Studying Virtual Math Teams PDF
Preview Studying Virtual Math Teams
Studying Virtual Math Teams COMPUTER-SUPPORTEDCOLLABORATIVELEARNING VOLUME11 SeriesEditor: ChrisHoadley,PennsylvaniaStateUniversity,Pennsylvania,USA NaomiMiyake,ChukyoUniversity,Aichi,Japan EditorialBoard: MichaelBaker,CNRS&UniversitéLumièreLyon,France CarlBereiter,OntarioInstituteforStudiesinEducation,Canada YrjöEngeström,UniversityofHelsinki,Finland GerhardFischer,UniversityofColorado,U.S.A. H.UlrichHoppe,UniversityofDuisburg-Essen,Germany TimothyKoschmann,SouthernIllinoisUniversity,U.S.A. ClaireO’Malley,UniversityofNottingham,U.K. RoyPea,SRIInternational,U.S.A. ClotildePontecorovo,University‘LaSapienza’,Italy JeremyRoschelle,SRIInternational,U.S.A. DanielSuthers,UniversityofHawaii,U.S.A. TheComputer-SupportedCollaborativeLearningBookSeriesisforpeopleworkinginthe CSCLfield.Thescopeoftheseriesextendsto‘collaborativelearning’initsbroadestsense; thetermisusedforsituationsrangingfromtwoindividualsperformingatasktogether,during ashortperiodoftime,togroupsof200studentsfollowingthesamecourseandinteracting viaelectronicmail.Thisvarietyalsoconcernsthecomputationaltoolsusedinlearning:elab- orated graphical whiteboards support peer interaction, while more rudimentary text-based discussionforumsareusedforlargegroupinteraction.Theserieswillintegrateissuesrelated to CSCL such as collaborative problem solving, collaborative learning without computers, negotiationpatternsoutsidecollaborativetasks,andmanyotherrelevanttopics.Itwillalso covercomputationalissuessuchasmodels,algorithmsorarchitectureswhichsupportinno- vativefunctionsrelevanttoCSCLsystems. Theeditedvolumesandmonographstobepublishedinthisseriesofferauthorswhohavecar- riedoutinterestingresearchworktheopportunitytointegratevariouspiecesoftheirrecent workintoalargerframework. Gerry Stahl Studying Virtual Math Teams 123 GerryStahl CollegeofInformationScience& Technology DrexelUniversity 3141ChestnutSt. Philadelphia,PA19104-2875 USA [email protected] ISBN978-1-4419-0227-6 e-ISBN978-1-4419-0228-3 DOI10.1007/978-1-4419-0228-3 SpringerNewYorkDordrechtHeidelbergLondon LibraryofCongressControlNumber:2009930753 ©SpringerScience+BusinessMedia,LLC2009 Allrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewritten permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY10013,USA),exceptforbriefexcerptsinconnectionwithreviewsorscholarlyanalysis.Usein connectionwithanyformofinformationstorageandretrieval,electronicadaptation,computersoftware, orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisforbidden. Theuseinthispublicationoftradenames,trademarks,servicemarks,andsimilarterms,eveniftheyare notidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyaresubject toproprietaryrights. Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Contents PartI IntroducingGroupCognitioninVirtualMathTeams IntroductiontoPartI . . . . . . . . . . . . . . . . . . . . . . . . . 3 1 AChatAboutChat . . . . . . . . . . . . . . . . . . . . . . . . . . 7 GerryStahl 2 TheVMTVision . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 GerryStahl 3 MathematicalDiscourseasGroupCognition . . . . . . . . . . . . 31 GerryStahl 4 InteractionalMethodsandSocialPracticesinVMT . . . . . . . . 41 GerryStahl 5 FromIndividualRepresentationstoGroupCognition . . . . . . . 57 GerryStahl PartII StudyingGroupCognitioninVirtualMathTeams IntroductiontoPartII . . . . . . . . . . . . . . . . . . . . . . . . 77 6 TheSequentialCo-ConstructionoftheJointProblemSpace . . . 83 JohannW.Sarmiento-Klapper 7 The Organization of Graphical, Narrative andSymbolicInteractions . . . . . . . . . . . . . . . . . . . . . . 99 MuratPeritÇakir 8 QuestionCo-ConstructioninVMTChats . . . . . . . . . . . . . . 141 NanZhou 9 ResolvingDifferencesofPerspectiveinaVMTSession . . . . . . 161 RamonPrudencioS.Toledo v vi Contents PartIII StudyingGroupDiscourseinVirtualMathTeams IntroductiontoPartIII . . . . . . . . . . . . . . . . . . . . . . . . 