith our predictionsthat the mental model of a sphericalearthsurroundedby spaceis a necessary,but not sufficient, condition for the acquisition of the scientific explanation of the day/night cycle. DISCUSSION Mental Models of the Day/Night

Cycle

The resultsof the presentstudyshowedthat 38out of the 60 childrenin our samplecouldbeassignedto a coherentmentalmodelof the day/night cycle. A graphicrepresentationof the subsetof modelsthat the children in our sample constructed(not including undeterminedor mixed models), is presentedin Figure 5. The mentalmodelsof the day/night cyclewhichwe obtainedweresimilar to the explanationsidentified in previous research(e.g., Baxter, 1989; Sadler,1987).The childrenprovidedaccountsof the alternationof day and night in terms of the sun going down behindthe hills or beingcoveredby clouds,or they gaveexplanationsbasedon the notion that the sunrevolves aroundthe earthor that the earthrevolvesaroundthe sunor rotatesaround its axis. There was one explanationidentified by Sadler and by Baxter (accordingto which the moon blocks the sunat night) which wasnot identified in the presentsample,but which has appearedin someof our text comprehensionstudies(seeVosniadou,1991b). Therewasalsonoticeablesimilarity betweenchildren’smentalmodelsof the day/night cycle and the kinds of explanationsof the day/night cycle found in the history of astronomy.Like the early astronomers,the young children in our sample explainedthe day/night cyclein terms of the sun moving to distant parts of the earth, hiding behind hills or mountains,or setting.underthe earthin the westto rise in the east. Three Kinds of Mental Models: Initial, Synthetic and Scientific

Our theoreticalframeworkled us to predictthat we would find threekinds of mentalmodelsof the day/night cycle:(a) initial models-models consistent with the observationsbased on everydayexperience;(b) synthetic models-representingattemptsto reconcilethe culturally accepted,scientific

DAY/NIGHT CYCLE

The sun is occluded by clouds or darkness. 4.

169

The sun moves out into space.

The sun and the moon move up/down on the ground.

0

*

DT

0

The sun and the moon revolve around the earth once every day

The sun and the moon move up/down to the other side of the earth. 7.

6.

c (a) or

(b)

The earth rotates up/down or west/east. Sun and moon are fixed at opposite sides.

The earth and the moon revolve around the sun every 24 hours.

The earth rotates west/east. Sun is fixed but moon revolves around earth. Figure

5. Mental models of the day/night

cycle.

explanationof the day/night cyclewith observationsbasedon experience; and(c) scientific models-models which agreewith the scientific view. The mentalmodelsof the day/night cyclewe obtainedin this studycan indeed be groupedin thesecategories. We considerthe modelswhich assumethat the earth is stationaryand that the sun is occludedby something,movesin an up/down direction, or movesfar away(Models 1,2, and3 in Figure5) to be clearexamplesof initial models. Thesemodels do not show any influencefrom the culturally acceptedview in which the alternationof day/night is causedby the earth’s

