how online small groups co-construct mathematical …

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1、196HowOnlineSmallGroupsCo-constructMathematicalArtifactstodoCollaborativeProblemSolvingAThesisSubmittedtotheFacultyOfDrexelUniversitybyMuratPeritÇakırinpartialfulfillmentoftherequirementsforthedegreeofDoctorofPhilosophyJune2009196Acknowledgements196TABLEOFCONTENTSLISTOFTABLESviLISTOFFIGURESviiABST

2、RACTxCHAPTER1.INTRODUCTION12CHAPTER2.LITERATUREREVIEW172.1.TheRoleofMathEducationintheAgeofParticipation172.2.ReviewofInstructionalTechnology192.2.1.Computer-AidedInstruction(CAI)202.2.2.IntelligentTutoringSystems(ITS)222.2.3.ConstructivistLearningEnvironments(Logo-as-Latin)242.2.4.Computer-Suppor

3、tedCollaborativeLearning(CSCL)262.2.4.1.SocialTheoriesofLearning272.2.4.2.EvolutionofResearchMethodsforStudyingCollaborativeLearning312.2.4.3.CSCLApplicationsinMathEducation322.2.5.SummaryofITResearch342.3.ACriticalSurveyofCSCLStudiesofMultimodalInteraction392.3.1.TheProblemofSocialOrganizationinC

4、SCL392.3.2.ApproachesinCSCLtoAnalyzingMultimodalInteraction412.3.3.TheUnitofAnalysis50CHAPTER3.RESEARCHDESIGN533.1.ResearchContext533.2.VMTProject:ADesign-basedApproachtoCSCLSystemDevelopment553.3.TheVMTOnlineCollaborativeLearningEnvironment593.4.MethodologyofChatInteractionAnalysis653.5.Historica

5、lBackgroundtotheChatInteractionAnalysisMethodology66CHAPTER4.CASESTUDYOFAVIRTUALMATHTEAM744.1.Data744.2.CaseStudyI:ConceptualBackground774.3.CaseStudyII–PartA921964.3.1.Co-constructionofthetriangulargrid934.3.2.Introductionofthehexagonalarray974.3.3.Achievementofindexicalsymmetrythroughreferential

6、work984.3.4.Decompositionofthehexagonalarrayintopartitions1034.3.5.Jointdiscoveryofacountingmethod1064.4.CaseStudyII–PartB1094.4.1.Constitutionofanewmathtask1094.4.2.Co-constructionofamethodforcountingsticks1154.4.3.Collectivenoticingofapatternofgrowth1214.4.4.Resolutionofreferentialambiguityviavi

7、sualproof1244.4.5.Re-initiatingthediscussiononthealgebraicformula1334.4.6.Co-reflectingonthejointachievementoftheteam1364.4.7.Overcomingtheproblemofoverlappingsticks1384.4.8.Derivationoftheformulaforthenumberofst