Factors promoting engaged exploration with computer simulations Noah S - PDF document

FactorspromotingengagedexplorationwithcomputersimulationsNoahS.Podolefsky,KatherineK.Perkins,andWendyK.AdamsDepartmentofPhysics,UniversityofColoradoatBoulder,Boulder,Colorado80309-0390,USAReceived10February2010;published5October2010Thispaperextendspriorresearchonstudentuseofcomputersimulationstoengagewithandexploresciencetopics,inthiscasewaveinterference.Wedescribeengagedexploration;aprocessthatinvolvesstudentsactivelyinteractingwitheducationalmaterials,sensemaking,andexploringprimarilyviatheirownquestioning.WeanalyzeinterviewswithcollegestudentsusingPhETsimsinordertodemonstrateengaged Correspondingauthor;noah.podolefsky@colorado.eduPHYSICALREVIEWSPECIALTOPICS-PHYSICSEDUCATIONRESEARCH,020117/020117©2010TheAmericanPhysicalSociety020117-1 processofbuildingconnectionsthroughexploration.ThenextsectiondescribesthesimthatwasusedinthisWaveInterference.Wethenoutlinethetheoreticalframeworkforanalyzingdatafrominterviewswithstudentsusingsims,followedbythemethodologyandresultsoftheinterviewswhichdemonstratestudentengagedexplorationanduseofanalogywiththesim.II.WAVEINTERFERENCESIMWaveInterferencesimisdesignedtoallowstudentstoexploreinterferenceinthecontextofwaterwaves,soundwaves,andlightwaves.Itiscurrentlytheeighthmostpopu-larsimonthePhETwebsite.ManyofthesimÕsdesignfea-turesarebasedongeneralguidelinesusedforallPhETsims,includingahighlevelofinteractivity,anintuitiveuserinterface,anduseofrepresentationsthatdrawonstudentsÕexistingideas.Inadditiontothesegeneralguidelines,thedesignofWaveInterferencemakesexplicituseofanalogies,asdescribedbelowThesimisdividedintothreepanels,orÒtabs,Óoneforeachwavephenomenonwater,sound,andlight.Eachtabusesthesamebasiclayout.Thislayoutusesconcen-triccirclesripplesviewtorepresentthewaveinanareacalledthewavepool.Thecirclesareblueforwater,grayforsound,andvaryincolorforlight,dependingonthewave-lengthoflightselected.Thefrequencyandamplitudeofthewavecanbeadjustedwithsliderstotheleftofthepool,andvariousotheradjustmentscanbemadeintheÒcontrolpanelÓontheright.Thewaterwavecanberotatedtoasideviewwhichshowsacrosssectionofawaterwaveoscillatingupanddown.Thesideviewservesasasecondrep-resentationofwatermeanttohelpstudentsmakethereal-worldconnectionthatthecircularshapesintheripplesviewdepictwaterwavesmovingupanddown.Inthesoundtab,usersmayselectgrayscaleview,asshowninFig.,orpar-ticlesview,whichdepictsairparticlesmovingbackandforth.Inthelighttab,userscanactivateascreentherightsideofthepool.ThisscreenshowsthelightpatternthatfallsonitÑiflightisinterfering,thescreenwillshowafringepatternWaveInterferencesimpromotesanalogyusewithvisualrepresentationsofwater,sound,andlightwaves.Useofanalogyinvolvesmappingcommonideassuchasfre-quencyandamplitudefromacrosswavephenomena.Inor-derfortheseanalogstobeusedproductivelyformakingsenseofwavephenomena,usershavetomakecomparisonsbetweenphenomenaanddrawconclusionsbasedonthesecomparisons.Thestrategyemployedinthesimistousegenericvisualrepresentationsacrossdifferenttabsascuestopromoteanalogyuse.Figureshowsthegenericrepresen-tationforsound.Slightvariationsofthisrepresentationareusedinthewaterandlighttabs.Inaddition,alternaterepre-suchasthesideviewofwaterareemployedtocuereal-worldconnections,promotetheuseofanalogy,andservetohelpstudentsmakemeaningofthegenericrepresen-III.THEORETICALFRAMEWORKInthisstudy,wefocusonengagedexplorationbystu-dentsusingsims,observedinthecontextofindividualstu-dentinterviews.FirstastudentispresentedwithoneortwoopenconceptualquestionsbeforeopeningthesimThesequestionsareconstructedtobecarefullybalanced,sufÞcientlydifÞcult,andopen-endedsothatstudentsshouldbeabletogiveareasonableanswertothequestionaftertheyhaveexploredthesim.Thegoalofaskingtheopenconcep-tualquestionisÞrsttodetermineastudentÕsinitialunder- ourceWavePoo