181 10 RepresentationalPracticesinVMT . . . . . . . . . . . . . . . . . 185 RichardMedina,DanielD.Suthers,andRaviVatrapu 11 StudentandTeamAgencyinVMT . . . . . . . . . . . . . . . . . 207 ElizabethS.CharlesandWesleyShumar 12 GroupCreativityinVMT . . . . . . . . . . . . . . . . . . . . . . 225 JohannW.Sarmiento-Klapper 13 Inscriptions,MathematicalIdeasandReasoninginVMT . . . . . 237 ArthurB.PowellandF.FrankLai 14 Reading’sWorkinVMT . . . . . . . . . . . . . . . . . . . . . . . 261 AlanZemelandMuratPeritÇakir PartIV DesigningtheVMTCollaborationEnvironment IntroductiontoPartIV . . . . . . . . . . . . . . . . . . . . . . . . 279 15 TheIntegrationofDual-InteractionSpaces . . . . . . . . . . . . . 281 MartinMühlpfordtandMartinWessner 16 Designing a Mix of Synchronous and Asynchronous MediaforVMT . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295 GerryStahl 17 DeicticReferencinginVMT . . . . . . . . . . . . . . . . . . . . . 311 GerryStahl 18 ScriptingGroupProcessesinVMT . . . . . . . . . . . . . . . . . 327 GerryStahl 19 HelpingAgentsinVMT . . . . . . . . . . . . . . . . . . . . . . . 335 YueCui,RohitKumar,SourishChaudhuri,GahgeneGweon, andCarolynPensteinRosé PartV RepresentingGroupInteractioninVMT IntroductiontoPartV . . . . . . . . . . . . . . . . . . . . . . . . 357 20 Thread-BasedAnalysisofPatternsinVMT. . . . . . . . . . . . . 359 MuratPeritÇakir,FatosXhafa,andNanZhou 21 StudyingResponse-StructureConfusioninVMT . . . . . . . . . 373 HugoFuksandMarianoPimentel 22 AMultidimensionalCodingSchemeforVMT . . . . . . . . . . . 399 Jan-WillemStrijbos Contents vii 23 CombiningCodingandConversationAnalysisofVMTChats . . 421 AlanZemel,FatosXhafa,andMuratPeritÇakir 24 PolyphonicInter-AnimationofVoicesinVMT . . . . . . . . . . . 451 StefanTrausan-MatuandTraianRebedea 25 AModelforAnalyzingMathKnowledgeBuildinginVMT . . . . 475 JuanDeeWeeandChee-KitLooi PartVI ConceptualizingGroupCognitioninVMT IntroductiontoPartVI . . . . . . . . . . . . . . . . . . . . . . . . 501 26 MeaningMakinginVMT . . . . . . . . . . . . . . . . . . . . . . 505 GerryStahl 27 CriticalEthnographyintheVMTProject . . . . . . . . . . . . . 529 TerrenceW.Epperson 28 TowardaScienceofGroupCognition . . . . . . . . . . . . . . . . 555 GerryStahl Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 581 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 585 NameIndex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 609 SubjectIndex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 615 List of Figures Figure2.1 SomeoftheVMTteam . . . . . . . . . . . . . . . . . . . 19 Figure2.2 TheVMTlobby . . . . . . . . . . . . . . . . . . . . . . . 21 Figure2.3 AVMTchatroom . . . . . . . . . . . . . . . . . . . . . . 22 Figure3.1 Three students chat about the mathematics of stackedblocks . . . . . . . . . . . . . . . . . . . . . . . . 32 Figure4.1 Screen view of the VMT environment with referencing . . . . . . . . . . . . . . . . . . . . . . . . . . 53 Figure6.1 Primaryfeaturesofachievingconvergentconceptual change . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 Figure6.2 Grid-worldtask . . . . . . . . . . . . . . . . . . . . . . . 87 Figure6.3 Snapshotsofgrid-worldproblemresourcescreated byVMTgroups . . . . . . . . . . . . . . . . . . . . . . . 88 Figure6.4 Threedimensionsofinteractioninbridgingwork . . . . . 91 Figure7.1 Taskdescription . . . . . . . . . . . . . . . . . . . . . . . 104 Figure7.2 Ascreen-shotoftheVMTenvironment . . . . . . . . . . . 105 Figure7.3 Sixstagesof137’sdrawingactionsobtainedfrom theReplayertool . . . . . . . . . . . . . . . . . . . . . . . 108 Figure7.4 TheevolutionofQwertyuiop’sdrawinginresponse to137’srequest . . . . . . . . . . . . . . . . . . . . . . . 109 Figure7.5 Theinterfaceatthe12thstageofFig.7.4 . . . . . . . . . . 110 Figure7.6 Snapshotsfromthesequenceofdrawingactions performedby137 . . . . . . . . . . . . . . . . . . . . . . 