JenniferGangerDepartmentofPsychologyUniversityofPittsburghMichaelRBrentDepartmentofComputerScienceWashingtonUniversityinSaintLouisDatainthisstudywereoriginallycollectedaspartoftheMassachusetts ID: 177637
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ReexaminingtheVocabularySpurtJenniferGangerUniversityofPittsburghMichaelR.BrentWashingtonUniversityinSaintLouisTheauthorsaskedwhetherthereisevidencetosupporttheexistenceofthevocabularyspurt,anincreaseintherateofwordlearningthatisthoughttooccurduringthe2ndyearoflife.Usinglongitudinaldatafrom38children,theymodeledtherateofwordlearningwithtwofunctions,onewithaninflectionpoint(logistic),whichwouldindicateaspurt,andonewithoutaninflectionpoint(quadratic).Comparingthefitsofthesetwofunctionsusinglikelihoodratios,theyfoundthatjust5childrenhadabetterlogisticfit, JenniferGanger,DepartmentofPsychology,UniversityofPittsburgh;MichaelR.Brent,DepartmentofComputerScience,WashingtonUniver-sityinSaintLouis.DatainthisstudywereoriginallycollectedaspartoftheMassachusettsInstituteofTechnologyTwinsStudyandarepartiallyreportedinJenniferGangersPhDdissertation.AnearlierversionofthisworkappearedintheProceedingsofthe25thAnnualBostonUniversityConferenceonLan-guageDevelopment.ThisstudywassupportedbyNationalInstituteofChildHealthandHumanDevelopmentGrantHD18381toStevenPinkerandGrantHD08493toJenniferGangerandbyNationalInstituteonDeafnessandOtherCommunicationDisordersGrantDC03082toMichael Anothertheoryisthatthespurtmarksachangeinchildrenobjectconcepts.Inoneversionofthistheory(Lifter&Bloom,1989),infantsbegintousewordswhentheyenterPiagetsSen-sorimotorSubstage6andthenshowavocabularyspurtastheirobjectconceptsbecomemoredetailedanddifferentiated,aroundthecloseofSubstage6.SimilarideashavebeenadvancedbyCorrigan(1978)andBates,Benigni,Bretherton,Camaioni,andVolterra(1979).AnothertheoryabouttherelationshipbetweenobjectconceptsandwordlearningcomesfromGopnikandMeltzoff(1987).Theyproposedthatthechildsabilitytosortobjectsintogroupsbasedoncategorymembership(usingataskknownastwo-categorysorting)improvesaroundthetimeofthevocabularyspurt(Gopnik&Meltzoff,1987;Mervis&Bertrand,1994;Poulin-Dubois,Gra-ham,&Sippola,1995).(Thiscorrelationhasbeendisputed,seeGershkoff-Stowe,Thal,Smith,&Namy,1997;Scha-fer&Plunkett,1998;Woodward,Markman,&Fitzsimmons,1994.)GopnikandMeltzoffs(1987)explanationisthatcatego-rizationreflectsthechildsrealizationthatobjectscanbesortedinbasic-levelcategoriesandthatsuchanunderstandingisnecessaryforlearningbasic-levelnames.Oncethisunderstandingisinplace,thechildsacquisitionofwordscanproceedatamorerapidpace,allowingavocabularyspurt.MervisandBertrand(1994)addedthatthenovelnamenamelesscategoryprinciple(N3C),aword-learningconstraintspecifyingthatnovelnamesareextendedtonovelobjects,alsoemergesatthesametimeasthevocabularyspurtandisaprerequisitebothforitandfortwo-categorysorting.Thevocabularyspurthasalsobeenrelatedtoadvancesofamorelinguisticnature.Plunkett(1993)suggestedthatthevocab-ularyspurtoccurswhenwordsegmentationhasbeensolved,implyingthattheabilitytopickthewordsoutfromrunningspeechopensthefloodgatestoproducingmanynewwords.Walley(1993)arguedthatthesegmentalrepresentationofwordschangesasthevocabularyspurtoccurs,leadingtotheabilitytorepresentwordsinmoreaccuratedetailasmoreandmorewordsarelearned(thoughseeSwingley&Aslin,2002,forconflictingideas).Ninio(1995)providedevidencethatadvancesinpragmaticsarecorre-latedwiththevocabularyspurt,suggestingthatgainsinsocialcognitionpermittheacquisitionofwordsatahigherrate.Finally,DaprettoandBjork(2000)contendedthatthespurtinproductivevocabularyisdrivenbythedevelopmentofwordretrievalabilities.TheVocabularySpurtasaDevelopmentalMilestoneInadditiontotheliteraturededicatedtouncoveringthemeaningofthevocabularyspurt,therearemanystudiesinwhichthephenomenonhasbeenusedsimplyasamilestoneoflinguisticandcognitivedevelopment(e.g.,L.Bloom&Capatides,1987;Choi&Gopnik,1995;Gershkoff-Stowe&Smith,1997)andasamarkerofdevelopmentalchange(e.g.,Fischer,Pipp,&Bullock,1984,citedinLifter&Bloom,1989).Althoughresearchershavenotreachedaconsensuseitherontheunderlyingcauseofthevocab-ularyspurtoronwhichcognitivemeasuresarecorrelatedwithit,thereseemstobelittledoubtabouttheexistenceofthevocabularyspurtitselforitsultimateimportancetocognitivedevelopment.EvenElmanetal.(1996),whoarguedthatthevocabularyspurtmaynotreflectanyunderlyingcognitivechange,assumedthatthereisanobservablespurtintherateofwordlearning(seealsoBates&Carnevale,1993;vanGeert,1991).TheexistenceofthevocabularyspurtseemsconfirmednotonlybyeyeballingdatafromstudiessuchasFensonetal.(1994),inwhichalarge,cross-sectionalsampleofchildrenappearedtoshowaspurttrend,andDromi(1987),inwhich1childstudiedlongi-tudinallyalsoappearedtoshowaspurt,butalsobythestudiescitedintheprevioussection,whichidentifiedaspurtinchildrenvocabularydevelopmentandtestedwhetheritwascorrelatedwithsomecognitiveorlinguisticchange.However,asisshowninthenextsection,themethodscurrentlyusedtoidentifythespurtcannotprovidedefinitiveevidenceaboutwhetherthespurtexists.IdentifyingtheSpurtTodeterminewhenachildundergoesthevocabularyspurt,oneofthreemethodsistypicallyused.Thefirstissimplytoestimateachildsoverallvocabularysizeandage.Ifthesizeissubstantiallygreaterthan50words,orifthechildsageisgreaterthan20months,itisassumedthatthechildhasundergoneaspurt.Thesize/agetestisaquickanddirtymeasure,usedbyresearcherswhosemainfocusisnotthespurtitselfbutsomeotherprocessthatisthoughttoberelatedtothespurt(e.g.,Schafer&Plunkett,1998).Thosewhousethismetricassumethatthereisaspurtandthatmostchildrenexperienceit.Avariantonthisapproachistoconsideraratioofcomprehensionandproductionvocabulary(Dapretto&Bjork,2000).Asecondmethodistoproduceagraphofvocabularysizeovertime,suchasthatgivenforthechildKerenbyDromi(1987),andtoeyeballitforaspurt.Althougheyeballingdatafortrendsisanimportantstepinallkindsofresearch,doingsomaybemisleadingwhenitcomestofindingavocabularyspurt,forreasonsthatwillbeelaboratedlater.Finally,themostcommonmethodforidentifyingwhenachildhasavocabularyspurtiswhatweshallcallthethresholdap-.Inthisapproach,athresholdofwordsperunitoftimemustbecrossed.Asurveyoftheliteraturerevealedthefollowingthresholds:MervisandBertrand(1994,1995)requiredthatchil-drenlearnatleast10newwordsinaperiodof14daysbeforetheywereconsideredtohaveenteredavocabularyspurt;GopnikandMeltzoff(1987)requiredatleast10newobjectwordsin3weeks;LifterandBloom(1989;seealsoL.Bloom&Capatides,1987)requireda20-wordminimumplus12newwordsin1month;ChoiandGopnik(1995)required10newobjectwordsin34weeksforanounspurtand10newverbsinthesameperiodforaverbspurt;Poulin-Duboisetal.