Download - Teaching and learning mathematics with technology.discovery.ucl.ac.uk/1474515/2/Clark-Wilson... · PRE-PRINT Cite as: Clark-Wilson, A., & Mostert, I. (2016). Teaching and learning

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Citeas:Clark-Wilson,A.,&Mostert,I.(2016).Teachingandlearningmathematicswithtechnology.InC.Hopkins,J.Anghileri,&J.Gage(Eds.),AIMSSECMathsTeacherSupportSeries:MathematicalThinkingintheLowerSecondaryClassroom.Cambridge:CambridgeUniversityPress.

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Teachingandlearningmathematicswithtechnology.

AlisonClark-Wilson

UCLInstituteofEducation,UniversityCollegeLondon,UK

IngridMostert

AfricanInstituteofMathematicalSciences,Muizenberg,SouthAfrica

Introduction

Thearrivalofdigitaltechnologiessuchascomputers,mobilephones,tablets(likeiPads

andAndroids)isrevolutionisingtheopportunitiesforbothteachersandlearnersalike

withineducationingeneralandwithinmathematicseducationinparticular.Alloverthe

worldteachersarelookingtodeveloptheirpersonalskillsandexpertisewith

technology.‘Technology’includesmanythings–fromcomputerstomobiledevices,

fromsoftwareandapplicationstoweb-sites.Thereisalotoftechnologyoutthereandit

keepschanging.

Inthischapterwearehopingtopointyouintherightdirectionsothatyoucanbeginto

explorearangeoftechnologiesthatyoucanuseinyourmathematicsteachingcareer

andbeyond.Technologycansupportbothteachersandlearners.

Forteachersofmathematics,technologyenablesustocreate(anddisplayorprint)our

ownteachingresourcesthatincludeaccuratemathematicaltextanddiagrams-and

sharethesewithotherteachers.Wearenolongerwhollyreliantonbuyingpublished

textbooksandworksheets-wecancreateourownandadaptthemyear-by-yearto

buildourownbankofteachingresources.Technologycanalsohelpustokeepadigital

recordoflearners’testscoresandhelpustoanalyselearners’progressovertime–we

canusetheinformationtoinformwhattopicswemightneedtorevisitorwhentobegin

toteachthenexttopic.

Forlearnersofmathematics,technologyoffersanopportunityforthemtobeintroduced

mathematicalideasandconceptsincompletelynewways.Mathematicalsoftwareand

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applicationsareavailablethatenablelearnerstoplaywithmathematicalobjectsina

waythatissimplynotpossibleusingtraditionalpaperandpencilmethods.

Inthischapteryouwilllearnaboutawiderangeoftechnologiesthatareavailableto

supportteachingandlearningmathematics.

Fig.1MakiNekhavhambeusingadataprojectorforthefirsttimeinherclassroom.

IMAGE1.jpg

Ofcourse,itmaynotbepossibleforyoutotrysomeoftheseideasrightaway.However

asyourpersonalaccesstotechnologyincreases,youcanreturntothischapterwhen

youareabletotrysomeoftheapproachesinyourownclassroom.

Differenttypesoftechnology

Technologyincludesaverywiderangeofdevices,software(orapplicationsor‘apps’),

websitesetc.thathaveallbeendesignedformanydifferentpurposesandaudiences.To

helpyouwithsomeoftheterminology,wehaveincludedaGlossaryattheendofthe

chapter-soifyoucomeacrosssomethingthatisnewtoyou,lookitup!

Also,becausetherearemanydifferenttechnologyproductsthatareavailable,we

cannotprovidethespecificinstructionsforalloftheideasweoffer–youwillneedto

usetheindividual‘Help’resourcesandproductmanualsthataccompanythedifferent

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technologyproducts-butwehopethatyouwillseethevalueinmakingthistime

investmentforyourself.

Inaddition,therearemanyonlinecommunitiesandaquickInternetsearchwilloften

takeyoutothehelpyouarelookingfor.ThemillionsofInternetusersaroundtheworld

meansthatusuallysomeoneelsehasalreadyasked(andpublishedananswer)tothe

exactquestionyouareaskingyourself!

