dynamic geometry environments (dge)动态几何环境（dge）

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1、Thedraggingprocessin3DenvironmentsandgenderdifferencesbyusingthedragmodeMathiasHattermannInstituteformathematicseducationJustusLiebig-University,Gießen,GermanyWorkinggroup3:InformationtechnologiesinteachingandlearningShortdescriptionofdynamicgeometryenvironments(DGE)Inthelastthreedecadestec

2、hnologyofferednewpossibilitiestoimproveteachingandlearningofgeometryinaspecialway.Mathematicseducatorsseedynamicgeometryenvironmentsasapowerfultooltoenrichandfurtherthelearningprocessinregularmathematicsclassrooms.Thefirstdynamicgeometryenvironments(DGEs)appearedintheeightieswiththegoaltopr

3、ovideafamilyofdiagramsasrepresentingasetofgeometricalobjectsandrelationsinsteadofasinglestaticdiagram.DGEstrytoimitateEuklids’geometryandarecharacterizedbythreeproperties.Thedrag-modeallowstheusertodrage.g.thepointsofagivendrawingandthediagramwillchangeaccordingtothenewpositionofthepoint,wh

4、ileallthegeometricalrelationsusedintheconstructionarepreserved,e.g.themid-perpendicularofasegmentwillstaythemidperpendicularafterapointofthesegmenthasbeendragged.ThesecondpropertyofDGEsisthepossibilityofmacro-constructions,whichallowtheusertogroupseveralconstructionstepsunderonecommand.Fore

5、xample,withthehelpofamacro-constructionitispossibletoconstructthetangentsofagivencirclethroughagivenpoint,whichislocatedoutsidethecirclewiththehelpofonecommand.ThethirdpropertyofDGEsisthecommand“traceorlocusofpoints”.Withthehelpofthiscommand,theuserisabletoinvestigatethelocusofaspecialpoint

6、,bydraggingabasicpoint.Forexample,theusercanfigureoutwhatcurveisdescribedbytheintersectionpointoftwoheightsofagiventrianglewhenthegivenpointCisdraggedonastraightline.ThemostpopularDGEsforplanegeometryareCabriIIPlus,Geometer’sSketchpad,Cinderella2.0.andothers.InGermanschools,“EuklidDynaGeo”i

7、susedveryoften.DGE,oneofthebest-researchedtypeofsoftwarewithindidacticsofmathematicsThedevelopersofDGEsachievedtheaimtodevelopprogramswhichfollowthelawsofgeometrywhiletheuserismanipulatingpoints,e.g.byusingthedragmode,justlikematerialobjectsreactbyfollow