l Detector FIG.1.SoundtabofWaveInterference.Eachtabusesthesamebasiclayout.Thesourceherealoudspeakercanalter-nativelybeafaucetwaterwaveorßashlightlightwave.Thegraywaveshownherecanrepresentawaterwave,soundwave,orlightwave.Thesource,wavecolor,andgraphlabelschangede-pendingonthephenomenonrepresented.Thegraphatthebottomshowsthewavealongthedashedlineinthepool.Aoneortwoslitscanbeplacedinthewavepoolisusedtomeasurethewaveactivityatdifferentpointsinthepool. FIG.2.Sideviewofwaterwave.Particlesviewofsoundwave FIG.3.Lightwavewith2slitbarrier.Interferencepat-ternisshownonthescreentotheright.PODOLEFSKY,PERKINS,ANDADAMSPHYS.REV.STPHYS.EDUC.RES.,020117020117-2 standingoftopicscoveredinthesim.ThesecondpurposeoftheopenconceptualquestionistodirectstudentsÕinitialin-teractionwiththesim.Studentsoftendeviatefromtheorigi-nalquestion,butifstudentscontinuetoengageandexplorewhileusingthesim,itisconsideredapositiveresult.Inthisstudy,themetricforsuccessisnottheoutcomeofthispro-cess,i.e.,whetherstudentscananswercertainquestionsorsolveparticularproblemsafterthefact;rather,effectivenessofthesimismeasuredthroughobservationofengagedex-plorationasithappensNotethatby,wedonotmeanwhatisoftendescribedaspurediscovery,whichmaynotprovidesufÞ-cientscaffoldingtosupportproductivestudentactivities.ThePhETsimsincludesigniÞcantscaffold-ing,whichsupportsstudentengagementandinquiry.Thisscaffoldingisimplicitinthatitconsistsofwhattheusercanandcannotdoaswellaswhattheuserisandisnotshown.AsigniÞcantpartofimplicitscaffoldingcanbedescribedintermsofaffordances,describedbelowAffordancesarewhatauserofatoolperceivesaspossibleandproductiveactionwiththattool.Affordancescanbepropertiesofnaturallyoccurringobjects,forinstanceonecouldusearocktopoundnailsintowoodbecausetherockÞtsthehandandisquiterigid.However,humansrecognizethatarockisfairlyawkwardfortaskslikepoundingnails.Wethereforedesignhammerswithuniquefeatures,i.e.,af-fordances,suchthattheyareparticularlygoodtoolsforpoundingnails.Similarly,wecanbuildaffordancesintosims.Forinstance,usersmightbegivencontroloverthewavelengthandamplitudeofalightwavewithslidersthatlooklikerealisticcontrols.Inthisway,usersreadilyperceivethatthesecontrolsarewaysofadjustingparametersinthesim,arereadilyabletomaketheseadjustments,andcanobservetheresults.Anotherexampleisslowingofphenom-enatowithinthelimitsofhumanperception,e.g.,slowingthespeedofalightwavesothatthewavenatureoflightisperceivablebytheuser.Inbothcases,thesefeaturesarede-signedsothatstudentsperceivethesimsasengagingandareinclinedtointeractwiththesiminproductiveways.restricttheactionsthatausercantakeand,likeaffordances,canbepurposefullybuiltintotools.Con-straintsareextremelyimportantforimplicitlyguidingtheuseofatoolsincetheyrestricttheuserfromtakinginappro-priateactions.Continuingtheanalogyofthehammer,onewouldneverthinktouseahammertoturnascrew.Withsims,weoftenwanttoconstrainactionsthatmaybeunpro-ductiveforengagedexploration.Examplesofthiswouldberestrictingtherangeofthewavelengthadjustmentforlighttothevisiblepartofthespectrum.Allowinguserstoviewul-travioletorinfraredwavelengthsmightbeadistractionthathindersproductiveexploration,dependingonthegoalsofaparticularsim-basedactivity.Similarly,inWaveInterferenceuserscanmovecertainobjectsinoneortwodimensions,butnotthree,andcanactivateoneortwowavesourcesthatarein-phase,butnotmoreandnotout-of-phase.Thesecon-straintskeepsimuserswithinaparameterspaceofthesimthatisproductiveforexploration,andoutoftherangeofparametersthatareunnecessaryandpotentiallyconfusing.Notethatsimsarenotdesignedtoaddressallpossiblelearn-inggoalse.g.,waterwavedispersionoroutofphaseinco-herentlightsourcesAcognitiveaffordancethatisbuiltintoPhETsimsistheuseofanalogy.Analogyisgenerallydescribedastheuseofideasfromafamiliartopictomakeinferencesaboutanunfamiliartopic.Formalmodelstreatananalogyasamappingofideasfromonetopictoanother,akintoamathematicalmapping.Forinstance,ideassuchasÒoscillat-ing,ÓÒadding,ÓandÒcancelingÓcanmapfromwaterwavesafamiliartopictolightwaveswhichislessfamiliarordertoexplaininterferenceoflight.Notably,waterandlightwavesarefairlybroadtopicswithmanycomplexitiesandnuances.Nonetheless,studentswithpartialunderstand-ingsofthesetopicscanstilluseanalogiestogenerateinfer-encesandnewideas.Furthermore,studentswhoaredeeplyengagedwithasimcanbuildconnectionsinrealtimeandtesttheseconnections.SuchisthecasewithstudentsusingWaveInterference,aswewilldemonstrate.Intheprocessofgeneratingnewideas,studentknowledgemaybecharacterizedasconsistingofpieces.Thesepiecesofknowledgecanbeusedtoconstructnewunder-standingsofunfamiliarphenomenaiftheyareactivatedandappliedappropriately.WecancharacterizeasigniÞcantamountofthisprocessasstudentuseofanalogy,whichissupportedinthesimsthroughtheuseofmultiplevisualrep-resentations.IntheWaveInterferencesim,visualrepresenta-tionsplaytwokeyrolesinpromotinganalogyusebystu-cueingknowledgeelementsforsensemakingwithinasingletopic,suchastransversewavemotionofwaterwaves,andconnectingknowledgeelementsacrosstopics,suchasconstructiveanddestructiveinterferenceofwaterandlightwaves.Thewayvisualrepresentationsareusedinthesimisdescribedindetailbelow.Insummary,affordancesandconstraintsprovideimplicitguidancetostudents,drivingproductiveactivity.WesuggestthismaylessentheneedforsigniÞcantexternalguidance.Thisframeworkdistinguishesengagedexplorationwithsimsfromothertypesofactivities,suchasheavilyguidedactivitiesorpurediscovery.Notably,simsarenotmeanttoreplaceotherpedagogicaltoolsentirely.Intheex-amplesabove,ourintentionistohighlightaprimarystrengthofsims:educationallybeneÞcialaffordancesandconstraintscanbebuiltintosimsthatmaynotbeeasilyaccessibleintherealworld.IV.METHODSThisstudyusesqualitativedatagatheredfrominterviewsinwhichstudentsexploretheWaveInterferencesimforabout1h.Weuseexemplarsfromthisdatasettodemon-stratecasesofengagedexplorationanduseofanalogy,asdescribedabove.Inparticular,welookforinstancesofaf-fordancesandconstraintsguidingproductiveexplorationbyInthese1hinterviews,studentsarenotexpectedtoarriveatacompleteandrobustunderstandingofwaveinterference,rather,thegoalisthattheywillbegintodevelopaframe-workaboutwaveinterferencebynoticingwhatisimportantandwhatisnotimportantforunderstandingthephenom-FACTORSPROMOTINGENGAGEDEXPLORATIONWITHPHYS.REV.STPHYS.EDUC.RES.,020117020117-3 enon.WaveinterferenceisafairlyadvancedanddifÞculttopic,andthestudentsweinterviewedinthisstudyhadnoformalinstructiononthetopicpreviously.BeforeusingtheWaveInterferencesim,thesestudentswerequestionedaboutinterferencephenomenabutnoneofthestudentsarticulatedthestandardscientiÞcexplanation.However,thesestudentsconstructedsigniÞcantunderstandingofthetopicthroughinteractionwiththesimand,whileengagedwiththesim,wereabletoarticulatemanyoftheideasnecessaryforex-plaininginterferencephenomena.Ourresearchfocusesonthefollowingquestions.Simsaredesignedwiththeintentofsupportingstudentsinmakingconceptualconnections,andweareparticularlyinterestedininvestigatingwhetherstudentsachievethesegoals.weidentifycasesofaffordancesandconstraintsdrivingpro-ductive,engagedexplorationbystudents?Dostudentsnoticeanduseconnectionsbetweendifferentwavephenom-enatomakesenseofwaveinterferenceÑthatis,dostudentsusetheanalogiesbuiltintotheWaveInterferenceDoesstudentuseofanalogyappeartobesupportedbytheparticularrepresentationsusedinthesim?Howdostudentsmakesenseoftheserepresentationsanddoesexplo-rationhelpthemmakeprogresstowardthestandardscien-tiÞcmodelofwaveinterference?WeseektoanswerthesequestionswithqualitativedatafrominterviewswithstudentsusingtheWaveInterferencesimulation.Interviewswereconductedwithundergraduatestudents,recruitedfromaÞrst-semester,algebra-basedintro-ductoryphysicscourseatalargeuniversity.Thiscourseisfairlytraditional,withthreelecturesandasinglelaboratorysectionperweek.AllofthestudentshadpreviouslyseenafewPhETsimsaspartofthiscourse,butnottheWaveIn-terferencesim.Interferencephenomenaarenotcovereduntilthesecondsemesterofthiscourse,sostudentshadnotyetbeenexposedtothismaterial.Thestudentsweremostlysci-encemajors,butnotinphysics.Studentswerepaidfortheirapproximately1h.Theseinterviewswerevideotapedforlateranalysis.Videorecordingcapturedthestudent,in-terviewer,andthecomputerscreenshowingthesim.Thestudybeganwithsixseparatepreliminarystudentin-terviews.Interviewsbeganwiththeinterviewergatheringbackgroundinformationsuchasmajor,yearinschool,andphysicsbackgroundofthestudent.Inthesepreliminaryin-terviews,studentswereaskedanopenconceptualquestionsimilartothefollowing:ÒIfyouhavetwolightsourcesshin-ingtowardascreen,youcancreatewhatiscalledaninter-ferencepattern.Howcanyouexplainthepatternthatyouseeonthescreen?ÓStudentswereaskedtogivetheirbestan-swerstothisquestionbeforeopeningthesim.Afteranswer-ing,thesestudentswerepresentedwiththeWaveInterfer-simandaskedtousethesimtoanswerthequestionasbesttheycould.Theinterviewerallowedthestudentstopro-ceedattheirownpace,occasionallyinterjectingpromptsorquestionstoprobestudentsÕthinking.Theseinterjectionswereusuallyminimalandclarifyinginnature,suchas,Òwhatdoyoumeanbythat?,ÓÒcanyouexplainthatmore?,Óor,Òdidyounoticethetabsatthetop?ÓOnoccasion,theinter-viewermightaskmorespeciÞcconceptualquestions.ThesepromptswereunscriptedandonlyprovidedafterstudentshadexploredsigniÞcantlyontheirown.Studentswereneverexplicitlytoldwhattodowiththesim.Withthisprotocol,studentsengagedwiththesimtoasigniÞcantdegree,buttherewassomeinitialdifÞcultyinthatstudentswerenotfamiliarwithinterferencepatterns.WiththeÞnaltwostudentsthatwereinterviewed,theopencon-ceptualquestionwasmodiÞedtoshowstudentstheinterfer-encepatternandpresentfourcontrastingcasesoflightinterferencepatterns.Beforestartingthesim,stu-dentswerepresentedwiththepictureinFig.onasheetofpaperandtoldthatitshowedlightsourcesontheleft,ascreenontherightwithaninterferencepattern,andbarrierswithoneortwoslitswhichletlightthroughcases3and4Studentswereaskedtotryandcomeupwithageneralmodelorexplanationforhowthepatternswerecreatedinthefourcases.Studentspresentedtheirinitialideas,andthenstartedthesimandweretoldtousethesimasbesttheycouldtoanswerthechallenge.WhileÞndingsfromall8interviewsweresimilarintermsofstudentengagementandexploration,onlytheÞnaltwointerviewsadheredstrictlytoaprotocolbasedontheopenconceptualquestionbasedonFig..WethereforefocusonresultsfromthesetwoÞnalinterviewsbelow.V.RESULTSInthissectionweanalyzetranscriptsegmentsfrominter-viewswithstudentsS1andS2.S1isasenior,majoringinmathandphilosophy,andhadpreviouslytakenphysicsinhighschool.S2isasophomoremajoringinbiologyandwasretakingthealgebra-basedphysicscourseafterreceivingaDinthecourse.S2hadnopriorformalphysicsinstruction.Neitherstudenthadpreviouslyreceivedanyformalinstruc-tiononwaveinterference.WhenpresentedwiththeopenconceptualquestionaboutthefourinterferencecasesinFig.beforeopeningthesim,bothstudentsÕexplanationsclearlyindicatedthattheydidnothaveagoodunderstandingof Source FIG.4.ImageoffourÒcontrastingcasesÓusedwithopenconceptualquestionforÞnaltwointerviews.PODOLEFSKY,PERKINS,ANDADAMSPHYS.REV.STPHYS.EDUC.RES.,020117020117-4 