Wehaveorganizedthechapterbydividingtechnologyintothetechnologiesthatmight

beusefulinsidetheclassroomwithlearnersandtechnologiesthatcanbeusedbyyou

and/oryourlearnersawayfromtheclassroom.

Technologyintheclassroomlooksattechnologyfor

1) exploringmathematicsina)number,b)algebra,c)geometryandd)statistics

andprobability;

2) projectingmathematicssuchasa)dataprojectors,b)visualisersandc)

webcams.

Technologyawayfromtheclassroomlooksatcreating

1) worksheetsbyinsertinga)symbolsandequations,b)tables,c)graphsandd)

geometricimages.

2) resourcestoprojectusinga)presentationsoftwareandb)interactive

whiteboardsoftware

3) electronicmarkbooksbya)enteringdataandthenb)makingsenseof

assessmentdata

andatonline

4) communitiesforteachersandlearnershostedbya)Ministryofeducationsites

b)AimingHighandc)theAfricanMathematicsInitiative

5) resourcessuchasa)MicrosoftMaths,b)EverythingMathsandScience,c)Khan

Academy,d)MathsExcellenceande)Math-Aid.

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Technologyintheclassroom

1) Technologyforexploringmathematics.

Thisistechnologythathasbeencreatedtochangethewaythatweengagein

mathematicsaltogether.Suchtechnologiesletusgettothe'nutsandbolts'of

mathematicsandhavethepotentialtoengagemanymorelearnersinthemore

challengingmathematicalconcepts.

a) Number

SpreadsheetsoftwaresuchasaGeoGebraspreadsheetorMicrosoftExcel(which

wasoriginallydesignedforbusinessandaccountancy)canbeusedvery

creativelytoexplorenumberproperties.Thebasicideaisthatthecolumnsand

rowsarelabeledwithlettersandnumbersandyouusethe‘Input’bartoenter

textornumbersintothespreadsheet‘cells’.Youcanthenenterdatamore

efficientlybysettingupsomemathematicalrulesorrelationships!Youarenot

expectedtoentereachnumberonebyone!

Forexample,inFig.2below,whichshowsa‘divisiontable’fornumeratorsand

denominatorsfrom1to10,onlythevaluesincellsA2andB1wereentered

manually.Alloftheothernumbersweremadebyenteringaformula,whichwas

thencopied–eitheracrossarowordownacolumnofdata.InFig.2,youcansee

thatthevalueof3÷4(incellD5)wascalculatedusingtheformula=$D$1/A5.

Inspreadsheetsoftwarethe‘$”notationiscalledabsolutereferencing–thisis

importantifyouwanttofixthevalueofanumberinaformula.

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Fig.2AdivisiontablecreatedusingaGeoGebraspreadsheet

IMAGE2_Spreadsheet_Division.jpg

Thepowerofaspreadsheetisthat,bychangingjustonenumberinthe

spreadsheet(thenumberincellA2froma1toa2),awholenewsetofdecimal

numberscanbecreated.Thiscreatesaverymotivatingspaceforpupilsto

explorefractiontodecimalconversionsandanswerquestionssuchas:

• Howmanytimesdoesthedecimalnumber0.5appear?Why?

• Canyoupredictfivedifferentfractionsthatwouldhaveadecimal

equivalenceof0.33?

b) Algebra

Manyofthe‘bigideas’andkeyconceptsinmathematicsarerelatedtoimportant

generalisations,suchasthatallfunctionsofthetypef(x)=a*x+b,whenplottedon

aCartesian(x-y)graphplane,producegraphsthathaveaparticulargeometric

feature(astraightline).Mostofuswillhavelearnedthisbyroteandbelievedit

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becauseourteachers(andthetextbook)toldusthatitwastrue.However,with

technology,itispossibleforthelearnerstoobservethegraphfeaturesfor

themselvesand,bychangingthevaluesofaandb,discovermuchmorebesides.

