Generating cultures for mathematical microworld development.docx

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