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axis rotation, nor do they includeany other information which reflectsexposureto other aspectsof scientific information, suchas, for example,information regardingthe sphericalshapeof the earthor therevolution of the eartharoundthe sun.Thirteenout of the20first-gradechildrenin our sample providedinitial modelsof the day/night cycle, while only two third-grade childrenandonefifth-gradechild adoptedaninitial model.Analysisof these data showsthat among the first-gradechildren there were reliably more childrenwith initial modelsthan with syntheticmodels,x2 (1, N= 16)= 6.25, p< .02. Syntheticmodelsrepresentattemptsto assimilatescientificinformation to an existinginitial model. The obtainedsyntheticmodels(Models4,5,6, and 7 in Figure 5) differed from the scientific explanationalong three dimensions:what movesto producethe day/night cycle,how theseobjects move, and whetherthe moon is causallyimplicatedin the day/night cycle. As we have seen, some children think that the day/night cycle results becausethe sun and the moon revolve around the earth, or becausethe earth revolvesarounda stationarysun. Older children think that the earth rotatesup/down and that the sun and moon are fixed at oppositesides.A number,,of the third-grade children and a majority of the fifth-grade children in our sampleprovided syntheticmodels of the day/night cycle (grade1: 3/20; grade3: 7/20; grade5: 11/20).Analysis of thesedata show that amongthe fifth-grade children therewerereliably more childrenwith syntheticmodelsthan with initial models, x2 = (1, N= 12)=8.33, pc .Ol. The model which comesclosestto the culturally-acceptedscientific explanationis Model 8 (Figure5), which includesa fixed sun,axisrotation of the earth, and revolution of the moon aroundthe earth. Only one child, a third grader,formed this model. The remaining22childreneitherdid not havecoherentmodelsor did not provideenoughdatafor usto understandtheir models.Threechildrengave models.inwhichthe directionof the earth’srotation wasunspecified(Model 12, Table 9), while threeadditional children were placedin a categoryin which the day/night model wascompletelyundetermined(Model 16,Table 9). Finally, 16childrenwereplacedin a mixed modelcategory.Five of them usedboth the up/down movementof the sunand the rotation of the earth to explainthe day/night cycle(Model 13,Table 9). Another five usedboth the earth’srevolutionaroundthe sunandthe earth’srotation to explainthe day/night cycle (Model 14, Table 9). The six remaining children useda variety of mechanismsin their explanations(Model 15, Table9). Age Trends in Mental Model Construction

Although the presentstudy was cross-sectionaland not longitudinal, the results clearly show that the majority of first-gradechildren enter school having formed an initial model of the day/night cycle. During the elementary school yearsthey appearto replacethe initial model with a synthetic

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171

model. By the end of their elementaryschool years,some children have replacedtheir syntheticmodel with the scientific model. It is interestingto note that the likelihood of children’smodelsbeinginconsistentincreasesafter the first grade.This finding is in agreementwith the hypothesisthat the mixed modelsare a product of children’sfailed attemptsto reconciletheir initial modelswith the culturally acceptedmodel ratherthan someoverall inability to form coherentmodels. Constraints on Children’s Mental Models of the

Day/Night

Cycle

In the Introductionwe discussedhow mental modelsof the day/night cycle areconstrainedby a hierarchyof constraints(presuppositions,beliefs,and mentalmodelsof the earthandthesun).Theseconstraintsweredescribedin the hypothetical knowledgeacquisition processshown in Figure 1. The mental models we have obtainedin this study are in agreementwith this hypothesizedconceptualstructure. Presuppositions

Thehypothesisthat certainontologicalandepistemologicalpresuppositions constrainchildren’s mental models was confirmed. The resultssuggested that the childrenhonoredseveralepistemologicalpresuppositions.All the children were capableof understandingth,at the alternation of day and night constitutesa phenomenonthat requiresan explanation.In addition, almostall of the children in our sampleprovided mechanistic/causalexplanationsof this phenomenon.Only one child said that “God makesit happens,”and noneof the children in this samplegaveanimistic explanations. It should be noted that the scientific explanationof the day/night cycledoesnot requirethe revisionof theseepistemologicalpresuppositions. It does,however,requirethe revisionof someontologicalpresuppositions which influencechildren’smental models of the day/night cycleindirectly through their mental models of the earth. Theseconstraintswill be discussedin the sectiontitled “Mental Models of the Earth.” Beliefs

Our resultsshowedthat most childreninferredfrom their observationsthat theday/night cycleis causallyrelatedto the appearanceand disappearance of boththe sunandthe moon. The erroneousbeliefthat themoon is causally implicatedin the day/night cycle appearedto be presentin the synthetic modelsof the oldestchildrenin our sample.It is not clearwhy this belief is sopersistent.It couldberelatedto the fact that in the usualpresentationsof thescientificexplanationof the day/night cyclethe role of the moon is not usuallyclarified. In an investigationof theastronomyunits on the day/night cyclein four widely-usedscienceseriesfor elementaryschoolstudents,we did not find any discussionof the role of the moon in the day/night cycle (Vosniadou,1991a,1991b).

