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HowCanTeachersUseVideoGamestoTeachTheirStudentsMathematics?

JeremiahI.HoldenandCarolineC.Williams

UniversityofWisconsin–Madison

APewreportpublishedin2008reportedthat97percentofteenagersplayvideogamesof

sometype(Lenhartetal.,2008).TheU.S.DepartmentofEducation’sTransformingAmerican

Education:LearningPoweredbyTechnology(2010)suggestsvideogamescansupportarange

ofteachingandlearningactivitiesinschool,fromembeddedassessmenttoengagementwith

locallyrelevantissues.Thisrecommendationechoesresearchdescribinghowwell-designed

videogamescansimulateprofessionalpracticesandmodelreal-worldproblemsolving(Gee,

2005,2007;Salen,2008;Shaffer,2006a;Squire,2006).Recently,asurveyofelementaryand

middleschoolteachersalreadyusingvideogamesintheirclassroomsfoundthatnearlyone-

fifthteachwithvideogameseveryday(Millstone,2012).

Concerningmathematicseducation,wesuggestitisnecessarytoask:Howcanteachers

usevideogamestoteachtheirstudentsmathematics?Ourprimaryconcernraisesadditional

questionsabouthowteachersselectandevaluatevideogames,andthevarioustypesofvideo

gamessuitableformathematicsinstruction.Weaddressthesequestionsbyreviewingcurrent

researchonvideogamesandmathematicseducation,andthendetailinghowtofindspecific

mathematicsvideogames.Afterhighlightingacaseofvideogameplaysupportingstatistical

reasoning,wediscusshowtoadaptvideogamestosupportclassroomteaching,andwethen

considerthefutureofteachingmathematicswithvideogames.

<H1>Background:VideogamesandMathematicsEducation

Formanyteachers,theirintroductiontoteachingmathematicswithvideogameswasMath

Blaster(Davidson&Associates,1983),“Astandarddrill-and-practice-typeinstructional

mechanism...withinashootergameidiom”(Ito,2008,p.93).Introducedin1983,Math

Blasterwasabest-sellingpieceofsoftware;today,mathematicsvideogamesareabroader,

dynamic,andprofitableenterprise.Videogameshavebeendesignedacrossgradelevelsandto

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meetCommonCoreStateStandardsforMathematics(2010)andNationalCouncilofTeachers

ofMathematics(2000)standards.TheynowrangefromthemobiledrillprogramFlashMath

(Kiger,Herro,&Prunty,2012)tonarrative-basedvirtualworldslikeQuestAtlantis(Gresalfi,

Barab,Siyahhan,&Christensen,2009;Robert,2013).

Becausedefinitionsof“game”arebroadandcontested(Salen&Zimmerman,2003;

Schell,2008),inthisbriefweconsidervideogamestobe“imaginaryworlds,hypothetical

spaceswhereplayerscantestideasandexperiencetheirconsequences”(Squire&Jenkins,

2003,p.8).Thisdefinitionisconsistentwithageneralconsensusthatvideogamesaremore

thandigitaltools;videogamesaredesignedenvironments,orpossibilityspaces(Squire,2008),

thatsupportlearningacrossmultiplesocialspaces,sharedpractices,andemergentformsof

knowledge(Barab,Gresalfi,Dodge,&Ingram-Goble,2010;Gee,2003;Shaffer,2006b).Our

understandingofvideogamescontrastswithdigitalsimulationslikeGeometer’sSketchpad(Key

CurriculumPress,1991;e.g.,Knuth,2002;Leong&Lim-Teo,2003)or“cognitivetutor”systems

(e.g.Anderson,Corbett,Koedinger,&Pelletier,1995),whichprimarilysupportconsistentand

accuratemeansofinteractingwithmathematicalobjectsandornotations.Videogameplay,on

theotherhand—likeplayingeneral—affordspositiveaffect,nonlinearity,intrinsicmotivation,

process,andfreechoice(Johnson,Christie,&Wardle,2005;Vygotsky,1978).