WithinasoftwarepackagessuchasGeoGebra,manylineargraphscanbe

exploredveryquickly,withouttheratherslowerprocessofplottingthe

individualfunctionsbyhandusingpaperandpencil.Thisdoesnotmeanthatthe

learners’graphplottingskillsarenolongerimportant–butitdoesmeanthatthe

moreimportantknowledgeabouttheeffectthatvaryingthevalesofaandbhas

ontheappearanceofthelineargraphscanbeaccessedbyalllearners.InFig.3

showsanexploratorytaskinGeoGebrathatuses‘sliders’tochangethevaluesof

aandb.

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Fig.3AGeoGebrafilethatusessliderstoexploretheeffectofchangingthe

valueson‘a’and‘b’inlinearfunctionsgivenbyf(x)=a*x+b

IMAGE3_Geogebra_Linear_functions.jpg

Itisusuallynotenoughtoonlypresentthisfiletothelearnersand‘show’them

whathappens.Itisbettertoarousethelearners’curiositybyaskingquestions

suchas:

• Whatdoyounoticeaboutallgraphsforwhichthevalueofb=0?(or3?Or

5?Or…)

• Whatdoyounoticeaboutallgraphsforwhichthevalueofa=3?(or1.5?

or-2?Or…)

• Canyoupredictwhatthegraphofy=-1x+2willlooklike?Howdoyou

know?

c) Geometry

Dynamicgeometrysoftwarehasrevolutionisedthewayinwhichwecan

understandandexploreideasfromgeometry.Thisisbecauseanydiagramcan

be‘interactive’aswecanchangeitsappearancebydragging-andexplorewhat

happens.Wecancreatemathematically‘robust’2-Dshapesthatkeeptheir

mathematicalproperties–evenwhenitsverticesandsidearetransformedby

dragging.Figs.4and5showasetoftriangles,eachofwhichhasbeencreatedin

thesoftwaresuchthatitretainsaparticularsetofproperties.Canyouspot

whichtriangleiswhich(andwhy?).

Fig.4ThreetrianglescreatedinGeogebra

IMAGE4_Three_triangles1.jpg

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Fig.5Thethreetriangleshavebeentransformedbydraggingonlyoneofeach

triangle’svertices!

IMAGE5_Three_triangles2.jpg

Youreallydoneedtoplaywithconstructingthesetrianglesinthesoftwareto

appreciatehowdynamicgeometryenvironmentsaredifferent–theequilateral

andisoscelestriangleswerecreatingusingadigitalsetofgeometricconstruction

tools.The‘Circlebycenterandradius’replacestheprotractorandmid-points

andperpendicularbisectorsarebuilt-indigitaltools.Aswiththegraphing

example,dynamicgeometrysoftwaredoesnotreplacepaperandpencil

constructiontechniques.Howeveritdoesprovideastimulatingenvironmentin

whichtoexploregeometricconstructionsandtheorems.

ManycountrieshaveGeoGebraInstitutesthatofferface-to-face

meetings/coursesandonlinesupportforteachers.(see

www.geogebra.org/institutes)

d) Statisticsandprobability

AnydatathathasbeenimportedintoamathematicaltoolsuchasExcelor

Geogebracanbeanalysed.Agoodsourceofinternationaldataonlearners’

lifestylesandinterestisprovidedbytheCensusatSchoolwebsite

(http://www.censusatschool.org.uk/).Theinternationalsectionofthewebsite

showsthemanycountriesthathavetakenpart–anditispossibletorequesta

randomiseddatasetwithwhichtocontrastyourownlearners’data.

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Fig.6TheinternationalpageoftheCensusatSchoolwebsite.

