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
middleschoolteachersalreadyusingvideogamesintheirclassroomsfoundthatnearlyonefifthteachwithvideogameseveryday(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
1
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.
2
Ke&Grabowski(2007)foundthatfifthgraderswhoplayedvideogamesoutperformed
non-gamingpeers,yetonlythosewhoplayedgamescooperatively(ratherthancompetitively)
hadeffectivegainsinmathematicsunderstandingandpositivechangesinattitude(as
measuredbyamodifiedversionoftheAttitudesTowardsMathsInventory;Tapia,Marsh,&
George,2004).Forhighschoolstudents,playingDimensionMwhenalignedwithonline
modulesandclassroomteachingincreasedmathematicsachievementincomparisontonongamingstudents;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
3
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).
4
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.
5
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
6
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.
7
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
8
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-basedlessonsaretheproductofwelldesignedenvironments.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–
9
entailsprofessionalbehaviorssimilartoacquiringanynewteachingmethod:research,planning,
implementation,reflection,anditeration.Teachersshouldinvestigategamesandrelated
teachingresources.Gameplayshouldbeacentralelementtoanyteachers’personalresearch
andlearning.Curricularmaterials,lessonplans,andassessmentsshouldalsobeprepared
beforeclassroomimplementation,yetremainflexibleenoughtoberevisediteratively.
Furthermore,itmaybeadvantageousforteacherstojoinonlineprofessional-amateur(“proam”)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.
10
Acknowledgements
WethankourthoughtfuladvisorsandmentorsattheUniversityofWisconsin–Madisonandthe
Games+Learning+SocietyCenterwhoreviewedthismanuscript:Dr.AmyB.Ellis,Dr.KurtSquire,
andDr.ConstanceSteinkuehler.WealsothanktwoanonymousreviewersandSeriesEditor
MichaelFishfortheirusefulcommentary.Authorshipwasalphabeticalbylastname.
References
Anderson,J.,Corbett,A.,Koedinger,K.,&Pelletier,R.(1995).Cognitivetutors:Lessonslearned.
JournaloftheLearningSciences,4(2),167–207.
Ball,D.L.,Thames,M.H.,&Phelps,G.(2008).Contentknowledgeforteaching:Whatmakesit
special?JournalofTeacherEducation,59(5),389–407.
Barab,S.,Gresalfi,M.,Dodge,T.,&Ingram-Goble,A.(2010).Narratizingdisciplinesand
disciplinizingnarratives.InternationalJournalofGamingandComputer-Mediated
Simulations,2(1),17–30.
Barab,S.,Zuiker,S.,Warren,S.,Hickey,D.,Ingram-Goble,A.,Kwon,E.,Kouper,I.,&Herring,S.
C.(2007).Curriculum:Relatingformalismsandcontexts.ScienceEducation,1–33.
BlizzardEntertainment(2004).WorldofWarcraft[computersoftware].Irvine,CA.
Clarke,J.,&Dede,C.(2009).Designforscalability:AcasestudyoftheRiverCity
curriculum.JournalofScienceEducationandTechnology,18(4),353–365.
Davidson&Associates(1983).MathBlaster[computersoftware].Torrance,CA.
Elford,S.(blog).MinecraftEduElfi:Oneteacher’sjourney.
http://minecrafteduelfie.blogspot.com
Gaydos,M.J.,&Squire,K.D.(2012).Roleplayinggamesforscientificcitizenship.Cultural
StudiesofScienceEducation,7(4),821–844.
Gee,J.P.(2003).Whatvideogameshavetoteachusaboutlearningandliteracy.NewYork,NY:
PalgraveMacMillan.
Gee,J.P.(2005).Learningbydesign:Goodvideogamesaslearningmachines.E-Learning,2(1),
5–16.
11
Gee,J.P.(2007).Whatvideogameshavetoteachusaboutlearningandliteracy.NewYork,NY:
PalgraveMacmillan.
Gresalfi,M.,Barab,S.,Siyahhan,S.,&Christensen,T.(2009).Virtualworlds,conceptual
understanding,andme:Designingforconsequentialengagement.OntheHorizon,17(1),
21–34.
Harris,A.,Yuill,N.,&Luckin,R.(2008).Theinfluenceofcontext-specificanddispositional
achievementgoalsonchildren’spairedcollaborativeinteraction.BritishJournalof
EducationalPsychology,78,355–374.
Ito,M.(2008).Educationvs.entertainment:Aculturalhistoryofchildren’ssoftware.InK.Salen
(Ed.),Theecologyofgames:Connectingyouth,games,andlearning(pp.89–116).
Cambridge,MA:MITPress.
Johnson,J.E.,Christie,J.F.,&Wardle,F.(2005).Play,development,andearlyeducation.
Boston,MA:PearsonEducation.
Ke,F.(2008).Acasestudyofcomputergamingformath:Engagedlearningfromgameplay?
Computers&Education,51,1609–1620.
Ke,F.,&Grabowski,B.(2007).Gameplayingformathslearning:Cooperativeornot?British
JournalofEducationalTechnology,38,249–259.
Kebritchi,M.(2008).Effectsofacomputergameonmathematicsachievementandclass
motivation:Anexperimentalstudy.DissertationAbstractsInternationalSectionA:
HumanitiesandSocialSciences,69(6-A),2121.
Kebritchi,M.,Hirumi,A.,&Bai,H.(2008).Theeffectsofmodernmathcomputergameson
learners’mathachievementandmathcoursemotivationinapublichighschoolsetting.
BritishJournalofEducationalTechnology,38(2),49–259.
KeyCurriculumPress(1991).Geometer’ssketchpad[computersoftware].Berkeley,CA.