Unlikeestablishedresearchabouttheimpactofvideogamesonstudents’science

learning(e.g.,Barabetal.,2007;Clarke&Dede,2009;Gaydos&Squire,2012;Squire,2010),

onlyahandfulofempiricalinvestigationshaveexploredhowvideogamesinfluencestudents’

mathematicsexperiencesandunderstanding(e.g.,Harris,Yuill,&Luckin,2008;Ke,2008;Ke&

Grabowski,2007;Kebritchi,2008).Youngandcolleagues(2012)recentlyexaminedthe

pedagogicalvalueofvideogamesinrespecttostudentachievement.Ninestudiesfromthe

mathematicsgamingliteraturewereincludedintheirmeta-analysis.Likepreviousreviews

whichidentifiedasparseliteraturebaseandinsufficientresearchaboutinstructionalgaming

amongspecificagegroups(Mitchell&Savill-Smith,2004),Youngetal.(2012)suggestbetter

“correspondence”bedevelopedbetweenagame’sobjectivesandstudents’mathematics

learningactivities.Teachingmathematicswithvideogamesdoesnotinvariablyequateto

studentslearningmathematicsfromvideogames.Inotherwords,theresultsaremixed.

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Ke&Grabowski(2007)foundthatfifthgraderswhoplayedvideogamesoutperformed

non-gamingpeers,yetonlythosewhoplayedgamescooperatively(ratherthancompetitively)

hadeffectivegainsinmathematicsunderstandingandpositivechangesinattitude(as

measuredbyamodifiedversionoftheAttitudesTowardsMathsInventory;Tapia,Marsh,&

George,2004).Forhighschoolstudents,playingDimensionMwhenalignedwithonline

modulesandclassroomteachingincreasedmathematicsachievementincomparisontonon-

gamingstudents;however,gameplaydidnotimprovemotivationtolearnmathematics

(Kebritchi,2008).Kebritchi,Hirumi,andBai(2008)foundstatisticallysignificantgainsforhigh

schoolstudentswhoplayedvideogames;theiraverageachievementgainbetweentwodistrict

examswasmorethandoublethatofnon-gamingpeers.Further,thesestudents’teachers

reportedvideogamesas“effective”learningtoolsbecausetheywereexperimental,offered

alternativeteachingapproaches,providedanengagingrationaleforlearning,andincreased

timeontask.Nonetheless,trendspersistacrossthisliterature;thesuccessandfailureof

teachingmathematicswithvideogamesreflectsmanyfactors,includingresearchdesign,game

mechanics,teachingstrategies,learningobjectives,andcontext(Youngetal.,2012).

Thevariedinfluenceofvideogameplayinmathematicsclassroomsisunsurprising:

gamesarenomagicbullet.LikeYoungetal.(2012),webelievethatsuccessfullearningdepends

uponteachersdevelopingandsupporting“correspondence”betweenplayandinstruction.

Effectivelyteachingmathematicswithvideogamesrequiresteacherswhocandevelop,support,

andreflectuponhowanygamecorrespondstoinstructionalgoalsandstudentlearningneeds.

Insum,mathematicallymeaningfulgameplayistheresultofthoughtfulandcreativeteaching.

Buthowdoesateachergoaboutfindingmathematicsvideogamestosupportteachingand

learninginhisorherclassroom?

<H1>FindingMathematicsVideoGames

Imagineaveteranmathematicseducatoreagertorefineherpractice.Oralternatively,imagine

the“digitallyable”first-yearteacher(Starkey,2010),anoviceconfidentinherabilitytoadapta

rangeofnewtechnologiestocommunicate,problem-solve,play,andshareinformationabout

teachingandstudentlearning.Howmighteitherteacheridentifywhatmakesgameplay

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effectiveinamathematicsclassroom?Whatwilleitherperceivetobetheadvantagesofvideo

gamesincontrasttomoretraditionalinstructionalstrategies?Cancommonpitfallsbeavoided,

hallmarksofsuccessrecognized,andchallengesmitigated?Eachoftheseeducatorscaneasily

visitthe“Education”sectionofApple’sAppStoreandsearchfor“mathgames.”AsofMay2014,

thissearchgave219results.Somegamesarefreewhileothersarecheap,andtheavailable

gamescoverarangeofcontentareasandgradelevels,withmanyclaimingtodramatically

improvestudents’learning.Wheremighttheseteachersgotofindwell-designedvideogames,

relatedcurricularmaterials,and—perhapsmostimportantly—acommunityofprofessionals

whocansupportimplementationandrefinementofteachingmathematicswithvideogames?