IMAGE6_Census_at_School.jpg

2) Technologyforprojectingmathematics

Thistechnologyisdesignedtoallowyoutoprojectimagesfromyourtabletor

computertotheclass.Itisnotlimitedtoprojectingmathematics.Youcanuseitto

projectanycontent.

a) Dataprojectors

Adataprojectorconnectstoyourcomputerortabletandprojectsitsdisplayontoa

wallorscreen.Ifyouhadaninteractivewhiteboard,itwouldbepossibletooperate

thesoftwareonyourcomputerortabletbytouchingthisprojectedimageand

annotateontopusing‘electronicwriting’.

b) Visualisers

Avisualiserisahighresolutioncameraonastandthatconnectstoadataprojector

and,whenyouplaceobjects,learners’workoratabletscreenunderneathit,this

imageisprojectedontothewalldisplay.Thisisparticularlyusefulwhenyouare

doingpracticaldemonstrationsasthelearnerscanseeyourhands!

c) Webcams

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Somecomputersandmosttabletshaveabuilt-inwebcam,whichisatinypin-sized

camera,usuallyfoundonthesideofthescreen.Whenthecameraisswitchedonand

youareconnectedtotheInternet(i.e.usingSkype,FaceTimeorsimilar),thisimage

(usuallyofyourface!)canbeseenbyothers.However,ifyoupointthecamera

towardssomelearners’work,youcanprojectthisimagetoadataprojectorforallin

theclasstosee.Itisalsopossibletobuyalow-costwebcamwithabendyarmthat

plugsintoyourcomputer/tablet–andmakesiteasiertoplacelearnerswork

underneath.Thisisalowcostvisualiser!

Technologyawayfromtheclassroom

1) Creatingworksheetsandtestswithaccuratemathematicaltextanddiagramsin

wordprocessingsoftwarehasthedistinct(andtime-saving)advantageinthatyou

caneditthedocumentagainandagaintomakemanydifferentversions.

OneofthefirstITapplicationsthatmanypeopleuseisawordprocessingpackage

suchas‘Word’toproducetypedtextthatcanbesaved,editedandprintedasand

whenyouneedit.Thismeansyoucanproduceyourowntasksandtests,writeyour

ownhelpfulnotesforyourlearnersandeven,bychoosingalargecleartext(orfont),

produceposterstodisplayintheclassroom.

a) Insertingsymbolsandequations.

Thebasicletters,numeralsandsimplesymbolssuchas+and–areallonthe

keyboard.Whenyouneedtousemoremathematicalsymbolssuchas÷,×,and

√youwillusuallygotoadropdownmenusuchas‘Insert’andchoose‘Symbols’

togetapaletteofothercommonsymbols.

Fig.11AtypicalpaletteofmoremathematicalsymbolsIMAGE11a_Symbols.jpg

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Towritemorecomplexnumericalandalgebraicexpressionsandequations,and

writingfractionsverticallyyouwillneedtousean‘equationeditor’whichis

normallyanoptionalfeatureofawordprocessingapplication.Asbefore,you

wouldselectan‘Insert’menuandchoose‘Equation’,whichwouldreveala

toolbarofdifferenttypes.

Fig.12Atoolbarofchoicesofdifferenttypesofequationsmathematicalsymbols

IMAGE12_Equations.jpg

b) Insertingtables

Therewillbemanyoccasionswhenyouwanttoproducetablesand,withyour

imagination,thesecanbequitecreative!

AlloftheimagesinFig.13belowhavebeencreatedastableswithinaword

processingpackage–thesecretistolearnhowtocontrolthesize,positioning,

textandshadingofeachcellinthetable.

Fig.13Aselectionofdifferentgraphics–allcreatedusingtablesinword

processingsoftware.IMAGE13_Tables.jpg

Herearesometoptips:

• Whenyouchoosetoinsertatable,onceyouhavecreateditwiththe

numberofrowsandcolumnsthatyouneed,selectthe‘Tableproperties’

totakecontrolofthesizeoftherowsandcolumns.Choosingawidthand

heightof1cmisveryusefulforproducingaccurateimages!

• Useborderlinescreatively–for,exampletocreatethe‘fractioncards’

above,whichcanbecutoutforlearnerstomatchandsort.

c) Insertinggraphs

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Firstly,youmusthaveaWorddocumentopen.

InGeoGebra,usethePointertooltodragaboxaroundthegraphthatyouwant

tocopy.OpentheFilemenuandchoose‘ExportgraphicsviewtoClipboard’(See

Fig.14below).