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The mechanismusedto explainthe appearanceand disappearance of the sun and the moon relied either on the notion that their movementtakes themsomewherewherethey cannotbe seen,or on the notion that something comesand occludesthem. We did not obtain any switch on/off explanations. The mechanismaccordingto which the viewerturns (or, rather, that the earth turns) so the viewer cannot seethe object anymoreseemsto be availablebut is not applieduntil the childrencanconceptualizethe earthas rotating or revolving. As we havealreadyseen,this doesnot happenuntil the children form the model of an earthsurroundedby space,eventhough this model may not be the scientific model of a sphericalearth with people living all aroundit on the outside. Mental Models of the Earth

Someof the most interestingfindings of the presentstudy haveto do with the constraints that mental models of the earth impose on the mental modelsof the day/night cycle.Mental modelsof the earthinfluencemental models of the day/night cyclein two ways: Fist, considerthe flat earthversussphericalearthdistinction. Flat earth modelsare constrainedby the presuppositionsthat the ground is flat and that unsupportedthingsfall (cf. Vosniadou& Brewer,1992).In Figure2 we describedhow thesepresuppositionsand the flat earth modelsthey entail constrain children’s mental models of the day/night cycle. Our results showedthat theseconstraintswere,in fact, observed.All the childrenin our samplewith a flat earthmentalmodelformedinitial modelsof the day/night cycle(seeTable 10). In addition to the flat vs. sphericalearth distinction, there were other aspectsof children’s specificmental modelsof the earth that appearedto imposeconstraintson how they explainedthe day/night cycle.An example of this canbefound in children’salternativeinterpretationsof the up/down movementof the sun dependingon their particular mental model of the earthas shownin Figure 3, explanationtype 4. We alsofound that childrenwith hollow spheremental modelshaddifficulty comingup with a coherentmodel of the day/night cycle.Sevenof the 12childrenwith hollow spheremodelsgaveunspecified,mixed, or undetermined,day/night cycle explanations.There wereonly two examplesof an up/down rotation mental model of the day/night cycle, a finding which is consistentwith the hypothesisthat these children have constructed the .__ hollow spheremodel underthe constraintsof an up/doGgravity presupposition. Obviously,the up/down rotation of the earthis not a very viable solution for thesechildren. A better solution of the day/night problem, givena hollow spheremodel of the earth, is to assumea west/eastrotation of the earth, which doesnot violate the up/down gravity presupposition.’ Two childrenwith hollow spheremodelsselectedthis solution. The mental model of a west/eastrotating hollow sphereis also a problem for children