Enthusiasmaboutvideogamesandlearninghasresultedinthegrowthofmanyonline

resourcesandcommunities,aswellasofflineconferencesandprofessionallearningevents.

WebsitessuchasGameDesk’sEducade(http://educade.org)andCommonSenseMedia’s

Graphite(http://www.graphite.org)providefreegamereviews,lessonplans,teachingtools,

andotherresources—manyofthemauthoredbyteachers.Manyeducatorshavealsocreated

andjoinedonlinecommunitiesdevotedtosinglegames.Forexample,thegameMinecraft

(Mojang,2009)hasinspiredMinecraftEdu(http://minecraftedu.com),anonlinecommunity

andcollaborativeeffortpromotingaffordabilityandschoolaccessibility.Additionally,the

PlayfulLearningInitiative(http://playfullearning.com)supportsanonlineknowledgebaseof

videogames,facilitatesregionalandnationalpartnershipsandprofessionallearningsummits,

andisguidedbyanadvisoryboardofK–12educators.

Asnewmathematicsvideogamesaredesigned,sotoowillthenumberofwebsites,

onlinecommunities,andotherresourcesproliferate.Eachwebsiteandonlinecommunityhas

differentcharacteristics;accordingly,weofferabriefoutlineofhowtofindrelevantgames

usingEducade(seefig.1).

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Fig.1.ScreenshotofEducadehomepage

Asearchbaratthetopofthewebsitemaybeused,forexample,tofindgamesfocusedon

middleandhighschoolalgebra.Sevenresultsarepresented.Fourare“teachingtools,”or

informationaboutspecificgamesandresourcesforteachingmathematics.Theremainingthree

are“lessonplans”focusedonimplementinggamesaccordingtospecificlearningobjectives.

One“teachingtool”isDragonbox(WeWantToKnow,2012).Accompaniedbytwolessonplans,

Dragonboxislikelyausefulresource,andselectingthegameleadstoadditionalinformation.A

screenshotfromDragonboxisincludedasfigure2.

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Fig.2.ScreenshotofalevelfromDragonbox

Dragonboxisrobustlydescribedwithtext,images,avideo,aswellasinformation

regardingalgebraiccontent,appropriategradelevels,platformssupportinggameplay,andhow

teacherscanimplementthegame.Therearealsotworelevantlessonplans,andalinktothe

officialDragonboxwebsite.WhilewestronglyrecommendDragonbox(particularlyfor

mathematicsteachersnewlyinterestedinvideogames),morethanafewpoorlydesigned

mathematicsgamesarealsoavailable.Weadviseplayingademobeforepurchasingany

mathematicsvideogame.Ifagamedoesnothaveafreelyavailabledemo,requestonefrom

thecompany.Inourexperience,acompanyunwillingtoshareademomaybeconcernedthat

theyaremarketinganinferiorproduct.

Afterdownloadingthedemo,playit!Whiledevelopingideasabouthowthegamefits

withclassroomteaching,requestfundingtopurchasethefullgameforclassroomuse.Consider

howthegamealignswithcurricula,andthe“correspondence”amongstudents’play,

mathematicscontent,andinstruction.Willstudentsplayintheclassroom,afterschool,orat

home?Whetherplayingatschoolorassigningashomeworkorextracredit,makesurethata

computerlabisavailableandthatthegameisproperlyinstalledsothatallstudentshaveaccess

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toit.

Finally,itiscrucialtofullyplayanygamebeforeimplementation.Whileplaying,

referencedesiredlearningobjectivesandnotewhicharesupportedbyplayandwhicharenot.

Considerhowthegamesupportsstandardsandcurricula,andwhatlessonandunitplanning

couldconnectstudentgameplaywithlearningobjectives.Teacherswhoareeagertoconsult

modelsofclassroomteachingandlearningcanfindonlinecommunitiesofteachersand

designers(listedearlier)whoopenlysharetalesoftriumphandfailure.Thesestoriescaninform

decisionsaboutwhetherorhowagameshouldbeplayed.Accordingly,wenowshareacase

studythathighlightswaysofconnectinggameplaytoclassroomteaching.