(Nothingmuchwillseemtohappen)

OpenyourWorddocumentandclickonPaste.

Fig.14ExportingagraphfromGeoGebraImage14_Geogebra_export.jpg

Youcanthenwritethetextaroundyourpicture.

d) Insertinggeometricimages

Therearealimitedrangeofbasicgeometricshapesavailableinmostword

processingapplicationswhenyouchooseInsertandShape.However,although

youcanchangethesizeofthembydragging,youhaveverylittlecontroloverthe

sizesofperimeters,areasandangles.Itismuchbettertocreatetheaccurate

shapethatyouwantinamathematicalapplicationsuchasGeoGebra,andthen

dragaroundyourimagetoselectitandthenusetheEditmenutocopyitfrom

GeoGebra-andpasteintoyourwordprocessingapplication,usingthesame

stepsfor‘Insertinggraphs’.

2) Creatingresourcestoprojecttotheclass

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Assoonasyoucanuseadataprojector,itislikelythatyouwillwanttomake

presentation‘slides’thatcanincludeimagesfromothersoftware(suchasgraphing

andgeometrysoftware)tosupportyoutointroduceyourlessonandprovide

stimulatingandmathematicallycorrectdiagrams,symbolsandtext.Youcancopy

andpasteimagesfromothersoftwareintosuchsoftwareinthesamewayas

describedearlierinthischapter.

a) Presentationsoftware

ThemostcommonlyusedpresentationsoftwareisMicrosoftPowerPointbutother

freesoftwarewithsimilarfeaturesisavailablefordownloadfromtheInternet.

Fig.15CreatingaslideinPowerPointIMAGE15_PowerPoint_Presentation.jpg

Asyouinserteachslideintoyourpresentation,youcanchoosethelayoutthatbest

suitsyourlesson.Acombinationofcleartextinalargefontsizeandimages(which

canbemovies)worksbest.

b) Interactivewhiteboardsoftware

Ifyouhaveaccesstoaninteractivewhiteboard,whichmustalwaysbeconnectedto

bothyourcomputerANDadataprojector,youcanusethespecialsoftwarethat

comeswiththeboardtocreatepresentationfiles.Thissoftwareisusuallyfreely

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downloadedfromthemanufacturer’swebsite,accompaniedbytutorialsandhelp

resourcestohelpyoumakethemostofthe‘fingertouch’functionality.

3) Creatinganelectronicmarkbook

Manyteachershavefoundspreadsheetsoftwaretobemostusefulforcreatingan

electronicmarkbookinwhichtheykeeparecordoflearners’outcomes.The

electronicnatureofthisbookmeansthatitisquickandeasytosortanynumeric

datafromhighesttolowestvalues,calculatemean.Modeandmedianaveragesand

producegraphsandtablestoshowlearners’progressovertime.Ofcoursethisdoes

relyonhighqualityassessmentdatainthefirstplace!

a) Enteringdata(Names/dates/marks)

Thestartingpointistoenterthestudents’names,genderandtheassessmentmarks.

Fig.16EnteringassessmentdatainaGeoGebraspreadsheet

IMAGE16_Assessment_data.jpg

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b) Makingsenseofassessmentdata

WithinGeoGebra,onceyourdataisentered,whenyouselectthecolumnofdatayou

cangenerateanumberofsummarystatisticsandgraphs.Soforthedataonthe

learners’achievementsinAssessment1,thisanalysiscouldbe:

Fig.17SummarystatisticsandBoxandWhiskerplotforassessment1.

IMAGE17_Box_whisker1.jpg

TheBoxandwhiskerplotisausefulgraphicthatshowstherangeofmarks(71–7=

64),andthat50%ofthestudentswereinthemarkrangefrom36to48.

IfthesummarystatisticsforAssessment2arealsogenerated,ASLONGASthescales

forthex-axisarethesame,yougetausefulgraphicthathelpsyoutoassesswhether

thestudentsaremakingprogressovertime.