(1995)required15newobjectwordsinamonth;GoldfieldandReznick(1990;seealsoReznick&Gold-field,1992)required10newwordsin2weeks;andNinio(1995)identifiedthespurtasthe2-monthperiodinwhichachildshowedthebiggestincreaseinvocabularyrelativetothepreviousmea-surement.Ultimately,allchildrenmustcrossallofthesethresh-oldstoreach60,000wordsbytheageof18;itisjustamatterofwhetherornottheycrossthethresholdduringtheperiodofaparticularstudy.Soperhapsunsurprisingly,noneoftheseauthorshadtroublefindingchildrenwithaspurt,confirmingintuitionsthatthespurtisarelativelywidespreadphenomenon.Forexample,intheirinfluential1990article,GoldfieldandReznickarguedthatthemajorityofchildren(13ofthe18theystudied)showedavocab-ularyspurt.AlthoughGoldfieldandReznickÕsstudyhasbeentakenasevidencethatsomechildrendonothaveaspurt,readersGANGERANDBRENT couldnonethelessremainunshakenintheirbeliefthatthemajorityofchildrendo.DefiningtheSpurtClearlyThekeypropertyofthevocabularyspurt,asdescribedintheDaprettoandBjork(2000)quoteinourintroduction,isthatitconsistsofdiscretedevelopmentalstagesratherthancontinuousincrementalimprovement.However,noneofthethreemethodsjustdescribed(vocabularylevel/age,eyeballing,orthreshold)issufficienttoidentifyavocabularyspurtconsistingofdiscretedevelopmentalstagesandtodistinguishitfromcontinuousincre-mentalimprovement.Atruedevelopmentalspurtmustbeatransitionbetweenaslowlearningstageandafasterlearningstage.Thelearningratemayincreasewithineachofthestages,butatthetransitionbetweenthestagesthelearningratemustchangefasterthanitdoesduringeitherstage.Mathematically,apointwheretherateofincreaseofacurveisgreaterthanitisbeforeorafteriscalledan.Thus,ifachildslearningrateundergoesatransitionbe-tweenalowstageandahighstage,therewillbeaninflectionpointinthelearningratecurveatthepointwherethetransitionoccurs.Furthermore,thelater,fasterlearningrateshouldbesustainedforsomeperiodoftime.Thisistruefortworeasons.First,theratemuststaythesameorincreaseifthechildistoreach300wordsby24months(and60,000wordsby18years).Second,thevocabularyspurtisthoughttobeareflectionofanunderlyingcognitivechange,suchasthenaminginsight,anincreaseinobjectknowl-edge,oranadvanceinwordsegmentationandphonologicalrep-resentation.Anincreaseintherateofwordlearningthatlastsonly1weekmaynotreflectacognitivechangejustabusyweek.Acognitivechangeshouldpersistovertime.Figures1and2illustratethesepointsandpreviewthestrategythatwillbeusedtoidentifyaspurt.Thesegraphsshowdatafrom1participant(Child041B),slightlymodifiedforexpositorypur-poses.Thegraphsdepictthechildsrateofwordlearning(newwordsperday)ontheverticalaxis,andcumulativevocabularysize,avariableofinterestinmanyvocabularystudies,onthehorizontalaxis.Notethatthisformofrepresentation(ratevs.size)departsfromtheusualvocabularygrowthcurve,whichtypicallycumulativevocabularyversustime(seebelowformoreonthispoint)Thequestionis,arethedatainFigures1and2betterdescribedashavingtwodistinctlearningrates(i.e.,aspurt)orashavingagraduallyincreasinglearningrate(i.e.,nospurt)?InFigure1,afunctionwithtwodistinctlevelsissuperimposedonthedata.Ifthischildhasavocabularyspurt,hisorherdatashouldbefitwellbythisfunction.Thisiswhataspurtshouldlooklike.InFigure2,ontheotherhand,afunctionwithagradualincreaseinrateissuperimposedonthesamedata.Theincreaseinword-learningrateiscontinual,withnopointoftransition.Ifthechildhasaspurt,hisorherdatashouldbefitlesswellbythisfunction.Keepingthesepointsinmind,itshouldbeclearnowthatthethreemethodstypicallyusedtoidentifyavocabularyspurtareinadequate.Ascertainingwhenachildsvocabularyexceeds50wordsassumestheexistenceofaspurtwithoutactuallycheckingforit.Eyeballingacurveofvocabularysizeversustimeisalsounreliable;whatlookslikeatakeoffpointinthecumulativevocabularycurvemayactuallyreflectagradualincreaseinrateratherthanaspurt,especiallyifoneiseyeballingacumulativevocabularycurve(totalwordsvs.age)insteadofrateofacquisi-tion.Finally,askingwhetherachildhascrossedathresholdrateofwordlearning(e.g.,10wordsin2weeks)isalsoinadequate.Achildwillcrossthisthresholdwhetherhisorherrateofwordlearningincreasesastheresultofatransitionbetweenstagesorastheresultofacontinualseriesofunrelatedprocesses.Furthermore,thethresholdcouldbecrossedinagoodweekwithoutheraldingapermanentchange.Wearenotthefirsttopointoutsuchshortcomingswithexistingmethodsofdetectingavocabularyspurt.P.Bloom(2000)alsopointedoutthedifferencebetweenacontinuousandadiscontin-uousincreaseinword-learningrateanddiscussedtheimplicationsofthisdifference.Reviewingtheavailableevidence,heconcludedthatthereprobablyisnovocabularyspurtinthe2ndyear(thoughhedidnotethepossibilityofalaterspurtinvocabularywhenchildrenlearntoread;however,becausethisspurtwouldbedrivenbythesuddenavailabilityofnewwordsratherthananinternalcognitivechange,wedonotconsiderithere).Regardingtheoriginalvocabularyspurt,Bloomdidnothavetherelevantdatafromindividualchildrentotesthisconclusion,nordidhespecifypreciselyhowtotestit.Toourknowledge,thepresentworkisthefirstrigoroustestofthevocabularyspurthypothesistouseempir-icaldatafromindividualchildren. Figure1.Aspurtlikefunction(logistic)superimposedonslightlymod-ifieddatafromChild041B. Figure2.Anonspurtlikecurve(quadratic)superimposedonthesamedatashowninFigure1.REEXAMININGTHEVOCABULARYSPURT ANewMethodWeproposeanewmethodforidentifyingthevocabularyspurt,onethattestswhetherthechangesinachildsrateofwordlearningrepresentdistinctstageswithatransitioninbetween.Inthelastsection,wearguedthatthefunctionsuperimposedonthedatainFigure1representsaspurt.Thisplotcanbegeneratedbyalogisticfunction,whichisafunctionofthegeneralform/(1xc)).Thisfunctionconformstothesigmoidcurvefamiliarfrommanypsychologicalprocessesinwhichthereisatransitionbetweenstates.Inthiscase,thestatesaretwodifferentratesofwordlearning.Inthelogisticfunction,therearethreeparameters,,and.Theparametercorrespondstotherateoflearningafterthetransition,orthe1.9inFigure1,forinstance).Theparametercorrespondstothelengthoftimeoverwhichthetransitionoccurs,ortheofthefunctionatthetransitionpoint.Itis0.25inFigure1.Parametercorrespondstothepointatwhichthetransitionoccurs,alsoknownasthetionpoint.Theinflectionpointisat45wordsinFigure1.Thelogisticfunctionisalogicalchoicetotestthevocabularyspurt.Itencompassesafamilyofcurvesthatrepresentstwosteadystateswithadiscretetransitioninbetween.Thereareotherfunc-tionswithinflectionpointsbutnonethatsoperfectlydepictthestatechangethatistheessenceofthevocabularyspurthypothesis.Themethodproposedhereinistotesthowwellalogisticfunctionfitseachchildsvocabularygrowthdata.Goodnessoffitofthelogisticfunctionistestedbyexaminingtheamountofvarianceaccountedforandalsobycomparingittothefitofamodelthatdoesnothaveaninflectionpoint,thequadraticfunction,showninFigure2.Aquadraticfunctionhasthegeneralformcorrespondstothesteadyincreaseinword-learningrate.0017inFigure2),correspondstothesteadyaccelerationinword-learningrate(.0004inFigure2),andisaconstantdefiningwherethefunctioncrossestheverticalaxis(.0239inFigure2).Dependingontheotherparametervalues,differencesinmayaffecteitherthetimeatwhichwordlearningbeginsortherateatwhichitbegins.Thequadraticfamilyofcurveswaschosenbecauseithascertainpropertiesonemightexpectavocabularycurvetohavenamely,itcanincreaseorleveloffdependingonwhetheritisconcaveupordown.However,noquadraticcurvehasaninflectionpoint(i.e.,apointofrapidchangesurroundedbypointsofslowerchange),anessentialhallmarkofatransitionbetweenslowerandfasterwordlearning.Thereare,ofcourse,aninfinitenumberofotherfunctionswithoutaninflectionpoint,butthequadraticismostsimilartothelogisticinformandnumberofparameters,soitwasalogicalchoice.Onemightwonderwhyasimplelinearfunctionisnotbeingusedasamodel.Theansweristhatalinearfunctionisaspecialkindofquadraticfunctioninwhich,thecoefficientofthequadraticterm,happenstobe0.Becausethefamilyofquadraticcurvescontainsthefamilyoflinearcurvesasaspecialcase,thereisalwaysaquadraticcurvethatfitsthedataatleastaswellasthebestlinearfunction.Toillustratethispoint,imagineasetoflearning-ratedatathatlieonaperfectstraightline.Theresultoffittingaquadraticcurvetothesedatawouldbeastraightlineis,acurveinwhich0.Thislinewouldaccountfor100%ofthevarianceinthedata.Furthermore,thefamilyofquadraticfunctions,unlikethemorerestrictedfamilyoflinearfunctions,hasthesamenumberofparametersasthelogisticfunction(three).Thismeansthatacomparisonbetweenquadraticandlogisticfitsismorefairthanacomparisonbetweenlinearandlogisticfits,wherethenumberofparametersisunequal.Onemightalsowonderwhyvocabularyrate,ratherthanvocab-ularysize,isbeingusedasthedependentmeasure.Rateisusedbecauseitisahypothesisaboutratethatisbeingexaminednamely,thatthelearningrateundergoesatransitionfromrela-tivelylowtorelativelyhigh.Itthereforemakessensetoexaminethechangeinratedirectly.Itispossibletoformulateamathemat-icallyequivalentmodelintermsofcumulativevocabularyintegralofrate.Thisisthegraphmostresearchersthinkofwhenimaginingaspurt(seeFigure3foranexample).Itistheonethatshouldhaveanifthereisavocabularyspurt.However,testingthenotionofanwouldrequiretheuseoftermssuchasanincreaseinacceleration,whicharemoredifficulttograspintuitively.Testingthechangeinrateinstead,whichismathematicallyequivalenttotestingchangeinaccelerationinthecumulativevocabularycurve,allowedustouseasimplelogisticfunctionandthereforeprovidedthesimplestandmostdirecttest.Tosummarize,boththelogisticfunctionandthequadraticfunctionhavethreeparameters,andbothareamongthemostplausiblerepresentationsofvocabularyrateovertime,butthelogisticfunctionhasaninflectionpoint(whichwouldindicateatransitionbetweenslowandfastwordlearning),whereasthequadraticfunctiondoesnot.Thus,comparingthefitsofthesetwofunctionstothedatacantelluswhetherachildsword-learningrateshowsthesignatureofavocabularyspurt.Wecomparedthelogisticandquadraticmodelsusinglikelihoodratios,whicharedescribedingreaterdetailinExperi-ment1.Weappliedthismethodtooriginalempiricaldatafrom20children.Wethenappliedthesamemethodtodatagleanedfrom17childreninastudybyGoldfieldandReznick(1990)andtothedataofKeren,achilddescribedbyDromi(1987).Theremainderofthisarticleisdividedintothreeexperiments.InExperiment1,wepresentthreedifferentwaysoflookingattheoriginaldata.First,theproposedspurttestwasappliedto20childrenastheyacquiredtheirfirst90words.Second,thewords Figure3.CumulativevocabularyasafunctionoftimeinChild214A.GANGERANDBRENT wererestrictedtonounstotestthehypothesisthatthevocabularyspurtisdrivenbynounlearning.Third,anothersetofchildrenfromourdatasetwhoreached150wordsduringthestudyweretestedinasearchforalaterspurt.Itisimportanttonotethatthesethreeanalysesrepresentthreedifferentwaysatlookingatessen-tiallythesamedata,notthreeindependenttests.Experiment2isatestoftheproposedmethodwithGoldfieldandReznicks(1990)data.Experiment3isatestoftheproposedmethodwithDromi(1987)data.Experiment1Participantswere35childrenselectedfrom98twinpairsrecruitedaspartofatwinstudyoflanguagedevelopment(Ganger,Pinker,Chawla,&Baker,2000).TwinswererecruitedfromthroughouttheUnitedStatesthroughMothersofMultiplesclubs,theinternet,newspapers,the1995TwinsDaysFestival(inTwinsburg,Ohio),advertisementsinTwinsMag-,andwordofmouth.Twinswerenotacceptedintothestudyif(a)oneorbothtwinshadahistoryofchronicearinfections(definedasmorethanthreeinfectionsortheprescribeduseofprophylacticantibiotics);(b)thetwinswereexposedtoalanguageotherthanEnglishonaregularbasis;(c)therewasahistoryofspeechorlanguagedisordersinthetwinsfamily;(d)eithertwinsbirthweightwaslessthan4pounds(1.8kg)orthegestationalagewaslessthan32weeks;or(e)eithertwinhadaprolongedhospitalstayafterbirth,definedas10daysorlongerowingtofactorstypicallyassociatedwithprematuritysuchasimmaturelungdevel-opmentorapnea.Becausetwinsmaybeatgreaterriskforlanguagedelaysanddisorders(Hay,Prior,Collett,&Williams,1987;Mittler,1970;Mog-ford,1993),theseratherstringentcriteriamadeitmorelikelythatourparticipantsexperiencednormallanguagedevelopment.Thefirstanalysisreportedbelowisbasedon20children(10girls,10boys;13fromidenticaltwinpairs,7fromsame-sexfraternaltwinpairs).Becauseofunavoidablebiasesinrecruitment,thissamplewasentirelyCaucasian.Onascalewhere0denotesthathighschoolwasnotcompleted,1denotesgraduationfromhighschool,2denotessomecollege,3denotesacollegedegree,and4denotesanadvanceddegree,theparentsinthefinalsamplereportedtheireducationalleveltobeanaverageof3.1.Fiveofthechildrenhadatleastoneadditionalsiblingwhowasolder;nonehadyoungersiblingsattheonsetofthestudy.Theaverageageofthissamplewhenparentsbegankeepingjournalswas15.3months(medianageChildrenwereselectedforthisstudyfromthe98pairsoftwinsaccord-ingtothefollowingthreecriteria.First,nomorethan10consecutivedayscouldbemissingfromthechildsvocabularyjournal,becausesuchholesmightproduceartifactualspurtlikejumpsinvocabularywhenthejournalresumed.Second,nomorethan20wordscouldbereportedinthe1stweekofdatacollection,becausesuchahighlevelofstartingvocabularyinthejournalmightindicatethatthechildalreadyknewmanymorethan20wordsandmayevenhavealreadyundergoneaspurt.Notethatexcludingsuchchildrendoesnotbiasusagainstfindingaspurt.Thereisnowaytoknowwhetherthe20wordsreportedinthe1stweekofdatacollectionwerelearnedthatweekorhadbeenlearnedpreviously.Becausethechildrenwererecruitedintothestudyatavarietyofages,thereisnoreasontothinkthatchildrenwhoalreadyhad20wordswhentheirparentsstartedkeepingdiarieslearnedthemquicklyand/orhadundergoneaspurt.Third,atleast90wordsmusthavebeenlearnedbythechildbeforethelast2weeksofjournalentries,becausethefinal2weeksofeachchildsdatawereremovedtoguardagainstthepossibilitythattheparentskeepingthejournalsmighthavedonealesscarefuljobofitinthefinalweeksbeforetheyleftthestudy.Sinceco-twinsarenotindependentsourcesofdata,onlyonetwinfromeachpaircouldbeused.Ifbothtwinsinapairmetthecriteria,onlythetwinwhosenamecamefirstalphabeticallywasincluded.Allofthesecriteriatakentogetherleft20children.ProcedureforCollectingVocabularyDataswordsweretrackedbyaskingparentstokeepjournalsoftheirtwinslanguageuse.Parentskeptalistofallthedifferentwordsusedbyeachtwineachday,evenifthewordshadbeensaidonpreviousdays.Theyweretoldtonotewhichwordswereimmediateimitationsandwhichwerespontaneouslyproduced(imitatedwordswerenotcreditedtothechild)andtowritedownanyaccompanyingcontextifitmighthelpelucidatethewordsmeaning.Incasesofuncertainty,parentsweretoldtousetheirintuitionandtobeasconsistentastheycouldfromonedaytothenextandfromonetwintotheother.Thedailylistsofwordswerekeptonformsprovidedbytheexperi-menters.Theformshadspacesforthedate,thetwinsnames,eachtwindailywordand/orphraselist,andcommentsonthewordsandphrases.Parentsmailedthesejournalsbacktothelaboratoryeachweekandwerecontactedbyexperimentersoverthephoneorbye-mailevery34weekstoaddressproblemsandquestions.Parentreporthasalongtraditioninstudiesofearlylanguageproduction(e.g.,Bates,Bretherton,&Snyder,1988;Fensonetal.,1994;Goldfield&Reznick,1990;Nelson,1973;Pine&Lieven,1990)becauseitallowsforlargersamplesizesthandoesdirectobservation.Itmayalsobemoreaccurate,becauseparentshaveaccesstoalargerrangeofcontextsinwhichtheirchildrenuseawordorconstruction.Oneparent-reportvocabularyinstrument,theMacArthurCommunicativeDevelopmentInventory(Fen-sonetal.,1994),achecklistof680words,hasbeenshowntohavehighretestreliability(.80to.90),highinternalconsistencybetweendifferentvocabularymeasureswithintheinventory(.95to.96),andhighreliabilitywhencomparedwithalaboratorymeasureofexpressivevocabulary(.72;Batesetal.,1988;Fensonetal.,1994).ThissuggeststhatparentsarereasonablygoodrecordersoftheirchildrenslanguageTheuseoffree-reportjournalsislesscommonbutwasnecessaryinthisstudytodocumenttrendsindevelopmentovertimeandtodecreasetheburdenonparentsoftwins.Thecorrelationbetweenfree-recallandcheck-listvocabularyestimatesrangedfrom.60to.86inanotherstudy(Reznick&Goldfield,1994)andwashighinatestwiththeoriginaltwinsampleofthisstudyaswell(.98;Gangeretal.,2000).ProcedureforTestingforaVocabularySpurtsdatawererepresentedasrateofnewwordacquisition(spe-cifically,newwordsperday)versuscumulativevocabulary.Therationaleforusingrateasthedependentmeasure,ratherthanvocabularysize,hasbeendescribedabove.Therationaleforusingcumulativevocabularyasanindependentvariableinsteadoftimeorageisthatthevocabularyspurtisthoughttooccuraroundthe50-wordmarkincumulativevocabularyratherthanbeingtiedtoaspecificageorlengthoftimeafterthefirstword.Inordertogivethereaderasenseofwhatthesedataarelike,Figures3through6showtherelationshipbetweendifferentrepresentationsofthesamedatausingplotsfrom1participant,Child214A.InFigure3thereisatypicalgraphofvocabularyversustime(cumulativevocabularyvs.ageinmonths).Figure4showsthesamedatagraphedasrateofvocabularyacquisition(newwordsperday)versustime(ageinmonths).Figure5showsnewwordsperdayversuscumulativevocabularytherepresenta-tionusedinthepresentstudy.Finally,Figure6showsasmoothedandcorrectedversionofthesedata,createdinaprocessdescribednext.Tosmooththedataoutoveroccasionalmissingdaysor1-daybursts,wecalculatedanaveragerateoveraspanof9words.Foreachlevelofvocabulary,thisaverageconsistedofawindowof9words(withthedayREEXAMININGTHEVOCABULARYSPURT ofinterestatthecenter)dividedbythenumberofdaysittooktolearnthose9words.Thisnumberofwords(9)waschosenarbitrarilybutwaschosenbecauseitlookedlikealargeenoughnumbertosmoothouttemporaryjumpsthatwerenotofinterestwhileatthesametimebeingasmallenoughnumberthatanyspurtingtrendswouldstillshowup.Truespurtingtrendswouldstillshowupbecauseitgenerallytookafewdays,onaverage,forachildtolearn9newwords,andsmoothingoverafewdaysshouldnotobscureatruespurt.Formissingdays,anaverageofthesurroundingdayswasfilledin.(Recallthatnochildinthisstudyhadmorethan10consecutivemissingdays.)Asdescribedintheintroduction,ourmethodofdeterminingwhetherachildhadavocabularyspurtwastiedtowhetherhisorherrateofacquiringnewwordscouldbemodeledwellbyalogisticfunction.AlogisticmodelwasfittoeachchildsdatabyusingthenonlinearregressionfunctionofSPSSforWindowsandenteringthemodelmodelslope(wordsÐinflectionpointbyhand.Thedependentvariablewasnewwordsperday.,thescumulativevocabularylevel,wastheindependentvariable.inflectionpoint,andareparametersthatarefittothechilddata.(Theirmeaningisdescribedinmoredetailintheintroduction.)TheparametersofthismodelwerefittoeachchildsdataindependentlyusingtheparametersoptionoftheSPSSnonlinearregressionfunction.ThismeansthatSPSSsmodel-fittingalgorithmtrieddozenstohundredsofcombinationsofparametervaluesuntilitfoundthosethatbestfitthedata.Initialvaluesoftheparametersweresetasfollows:inflectionpoint0.1,and0.1.Thesevaluesmayappeararbitrary,buttheywerevariedduringexploratoryanalysis,andtheyhadlittleeffectontheresultaslongastheywerenotextremelyfarfromreasonablefinalvalues.Furthermore,SPSSsalgorithmusesthesevaluesmerelyasstartingpoints;itstilltestsawiderangeofvaluesandselectsthosethatbestfitthedata.Themostimportantparameterforourpurposesistheinflectionpointbecauseitrepresentsthecenterofthetransitionifthereisoneastageduringwhichtherateofvocabularygrowthislowandastageduringwhichitishigh.Inthisanalysisandinthenouns-onlyanalysis,describedbelow,aninflectionpointanywherebetween20and90wordswasaccepted,becausethevocabularyspurtisthoughttooccurataround50words.Aminimumof20wordswasdecideduponbecausemanyinvestigatorsagreethatbefore20wordsistooearlyforatruespurt(e.g.,Lifter&Bloom,1989).Amaximumof90waschosenbecausedatafrommostofourparticipantsendedat90wordsafterthelast2weeksofdatawereremoved.Ifachilddidnothaveaninflectionpointbetween20and90words,weconcludedthatthechilddidnothaveavocabularyspurt.However,whilehavinganinflectionpointattherightplaceisnecessaryforhavingaspurtlikecurve,itisnotsufficient.SPSSslogisticmodel-fittingalgorithmwillfindaninflectionpointsomewhereinthedataevenifthedatacouldbebetterfitbyafunctionwithoutaninflectionpoint.Therefore,wealsotestedthefitofaquadraticmodel(discussedinmoredetailintheintroduction)byusingthecurve-fittingfunctionofSPSSforWindowsandcheckingthequadraticoption.Thetwomodelswerecomparedfortheirgoodnessoffitbyusinglikelihoodratios.Themodelwiththehigherwasconsideredpotentiallytobethebetterfit,buttomakethecomparisonmorerigorous,wealsocomputedlikelihoodratiosforthetwomodels.Alikelihoodratioistheratiooftheprobabilityoftheobserveddatapointsunderonemodel(thelogistic)totheirprobabilityunderanalternativemodel(thequadratic).Therefore,thelargertheratio,thebetterthelogisticcurvefitsthedatarelativetothequadraticcurve.Notethatthisisnottheratiooftheprobabilitiesofthemodelsbutrathertheratiooftheprobabilitiesofthedataifthemodeliscorrect.Likeatraditionalsignificancevalue,itisa