lightinterference.CommonideaswerethatthebarriersÒblockedÓthelight,orthatthelightÒcrossedÓandgavethepatterns;but,bothS1andS2statedexplicitlythattheycouldnotexplainwhycases2and4hadthreebrightspots.Fol-lowingthis,studentsopenedtheWaveInterferencesim.Wepresentinterviewdatafromthepointatwhichstudentsbe-ganinteractingwiththesimbelow.Student1InterviewAfterattemptingtoexplainthefourcases,S1openedthesimandbegantoexplore,startingwiththewatertab.Afterspendingseveralminutesbecomingfamiliarwiththebasicoperationofthesim,suchasmovingsliderstomakechanges,S1engagedintheÞrstofmanyexploratoryactivi-ties.S1adjustedthefrequencyandamplitudeofthewaterwaveandactivatedthetapemeasure.Withoutpromptingbytheinterviewer,S1said,ÒOutofcuriosity,doeschangingtheamplitudeaffectthatbetweencircles;wavelength.ÓTheinterviewerdidnotre-spond.S1thenadjustedtheamplitudeofthewaterwavetobeverysmall,thenverylarge,andthenpausedthesim.Pausingfreezesthewaverepresentationshowninthewavepool.S1usedthetapemeasuretodeterminethedistancebetweenthecircles,concluding,ÒNo,itdidnÕtappeartoaf-fectthelengthofit.ÓThisshortsegmentisjustoneexampleofthesortofexplorationthatstudentsengageinwhenusingthesim.Thisexplorationfollowsacommonpattern.First,someelementofthesimdrawstheuserÕsattention,leadingtheusertomanipulatetheelementandseetheresultinrealtime.Uponseeingthisresult,theusergeneratesfurtherquestions,andthenexploresthesimfurtherinordertoanswertheseques-tions.Notethatthissortofproductiveexplorationhingesonseveralaffordancesbuiltintothesim:theadjustmentofam-plitude,thereal-timechangeinrepresentationinreactiontotheadjustment,theavailabilityofatoolthetapemeasurethatallowsforthemeasurementoflength,andtheabilitytopausethesim.Built-inconstraintsalsosupportengagedex-ploration:witharealfaucet,increasingthewaterßowinordertogeneratealargeramplitudewouldnecessarilyin-creasethefrequencyofdrips.However,thisisanartifactoffaucets,notageneralpropertyofwaves.Inthesim,thefaucetisdesignedsuchthatincreasingthewaterßowaffectsthedripsizeandthustheamplitudeofthewaves,butiskeptfromaffectingthefrequency.Thisconstraintontheef-fectofamplitudesupportsstudentsingeneratingtheideathatamplitudeandfrequencyareindependentquantitiesofaS1spentseveralminutesfurtherexploringthesim,ma-nipulatingcontrols,changingtothesideviewofwater,andusingthedetectortoprobedifferentareasofthewavepool.Aboutfourteenminutesintotheinterview,stillworkinginthewaterwavetab,S1activatedtheoptionfortwofaucetsandsawthatadifferentpatternwascreatedinthewavepool.Thispatternshowslightanddarkcirclesmovingawayfromthesources,aswellasfuzzylinesthatrepresentnodallineswherethewaveamplitudeiszero.S1usedthedetectortoseethatthewaterheightwasnotchangingalongthenodallines,butoscillatedinotherareas.Noticingthesefeatures,S1said,S1:IwonderwhatdeÞnestheselinespointingalongthenodallinesnowaveactivityrightinbetweenthemiswherethewavesarethebiggest,andheretheymellowout.SowhatIwaswonderingishowyoude-terminethat.S1thenspentseveralminutesmovingthedetectoraroundthewavepool,thenchangedbacktoasinglefaucetandactivatedabarrierwithasingleslit.Thiscreatesadiffractionsimilartointerference,butforasingleslitingfromtheslit,whichS1continuedtoexaminewiththedetector.ThefollowingdiscussionthenensuedbetweenS1andtheinterviewerS1:ThatÕsintriguing.Youhavethesamethingrighthereinthemiddle,justlikewhenwehadtwodrips,theyinterferedwitheachotherandandcalmedthewater.I:Sowhatdoyoumeanwhenyousayinterfere?S1:IÕmnotsure.Thewavesaregoinginthesamespotandtheendresultisashallowerwavewithaloweramplitude.Here,theamplitudehereonthesetwolinesis,um,aheightwithoutnumbers,andoverhereitÕsless.Andsoifyouputascreenouthere,outhere,youÕdhave,um,twowhitespots,andthenadarkerspotinbetweenthem.Here,S1makesacomparisonbetweenthepatterncreatedbytwodripsandthepatterncreatedbytheslit.Initially,thelanguagethatS1usesisveryspeciÞctowaterÑS1talksaboutÒwherethewavesarethebiggest,andheretheymel-lowout.