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CYCLE

173

with hollow spheremodels,however,becauseit doesnot easilyexplainthe disappearance of the sunat night. In orderto makethesundisappear at night somechildrencreatea “day side” of the earth and a “night side” of the earth,Giventhis model, the sundisappearsfrom our sightwhenwe moveto the “night side” of the earth, as the earth rotatesfrom west to east(see drawingnumber 12, Figure 4, and explanationtype 12,Table 4). Anotherinterestingempiricalrelationshipexistsbetweenthe directionof theearth’srotation and children’searthshapeand day/night cyclemodels. Therewereonly threechildrenwho formed west/eastrotation modelsof the earth.Two of them had a hollow sphereearth model and one a flattened sphereearth model. On the other hand, there were 23 children with sphericalearth models, 13 of whom attributed the day/night cycleto the rotational movementof the earth. All of these13 children conceptualized the earthasrotating in an up/down direction(i.e., rotation aroundan axis throughthe equator).There are a number of possibleexplanationsof the preferencesphericalearth children show for an up/down rotation of the earth.One explanationis basedon the similaritiesthat exist in the model of a rotatingearthanda fixed sun(model7a, Figure5), and the model of a stationaryearthand anup/down movingsunandmoon (seemodel4, Figure 5). The two models are identical with the exception that in one the day/night cycle is explainedin terms of the rotational movementof the earth(up/down rotation) whereasin the otherit is explainedin termsof the up/down linear movementof the sun and the moon. It appearsthat childrenwith a sphericalearthmodelwho haveformed modelnumber4 (Figure 5)may tendto moveto model 7a, whenthey aretold that the reasonfor the disappearance of the sun is the rotational movementof the earth. Model 7a (Figure 5) is also consistentwith the belief that the sun is locatedabovethe top of the sphericalearth,ratherthan in the planeof the earth’sequator.Sucha belief may be a remnantof an initial model of the day/night cycle,basedon everydayexperience,which children continueto hold evenwhenthey haveunderstoodthat the shapeof the earthis spherical. Givensucha belief, the creationof a model of the day/night cyclewith explanatoryadequacyrequiresan up/down rotation of the earth, so that thepersonlocatedon the top part of the earth, facingthe sun,will be away from the sun when it is night. Our analysesof the direction of the earth’s rotation suggestthat the up/down rotation of the earth is a rather subtle form of syntheticmodel construction. To conclude,the resultsof the presentstudyconfirm our originalhypothesisthat children’s mental models are influencedby a hierarchyof constraints,which we havecalledpresuppositions,beliefs,and mentalmodels, that operatesimultaneouslyon the knowledgeacquisitionprocess.Someof theseconstraints(e.g., the ontologicalpresuppositionswe haveidentified, thebelief that the sun moves,etc.), operatein a similar fashionin the case of childrenwho grow up in different cultures(seeVosniadou,in press-b),as

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well as in the early astronomerswho tried to explain the day/night cycle, The latter finding supportsa limited form of recapitulation(cf. Brewer& Samarapungavan,1991)to the extentthat someof the presuppositionsand beliefsconstrainingthe constructionof mentalmodelsin childrenandearly astronomersaresimilar. Explanations of the Construction of Synthetic Models of the Day/Night Cycle

In our previouswork (Vosniadou& Brewer, 1992)we explainedthe formation of syntheticmodelsof the earthasthe productsof the graduallifting of the constraintswhich operateon initial modelsof the earthunderthe influenceof the information providedby the culture. The resultsof the present investigationshowthat this analysiscanalso explainthe formation of synthetic modelsof the day/night cycle. For easeof expositionwe will basethis discussionon the subsetof day/ night models presentedin Figure 5. The three initial day/night models (Models 1, 2, 3) are constrainedby the initial earth shapemodel of a flat andstationaryearth. In thesemodelsthe day/night cycleis producedeither by the up/down movementof the sun (moon) to the earth’ssurfaceor by the occlusionof the sun (moon). The first fundamentalchangewhich allows the formation of synthetic modelsof the day/night cyclerequiresthe lifting of the constraintimposed by the model of a flat earth, and, therefore,indirectly, of the constraints imposedby the ontologicalpresuppositionsthat the groundis flat andthat unsupportedobjectsfall in a downwarddirection.By adoptingthe modelof a sphericalearthasan object (motionless)in spacechildrencan explainthe day/night cycleby havingthe sun (moon) go down to the other sideof the earth (Model 4). Acceptingthe model of a sphericalearth surroundedby spaceallows a number of additional syntheticday/night models.The children who hold Model 5 believethat the sun and moon revolvearoundthe earthevery24 hours. This model is similar to Model 4 exceptthat the postulatedmovement of the solarobjectsis revolutionratherthan up/down. It seemslikely that the children holding Model 5 have been influencedby information from the culture about the revolution of the moon aroundthe earth or of the eartharoundthe sunwhich they haveusedto generatea classicgeocentric model of the day/night cycle. The childrenwith Model 6 havegiven up the belief that the earth does not move. Thesechildren believethat the earth revolvesaround the sun every24hours. Note that if oneassumesthat the earthdoesnot revolveon its axis, then this model providesan explanatoryaccountof the day/night cycle.Nevertheless,we think it is unlikely that elementaryschoolchildren havearticulatedtheir modelswell enoughto understandthis point andthat it is more likely that most of thesechildren haveassimilatedinformation