<H1>CaseStudy:StatisticalReasoningandWorldofWarcraft

TeachingmathematicswithvideogamesneednotconjureupagedimagesofMathBlaster;

classroomteachersareadaptingvariousgamingenvironmentstosupportthedevelopmentof

sophisticatedmathematicalinvestigations.ConsiderthecaseofScottMcClintock,astatistics

teacheratWestChesterUniversityinWestChester,Pennsylvania.WritinginNCTM’s

MathematicsTeacher,McClintock(2011)describeshowthegameWorldofWarcraft(Blizzard

Entertainment,2004;fig.3,below)supportedhisstudents’understandingofstatistical

reasoning.AprimaryconcernforMcClintockhadbeendatacollectionandanalysis;he

perceivedissuesofsamplesizeandsurveyrelevancetobepedagogicalchallengesforquality

teachingandlearning.However,withWorldofWarcraftMcClintockrealizedhecouldaddress

thesechallengesbycreatingassignmentsthatengageda“widevarietyofstatisticalpractices”

(p.215).OnekeytoMcClintock’ssuccesses—andhisstudents’learning—wastheopportunities

forengagementandreflectionfoundwithinthegameworldandalsoinclassaftergameplay

ended.

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Fig.3.ScreenshotoftheOrcstartingzoneinWorldofWarcraft

Oneassignmentconcernsthestatisticalconceptofsampling.McClintockdirectedhis

studentstosurveytheraceandclassof50WorldofWarcraftplayersineachofthreedifferent

cities.Knowledgeableaboutthedifferentracesanddifferentclasscategoriespossibleforany

givenplayer,studentssampled50playersinthehumancapital,50intheelvencapital,and50

inaraciallyneutralcity.Aftercollectingdata,studentscalculatedthepercentageofhumansin

eachsample,andthendeterminedwhichsampleproportionmostlikelyrepresentedthetrue

proportionoftotalhumanplayers.

AlthoughWorldofWarcraftwasnotdesignedtoteachstatistics,anumberofgame

featuressupportedstudents’statisticalreasoning.First,randomsamplingmethodswouldnot

workinthisvirtualcontext;instead,systematicsamplingwaspossibleastheraceandclassofa

givenplayercouldbeobtainedthroughanunobtrusivemouseclick.Second,thedesignof

particularcitiesbiasesthesample;samplinginthehumancapitalwouldlikelyoverestimatethe

totalproportionofhumans,whereassamplingintheelvencapitalwouldlikelyunderestimate

thatproportion.Thus,onlyinarace-neutralcitycouldstudentsobtaintheleastbiased

statisticalsample.Itwasbecauseofthegame’scontextualfeaturesthatmoresophisticated

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mathematics,abouttheprobabilitiesofplayers’raceandclass,becamepossible.McClintock

alsoaddressedtheimportanceofcontinuingtosupportstudents’investigationsbeyond

gameplay.

Reflectinguponhisownlimitations,hesuggeststeachersprovidewrittenfeedbackto

studentsaboutfindings,encouragestudentstoaskquestionsoftheirdata,andconduct

iterativeroundsofdatacollectionandanalysisbackinWorldofWarcrafttotestnew

hypotheses.Ultimately,McClintockarguesthatbothgamefeaturesandteachers’pedagogycan

appropriatelysupportstudents’learningofcomplexstatistics,andthatteachersshould

“considerhowwemightadapt[videogames]toenhancethereachandscopeoftheclassroom”

(p.217).

<H1>Discussion:PlayingandAdaptingVideoGamesforTeachingMathematics

Theintentofthisbriefisnottosupportanymathematicsteacherinonlyvisitinganonline

database,downloadingagameandrelatedmaterials,andthenhavingstudentsplay“forfun”

orasa“reward”aftercompletinganotherassignment.Rather,weadvocateadaptingvideo

gamestocomplementthecharacteristicsofaclassroom.McCall(2011),writingabouthisown

useofgamesintheclassroom,argues,“Successfulgame-basedlessonsaretheproductofwell-

designedenvironments.Teacher/designersmustthoughtfullyembedthesegamesinan

environmentandsetoflearningactivitieswherestudents,learningtools,andresourceswork

togetherinpursuitofthedesiredoutcomes”(p.61).