ÓWhileS1usesthewordÒamplitude,ÓwhichisnotspeciÞctowater,hereS1explicitlyrelatesamplitudetoÒshallower.ÓS1isexploringthesimandtryingtomakesenseoftherepresentationsofwaterwaves.Inusingthedetector,S1iscoordinatingtworepresentationsofthewaterwaveÑthewavepoolripplesandthesinewaveinthedetectorÑandisusingthedetectorrepresentationtomakesenseofthewavepoolrepresentation.S1generatestwospontaneousanalogiesinthesegmentsabove.First,withthesingleslit,S1saysÒyouhavethesame FIG.5.Twosourceinterferenceofwaterwaves.Fuzzylinesrepresentnodallineswherewaveamplitudeiszero.Detectorsareplacedinanareaoflargewaveactivityandonanodalline,resultinginalargeamplitudecurveandaßatlineonthedetectorgraphs,respectively.FACTORSPROMOTINGENGAGEDEXPLORATIONWITHPHYS.REV.STPHYS.EDUC.RES.,020117020117-5 thingagain,Órelatingtheinterferencepatterntothetwo-sourcecase.NotethatS1setsupthesetwosituationsandthennoticesthesimilaritybetweenthem.S1alsomakesaspontaneousanalogicalconnectionbetweenwaterandlight.Inthelastline,S1saysÒifyouputascreenouthere,Óthatthereisnoscreenshowninthewatertab.S1isusingtherepresentationshowninthewatertabtomakesenseoftheinitialquestionaboutlight,inwhichonlytheÞnalinter-ferencepatternonthescreenisshown.Next,S1activatedtwoslitsandcontinuedinasimilarprocessofprobingwiththedetector,manipulatingthesim,andobservingtheeffects.Duringthistime,S1notedhowthetwoslitscreatedaninterferencepatternsimilartotwosourcesorasingleslit.S1continuedtoexplorethewatertab,andataboutthirty-Þveminutes,theinterviewersaid,ÒDidyounoticethetabsupatthetop?ÓS1said,ÒNo,Iwasjustplayingwithwater,Óandimmediatelyswitchedtothesoundtab.S1spentafewminutesexploringsound,andthenataboutfortyminutesintotheinterview,S1beganexploringthelighttab.S1Þrstactivatedtwolightsources,thenpausedthesimtoexaminethepatternshown.S1:Again,wehavethelineswherethewavesdonÕthappen,andthatÕswhyweÕvegotdarknessinthemiddle.Becausejustlikewiththewater,thewavesareinterferingwitheachothersomehow.AndsoweÕllhaveanother,um,whitespot,orblackspotouthereandoneouthereaswell.Here,S1isdescribingwhatisseeninthewavepoolandspontaneouslymakesareferencetowater,basedonthelightwaveinterferencepatternshown.S1ismakinganotherana-logicalcomparisonbetweenwaterandlight,thistimecom-paringtwotabsofthesimwhereasearlierS1comparedwaterwavesinthesimtothelightinterferencepatternonasheetofpaper.WaterservesasafamiliarresourceforS1togenerateideasaboutlight.ThoughS1hadmadeacompari-sonbetweenwaterandlightearlier,therepresentationusingbrightanddarkareasinthewavepoolappearstobecriticalforS1noticingthespeciÞcsimilaritiesbetweenwaterandlightwavese.g.,referringtotheÒwhitespot,orblack.S1continuedexaminingtheinterferencepattern,andtheinterviewerpromptsS1.I:Sowhatdoyouthinkisgoingonoutthere?S1:Whatdoyoumean?I:Um,whydoyouthinkyougetthesedifferentpat-terns?I:HowwouldyouexplainthesedifferentcasesS1:Um,Ithinkthatthe,likeIÕvebeensayingitthewholetime,thewavesareinterferingwitheachother.AndmaybeitÕsthatonewaveishereraisesrighthandup,palmdownandtheotheroneishereputslefthandlower,palmdownandtheycrashintoeachotherbringinghandstogether,theyhittinghandsto-getherseveraltimes.IdonÕtknow,theyI:Whatwouldgiveyouthatidea?S1:Um,IÕmnotreallysure.Iguessthatwhenthey,whenthewavesinteract,um,thelikepartsoftheitdoesnÕtmatterwhyyouÕvegotseparatewaves.WhetheryouÕvegottwolightsandthewavesareinteracting,ortwodrips,ortwospeakersorwhat-everandthewavesareinteracting.OrifyouÕvegotabarrierandandnowweÕvegotwavescomingoff,separatewavescomingoffofeachoftheseslits,andweaddedeachoftheseslitssothedifferentwavesinteractwitheachotherbringinghandsto-andyouseethattheyinteract,andtheyÕvebeendoingthatthewholetime,butumIjustwouldwanttoknow,like,exactlywhatthatinteractionishandstogetheragain.Whathappensthere.