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175

about the earth’s yearly revolution around the sun into their day/night model without developing a completely specified model. The children with Model 7 have also given up the constraint that the earth is motionless but use the earth’s rotation (either up/down or west/east) to explain the day/night cycle. This model begins to converge on the scientific model but still contains an important synthetic component. The children with this model assume that the sun and moon are fixed in space at opposite sides of the earth and thus have generated an elegant solution to the day/night cycle. The children with Model 8 have finally attained the essence of the culturally accepted scientific model with a rotating earth, a fixed sun, and the moon rotating around the earth. It seems likely that even children with this model have not articuluted their models fully to capture phenomena such as the time it takes the moon to rotate around the earth or the occurrence of the phases of the moon. Contrary to our original hypothesis that the stars would also be causally implicated in the day/night cycle, this belief is not as strong as the belief that the moon is associated with night. While most of the young children provided explanations for the disappearance of the stars during the day, which were similar in kind to the explanations for the disappearance of the moon, the great majority of the children in our sample thought that the stars are stationary and knew that it is possible for them to be in the sky during the day but not to be seen because of the brightness of the sun’s light. Criteria Honored by Children in Constructing Mental Models We will now examine children’s mental models of the day/night cycle in terms of the criteria of accuracy, logical consistency, and simplicity. Accuracy The mental models of the day/night cycle that the children constructed were for the most part empirically accurate, in that they were consistent with children’s observations. One of these observations is that the sun is in the sky only during the day. The other is the erroneous observation that the moon is in the sky only during the night. Note that empirical accuracy was present even in the case of the synthetic models, despite the fact that synthetic models are the products of significant misrepresentations of scientific information. In fact, it is often the case that the “errors” in the synthetic models actually increase their empirical accuracy, given the range of observations available to children. For example, the children with models 8 and 9 (Table 9), who assumed that the sun and the moon are fixed on the opposite sides of a rotating earth, formed models which were empirically accurate given the (erroneous) observation that the moon is present in the sky only during the night.

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Logical Consistency

The 38 childrenassignedto a mental model of the earthgavelogically consistent responsesto the four sets of questionswhich investigatedtheir explanationsof the disappearance of the sunat night, the disappearance of the starsduringthe day, the movementof the moon, andthe alternationof day and night. In addition, the obtainedmental modelsof the day/night cyclewereconsistentwith thehypothesizedconstraintsimposedby children’s mentalmodelsof the earth.Roughlya third of the childrenwho wereput in the mixed categoriesappearedto be in a transitory state from an initial model of an up/down moving sunto an earthrotation explanation(Model 13,Table9). Another third appearedto be confusingthe earth’srevolution aroundthe sunandthe earth’srotation on its axis (Model 14,Table 9). The final third of the childrenwith mixed modelsgaveresponsesthat werecomplex combinationsof various models.The remaining children’sresponses wereeitherunspecified(Model 12,Table9) or underdetermined(Model 16, Table 9). While our resultsmay appearto contradictreportsthat not only young children but alsohigh schooland collegestudentsgive internally inconsistent responsesto questionstapping aspectsof their knowledgeof science (e.g., disessa,1988,1993;Reif & Allen, 1992;Solomon, 1983),this may not be necessarilythe case.In most of the existingresearchwheresuchinconsistencies are noted,a studentis consideredto beinternally inconsistent if he or sheusesa givenscientificconceptcorrectlyin somecasesbut not in others.The possibility that this studentis using a representationwhich is different from the scientificone,but which is nevertheless well-definedand internally consistentand which can account for the obtained pattern of “correct” and “erroneous” responses,is usually not exploredin a systematic fashion.Until more detailedanalysisof students’mental representations in theseother domainsis carriedout we will not know if the conflict betweentheseliteraturesis apparentor real. Simplicity