Figure4.RateofvocabularylearningasafunctionoftimeinthesamechildshowninFigure3(Child214A). Figure5.Rateofvocabularylearningasafunctionofcumulativevo-cabularyinthesamechildshowninFigures3and4(Child214A). Figure6.Rateofvocabularylearningasafunctionofcumulativevo-cabularyinthesamechildshowninFigures3,4,and5(Child214A)withsmoothingovera9-wordwindowandcorrectionformissingdays.GANGERANDBRENT functionofthesamplesizeaswellastheeffectsize.Byconvention,aratioof100:1isrequiredtobeveryconfidentoftheresult,aratioof10:1isworthasecondglance,andanythingsmallerisnotacceptable.Likelihoodratiosaretypicallygivenin(base10)logarithms.Thus,aratioof100:1isalogof2,and10:1yieldsalogof1.Followingthisconvention,thelogofthelikelihoodratio(henceforthLLR)hadtobe2orlargertoshowthatthelogisticmodelfitbetterthanthequadraticmodel.Whenthedeviationofthedatafromthetruemodelisnormallydistrib-uted,theLLRcanbecomputedusingtheformulaformula(QuadraticRMSResiduals)LogisticRMSResidualsnumberofobservationsRMSResidualsistherootmeansquareoftheresiduals,orthesquarerootoftheoftheregression.Theresidualsbecomesmallerasgoodnessoffitincreases.Totestwhetherthelogisticmodelfitsbetterthanthequadraticmodel,oneputsthequadraticresidualsinthenumeratorandthelogisticresidualsinthedenominator.Asthefitofthequadraticmodelimproves,theresidualsinthenumeratorwilldecrease,andthewholeratiowillthereforegetsmaller.Asthefitofthelogisticmodelimproves,theresidualsinthedenominatorwilldecrease,andthewholeratiowillinsteadgetlarger.Table1displaystheinflectionpoints,values,andLLRsforeachofthe20children.Nineofthe20hadaninflectionpointbetween20and90words.These9werethereforetheonlycan-didatesforavocabularyspurt.Sixofthese9childrenhadalargerforthelogisticmodelthanforthequadraticmodel,and4ofthosehadLLRs2,indicatingabetterlogisticfit.Oneadditionalchild(037B)hadanLLRthatwasbetween1and2.Ofthe20childrenconsidered,4(perhaps5,ifoneborderlinecaseisincluded)showedevidenceofavocabularyspurt.Thisfindingdoesnotsupportthenotionthatthevocabularyspurtisawidespreadoruniversalphenomenon.Itisnotevenclosetothe72%ofchildren(13/18)thatGoldfieldandReznick(1990),usingathresholdapproach,foundtohaveaspurt.Thereareseveralpossibleobjectionstothisfinding.Oneisthatanumberofstudieshaveindicatedthatthevocabularyspurtisbasedpredominantlyonnouns(e.g.,Gopnik&Meltzoff,1987),andinfactthetermnamingexplosionusuallyrefersnottothevocabularyspurtasawholebuttoajumpinnounlearningalone.Similarly,GoldfieldandReznick(1990)foundthatspurterstendedtohaveapreponderanceofnounsintheirvocabularywhereasnonspurtershadamorebalancedvocabularycomposition.Thispossibilitycanbeaddressedbycomparingtheproportionsofnounsinthevocabulariesofspurtersandnonspurters.The4spurtershadameanproportionof.70nounsintheirvocabulary.10),whereasthe15nonspurtershadameanproportionof.63nouns(.10).Thedifferencewasnotsignificant,one-.13,buttheeffectwasintherightdirectionand,giventhesmallnumberofsubjectsinthespurtgroup,shouldprobablybeconsideredborderline.Thisfindingprovidedtherationaleforasecondanalysis,inwhichnounsalonewereconsidered.Fromthesampleof20chil-drenintheoriginalanalysis,weselectedasubsetwithwhichtoexaminethehypothesisthatthevocabularyspurtmightinvolveonlynouns.Allwordswerefirstclassifiedasnounsornon-nounsbyanundergraduateresearchassistantanddouble-checkedbyoneoftheauthors.Later,theprocesswasrepeatedbyasecondre-searchassistant(withoutdoublecheckingbytheauthors)topro-videreliabilitystatistics.Allcommonnouns(countandmass)wereincluded,aswerepropernamesandbrandnames(e.g.,Cheerios).Personal,demonstrative,andpossessivepronouns(e.g.,he,this,mine,respectively)werenotincluded.Inpotentiallyambiguouscases(e.g.,)wheretheparentdidnotprovidesufficientcontexttodifferentiatethepartofspeech,thewordwasclassifiedfollowingtheratersintuitionsofwhichcategorythechildwaslikelytohavemeant.Suchdecisionswerebasedontheintuitivelikelihoodthatayoungchildwouldsaytheword.Incasesofuncertainty,frequencycountsfromFrancisandKucera(1982)wereconsulted,andthewordwasclassifiedasthemorefrequentform.Boththeinitialclassificationofwordsintonounsandnon-nounsandtheresolutionofdifficultcasesweredoneforadifferentstudybyraterswithnoknowledgeofwhichchildrenwereclassifiedasspurtersinthepresentstudy.Thepercentageofagreementbetweenthetworaterswas91%(calculatedbydividingthenumberofwordsbothratersidentifiedasnounsbythenumberofnounsidentifiedbyoneraterortheother).Thereliabilitycoefficientwas.82.Childrenwereusedinthenounanalysisiftheyhadatleast90commonnounsaftertheirlast2weeksofdatawereremovedandhadnomorethan20commonnounsreportedinthe1stweekofdatacollection.The90-wordminimumwaschosensotheresultswouldbecomparabletothoseinthefirstanalysis.Becauseex-cludingnon-nounsreducedthetotalvocabularyconsiderably,thesecriterialeftonly11childrenwithwhichtotestthenouns-onlyspurthypothesis(7girls,4boys;6fromidenticaltwinpairs,Table1ResultsofExperiment1InitialAnalysis:TestingforaSpurtBetween20and90Words 3700.0000.5661890.0000.5631280.0000.6221270.0000.512940.0000.400600.0000.138062A120.1450.148230B180.2570.448yes218A220.2190.234012A250.3280.337237A260.8230.781050A290.2990.201024A310.6120.620022A330.7830.755227A440.5450.508037B550.3930.3801yes243A560.8880.8312yes009A3170.6920.716yes030A3380.0000.684yes010A5540.4650.528loglikelihoodratio.Inflectionpointslessthanzeroorgreaterthan90arenotpossiblegiventherangeofthedata(090words).Insuchcases,theprogramcouldnotfindareasonablefitwithintherangeofactualdata.1arenotREEXAMININGTHEVOCABULARYSPURT 