Generating cultures for mathematical microworld development.docx
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Generating cultures for mathematical microworld development.docx
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Generatingculturesformathematicalmicroworlddevelopment
Generatingcultures
formathematicalmicroworlddevelopment
inamulti-organizationalcontext
ChronisKynigos
EducationalTechnologyLab,
UniversityofAthens
SchoolofPhilosophy,
FacultyofPhilosophy,EducationandPsychology,
Dept.ofEducation.
andComputerTechnologyInstitute.
Kynigos@cti.gr
Abstract
Thispaperdiscussesmethodologicalissuesofmathematicalmicroworlddevelopmentintegratedwithgeneratinginnovationintheschoolsetting.Thisisdonebymeansofvignettesofkeyepisodesinoureightyear-longexperienceofdevelopingacomponentarchitectureforeducationalsoftwarebasedonLogoasascriptinglanguage.Thevignettestouchontheproblemsofcollaborationbetweenorganizationsandpeopleofdifferentexpertise.Theyalsoaddressissuestodowiththeschoolandtheclassroomassocialsystems,withthemethodforimplementinginnovationandwithcurriculumdesign,teachingandlearning.Asetofissueswhichemergedtobeproblematicareoutlinedanddiscussed;thedifferentprioritysystemsinvolved,theamountofinvestmentincollaboration,thedifferingdiscoursesandepistemologies,thenotionofaproduct,theinterdependenciesandthecontrastbetweenreformandinnovationversusinstantfit.Itissuggestedthatawarenessneedstoberaisedaswellasmethodsfordealingwiththesefactorsinordertogenerateculturesdevelopingandusingexploratorysoftware.
Introduction
Thisarticlediscussesemergingorganizationalcontextswithinwhichmathematicalmicroworldsandcorrespondingpedagogiesmayfindnewgroundstodevelop.Iarguethatbesidesdevelopmentsinthefieldsoftechnologicalandeducationalresearch,thedevelopmentofthesemicroworldsandpedagogiesisinfluencedbythewaysinwhichamuchlargervarietyoforganizationsandcommunitiesareprogressivelyparticipatingintheshapingofperspectivesrelatedtotheuseofcomputationalandcommunicationtechnologiesforeducationandthewaysinwhichtheseorganizationsinfluencecorrespondingeducationalreform.Thediscussionattemptstoidentifysomeissuesthatmaybecrucialtotheroleofthemathematicalmicroworldcommunityinthiswidersettingoftechnologicalinfusionineducationalsystems.Thisisdonebymeansofasetofilluminativevignettes,groundedinalongitudinaleightyear-longexperienceofinfusingamathematical–constructionistperspectiveintoaseriesofconsecutiveprojects.ThesewereallfundedbytheEuropeanCommunity,whichexplicitlysupportscollaborationsbetweenadiversityofinstitutionsandeducationalsystems.Theysharedascentralobjectivetogeneratecommunitiesofpeoplecollaboratingindeveloping,reflectingonandproliferatingtheuseofexploratorysoftware.Theyinvolvedtheon–goingdevelopmentofE-slate,atoolkitfordevelopingawiderangeofexploratorysoftware,thedesign,managementandsupportofalarge–scalesystemicinitiativetointegratetechnologyintotheGreekeducationsystemandclassroom-basedresearchonteachingandlearningprocessesemergingfromimplementinginnovativeprogramsbasedontheuseofE-slatesoftware.
Emergingorganizationalcontexts
Theprocessofdevelopingexploratorysoftwareformathematicsrequiresasynthesisofexpertise:
incomputerscienceforsoftwaredevelopment;inmathematicalteachingandlearningtheory;inthemethodofintegrationandsupportoftheuseofthesoftwareinrealschoolsettings,andintheproductionofpolishedsoftwareandrespectivematerialstothelevelofprofessional-lookingproducts.Thesetypesofexpertisearetypicallyfoundindifferentorganizationsanddepartments,eachwithitsownhistoryofevolutionandagendaforprogress.Inthepasttwentyyears,however,thedevelopmentofsuchsoftwarewasfundedmainlyasfocusedresearchandwasbasedinauniversity,researchinstituteandoccasionally,acompanytypicallywithsomestateorfederalfundingandtightconnectionstoacademia.Todealwiththeneedforcompositeexpertise,theseorganizationswouldmostoftenemploycomplementaryactors,e.g.eitheraprogrammeroraneducationalist,dependingontheexpertisemissingattherespectivedepartment.Inmanycases,thesepeoplewouldbecomehybridactors,inthesensethattheywouldacquireenoughcomplementaryunderstandingsoastoeffectivelyactaspartofateambasedonalienexpertise.Itwasthroughthistypeofuni–organizationalsettingthatthecommunityworkingontheconceptionoftechnologiessupportingthegenerationofmathematicalmeaningsandthedevelopmentofourunderstandingofthisprocessasessentialforlearningmathematicswasdeveloped.
