EuropeanErasmus+ProjectMath-GAMES
www.math-games.eu
MATHEMATICSANDTHEROLEOFGAMESINLEARNINGANDTEACHING-
WHYUSINGGAMESINLEARNINGMATHEMATICS?
THEMATH-GAMESMETHODOLOGY
byAndreasSkotinos,Cyprus
TheGoalsofMathematicsanditscentralityinan
adult’slife
importantinthecaseofSlowAdultsLearners.The
Backgroundthatcansupportasuccessfulpromotionof
Gamesinthelearningprocesscanstemoutof
expectationsthatcanhavepositiveimpactonthe
followingaspectsofhumanbehavior:cognitive,
motivational,emotionalandsocial.Existingresearch,
althoughnotextensiveasyet,supportsthispositive
impact.ParticularlyinthecaseofSlowAdultsLearners
thepositiveimpactonthemotivational,emotionaland
socialaspectsiscrucialanditisexpectedtohave
positiveinfluenceonthecognitiveaspectsaswell.
Itisgenerallyagreedthatdoingmathematicsisacritical
skillforall,adultsandchildren,geniusesandpeople
withlimitedintelligence,personswithhigheducation
andindividualswithlowliteracyandknowledge.
Inquiteanumberofreportsitisrecognizedand
stressedthatinorderforadultstofunction(reasonably
well)inanincreasinglycomplexworld,theyrequirea
basiclevelofnumeracy,whichisincreasinglynecessary
inarangeoflife-skills,suchaspersonalfinanceanddata
handling.Itisalsoacceptedthatmathematicalskills(at
leastattheveryelementarylevel)areincreasingly
neededintheworkplaceandineverydaytransactions
betweenpeople.
InPsychologyitisrecognizedthatPlaybringsjoy.Andit
isvitalforproblemsolving,creativityandrelationships.
Thisistrueforeverypersoneitherachildoranadult.In
particularthisisvitalforslowlearnersasitisoneofthe
veryfewsourcestoprovidetheseelements,whilefor
otheradultstheremaybeothersourcesaswell.
FurthermoreresearchinPsychologyrelatesPlaywith
muchsocialbehaviorthatwewanteithertoenhance(if
theyaredirectingtotherightdirection)ortodiminish(if
theyareleadingtothewrongdirection).
ItisnotachancethatAeschylus,25centuriesago,inthe
“PrometheusBound”isaddingthatbesidesthefire,
whichPrometheusgavetopeople,hepointsout“And
yes,Iinventedforthemnumbers,too,themost
importantscience”.Thisrevealsthecloserelationof
humanstomathematicalliteracyandtheirneedto
developmathematicalskills,atleastattheelementary
level.
Forinstance,apsychologistfoundthatlackofPlaywas
justasimportantasotherfactorsinpredictingcriminal
behavioramongmurderersinTexasprisons.
Thesebasicskillsareobviouslyreflectedinthemain
goalsofmathematicseducation,whicharetoprepare
studentsto:
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ThuswhenwearedealingwiththeuseofGamesinthe
processesofteaching(andhencelearning)wewould
betteremploytechniquesandmethodsaimingat:
Solveproblems
Communicateandreason
Makeconnectionsbetweenmathematicsand
itsapplications
Becomemathematicallyliterate
Appreciateandvaluemathematics
Makeinformeddecisionsascontributorsto
society.
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Ascanbeseenthemajorityofthesegoalsare
immediatelyrelatedtogenerallifeskills,thatare
expectedforanyadultandconsequentlyitisjustifiable
topromotethelearningofthissubjecttoanyperson
irrespectiveofhis/herabilityanddegreeofintelligence.
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TheroleofGamesinLearningMathematics
SowehavetopromoteMathematicslearningbyany
means.Inviewofthisneedthequestionnowbecomes
“HowcanGamespromotetheLearningof
Mathematics?”Particularlythisquestionbecomesmore
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CreatingInterestandPromotingMotivation
AGameisasequenceofinterestingchoices.By
engagingthelearnerinsuchaprocess
motivationisactivatedandthinking(including
criticalone)istakingplace.
UtilizingtheBenefitsThatGamesProvidein
EngagingLearnersinanEnvironmentof
ExperientialandActiveLearning
Theinteractioninagamecreatesabetter
understandingforthelearnersinregardstothe
objects,concepts,processesandeventhe
otherlearnersinvolved
SocializingthePersonsInvolvedandExploiting
theCompetitionandChallengeElement
Gamesarepartofeverydaylife-socialization.
Thisisparticularlyimportantinthecaseofslow
learnersastheirslownessmighthaveitsroots
intheirlackofsocialrelationsand
interchangingeliminatingideasorlowmorale.
EuropeanErasmus+ProjectMath-GAMES
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www.math-games.eu
ConnectingtoRealLifeSituations
Quitemanygamesreflectactualactivitiesof
lifeandthustheyprovidetheelementof
usefulness.
DevelopingaHappyandJoyfulEnvironment
Asalreadymentionedthejoyelementisaplus
inthelearningprocess.
UtilizingtheDesign(Structure,Rules,
Equipment,ProblemPosingetc)ofaGamein
OrdertoDevelopanAppropriateLearning
Approach
Thecomponentsofagame,particularlythe
onescharacterizedbyaesthetic,illustrative,
energeticactivitiescanbeexploitedfor
meaningfullearning.Alsotheproblemsolving
elementsprovideampleideasforstrategicand
criticalthinking.
metacognitionproblemshavetroubleselecting
andusingeffectivelearningstrategies.Games
couldprovidetheforumtofacesuch
difficulties.
MotorFactors
Motorskills,likeperceptualones,involvemore
thanoneprocess.Theymayinvolvememoryof
thesymbolalongwithitsactualformation
(visualandmotormemories).Theymayinvolve
visualperceptionandtransfer(copying).Or
theymayinvolveintegrationoffinemuscles
withtaskdemands.Indicatorsofmotor
problemsarehighlyvisible:poorlyformed
symbols,littlecontrolofspacing,excessivetime
foratask,andavoidanceofwrittenwork.
SocialandEmotionalFactors
Suchfactorscoveraverybroadspectrum
includingpeerrelations,cooperation,selfesteemetc.Gamesagaincouldprovidea
mediumforfacingthem.
HabitsofLearning
“Habitsoflearning”referstohowindividuals
viewandparticipateinlearning,theirselfdisciplineandself-motivation,goalsetting,
engagementinlearningactivities,and
acceptanceofchallenges.
PreviousExperiences
Particularlyinthecasethelearnerhadnegative
previousexperienceherefusestogetinvolved
inthelearningprocess.Gamesagaincould
alleviatesuchnegativeexperiences.
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TheMath-Gamesmethodology
TheMath-Gamesmethodologyencompassesaseriesof
activitiesthatwillprovideateacher(andinparticulara
teacherofslowlearnersadults)thebackgroundfor
usingGamesasaneducationalmediumindeveloping
mathematicalliteracy.Inthiscontextitincludesthree
mainoutcomes(aMath-GamesCompendium,aMathGamesGuidebookandaMath-GamesTeacherTraining
Course)thatsupportvariousapproachesandmethods
forlearningandteaching.
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FactorsthataretobeconsideredinadoptingtheMathGamesmethodology
IndesigningalessonthroughtheadoptionoftheMathGamesmethodologyandconsideringthatthemain
targetgroupoflearnersaregoingtobeslowadult
learnersitisusefultotakeintoconsiderationanumber
offactorsreflectingsomeofthepossibledifficultiesof
theselearners.Theeffortwillbetoexploitthepowerof
Gamesinordertoalleviateordiminishthesedifficulties.
Suchfactorsincludethefollowingones:
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Consequentlywhatwehavetotakeintoconsideration
indesigningourplanforteachingusingtheMath-Games
methodologycouldbesummarizedas:
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LanguageIssues
Inmathematicsclasses,languageproblemsare
evidentwhenstudentshavetroubleusing
symbolsofmath,expressingmathconceptsto
others,andlisteningtomathematics
explanations.Problemsalsoappearin
expressingmath“sentences”.
CognitiveFactors
Thesemaybeattributedtoperceptual,
memory,attentionorreasoningfactors.
Perceptioninvolvestakingininformationfrom
theenvironmentandprocessingthat
informationforstorageoruse.
MetacognitiveFactors
Metacognitionisanawarenessoftheskills,
strategies,andresourcesthatareneededto
performataskandtheabilitytouseselfregulatorymechanisms,includingadjustments,
tocompletethetask.Studentswith
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Typeofslowlearner(istheslownessdueto
otherlearningareas?)
BackgroundinMath
Socializationneedsoftheperson
Motivationneedsandindicationsthatthe
mathematicalcontentofthegamerelatesto
everydaylife
Provisionofopportunitiesfortheuseofthe
previouslymentionedbenefits
GeneralApproachesforUsingGamesinLearning
Mathematics
ObviouslytheapproachonewilladoptforusingGames
inthelearningprocessdependsonanumberofgoals
thatwewanttoachieverangingfromthemathematical
areaortopictotheconsiderationsmentionedjustinthe
previousparagraphs,reflectingthebenefitsofthe
methodology.Inthiscontextwecansuggestthe
followingapproaches:
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UsingtheMethodologyasanIntroductiontoa
MathematicalTopic
Theideaistoaskthelearnerstoplayagame
thatcanbeassociatedwiththelearning
EuropeanErasmus+ProjectMath-GAMES
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www.math-games.eu
objectivesoftheparticulargame.Playinga
gamecanbeusedasabrainstorming.Thisidea
isexpectedtobethebasisformotivationand
developingofinterest.Itcanalsobeusedasan
icebreakerbothfortherelationsofthepeople
involvedinthelearningprocess(learnersand
teacher)andfortheattitudesofthelearners
towardsmathematics(whichareusually
negative).
UsingtheMethodologyforCreatingaHappy
andJoyfulEnvironment
Thisideadevelopspositiveconditionsfor
learningandthusovercomingnegative
attitudesandanxiety.
UsingtheMethodologyasanActual
EducationalMediumforComprehensionof
MathematicalConceptsandProcesses
Obviouslysuchanapproachisasubstitutefora
moretraditionalonewiththeadvantagethatit
exploitsthebenefitsofthemethodology.
UsingtheMethodologyforConsolidationof
OtherwiseLearnedConceptsorProcesses
Itisafactthatlearningprocess,particularlyfor
mathematics,demandssuchanapproach.
UsingtheMethodologyforRelating
MathematicstoRealLifeSituations
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Theidentificationofusesofmathematicsfor
reallifesituationisanassetforadultsasthe
needtoseeapplicationsofwhattheyhaveto
learn.
UsingtheMethodologyforDeveloping
ProblemSolvingandCriticalThinkingSkills
Itisamajorgoalthateverylearnerdevelops
suchskills.Gamesareidealforstrategic
thinking,planninganddesigningapproachesto
faceproblematicissues.Itprovidestheforum
formeaningfullearningandnotjustrote
memorization.
UsingtheMethodologyforBoosting
Creativity,ProductivityandInnovation
Thisideaenhancestheskillsofthelearnersand
providesafruitfulapproachforlearning.Itcan
beutilizedforadaptationofgamesor
constructingnewonesbytheplayers.
UsingtheMethodologyforFixingRelationship
DifficultiesAmongtheLearners
Asmentionedearliersuchanapproachcan
createacooperative,challengingandjoyful
environment,thuscreatingidealconditionsfor
learning.
ThefollowingtableindicatessomeexamplesforthevariousapproachesthatarepresentedinthisGuidebook:
Approach
Gamepresentedinthe
Math-GamesCompendium
Sectioninthepresent
Guidebook
IntroductiontoaTopic
JoyfulEnvironment
Educationalmedium
Consolidation
MathinRealLife
ProblemSolvingandCritical
Thinking
Creativity,Productivity,Innovation FixingRelationships
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Mankind and Mathematics
Prometheus was chained for punishment on a high rock
because he brought salvation to man, not only by steeling the
gods’ fire, but also by giving man also numbers and their
meaning. Thus, already 2,500 years ago, Aeschylus in his
“Prometheus Bound” confirms the importance of numbers for
mankind.
https://www.youtube.com/watch?v=kcWdcGwd844
Fact is, that adults need a minimum knowledge of numeracy to
survive in our world. Numeracy is increasingly necessary in a
wide range of life-skills, such as
• personal finance,
• data handling,
• at daily work and
• in everyday transactions.
Each person needs a minimum knowledge of numeracy.
Numeracy is like literacy increasingly necessary in a wide range of life-skills.
The basic life-skills are obviously reflected in the main goals of mathematics education,
which will prepare people to
• solve problems
• communicate and reason
• make connections between mathematics and its applications
• become mathematically literate
• appreciate and value mathematics
• make informed decisions as contributors to society.
Particularly in the case of Slow Adults Learners the impact during regular lessons shows
deficits on the
• motivational,
• emotional,
• cognitive and
• social aspects.
The result is: 13% of all adults have a lack of knowledge in arithmetic.
This causes playing when learning
Mathematics:
This causes playing in
humans:
This causes playing with
the learning behaviour:
• Playing is fun
• Playing together
builds human
relationships
• Playing strengthens
creativity
• Playfully problems
are solved
• When playing, you
have to pay
attention to the
rules
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Interest is aroused
Motivation is
encouraged
Competition is
socialization
Games represent
reality as a model
A relaxed and
cheerful
environment is
created when
playing
• Great learning motivation by
working with things that make
pleasure
• High learning effect by joy in the
matter
• Social behaviour in solving
problems is promoted
• Speaking and language skills are
encouraged to play, important
for the understanding of
mathematical tasks
• In Mathematics, as in the game,
there is always a model for
reality
• When playing certain games, the
motoric skills are encouraged
• Solution strategy and
mathematical rules are applied
The result is: Play Games and and learn Mathematics more easily.
Our Project-Website will help you:
www.math-games.eu