5fromfraternaltwinpairs).Themeanageattheonsetofdatacollectionforthissubsetwas16.0months(medianageTable2displaystheresults.Fiveofthe11childrenhadnoundatathatweremodeledbyalogisticcurvewithaninflectionpointbetween20and90words.These5werethereforetheonlycan-didatesforavocabularyspurtbasedonnounsalone.Fourofthe5childrenwithinflectionpointsinthetargetrangehadalargerforthelogisticmodelthanforthequadraticmodel,butonly1(Child243A)hadanLLR2,indicatingabetterlogisticfit.Itshouldbenotedthatanotherchild(Child050A)hadaninflectionpointof19andanLLR2.Iftheinflectionpointsearchwereexpandedonlyslightly,thischildwouldalsobeincluded.Thisresultsuggeststhatnounlearningalonedoesnotundergoaspurtand,likewise,thatthevocabularyspurtwasnotbeingmasked(intheoriginalanalysis)bynon-nouns.Why,then,havesomanyothersconcludedthatnounlearningiscentraltothevocabularyspurt?Onepossibilityisthatnounslendthemselvestobeinglearnedinburstsbecausegroupsofnounsoftenco-occurintherealworld.Avisittothezoo,forexample,mayresultinadozennewanimalkindnames,butfewornonewverbs,adjectives,orsocialwords.Ifathresholdapproachisused(requiring,forinstance,10newwordsin2.5weeks),atriptothezoomightmakethechildsvocabularycrossthatthreshold.How-ever,justbecausethechildcanlearn10newnounsatoncedoesnotnecessarilymeanheorshehasundergoneasignificantcog-nitivechangeinhisorherword-learningability.Rather,theburstwasdrivencompletelybyexperientialfactors(atriptothezoo).Althoughvocabularycompositiondoesnotappeartohavedriventheresults,anotherpossibleobjectiontotheoriginalanal-ysis(andtothesecond)mightbethatthecumulativevocabularyofthechildrenhasbeencutoffat90words.Infact,MervisandBertrand(1995),inaresponsetoGoldfieldandReznick(1990),madeexactlythisargument,pointingoutthatGoldfieldandsnonspurtersonlyreachedanaverageof86wordsduringthestudy.MervisandBertrandpresentedevidence,usingathresh-oldcriterion,thatsomechildrenshowaspurtlaterinvocabularylearning,atanaverageof112words.Toaddressthispossibility,wepresentafinalanalysisthataddressesthepossibilitythatthereisaspurtbeyondthe90-wordmark.Forthisanalysis,wereexaminedtheoriginalsetof98twinstofindchildrenwhohadatleast150wordsintheirlexiconbeforetheirlast2weeksofdatacollection.Theywereincludedeveniftheyhadasmanyas39wordsinthefirst2weeksofdatacollection.Thesecriterialeft18children(10girls,8boys;9identicaltwins,9fraternaltwins).Theiraveragestartingagewas17.5months(4.2).Threeofthese18childrenwerealsoincludedintheoriginalanalysis,andanother7aretwinsofchildreninthatanalysis.Table3displaystheresults.Inadditiontotheinflectionpoints,values,andLLRs,wordsrecordedinthefirst2weeksofdatacollectionareincludedtogivethereaderanideaofwhetheranearlyspurtcouldhavebeenmissed.Sixofthe18childrenhadvocabularydatathatweremodeledbyalogisticcurvewithaninflectionpointbetween20and150words,butthehighestinflec-tionpointwas91.All6hadalargerforthelogisticmodelthanforthequadraticmodel,butonly3ofthe6hadLLRsindicatingabetterlogisticfit.TwoadditionalchildrenhadLLRsbetween1and2.So,muchasinourfirsttwoanalyses,3of18(17%)hadaspurtinthisanalysisofhighervocabularylevels(5of18,or28%,if2borderlinecasesareincluded).Furthermore,becausenochildhasaspurtafter91words,itappearsthatrestrictingthesearchtothefirst90wordsintheoriginalanalysisdidnothinderourabilitytofindaspurt.Athirdobjectiontothestudypresentedheremightbethattheparticipantsarealltwins.Asnotedinthetwinsaremorepronetolanguagedisordersanddelays,partlybecauseofprematurityandotherperinatalfactors.Asalsonoted,therewasacutoffforgestationalageandbirthweightinthisstudytoavoidsuchproblems.Nonetheless,threeadditionalproblemsrelatedtothetwinsampleremain.First,althoughsomelanguageproblemsintwinsareduetobiologicalfactors,somearethoughttobeduetosocialfactors(Mogford,1993;Tomasello,Mannle,&Kruger,1986).Itisthere-forepossiblethattwinslearnlanguageataslowerratethansingletons,whichcouldmakethemanoncomparablepopulationand,moreimportantly,couldbiasagainstfindingaspurt.Second,GoldfieldandReznick(1990)reportedthatbirthorderwasonemajordifferencebetweentheirspurtersandnonspurters,withspurtersbeingmorelikelytobefirstborn.GoldfieldandReznickarguedthatthereisameaningfulrelationshipbetweenbirthorderandnounlearning,whichisthatparentswithonlyonechildhavemoretimetoplaythenaminggamethepracticeofincessantlylabelingobjectsandencouragingthechildtorepeatandlearnthelabels.Poulin-Duboisetal.s(1995)study,whichreportsacorrelationbetweennamingpracticesinparentsandnounlearninginchildren(aswellasbettercategorizationskillsandearlierspurting),supportsthisconjecture.Asnotedinthedescriptionoftheparticipants,5ofthe20childreninExperiment1hadanoldersibling.Oneofthose5wasaspurterandanotherwasaborderlinespurter(Child037B),whereastheremaining3werenotspurters(seeTable1),whichsuggeststhatbirthorderhaslittleimpactonthepresenceofavocabularyspurt.However,becauseallofthechildreninthisstudyaretwins,theyallhaveasame-agesibling.Thereforetheirparentspresumablyhadlesstimethanparentsofsingletonstoplaythenaminggame.Indeed,itisknownthattwinshavelessindi-Table2ResultsofExperiment1Nouns-OnlyAnalysis SubjectInflectionpoint230A120.1970.582024A160.1060.108050A190.3920.310214A230.4170.412037B320.2450.229243A410.7850.576025A540.8600.855012A620.3750.376204A3210.3790.384218A4350.4360.497067A1,1160.0860.413loglikelihoodratio.Inflectionpointslessthanzeroorgreaterthan90arenotpossiblegiventherangeofthedata(090words).Insuchcases,theprogramcouldnotfindareasonablefitwithintherangeofactualdata.1arenotGANGERANDBRENT vidualinteractionwiththeirmothersandfewerinstancesofjointattention(Tomasello,Mannle,&Kruger,1986).Third,thefactthattheparticipantsaretwinscomplicatesdatarecording.Itispossiblethatparentsoftwinscannotaccuratelyseparatetheexpressivevocabularyofthetwochildrenwhenkeepingwrittenjournals.Indeed,Reznick,Corley,andRobinson(1997)showedthatparentratingsofexpressivelanguageintheir14-month-oldtwinsresultedinmuchhigherestimatesofco-twinsimilaritythandidobjectiveobserverratings.Althoughtheuseofadailyjournalinthepresentstudy(asopposedtoaone-timeretrospectivechecklist,asinReznicketal.)shouldattenuatesuchaneffect,itcannotberuledout.Ifco-twinsundergoaspurtatdifferenttimes,orifonehasaspurtandtheotherdoesnot,thenconfusingthelanguageofthetwotwinscouldobscureanactualspurtinoneorbothchildren.ThusthefactthattheparticipantsaretwinscouldberesponsibleforthesmallernumberofspurtersinthisstudyrelativetothenumberinGoldfieldandReznick(1990).Allthreeoftheseobjectionstousingtwinscouldbeansweredbyapplyingthesametechniquetonontwins.ThiswasthegoalinExperiments2and3.InExperiment2,datafromGoldfieldandReznick(1990)wereusedtotestdirectlywhetherthefactthattheyfoundmorespurterswasduetofundamentaldifferencesintwinsversussingletonsorifitwas,asweargue,duetoourmorerefineddecisionprocedureforidentifyingaspurt.InExperiment3,thetechniquewasappliedtoDromis(1987)data.Experiment2:GoldfieldandReznick(1990)DataBecauseweproposeusingGoldfieldandReznicks(1990)dataasatestofwhetherourresultshavebeenbiasedbytheuseoftwins,itisworthconsideringinsomedetailthecharacteristicsoftheirparticipantsandtheprocedurestheyusedforcollectingandcompressingdata.ThechildrenaredescribedindetailinGoldfieldandReznick(1990).TherelevantdetailsarethattheywererecruitedthroughbirthrecordsandcamefromCaucasian,middle-class,English-speakingfamilies.Thesam-pleconsistedof9girls(5firstborn,4later-born)and9boys(3firstborn,6later-born).ThissampleisthereforequitesimilartothetwinsampledescribedinExperiment1.ProcedureforCollectingDataThemethodofdatacollectioninGoldfieldandReznicks(1990)studywasalsoremarkablysimilartothatinExperiment1.Childrenswordusewasalsoassessedbymothersdiaries,andcontacttodiscusstherecordswasalsomadewiththemotherseveryfewweeks(2.5weeksinGoldfield&Reznick,34weeksinthepresentstudy).Asdescribedinourintro-duction,GoldfieldandReznickrequiredthat10newwordsbelearnedbyachildina2.5-weekintervalinorderforaspurttobeattributedtothatchild.Thisdifferencenecessitatedminorchangestoouranalyticproce-dure,whicharedescribedinthenextsection.Oneotherproceduraldifferencewasthatincompressingtheirdata,GoldfieldandReznick(1990)attributedawordtoachildonlyifthatwordhadbeenreportedbythemotheratleasttwotimes.InExperiment1,wordswereattributedafterjustoneparentreport.Itispossible(thoughfarfromcertain)thatthisdifferencecouldmakethechildreninGoldfieldandsstudylesslikelytoshowaspurt,becauseeachchildsvocabu-larywouldundoubtedlybeincreasedbytheinclusionofwordsheorshesaidonlyonce.Ifthisistrue,thenGoldfieldandReznicksdatawouldnotbeafairtestofournewtechnique.However,thereisnoreasontothink,apriori,thatreportingmorewordsacrosstheboardwouldmakeachildmorelikelytoshowaspurtthiswouldonlybetrueiftheextrawordsalloccurredatthesametime.Iftheyarespreadacrossthereportingperiod,oriftheyincreasesteadilyduringthereportingperiod(asonemightexpect,becauseachildmightuseeachwordlessoftenashisorhertotalvocab-ularyincreased),theseone-timewordswouldnotincreasethelikelihoodofshowingaspurt.ProcedureforReanalyzingGoldfieldandReznick(1990)DataForeachofthechildrenreportedbyGoldfieldandReznick(1990),oneoftheauthorsandoneundergraduateresearchassistantindependentlyestimatedthedatafromthegraphsprovidedbyGoldfieldandReznickbyenlargingthegraphs,affixingthemtogridpaper,andtapingthemuptoawindowforlight.Usingthismethod,datacouldbeestimatedfor17ofthe18children.Estimatesmadebytheauthorandthosemadebytheassistantwerehighlycorrelatedforeachsubject.TheaveragePearsonwas.998,andtheeffectiveorcomposite(Spearman-Brown)reliabilitywas1.00forallsubjectsexceptone,whohadacompositereliabilityof.985.Becausethenumberofwordslearnedin2weeksismuchhigherthanthatlearnedinaday,alloftherawnumberswereconsiderablyhigherforthesechildren,andsomeadjustmentstoouranalyticprocedurehadtobemadetocompensate.Specifically,alltheratesweredividedby10tobringthemdowntothesameorderofmagnitude.ThedatafromSubject8hadtobedividedby100insteadof10fortheprogramtoconverge.BecausethenumberswerestilllargerthanthoseinourExperiment1,thestartingvaluesoftheparametersgiventoSPSSalsohadtobeadjusted.Weusedthefollowingvalues:inflectionpoint1,andAllresultingparameterestimatesthenhadtobeadjustedaccordingly(i.e.,multipliedby10forallsubjectsexceptSubject8,whosefinalparametervaluesweremultipliedby100).ThesechangeshadnoeffectontheshapeTable3ResultsofExperiment1,Analysis3:TestingforaVocabularySpurtAfter100Words Wordsreportedinfirst2weeks1700.0000.30901440.0000.009331050.0000.3730770.0000.06512150.0000.36539067A30.0090.1420050A290.2670.239227B360.4810.436239A560.3190.31416037A620.2630.231025B880.7290.708218B910.4260.372215235B1640.2900.29133208B5740.4490.4380001B5870.6140.63229039A5900.4330.50139225A7200.5520.59718065B1,1210.0520.06130loglikelihoodratio.Inflectionpointslessthanzeroorgreaterthan90arenotpossiblegiventherangeofthedata(090words).Insuchcases,theprogramcouldnotfindareasonablefitwithintherangeofactualdata.1arenotREEXAMININGTHEVOCABULARYSPURT ofthecurveortheestimatedlocationoftheinflectionpoint;theyjustputthedataontothesamescaleasthedatainExperiment1.Asidefromthisminorchange,thesameprocedureoutlinedinExperiment1wasfollowedTable4displays,foreachofthe17childrenfromGoldfieldands(1990)study,inflectionpoints,values,andLLRs,aswellasGoldfieldandReznicksclassification(spurtornospurt).ThesubjectnumberingfollowsthatgivenbyGoldfieldandThirteenofthe17childrenhaddatathatweremodeledbyalogisticcurvewithaninflectionpointbetween20and90words.These13werethereforecandidatesforavocabularyspurt.Fourofthese13hadalargerforthelogisticmodelthanforthequadraticmodel,butonly1ofthem(Subject2)hadanLLRindicatingabetterlogisticfit.Oneotherchild(Subject5)hadanLLRbetween1and2.Evenincludingtheborderlinecase,thereareonly2spurters(12%)amongGoldfieldandReznicks(1990)17subjects.BothwereconsideredspurtersbyGoldfieldandReznick,butsowere11others.Wethereforeconcludethatitisadifferenceinprocedure,notinsamplecharacteristics(twinvs.singleton,birthorder,etc.)ordatacollectionmethods,thatledtoourfindingarelativelysmallnumberofchildrenwithavocabularyspurtinExperiment1.Experiment3:Dromis(1987)DataInafinaltestofthemethodpresentedhere,weusedDromis1987datafromherdaughterKeren.ThedetailsofdatacollectionaswellasKerenvitalstatisticsaregiveninDromi(1987).ThedataweretakenfromtablesgiveninDromi(1987),andthestatisticalprocedurefollowedwasthesameasthatoutlinedinExperi-ment1.LogisticmodelfittingidentifiedaninflectionpointforKerenat95words.Thelogistic.732,thequadratic.724,andtheAlthoughKerensdatawerefitwellbythelogisticfunction,theywerefitjustaswellbyafunctionwithoutaninflectionpoint,thequadraticfunction.Giventhesimilarityofthetwofits,wecannotconcludethatKerenhadaspurt.GeneralDiscussionWehavearguedthattherehasbeenafundamentalflawwithmeasuresofthevocabularyspurtusedinthepast:Eventhemostsophisticatedofthem,thethresholdapproach,requiredonlythatasrateofwordlearningcrossanarbitrarythreshold,notthatitexhibitaninflectionpoint.Insteadofusingathreshold,weexaminedvocabularyratedatadirectlyforaninflectionpoint.Thepresenceofaninflectionpointinthelearning-ratecurveisaninevitableconsequenceofatransitionfromastagecharacterizedbyalowratetoonecharacterizedbyahigherrate.Althoughsuchmethodshadbeensuggestedpreviously,thisreportrepresentsthefirstattempt,toourknowledge,toapplythemtolongitudinaldatafromindividualchildren.Ourhopeisthatotherswilladoptthismethodandapplyittomoredatasothatthefieldcanultimatelyprovideanaccurateestimateofhowmanychildrenundergoavocabularyspurt.Inthepresentreport,theresultwasthatonlyaminorityofchildrenhadareliableinflectionpointintheirvocabularyratefunctions.First,weconsidereddatafromanewsampleof20children,usingrateofwordlearningasthedependentmeasureandcumulativevocabularysizeastheindependentvariable.Fromthatsample,therewereonly4orperhaps5childrenwithgoodenoughlogisticfitstoindicateapossiblespurt.Wethenreanalyzedthedatainordertotestwhetherchildrenlearningnounsaloneshowedaspurt,andwefoundthat1orperhaps2outof11childrenshowedaspurtunderthoseconditions.Wethenexpandedtheinflectionpointsearchto150wordsandfoundthat3orperhaps5of18childrenshowedaspurt,nonelaterthan91words.WethenreanalyzeddatafromGoldfieldandReznick(1990)andfoundthat1orperhaps2oftheir17childrenshowedaspurt.Finally,s1987datafromherdaughterKerenweresubjectedtoourTable4ResultsofExperiment2:GoldfieldandReznicks(1990)Data