Intheearlyeighties,however,thiskindofsettingandthiskindofperspectiveinusingtechnologyforlearningwasthenorm.Mathematicalmicroworldswereoneoftheveryfewcomputationalenvironmentsdesignedforlearning.Inthesecomputationalenvironments,gettingacomputertodothingsinvolvedaveryneatwayofmakinguseoftheavailabletechnology.Itenabledthelearnertoexpressideasinsymbolic(mathematical)formbymeansoftextandwhenappropriate,toseetheresultsrepresentedinfunction-derivedgraphics(asintheturtlegraphicspartoftheLogolanguage).Initself,constructingandexploringthroughexecutableideas,andreflectingonthesethroughcomputerfeedbackandeditingisanimportantmechanismformicroworldfunctionality.Thecreationoffocusedandcoherentenvironmentsalongwithasetoftoolsformakingconstructionsormeansforexploring(toparaphraseClementsandSarama’sdefinitionofmicroworldsinthisvolume)istoasignificantextentpossiblewiththesetechnologicalmeansalone.
Furthermore,symbolicexpressionandconstructionbymeansofmathematicalformalismwasnotonlyseenasanimportantpartofsuchsoftware,butalsoascentraltothenatureofmathematicallearning(Harelet.al.,1991,NossandHoyles,1992,Kynigosetal.,1997).Theconstructionist-exploratory(KafaiandResnick,1996,diSessa,et.al.,1995)perspectivesforlearningwithtechnologyconstitutedsignificantadvancestoourunderstandingofthemathematicallearningprocess.Appliedresearchinimplementingorattemptingtoinstitutionalizeeducationalpracticesbasedonthese,suchasNoss,1985,HoylesandSutherland,1989,wereamongstthefirstexperiencesofusingcomputationaltechnologyintheschoolsystem.Acentralideastemmingfromthiscommunityisthedistinctionbetweenacomputationaltoolandaninstrument(Lagrangeet.al,2001):
atoolisacomputationalartifact,whileaninstrumentreferstohowthatartifactwasmentallyconstructedbytheuser,thatis,howtheuserconceivesitsconstraintsandpossibilities.Another,istheprocessofintegratingsoftwaredevelopmentwiththestudyofeducationalprocessesemergingfromitsuse-whereasinglepieceofsoftwaremaybecomeasetofdifferentinstruments-andfinallywiththeinstitutionalizationofitsuseintheeducationalsetting(Papert,1993,Hoyles,1993).
Sincethen,however,theadventofnewinterfaces,media,technologicalpowerandspeedprovidedthepossibilityofextendingmathematicalmicroworlds’functionalitiesinavarietyofways,asforinstance,usingdirectmanipulationindynamicgeometryenvironments,multimediaauthoring,realisticsimulations,datahandlingandtheuseofaseriesofcomputationalideassuchasparallelorobjectorientedprogramming.Thesedevelopmentshavegivenrisetoawidervarietyofrepresentationsofmathematicalideasandobjectsandthemeansformanipulatingoroperatingonthese(seeEdwards,1998foradiscussiononthenotionofmicroworldsasrepresentations).Suchenvironmentshavealsoprovidedthepossibilitytohighlightthemathematicalaspectsofawidersetofsituations,suchassimulations(seeSimCalc,endoftext).
Inparallel,thesenewtechnologiestogetherwiththeexplosivedevelopmentsincommunicationstechnologieshavebeenusedtodevelopalargevarietyoftechnologicalenvironmentsoutsidemathematics,respectivelyembodyingabreadthofperspectivesonlearningacrossavarietyofsubjectareasandthemes.Experimentsorexplorationswithsimulations(InteractivePhysics),withtheuseoflargeandwellorganizedrepositoriesofinformation(Perseus),withdatahandling(Tabletop)andthroughparticipationin‘knowledgebuilding’debates(CSILE)aresomekeystudentactivitiesmadepossiblewiththenewtypesofsoftwareavailable.Thedevelopmentofthiskindandspanofsoftwarehasplayedanimportantroleinbringingamuchlargernumberofcommunitiesintothegame,andveryoftenperspectivesoflearningwithinthesecommunitiesdifferwidely.
Forinstance,therearecommunitiesoutsideeducationalresearchtakinganinterestinintegratingtheuseofcommunicationandcomputertechnologyintheeducationalsystem:
thecomputerapplicationsbranchoftheR&Dcommunity,thesoftwaredevelopmentindustry,thetelecommunicationsagenciesandorganizationsandtheeducationalpolicymakers(oftenassumingtheroleof‘reformists’).Thesecommunitiesbringalternativeperspectivesontheessenceofandthemethodfordevelopingandusingsoftwareineducation.
Moreover,insomepartsoftheworld,suchastheEuropeanCommunity(E.E.C.),thereisaconsistentandexplicitencouragementfortheseperspectivestointegratewitheachotherinthelastfiveyearsorso.InthecaseoftheE.E.C.,theagendaforthisisnoteducationalinthenarrowsense,butmoresocio-politicalanddevelopmentalinnature:
tocreateinterculturalsensitivityandtogeneratemoresynergybetweenacademiaandindustry.ResearchersarethusfacedwithexplicitencouragementtoengageinR&Dactivityparticipating
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