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Fig.18SummarystatisticsandBoxandWhiskerplotforassessment2.

IMAGE18_Box_whisker1.jpg

Soitappearsthattheclassismakingsomeprogress!!

4) Onlinecommunitiesforteachersandlearners

a) Ministryofeducationsites

Manycountriesaredevelopingtheirwebsitestoincludeinformationaboutthe

curriculum,detailsofanyregionalandnationaltestingarrangementsandasa

gatewayor‘portal’forresourcestosupportteachingandlearning.

Forexample,

SouthAfrica:theThutongwebsitewww.thutong.doe.gov.za.

Zimbabwe:theMinistryofPrimaryandSecondaryeducationwebsite

www.mopse.gov.zw

b) Aiminghigh

TheAimingHighteachernetworkhasgrownfromthehundredsofteacherswho

haveattendedtheAfricanInstituteforMathematicalSciencesSchoolEnrichment

Centre’s(AIMSSEC)coursesinSouthAfricasince2005.

ThewebsiteincludesTeachingresources,anonlineForumandNewsaboutthe

AIMSSECcourses.AIMSSECworkcloselywiththeGeogebraInstituteinSouth

Africatooffercoursesandsupportfortechnologyuse.

aiminghigh.aimssec.ac.za

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Fig.20TheAimingHighTeacherNetworkhomepage

IMAGE20_Aiming_high.jpg

c) AfricanMathematicsInitiative

TheAfricanMathematicsInitiative(AMI)isaKenyanNGOformedby

mathematiciansandmathematicseducatorswhoareworkingtocreatea

strongermathematicalcommunityandcultureofmathematicsacrossAfrica.

AMIhasproducedresourcestosupporttheuseofdigitaltoolsformathematics

suchasGeoGebraandScratch,whichareavailableonitswebsite.

www.africanmathsinitiative.net

5) Onlineresourcesforteachersandlearners

a) MicrosoftMath

MicrosoftMathisafreeresourcethatcanbeaccessedbyhighschoollearnerson

theircellphones.Itincludestheorypagesandquizzes.Learnerscancompete

againsteachother.Teacherscancreateagroupfortheirclassandcanthenkeep

trackofthenumberofpointsearnedbyeachlearner.Tocreateanaccount,goto

math.microsoft.com.

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Fig.21MicrosoftMathmenuandexampleofapracticequestion

IMAGE21a_MicrosoftMath_Menu.pngIMAGE21b_MicrosoftMaths_Example.png

b) EverythingMathsandScience

EverythingMathsandSciencehasfreehighschooltextbookswithvideosand

simulations.ThecontentisspecificallycreatedfortheSouthAfricancurriculum

butcanbeusedbyanybody.Thetextbookscanbeviewedonlineordownloaded

andprinted.Thesitealsohasafreeonlinepracticeservicethatallowsteachers

tosetproblemsfortheirlearners.Teacherscancreateagroupfortheirclass,set

problemsandthenkeeptrackofthenumberofpointsearnedbyeachlearner.

www.everythingmaths.co.za.

c) KhanAcademy

TheKhanAcademyisanonlineresourcethatincludestestquestionsandvideos

tosupportlearnersawayfromtheclassroom.Youwillneedtowatchthevideos

carefullytoo-astheymayintroduceyourlearnerstoarangeofdifferent

problemsolvingapproaches,mathematicalvocabularyandnotation.The

resourcesareorganisedbymathematicaltopicsandtheyarenotalignedtoany

particularcountry’scurriculumorexaminationsystem.Iflearnerscreatean

account,thentheirprogressthroughthetopicsisrecordedandtheyareawarded

pointsandrewardsfortheirwork.www.khanacademy.org

d) MathsExcellence

MathsExcellenceisawebsitestartedbySouthAfricanteacherstoimprovethe

standardofMathseducationandtomakemathsmoreaccessible.Itcontains

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manydifferentfreeresourcessuchastextbooks,videos,tutorialsandexam

papers.