In the previoussectionwe arguedthat we were ableto accountfor a large percentageof our databy assumingthat the childrenin our sampleadopted well-definedmental models of the day/night cycle which they usedconsistently to answer a number of different questions related to this phenomenon.In addition to beingsensitiveto issuesto logical consistency, the childrenalso seemedto showsomesensitivityto issuesof simplicity in their explanations. The term simplicity is usedhereto referto the useof the samemechanism to accountfor different,althoughrelated,phenomenasuchasthe disappearanceof the sunduringthe night andthe apparentdisappearance of the moon and starsduringthe day. The findingsof this studyindicatethat the majority

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of the childrenin our sampleusedthe samemechanismto explainthe disappearance of the sunandthe disappearance of the moon.With the exception of the children assignedto the occlusionmodel (Model 1, Table 9), there wasa strongrelationshipbetweenthe specificexplanationgivenfor the disappearance of the sun during the night and of the moon during the day. Theserelationshipscan be examinedin detail in Table 9. As can be seenin this table, the children who assertedthat the sun goesdown behind the mountainsor down to the other sideof the earth alsostatedthat the moon comesup when the sun goesdown. We call this the “hydraulic model” becauseit is as if the two movementsare dependenton eachother. The downwardmovementof the suncausesthe upwardmovementof the moon. The interdependencyof the movementsof the sun and the moon is apparentin the other explanationsof the day/night cycle.For example,the childrenwho said that the sun revolvesaroundthe earth also mentioned revolutionto be the movementof the moon. We did not find any models wherethesunrevolvesaroundtheearthbut themoon movesin an up/down directionor the reverse.Finally, most of the childrenwho adoptedthe explanationin which the day/night cycleis causedby the earth’srotation conceptualizedboth the sunandthe moon asstationary.Again, wedid not find any instanceswherethe earth wasseenas rotating aroundits axis, the sun wasstationary,andthe moon movedin an up/down direction,althoughwe hadthe scientific model wherethe earth rotatesaround its axis, the sun is stationaryand the moon revolvesaround the earth. Note that children’smodel of an earthrotating in an up/down direction with the sun and moon fixed at oppositesidesis a simpler model than the scientificmodelin which the moon revolvesaroundthe earth.It is the occurrenceof modelssuch as this that lend such strong support to the overall “constructivist” position. Explanationsof the disappearance of the starsat night werenot ascoordinatedwith the disappearance of the sunand the moon aswasthe caseof themoonand sunthemselves.With theexceptionof the childrenwho attributedtheday/night cycleto the up/down movementof the sun,of the moon, andof the starson the othersideof the earth,a differentspecificmechanism wasusedto explainthe disappearance of the starsduringthe night than the oneusedto explainthedisappearance of thesunandthe moon. In addition, thegreatmajority of the olderchildrenin our sampleknewthat the starsare presentduringthe daybut that wecannotseethem becauseof the brightness Of the sun’s light and gavethis as the explanationfor their apparentdisappearance during the day. TOconclude,the findings from the presentstudyshowthat the majority of the childrenin our sampleformed empiricallyaccurateandlogicallyconsistentmental modelsof the day/night cycle.In addition, their modelsexhibited systematicrelationsbetweenthe mechanismsused to explain the

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disappearance of the sunandthoseusedto explainthe disappearance of the moon which showedconsiderablesensitivityto issuesto simplicity. These findings agreein generalwith resultsobtainedby Samarapungavan (1992) showingthat whenchildrenchoosebetweentheoriestheypreferexplanations which are empirically accurateand logically consistent.While children demonstrateconsiderableskills in constructingand modifying their mental modelsto fit the availabledata,the presentresultsdo not showthat children have developedmetaconceptualawarenessand consciouscontrol of their mental models(D. Kuhn, 1989). The Nature of Conceptual Change

