Title Geometric Algebra New Foundations, New Insights标题的几何代数的新基础新的见解.docx

TheworkofAmbjornNaevewithinthefieldofMathematicsEducationalReformAmbjornNaeveMarch2001(I)CIDCentreforUserOrientedITDesignTableofContentTableofContent21. ProblemStatement42. Background52.1. TheCVAPresearchgroup62.2. TheGeometricToolboxproject62.3. PrqjectiveDrawingBoard:dynamicgeometricexplorations72.4. TheCentreforuser-orientedITDesign(CID)92.5. TheGardenofKnowledgeproject102.6. SomeILEprojectsatCID113. ConceptBrowsing123.1. Conceptualtopologies123.1.1. Traditionalconceptualtopologies123.1.2. Dynamicconceptualtopologies-hyperlinkedinformationsystems123.1.3. Problemswiththeabovementionedconceptualtopologies133.2. BasicDesignPrinciplesforConceptBrowsers143.3. Conzilla144. KnowledgeManifolds164.1. CreatingMultiplyNarratedKnowledgeComponents164.2. ComposingKnowledgeComponentsintoLearningModules175. MathematicalILEworkatCID195.1. TheVirtualMathematicalExploratorium195.1.1. Introduction195.1.2. Surfingthecontext215.1.3. Displayingmeta-datadescriptions235.1.4. Viewingthelistofcontentcomponentsthroughdifferentfilters245.1.5. Viewingtheactualcontentofacomponent275.1.6. Displayingthedecriptionofthecontentcomponents285.1.7. DesigngoalsandeducationalapplicationsoftheVME295.2. LiveGraphics3D-makingMathematicagraphicscomealive315.3. MathematicalComponentArchives325.3.1. GeneralgoalsoftheMCAproject335.4. CyberMath336. TheSwedishLearningLab376.1. Excerptfromtheproposalsummary376.2. NewMeetingPlacesforLearning386.2.1. Summary386.2.2. Projectoverview387. Archives,Portfoliosand3DEnvironments(APE)397.1. APE:TrackA:ContentandContextofMathematicsinEngineeringEducation397.1.1. Goals397.1.2. ActivityplanforstudywithintheMScprograminITatKTH397.1.3. ExcerptsfromtheProgressReportyear2000407.1.4. Currentstateoftheprojectcomparedtotheactivityplan417.1.5. Implementationofinteractivecontentandappropriatetools437.1.6. Educationalevaluation/assessmentresults(Study1)437.2. APE:TrackC:3DCommunicationandVisualizationEnvironmentsforLearning(CVEL)447.2.1. GoalsoftheCVEL-Project447.2.2. Activityplanyear2000(Workpackages)447.2.3. ExcerptsfromtheProgressReportyear20(X)-ResultsatDIS467.2.4. ExcerptsfromtheProgressReportyear2000-ResultsatCID468. PlannedLearningLabProjects:PersonalizedAccesstoDistributedLearningResources528.1. ProposalSummary528.2. Module:InfrastructureandIntelligentServices538.2.1. Contributors538.2.3. ProblemDescription,ResearchAspects538.2.4. ResearchGoalsZDeliverables538.2.5. Interactionwithothermodules558.2.6. CIDteam558.3. Module:Personalizedaccesstoeducationalmedia558.3.1. Contributors558.3.2. ResearchIssues569. GeometricAlgebraandMathEducationalReform589.3. DavidHestenes589.4. Modelingprogramexcellenceaward589.4.1. Exemplary&promisingeducationaltechnologyprograms(2000)599.5. SIGGRAPH-2000:GeometricAlgebraCourse609.5.1. CourseTitle:GeometricAlgebra:NewFoundations,NewInsights609.6. MathXplor-aVirtualMathematicsExploraioriumgroup629.7. DavidHestenesatKTH659.8. EducationalReformbasedonSoftwaredevelopment659.8.1. TheSimCalcProject659.8.2. OverallStrategy6710. CILTandEdGrid6710.3. TheCILT2000conferenceandtheM&Vworkshop6711. References6911.3. SelectedpublicationsbyAmbjomNaeve6911.4. SupervisoryActivitiesbyAmbjornNaeve701. ProblemStatementDuringthelasttwodecades,thespectacularadvancementswithinthefieldofinformationtechnologyhavecreatedpowerfulgraphicalworkstationswithpossibilitiestostudymathematicsinnewandexitingways.Todayitisevidenthowcomputerbasedanimationsandsimulationshaveaffectedmostfieldsthatinvolvemathematicalapplicationsinsomeway.Visualizationofstructuralrelationshipsanddynamicprocesseshasemergedasafieldofitsown,withapplicationswithinscienceandtechnologyaswellaswithineconomicsandsocialsciences.Itisthereforesomethingofaparadoxthatoneofthefieldsthatseemstohavebeenleastaffectedbythisdevelopmentisthefieldofmathematicsitself.Thisisespeciallytrueofmathematicseducation,i.e.mathematicaldidactics.Atouruniversitieswearestillcarryingonthetraditionalwaysofmathematicsteaching-executingourcoursesintheoverallspiritofuthesameprocedureaslastyear11!Amongmathematicsteachers,computersareoftenconsideredathreateningelement,thatfocusesthestudents'attentioninthewrongdirection.Thisattitudeiseasilyreinforcedbythemultitudeoflow-qualityeducationalsoftwarethatsupportsmathematicallytrivialpursuitsinonewayoranother.Infact,thisdeplorablestateofaffairshascausedtheissueofcomputer-supportedorcomputer-disturbedmathematicstosurfaceasamajordiscussionthemeamongmathematicaleducationalists. See the report titled Datorstddd eller (Iatorstord mutenutikundervisning ?, Hogskoleverkets Skriftserie I999:4S, ISSN 1400-9498.Ofcourse,therearemanyexceptionsfromthisbasicpatternintheformofindividualteachersthatinvolvethemselvesintryingtomakeintelligentuseofthepossibilitiesofpedagogicalrenewalthatareofferedbytheemergingICTt