115 Figure7.7 Useofthereferencingtooltopointtoastageofthe hexagonalarray . . . . . . . . . . . . . . . . . . . . . . . 116 Figure7.8 137splitsthehexagoninto6parts . . . . . . . . . . . . . 119 Figure7.9 Areconstructionofthefirstthreeiterationsofthe geometricpattern . . . . . . . . . . . . . . . . . . . . . . 121 Figure8.1 ThesessionintheReplayertool . . . . . . . . . . . . . . . 150 Figure9.1 Theperimeter-of-an-octagonproblem . . . . . . . . . . . . 167 Figure9.2 Thediagrampriorto“labeling”byparticipants . . . . . . . 168 Figure9.3 Thelabeleddiagram . . . . . . . . . . . . . . . . . . . . . 169 Figure9.4 Hexagon . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 Figure9.5 Octagon . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 ix x ListofFigures Figure10.1 TeamBintheVMTsoftwareenvironment . . . . . . . . . 187 Figure10.2 InstructionsforSession1 . . . . . . . . . . . . . . . . . . 190 Figure10.3 Initiating the practice of visualizing problem decomposition . . . . . . . . . . . . . . . . . . . . . . . . 192 Figure10.4 Sideviewofpyramid . . . . . . . . . . . . . . . . . . . . 195 Figure10.5 Topviewofpyramid . . . . . . . . . . . . . . . . . . . . . 195 Figure10.6 Colorusedtoshowlayersofpyramid . . . . . . . . . . . . 197 Figure10.7 TeamC’ssolutioninthewiki . . . . . . . . . . . . . . . . 199 Figure10.8 Growthofadiamondpattern . . . . . . . . . . . . . . . . 199 Figure10.9 Whiteboardatline4096inLog10-5 . . . . . . . . . . . . 200 Figure10.10 Representational practices across people and artifacts . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 Figure12.1 Grid-worldtask . . . . . . . . . . . . . . . . . . . . . . . 228 Figure12.2 Labelingtosupportreference . . . . . . . . . . . . . . . . 229 Figure12.3 Multiplerepresentationsonthesharedwhiteboard . . . . . 232 Figure13.1 Thepizzaproblem . . . . . . . . . . . . . . . . . . . . . . 242 Figure13.2 Screenshotofphase3 . . . . . . . . . . . . . . . . . . . . 247 Figure13.3 Screenshotofphase4 . . . . . . . . . . . . . . . . . . . . 248 Figure13.4 ScreenshotofSilvestre’sfinalsolution . . . . . . . . . . . 254 Figure13.5 TheinitialrowsofPascal’striangle . . . . . . . . . . . . . 257 Figure14.1 Movement of graphical objects to do practical reasoning . . . . . . . . . . . . . . . . . . . . . . . . . . . 275 Figure14.2 Jasonindexesanareaofthewhiteboard . . . . . . . . . . . 276 Figure15.1 FunctionalityintheVMTinterface . . . . . . . . . . . . . 286 Figure15.2 Explicitreferencingmustbelearned . . . . . . . . . . . . 289 Figure15.3 Bwangusesanexplicitreference . . . . . . . . . . . . . . 290 Figure15.4 Screenshotaftermessage1546 . . . . . . . . . . . . . . . 292 Figure16.1 TheVMTLobby . . . . . . . . . . . . . . . . . . . . . . . 306 Figure16.2 TheVMTtabbedworkspace . . . . . . . . . . . . . . . . 307 Figure16.3 TheVMTcoursewiki . . . . . . . . . . . . . . . . . . . . 308 Figure16.4 TheVMTprobabilitywikipage . . . . . . . . . . . . . . . 309 Figure17.1 Screenviewofreferencing . . . . . . . . . . . . . . . . . 316 Figure19.1 Earlyenvironmentforcollaborativemathproblem solving . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339 Figure19.2 IntegratedversionoftheVMTenvironment . . . . . . . . 350 Figure19.3 ConfigurationofBasilica . . . . . . . . . . . . . . . . . . 353 Figure21.1 Relation-distancedistribution . . . . . . . . . . . . . . . . 376 Figure21.2 Subjectdistribution(first30messagesindetail above) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377 Figure21.3 Subjectsinparallel . . . . . . . . . . . . . . . . . . . . . . 378 Figure21.4 Subjectalternation . . . . . . . . . . . . . . . . . . . . . . 378 Figure21.5 Subjectwaves . . . . . . . . . . . . . . . . . . . . . . . . 379 Figure21.6 Concentrationandconfluence . . . . . . . . . . . . . . . . 379 Figure22.1 Samplerulesforconversationcodes . . . . . . . . . . . . 414
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