Goldfield&Reznickspurt?1000.0000.616yes60.0830.086(22190.8650.714yes7250.5910.4755260.9950.9851yes12330.5210.568yes2440.9990.9802yes10450.4620.45313450.3750.5623500.9940.998yes15500.9540.950yes17500.9880.975yes4530.9930.999yes11600.9880.995yes9610.9470.936yes24720.7830.789yes81700.6281.000Dashindicatesthattheloglikelihoodratio(LLR)couldnotbecomputedbecausethereweretoofewobservations.Inflectionpointslessthanzeroorgreaterthan90arenotpossiblegiventherangeofthedata(090words).Insuchcases,theprogramcouldnotfindareasonablefitwithintherangeofactualdata.1arenotGANGERANDBRENT methodandrevealednoevidenceforaspurt.IfwetaketheresultsfromthefirstanalysisofExperiment1asrepresentativeofourowndataandcombinethemwithourreanalysisofGoldfieldandsparticipantsinExperiment2andofKereninExperi-ment3toyield38children,wefindthat5(perhaps7)ofthe38children,or13%(perhaps18%),hadavocabularyspurt.Readersmustdecideforthemselveswhethertheywishtofollowourstrictestorloosestcriteriaorsomecompromisebetweentheminordertosettleonapointestimate.Althoughthesefindingsindicatethatafairnumberofchildrenhaveavocabularyspurt,thefindingsdonotsupportthenotionthatitisauniversalriteofpassageinlanguagedevelopment.Thisoutcomemeansthatwemustrethinkwhetherthevocabularyspurtreflectsanimportantchangeincognitivedevelopment.Theoriesthatpositafundamentalchangeinthewaychildrenusewordsappearnolongertohavesupport.Forinstance,theinsightthatwordsrefertothingsorthatallthingshavenames(e.g.,Dore,1978;Reznick&Goldfield,1992)wasproposedspecificallytoaccountforthevocabularyspurt.Ifmostchildrendonothaveaspurt,thereislittleremainingsupportforthenaming-insightclassofhypotheses.Claimsthatchildrensobjectconceptsarefundamentallyre-structuredwouldalsolosesupportifmostchildrendonotundergoavocabularyspurt.AlthoughPiagetstheoryisnotdirectlyaf-fected,thenotionthatadvancesinobjectknowledgeduringSen-sorimotorSubstage6spurredaspurt(Lifter&Bloom,1989)isnolongernecessary.Likewise,GopnikandMeltzoffs(1987)empha-sisonsortingobjectsasasignofbasic-levelknowledgethatenablesfastwordlearningnowseemsmisplaced;inmostchildren,thereisnoevidenceforanonsetoffasterwordlearningthatneedstobeexplainedLikewiseformanyotherclaimsdescribedintheintroduction.Discontinuouschangesinwordrepresentation(Walley,1993),wordsegmentation(Plunkett,1993),pragmatics(Ninio,1995),andwordretrieval(Dapretto&Bjork,2000)arenolongerneces-saryasdrivingforcesbehindthevocabularyspurt.Ontheotherhand,itispossiblethatacontinuouschangeinwordlearningcausesadiscontinuityinotherdomains.Forin-stance,wordrepresentationchanges(Walley,1993)andnamingerrors(Gershkoff-Stowe&Smith,1997)havebothbeenreportedataround50words.Althoughbotharesupposedtoberelatedtothevocabularyspurt,itispossiblethatthesechangesactuallyoccurbecauseofsomereorganizationofthementallexiconthattakesplacewhenitexceedsacertainsizeinordertoaccommodatethephonologicalandsemanticpropertiesofmorewordsandtheirrelationships.Forinstance,achildwithalexiconcontainingonlyonewordstartingwith/m/,,canberatherlazyabouthowtorepresentandproduceitsphonologicalform(e.g.,).Oncemorewordsthatbeginwith/m/areadded(e.g.,phonologicalrepresentationsmustbecomemorecomplexinordertodiscriminatethewords.Thesamecouldbetrueofsemanticrepresentations,causingnamingerrorsasthechildattemptstoconvergeonmoreexactmeanings.Allofthesecouldbetruewithoutthepresenceofaspurt;areorganizationofthementallexiconmaynotincreasetherateofwordlearningitmayevenbenecessaryjusttomaintaintherate.Butifthereisnovocabularyspurt,westillhavethetaskofexplainingwhytherateofvocabularylearningincreases.Oneexplanationisthatinsteadofasingledramaticcognitivechange,therearemanysmall,unsynchronizedchangesinbothhighercognitiveandlowerlevelprocessingabilities.Thesewouldleadtowhatappeartobesteadyincreasesinword-learningability.P.Bloom,inhis2000bookHowChildrenLearntheMeaningsofWords,wrote:Itwouldnotbedifficulttoseeifit[aspurt]didoccur.Onecouldgraphthechildsvocabularygrowthandlookforadramatic(oratleaststatisticallysignificant)changeintheslopeofthelinedenotingrateofgrowth.(Notethatthegraphhastobeofanindividualchild,notaggregatedata,andhastobeofrate,notsize.)Thisisasimplecriterion,but,asfarasIknow,noevidenceisavailablethatanychildhasevermetit.(p.43)Theevidenceisnowin.Wehavegivenadetailed,quantitativemethodfordetectingavocabularyspurtinindividualchildrenandapplieditforthefirsttime.Aminorityofchildrenabout1indohaveaspurt,butmostdonot.Aitchinson,J.(1994).Wordsinthemind:Anintroductiontothemental(2nded.).Oxford,England:Blackwell.Bates,E.,Benigni,L.,Bretherton,I.,Camaioni,L.,&Volterra,V.(1979).Theemergenceofsymbols:Communicationandcognitionininfancy.NewYork:AcademicPress.Bates,E.,Bretherton,I.,&Snyder,L.(1988).Fromfirstwordstogram-Cambridge,England:CambridgeUniversityPress.Bates,E.,&Carnevale,G.(1993).NewdirectionsinresearchonlanguageDevelopmentalReview,13,Berk,L.(2003).Childdevelopment(6thed).Boston,MA:Allyn&Bacon.Bloom,L.(1973).Onewordatatime:Theuseofsingle-wordutterancesbeforesyntax.TheHague:Mouton.Bloom,L.,&Capatides,J.B.(1987).Expressionofaffectandtheemer-genceoflanguage.ChildDevelopment,58,Bloom,P.(2000).Howchildrenlearnthemeaningsofwords.MA:MITPress.Choi,S.,&Gopnik,A.(1995).EarlyacquisitionofverbsinKorean:Across-linguisticstudy.JournalofChildLanguage,22,Corrigan,R.(1978).LanguagedevelopmentasrelatedtoStage6objectpermanencedevelopment.JournalofChildLanguage,5,Dapretto,M.,&Bjork,E.(2000).Thedevelopmentofwordretrievalabilitiesinthesecondyearanditsrelationtoearlyvocabularygrowth.ChildDevelopment,71,Dore,J.(1978).Conditionsfortheacquisitionofspeechacts.InI.MarkovaThesocialcontextoflanguage(pp.87111).Chichester,England:Dore,J.,Franklin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