The initial models of the day/night cycle in which the sun moves down behindthe mountains,goesout into space,or is occludedby oloudsarevery different from the culturally acceptedmodel of a stationarysun, the earth rotating around its axis, and the moon revolving around the earth. Our resultsshow that six-year-oldchildren come to school having formed an initial model of the day/night cyclewhich, over a period of years,changes to a syntheticmodel and then to a scientific model. How canwe bestcharacterizethe kind of conceptualchangewhich takes place during the elementary school yearsas the cultural knowledgehas a greaterand greater impact on the children’smodelsof the day/night cycle? Accordingto Spelke(Ml), conceptionsof physicalobjectsdo not undergo fundamentalchangewith development,and knowledgeof the sort we have calledontologicalpresuppositions (e.g.,the continuityandsolidityof physical objects)continuesto beentertainedin adults’commonsense reasoningabout physicalobjects.One kind of fundamentalknowledgeabout the behavior of physicalbodiesrelevantto the issuesdiscussedin this paperis the concept of an up/down gravity. This is the knowledgethat “unsupportedthingsfall in a downwarddirection,” which appearsto be presentevenin 6-month-old infants (Needham& Baillargeon,1993;Spelke,1991).Our resultsshowthat children’spresuppositionsregardingan up/down gravity needto berevised and arerevisedby the elementaryschoolchildrenwho providescientific or even synthetic explanationsof the day/night cycle. We interpret these resultsto indicatethat the processof knowledgeacquisitioncannotbe fully accountedfor using the notion of enrichment(Spelke,1991). In an important recentbook on conceptualchangein scienceThagard (1992)arguesthat conceptsare organizedin theorieswhich are primarily structuredvia kind and part-wholehierarchies.Viewed in this way, conceptual changemay involve the addition or deletionof concepts,or their transformations.The transformationscan be simple-when they involve differentiation or coalescence;or complex-when they involve alterations in kind relationsor part relations.Thagardcalls onesuchchange“branch jumping” sinceit involvesthe movementof a conceptfrom onebranchof

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(A) From Ptolemy to Copernicus Major Bodies

(B) From Grade 1 to Grade 5

Figure

6. Changes

in the system

of categorization

of the major

astronomical

bodies.

the kind-hierarchy to another. An example of branch jumping which, according to Thagard, is one of the most radical kinds of conceptual change characterizing scientific revolutions, is illustrated in Figure 6. This figure describes the move from the Ptolemaic system’s classification of the celestial bodies (Figure 6a) to the modern, Copernican view. Copernicus reconceptualized the earth as a planet and reclassified the moon as a satellite of the earth. (The sun was not recognized as a star until around 1800.) Another important recent approach to conceptual change is found in the work of Chi and her colleagues (Chi, 1992; Chi, Slotta, & de Leeuw, in press). Chi has described conceptual change in terms of a special kind of branch jumping which involves two ontologically distinct categories. According to this theory, conceptual changes take place when a concept belonging to one ontological category (e.g., matter) is re-assigned to a different ontological category (e.g., process) as was the case historically with the concept of heat. The results of the present study support Thagard’s (1992) and Chi et al.‘s (in press) analysis. Children’s categorization of astronomical objects seems