Robustmathematicseducationhasneverbeenachievedthroughtheblindadoptionof

newcurricula,tools,ormethodsdevoidofteachers’skillfulfacilitation;videogamesarenot—

and,webelieve,willneverbe—anexception.Teachingmathematicswithvideogameswill

requirethatteachersdeftlyconsidertrends,limitations,andtheinsightsofcasestudiessuchas

theonenotedabove;makeprofessionaljudgmentsrelevanttolocalcontext;andreflectupon

thesuccessesandchallengesassociatedwithteachingandstudentlearning.

Wesuggestthateducatorsinterestedinteachingmathematicswithvideogames

recognizethesubstantialeffortandintellectualengagementrequiredofsuchanendeavor.

Learningtoplayanygametosupportlearning–and,inparticular,amathematicsvideogame–

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entailsprofessionalbehaviorssimilartoacquiringanynewteachingmethod:research,planning,

implementation,reflection,anditeration.Teachersshouldinvestigategamesandrelated

teachingresources.Gameplayshouldbeacentralelementtoanyteachers’personalresearch

andlearning.Curricularmaterials,lessonplans,andassessmentsshouldalsobeprepared

beforeclassroomimplementation,yetremainflexibleenoughtoberevisediteratively.

Furthermore,itmaybeadvantageousforteacherstojoinonlineprofessional-amateur(“pro-

am”)gamingcommunities,likethoseassociatedwithMinecraft,inordertodiscussexperiences,

shareinsights,andgrowaprofessionalnetworkofteachers-as-players.

[H1>TheFutureofGame-BasedMathematicsEducation

Asbothliteratureandpopularmediaindicate,teachersandtheirstudentsareplayingand

increasinglydesigningvideogames(Squire,2011).Withagrowingnumberofteacherswriting

abouttheirownexperiencedesigningandteachingwithvideogames(e.g.,Elford[blog];McCall,

2011;Williams[Ed.],inprogress),webelievethisisaveryexcitingtimetobeamathematics

educatorinterestedinusingvideogames(andothergames)forlearning.Classroomteachers

arebeginningtorefinehowresearchersanddesignerscreatemathematicsvideogames,so

contentandgameplaybothaligntostandardsandalsoadapttoindividualstudents’learning

needs(e.g.Riconscente,2011).Whatnewformsofpedagogical,technological(cf.Mishra&

Koehler,2006),andmathematicalknowledgeforteaching(cf.Ball,Thames,&Phelps,2008)

mightteachersdemonstratewhenteachingwithvideogamesacrossbothformalandinformal

settings?Mightvirtualgameworlds,likeWorldofWarcraft,becomeacommunalmathematics

“thirdplace”(Steinkuehler&D.Williams,2006)amongnetworkedlearnersaroundtheworld?

Andhowmightplayfulpedagogyandgame-basedcurriculaalterhowresearchersand

practitionersunderstand“ambitious”instruction(cf.Lampertetal.,2010)?AsYoungand

colleagues(2012)suggest,thefutureofgame-basededucationwillbeshapedbyeducatorsand

researcherswhocollaborativelyexamine“howgamingcombinedwithinstructionalfacilitation

byamasterteacheraffectsengagement,studentbehavior,andoverallacademicachievement”

(p.83).Itisanexcitingtimetobeaneducatorinterestedinteachingmathematicswithvideo

games.

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Acknowledgements

WethankourthoughtfuladvisorsandmentorsattheUniversityofWisconsin–Madisonandthe

Games+Learning+SocietyCenterwhoreviewedthismanuscript:Dr.AmyB.Ellis,Dr.KurtSquire,

andDr.ConstanceSteinkuehler.WealsothanktwoanonymousreviewersandSeriesEditor

MichaelFishfortheirusefulcommentary.Authorshipwasalphabeticalbylastname.

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