ÓS1ÞrstexplainsthatÒthewavesareinterferingwitheachotherÓandmakesagestureanotherrepresentationofsome-thingbeingupandsomethingbeingdowncomingtogether.S1isnotabletoarticulatetheseideasverywellinwords,butS1Õsgesturesaresuggestiveofwavescancellingakintode-structiveinterference.NotethatS1endsthelaststatementbysuggestingfurtherquestionstobeanswered.Whilethisindi-catesthatS1Õsideasaboutinterferencearetenuous,thissortofquestioningbystudentsisexemplaryofengagedexplora-tionsinceitindicatesthatstudentsarechoosingandexplor-ingtheirowninquirypath.Furthermore,S1generatesmanyusefulideasaboutwaveinterferenceandmaybeinthepro-cessofdevelopingacoherentconceptualframeworkofthephenomena.Thisprocessofdevelopingaframeworkisim-portantforstudentstomakesenseofcontenttheyencounterinthefuture.Alongtheselines,wewillsoonseethatS1isabletodemonstrateafairlyrobustunderstandingofwaveinterference.S1isalsobeginningtogeneralizetheideaofwaves.S1says,ÒitdoesnÕtmatterwhyyouÕvegotseparatewaves,ÓandtherestofS1ÕstalkmakesitclearwhatismeantisthatitdoesnotmatterwhatspeciÞcwavephenomenonisbeingdescribed.S1isgeneralizing,sayingthatwater,sound,andlightwavesallbehavethesameway.I:SowhatwouldbeyourbestexplanationforwhatÕsgoingonatthedarkspotsandwhatÕsgoingonatthelightspotsonthescreen?ÓS1:The,um,amplitudeofthewavedeterminesthebrightnessofthe,um,thespotonthescreen.Andsohere,wheretheinterferingwaves,likebeforethebar-rierhaskindofbrokenupthewavealittlebit,soyoujustgetwhatÕscomingtoaslit,andsotheyinterferewitheachotherandsotheamplitudeissmaller.Youget,um,adarkerspot.But,likeyouÕvegotlighthereandhereandherepointingatthescreen,um,justlikewhenweweretalkingwiththewaterswitchestothewatertab.Wherewehadthetwoslitsandtheyinter-feredwitheachotherandthelinebetweenthem.Butthentheyhadthespaceinthemiddle.S1continuestodrawonwatertoexplainwhatishappen-ingwithlight.However,nowS1actuallyswitchestothewatertab,usingthiselementofthesimasaresourceforexplaininghisreasoning.ThisisasigniÞcantshiftinhowS1isusingthesim.Theactivityisnolongeramatterofinter-actionbetweenstudentandsimÑS1isnowusingthesimasatoolforwiththeinterviewer.Inasense,thesimprovidesnotonlyscaffoldingforthestudentÕsexplora-PODOLEFSKY,PERKINS,ANDADAMSPHYS.REV.STPHYS.EDUC.RES.,020117020117-6 pliÞednatureoftherepresentationalsoconstrainsusersbyreducingÒnoise,Óthatis,extraneousvisualinformationthatisnotrelevanttothesimlearninggoals.Thefactthatthedetectorgivesusersawayofmakingsenseofthelightwave,butlimitsuserstojusttheinformationthatisnecessary,isaperfectexampleofagoodbalancebetweenaffordancesandconstraintsbuiltintothesim.Putanotherway,thechallengeinthisactivityistoÞgureoutwhywavesinterfere,andthesimprovidesjusttherightamountofscaffoldingsuchthatthischallengeisbalancedbetweentooeasyandthereforenotinterestingandtoodifÞcultandthereforefrustratingTheresultofthesedesignchoicesisthatstudentsfocusontheessentialfeaturesforbuildingunderstandingofwavein-terference:lightanddarkareasandareasthatmakeÒfuzzylinesÓthroughthepattern.LikeS1,S2madeanalogicalconnectionsbetweendiffer-entwavephenomena,whichsupportedS2Õsexploration.About30minintotheinterview,S2switchedfromthelighttabtothesoundtab.S2createdaninterferencepatternwithtwospeakers,thenswitchedtotheparticlesviewandbegantocommentonwhatwasshown.stilltryingtoÞgureoutwhyitbreaks.CausetheyÕredoingthesamethingthatthelightdid,andtheyÕrebreaking,whenthewavelengthbreakssplitsatthebarrier,itcausesittochangeshapes.I:WhatÕsthesameaboutthem?S2:Thewaythey,um,whentheycombinetheydonÕtstaythesamestraightpatternthatitwould.AndsoitÕshittingdifferentlyonthewall.ItÕshittingonthethreespotsinsteadofjustone.WenotethatS2initiatedtheideathatsoundandlightweresimilarinthepatternsshowninthewavepool.S2stillcannotquiteexplainthesepatterns,buttheanalogicalcon-nectionsarebeginningtotakeshape.S2nextswitchedtothewatertabandcreatedaninterferencepatternwithtwofau-cets,thenactivatedthedetectorandbeganexaminingthewaterwaveswiththedetectorprobe.S2:SohereIhavethewaterdrippingin,andIhaveitsetsoitÕlldripreallyfast,thefrequencyishigher.And,likeonthelightwaves,theybreakupandtheyhitthewalldifferently.Andherethewaterlevelisthesmall-movingtheprobetoanodalline,wherethelightwavehadthesmallestelectricÞeld.Andthesamething,thewaterlevelishighestwhenitÞrstcomesoutofthespoutmovingtheprobeneartooneofthefau-I:Sowhatdoyouthinkiscausingthatpatternhere?S2:WhenitÞrstcomesout,ithasahighervelocitysothewaveisgoingtohaveahigherimpactonit,whenithitsthewater.Whichcausesthewatertohaveahigherwaterlevel.Andasitgoesclosertothewall,itlosesenergyandsothewavesarenÕtashigh.Sothewaterleveldecreases.SoIguessifyouappliedthattothelightswitchestolighttab,itwouldkindofbethesamethingIguess.WhenthelightÞrstcomesoutofthelightbulb,itwouldbeatitshighestintensityandmovingthefastest,andsowhenitgetsclosertothewallitÕsslowingdown.AndthenitwonÕt,asitslowsdownitlosesenergy?S2continuedtoexplorethewater,sound,andlighttabswiththedetector.S2madeseveralmorereferencestothethreephenomenabeingsimilar,activatedmanypiecesofknowledgeaboutinterferenceandmadeconnectionsbe-tweenphenomena.About45minin,theinterviewerdecidedtoprobemorespeciÞcallywhatideasS2hadgeneratedbyusingthesim.I:Inthewaterone,whatdoyouthinkthelightplacesandthedarkplacesare?S2:ItÕsthewaterlevel.I:Whichiswhich?ÞrsttakingsometimetoexplorewiththedetectorThedarkplacesaregoingtobethedeeper.Ithinkthelightonesaregoingtobelikethetopofthewave,andthedarkonesaretheinbetweenthem.Noticethatinthelastline,S2didnotanswerrightaway.S2tooktimetousethedetector,movingtheprobearoundthewavepooltoÞndananswer,thenresponded.S2hadbeendoingasimilarexplorationwiththedetectorwithwa-ter,sound,andlightthroughouttheinterview,andsoatthispointwaswellpreparedandknewwhatactionwasneededtodoinordertoanswertheinterviewerÕsquestion.About50minin,S2wasexploringthewatertabwhentheinterviewerbegantoaskaseriesofprobingquestions.I:WhatdoyouthinkwouldhappeniftwowaveswerecomingalongandoneofthemwasgoingupandonewasgoingdownS2:Andtheyhit?andtheyhit.S2:Itwouldgobacktozero.Theywouldneutralizeeachother,Iguess.I:Andso,doesthathelpyouthinkaboutthisatall?switchestolighttabSo,whentheycollide,theamplitudesareoppositesooneisatthetop,oneisatthebottomraisesonehandup,onehanddown.AndwhentheycollidetheyzerooutbringshandstogetherandthatÕswhyyougetthe,youdonÕthavethelight.Afewmomentslater,theintervieweraskedS2toexplainagainhowthepatternwasformed,andwhatS2didistelling.S2wasinthelighttab,butswitchedtowatertobeginanexplanation,groundingtheideasinwaterwaves.I:Socanyouexplainittomeagain,thewayitmakessensetoyou.S2:So,withthewaterswitchestowatertab,thetwowavestheycomeateachotherandoneÕshighandoneÕsdownlow.Whentheycollidetheycanceloutandtheygobackdowntothenormalwaterlevel.Andsoforthelight,whentheydothatswitchestolight,itwouldbethesamethingwiththewavelengths.Theonewavelengthwouldbeuphigh,theonewouldbeonthebottom,andtheycollide.Andsowhentheycollidetheycancelout.WhentheycanceloutyoudonÕtgetthelightanymore.YoucanÕtseethewavelengthifitÕsAtthispoint,S2isabletogiveaverygoodexplanationfortheinterferencepattern.NoteparticularlyhowS2useswatertoexplaintheideas,eventotheinterviewerwhopre-PODOLEFSKY,PERKINS,ANDADAMSPHYS.REV.STPHYS.EDUC.RES.,020117020117-8