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to undergoa kind of branchjumping which is similar to the onewhich took placein the history of science.As shownin Figure6b, six-year-oldchildren with initial mental modelsof the day/night cyclethink that the earth is a physicalobject while the sun and the moon are celestialobjects.We have arguedthat the mental representationof the earth as a spheresurrounded by spaceis a precondition for understandingthe scientific explanationof the day/night cycle. In the cosmologyof the third graderwho providesa scientificexplanationof the day/night cycle,the earthhasbeenreclassified asa celestialbody, a planet,whichrotatesaroundits axisandrevolvesaround the sun. At the sametime, the sun, the moon, and the starsare clearlydifferentiated,the child havingrecognizedthat the moon is not causallyrelated to the day/nightcycle,andthat the starsaredifferent from theothercelestial bodies.Thus, our datashowthat the developmentof children’scosmologies provide evidencefor the sametypesof radical conceptualreorganizations that haveoccurredin the history of science,. Onelimitation of theThagard(1992)and Chi et al. (in press)approaches, however,is that they do not explainwhy the reorganizationsof knowledge which are characterizedas branchjumping are so difficult for scientistsin the developmentof scienceor for childrenacquiringnewknowledge.Thagard (1992)acknowledgesthat branchjumping is the product of revolutionary changesin scientists’underlyingsystemsof beliefs,but doesnot go further to explainthe natureof thesebeliefsandtheir changes.In our work wehave adopteda semanticratherthan a syntacticdescriptionof conceptualchange. We try to characterizethe kinds of knowledgestructuresthat underly children’s mental models of the day/night cycle and to describethe changes that happenin thesestructuresduring the knowledgeacquisitionprocess. Fundamentalto our way of thinking is the notion of constraint.We have argued that the reorganizationsof knowledgetaking place during the knowledgeacquisitionprocessoccur via the reinterpretationof a hierarchy of constraintswhich differ in their degreeof entrenchment.The deepestand most difficult constraintsto changearethoseweterm presuppositions.Presuppositionsform the basisof an individual’s ontology and epistemology and exert an enormousinfluenceon the knowledgeacquisitionprocess. In addition to the presuppositions,our theoreticalframeworkincludesa number of additional constructssuchas beliefs and mental modelswhich appearto act as second-orderconstraintson the knowledgeacquisition process,Beliefsand mental models are examplesof what Keil (1990)calls “acquired-domain-specific”constraints.Thesearethe kinds of constraints which developwith the acquisitionof expertise,asthestructureof the information learnedcomesto exertits own uniqueinfluenceon the knowledge acquisition process.Our data suggestthat constraintsof this type come to exert a powerful role in the child’s understandingof complexphysical phenomena.

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The accountof conceptualchangepresentedin this paperis in someways similar to the accountof theorychangedevelopedby Carey(1985;1991)but &O differs from it in important respects.Careyproposesthat childrenstart by holding theory A and then switch to theory B which differs from the originaltheoryin termsof its structure,the phenomenait explains,and the individual conceptsit includes.In our approachthe theory-like natureof the structuresunderlyingchildren’sperformanceis tracedto a set of presuppositions,beliefs, and mental modelswhich constrainthe way a given child will representa specificsituation. Within this theoreticalframework, conceptualchangeis a continuousprocesswhich happensasthe different kindsof constraintsmentionedabovearereinterpretedduringthe knowledge aquisitionprocess.Oneof the advantagesof the presentapproachis that it canaccountfor thegradualnatureof conceptualchangeandfor the formation of syntheticmodelsof the world. CONCLUSIONS Theresearchdescribedin this article attemptedto identify and characterize elementaryschool children’s mental models of the day/night cycle. The resultsshowedthat the majority of the studentsin our sample(38out of 60) useda well-definedmentalmodel of the day/night cycleto answerour questions.Thesemodelswerelogicallyconsistentand for the most part werealso characterizedby empirical accuracyand simplicity. Initial mental models showedno influencefrom the currently acceptedscientific explanationof theday/night cycle,while syntheticmental modelsrepresentedattemptsto assimilatethe scientific explanationsto existing conceptualstructures.A theoreticalframework wasoutlined which is capableof explainingthe formationof initial andsyntheticmodelsby postulatingthat thereis a hierarchy of constraints-presuppositions, beliefs,andmentalmodels-some of which arepresentearlyin the child’s life and otherswhich emergelater out of the structureof the acquiredknowledge,andwhich guidethe knowledgeacquisition process.

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