www.mathsexcellence.co.za

e) MathAids

MathAidsprovidesfreemathsworksheetsforteachersandlearners.Thereare

manydifferenttopicstochoosefromandbecausetheworksheetsarerandomly

theyarealldifferent.Theworksheetscanbedownloadedandprinted.

www.math-aids.com

Nextsteps

Anychangestoourteachingpracticescomeatapersonalcost.Ittakestimetolearnto

usenewtoolsandresources;weoftenmakeapersonalfinancialinvestmentin

technologythatwillsupportusinourwork;andintheclassroomthingsmightnot

alwaysgoasexpected.However,thereareveryfewteacherswhodisagreewiththe

needtodeveloppersonallyandprofessionallyasameanstosupportingourlearnersto

achievemathematicstotheverybestoftheirabilities.

Glossary

Dynamicgeometry:aninteractivemathematicsenvironmentthatenablesgeometric

constructionstobecreatedandmanipulated.Forexample,2-Dshapescanbecreated

andtheirangles,sidelengths,areasandperimeterscanbemeasured.Usingthe

software,theseshapescanbetransformedbydraggingandtheyretaintheirunderlying

mathematicalproperties,althoughthemeasurementsmaychange.Theaccurateimages

canbecopiedandpastedintoothersoftware,suchasMSWord.

Examples:GeoGebra,Cabri-geometry,TheGeometer’sSketchpad,Cinderella

Dynamicgraphing:aninteractivemathematicsenvironmentthatenablesCartesian

andpolargraphstobeplottedautomaticallybyenteringthefunction.The

accompanyingtablesofvaluescanbedisplayedandthefunctionscanbetransformed.

Examples:GeoGebra,Desmos,Autograph

Spreadsheet:aninteractiveenvironmentwhereyoucaninput,organiseanalyseand

storetextandnumericaldataasatable.Thisdatacanbedisplayedgraphicallyanda

numberofstatisticalanalysescanbeusedtoqueryandinterpretthedata.

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Examples:Excel,GeoGebra,

ApplicationorApp:Theseareusuallydigitaltoolsthathavebeendesignedtoonlyrun

onSmartPhones,iPadsandAndroidtablets,althoughsomepeoplearenowusingthis

wordtodescribesoftware.However,manyAppshavelimitededitingandfile-saving

features.Forexample,GeoGebraisavailableasanApp,butthereislimited

functionalitywhencomparedtothesoftwareversion.

Software:Aparticulardigitaltoolthathasbeendesignedforaspecificpurposeiscalled

‘software’.Forexample‘word-processingsoftware’allowsyoutocreate,edit,saveand

sharefiles.Thistexthasbeenwritteninwordprocessingsoftware.

Web-based:Ifaparticularresourceisweb-based,youwillneedtohaveanInternet

connectiontobeabletoaccessandusetheresource.Sometimesyoucansavethe

resourceontoyourowncomputersothatyoucanuseit‘off-line’.

Searchengine:Whenyouhaveaninternetconnection,youuseasearchenginetolook

forresourcesandinformationontheinternet.Themostcommonsearchenginesare

Google,InternetExplorerandYahoo.

Internet(orWorldWideWeb):Thisisaglobalnetworkthatconnectseveryone’s

computerstotheresourcesthatdifferentindividualsandcommunitieshavepublished

ontheirwebsites.

Mobilemessagingapplication:Thisisaninstantmessagingservicethatcanbeused

onmobile‘phonesandcomputers.Itcanbeaquickwaytocommunicateinformationin

‘real-time’.

Dataprojector:Adataprojectorprojectstheimagefromyourcomputerscreenontoa

wallorscreensothateveryonecanseetheimage.Itwillusuallyneedapowersource

andaconnectioncablefromyourcomputerortablet.Themoreexpensiveversions

haveamorepowerfulbulb,whichmeanstheywillprojectabrighterimage.

Download - Teaching and learning mathematics with technology.discovery.ucl.ac.uk/1474515/2/Clark-Wilson... · PRE-PRINT Cite as: Clark-Wilson, A., & Mostert, I. (2016). Teaching and learning

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