Kiger,D.,Herro,D.,&Prunty,D.(2012).ExaminingtheInfluenceofaMobileLearning
InterventiononThirdGradeMathAchievement.JournalofResearchonTechnologyin
Education,45(1).
Knuth,E.J.(2002).Fosteringmathematicalcuriosity.MathematicsTeacher,95(2),126–130.
Lampert,M.,Beasley,H.,Ghousseini,H.,Kazemi,E.,&Franke,M.(2010).Usingdesigned
12
instructionalactivitiestoenablenovicestomanageambitiousmathematicsteaching.In
Instructionalexplanationsinthedisciplines(pp.129–141).NewYork,NY:Springer.
Lenhart,A.,Kahne,J.,Middaugh,E.,Macgill,A.R.,Evans,C.,&Vitak,J.(2008).Teens,video
games,andcivics.Washington,D.C.:PewInternet&AmericanLifeProject.
Leong,Y.H.,&Lim-Teo,S.K.(2003).Effectsofgeometer'ssketchpadonspatialabilityand
achievementintransformationgeometryamongsecondarytwostudentsinSingapore.
TheMathematicsEducator,7(1),32–48.
McCall,J.(2011).Gamingthepast:Usingvideogamestoteachsecondaryhistory.NewYork,
NY:Routledge,Taylor&FrancisGroup.
McClintock,S.(2011).Countingpriests,paladins,pets.MathematicsTeacher,105(3).
Millstone,J.(2012).Teacherattitudesaboutdigitalgamesintheclassroom.NewYork,NY:The
JoanGanzCooneyCenteratSesameWorkshop.
Mishra,P.,&Koehler,M.J.(2006).TechnologicalPedagogicalContentKnowledge:Anew
frameworkforteacherknowledge.TeachersCollegeRecord108(6),1017–1054.
Mitchell,A.,&Savill-Smith,C.(2004).Theuseofcomputerandvideogamesforlearning:A
reviewoftheliterature.London,UK:TheLearningandSkillsDevelopmentAgency.
Mojang(2009).Minecraft[computersoftware].Stockholm,Sweden.
NationalCouncilofTeachersofMathematics(2000).Principlesandstandardsforschool
mathematics.Reston,VA:NCTM.
NationalGovernorsAssociationCenterforBestPracticesandCouncilofChiefStateSchool
Officers(NGACenterandCCSSO).(2010).Commoncorestatestandardsfor
mathematics.Washington,D.C.:NGACenterandCCSSO.http://
Riconscente,M.(2011).Mobilelearninggameimproves5thgraders’fractionsknowledgeand
attitudes.LosAngeles:GameDeskInstitute.
Robert,L.(2013).Adescriptivecasestudyofmeaningfulonlinelearningexperiencesinthe3D
virtualgameQuestAtlantis.Unpublishedmastersthesis.UniversityofCalgary:Calgary,
Alberta.
Salen,K.(2008).(Ed).Theecologyofgames:Connectingyouth,games,andlearning.Cambridge,
MA:MITPress.
13
Salen,K.,&Zimmerman,E.(2003).Rulesofplay.Cambridge,MA:MITPress.
Schell,J.(2008).Theartofgamedesign:Abookoflenses.Burlington,MA:MorganKaufmann
Publishers.
Shaffer,D.W.(2006a).Howcomputergameshelpchildrenlearn.NewYork,NY:Palgrave
Macmillan.
Shaffer,D.W.(2006b).Epistemicframesforepistemicgames.Computers&Education,46(3),
223–234.
Squire,K.(2006).Fromcontenttocontext:Videogamesasdesignedexperience.Educational
Researcher,35(8),19–29.
Squire,K.D.(2008).Videogamesandeducation:Designinglearningsystemsforaninteractive
age.EducationalTechnology,48(2),17.
Squire,K.(2010).Frominformationtoexperience:Place-basedaugmentedrealitygamesasa
modelforlearninginagloballynetworkedsociety.TeachersCollegeRecord,112(10),
2565–2602.
Squire,K.(2011).Videogamesandlearning:Teachingandparticipatorycultureinthedigital
age.NewYork,NY:TeachersCollegePress.
Squire,K.D.&Jenkins,H.(2003).Harnessingthepowerofgamesineducation.Insight,3,5–33.
Starkey,L.(2010).Supportingthedigitallyablebeginningteacher.TeachingandTeacher
Education,26(7),1429–1438.
Steinkuehler,C.A.,&Williams,D.(2006).Whereeverybodyknowsyour(screen)name:Online
gamesas“thirdplaces.”JournalofComputer‐MediatedCommunication,11(4),885–909.
Tapia,M.,Marsh,I.I.,&George,E.(2004).Aninstrumenttomeasuremathematics
attitudes.AcademicExchangeQuarterly,8(2),16–21.
U.S.DepartmentofEducation,OfficeofEducationalTechnology(2010).TransformingAmerican
education:Learningpoweredbytechnology.Washington,D.C.:U.S.Departmentof
Education.
Vygotsky,L.S.(1978).Mindandsociety:Thedevelopmentofhighermentalprocesses.
Cambridge,MA:HarvardUniversity.
WeWantToKnow(2012).Dragonbox[computersoftware].Oslo,Norway.
14
Williams,C.(Ed.).(inprogress).Teacherpioneers:Visionsfromtheedgeofthemap.Pittsburgh,
PA:ETCPress.
Young,M.F.,Slota,S.,Cutter,A.B.,Jalette,G.,Mullin,G.,Lai,B.,Simeoni,Z.,Tran,M.,&
Yukhymenko,M.(2012).Ourprincessisinanothercastle:Areviewoftrendsinserious
gamingforeducation.ReviewofEducationalResearch,82(1),61–89.
15