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Ewing, Bronwyn(2017)Theorizing critical discourse theory and analysis for investigating mathe-matics classrooms.Creative Education, 8(13), Article number: 79759 2064-2090.
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https://doi.org/10.4236/ce.2017.813140
Creative Education, 2017, *, *‐*
http://www.scirp.org/journal/ce
ISSN Online: 2151‐4771
ISSN Print: 2151‐4755
DOI: 10.4236/***.2017.***** **** **, 2017 1 Creative Education
TheorizingCriticalDiscourseTheoryandAnalysisforInvestigatingMathematicsClassrooms
BronwynEwing
SchoolofTeacherEducationandLeadership,QueenslandUniversityofTechnology,Brisbane,AustraliaEmail:[email protected]
Howtocitethispaper:Ewing,B.(2017).PaperTitle.****,*,**‐**.http://dx.doi.org/10.4236/***.2017.*****Received:******,***Accepted:******,***Published:******,***Copyright©2017byauthor(s)andScientificResearchPublishingInc.ThisworkislicensedundertheCreativeCommonsAttributionInternationalLicense(CCBY4.0).http://creativecommons.org/licenses/by/4.0/
Abstract
Critical Discourse Theory and its elements, discourse, language, power, ideology, sub-ject positioning, struggle and discursive practice, allow a critical understanding of theissues of the working of power and its contestation, and the processes of inclusion and exclusion from social contexts such as mathematics classrooms. Critical Discourse Anal-ysis as a method brings together the theoretical understandings of critical discourse the-ory to analyse social contexts as well as the language of research participants’ accounts. It enables an understanding of how power, discourse, and ideology are realised in ac-counts.
Keywords
Critical Discourse Theory, Critical Discourse Analysis, Mathematics education
1.Introduction(Heading1)
Intheapproachtounderstandingdiscoursetakeninthispaper,Fairclough’s(1995,
2001,2003)adaptationofFoucault’s(1972)ideasofdiscourseforcriticaldiscourse
analysis[CDA]iscentral.Cognateapproachesbyothersignificantdiscourseanalysts
(seeforexample,vanDijk,2001)orfromcriticaltheory(seeforexample,Hall,2001a,
2001b)aredrawnonwhereappropriate,thususingatoolboxapproachtoexplain
ideas.TheworkofBakhtin(Clark&Holquist,1984;Emerson&Holquist,1986)and
Volosinov(1973)isdrawnonforitsdevelopmentofa“dialogicaltheoryoflanguage”
(Fairclough,2003,p.42)andthecontingencyofmeaningonsocialcontext.Thepaper
drawsonelementsofparticipantaccountsfromastudyconductedbytheauthorto
exemplify ideasaboutthetheorypresentedandused inthestudyonly.The larger
studyisnotthefocusinthisinstance.
2.Discourse
ForCriticalDiscoursetheoryandforthispaper,then,discourseis“languageas
Open Access
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DOI: 10.4236/***.2017.***** 2 Creative Education
socialpracticedeterminedbysocialstructures”(Fairclough,2001,p.14).Following
Foucault(1972),adiscourseisagroupofstatementsthatprovidesalanguageforrep‐
resentingknowledgeaboutaparticulartopicataparticularhistoricalmoment;indeed
itconstructs the topic.That is,asasocialpractice,discourseconstitutessituations,
objectsofknowledge,thesocialidentitiesof,andrelationshipsbetween,peopleand
groups (Fairclough &Wodak, 1997). It is about knowledge defined and produced
throughlanguagewithinaparticularcontextandhistory(Hall,2001a).Inshort,dis‐
courseconstructsmeaningthroughsocialpractice.
Discoursethenisnotsimplyalinguisticconcept:itisthesocialpracticeoflan‐
guage and its consequences (Fairclough, 2001;Thomas, 2006). It is “a complexof
threeelements:socialpractice,discoursalpractice(textproduction,distributionand
consumption),andtext”(Fairclough,1995,p.74).Heresociallifeismadeupofsocial
practices,“habitualisedways,tiedtoparticulartimesandplaces,inwhichpeopleap‐
plyresources(materialorsymbolic)toacttogetherintheworld”(Chouliaraki&Fair‐
clough,1999,p.21).Discoursalpracticeandtextcomprehendthetwowaysinwhich
discoursearticulateswithpractice,sothatwhile“practicesarepartlydiscursive(talk‐
ing,writing, etc. is oneway of acting) . . . they are also discursively represented”
(Chouliaraki&Fairclough,1999,p.37).Further,“eachpracticeislocatedinanetwork
ofpractices”(Chouliaraki&Fairclough,1999,p.23),andthesenetworks“areheldin
placebysocialrelationsofpower”(Chouliaraki&Fairclough,1999,pp.23‐24).
Thisconceptualisationofdiscourseremoves thearbitrarydistinctionbetween
“whatonesays(language)andwhatonedoes(practice)”(Hall,2001a,p.72).Here,as
notedabove,socialpracticeentailsmeaning,andsince“allpracticeshaveadiscursive
aspect”(Hall,2001a,p.72),meaningsshapewhatanindividualdoes,andhows/he
conductsher/himself.That is tosay,discoursegovernshowatopicor ideacanbe
spokenaboutandputintopractice,itregulateshowpeopleconductthemselves(Hall,
2001a).Justasadiscoursedefinesacceptablewaysoftalkingandwritingintelligibly
aboutatopicandofconductingoneself,sobydefinitionitalsolimitsandrestricts
otherwaysoftalkingandwriting“inrelationtothetopicorconstructingknowledge
aboutit”(Hall,2001a,p.72).Knowledgeisputtoworkthroughdiscursivepractices
insocialinstitutionsasawayofregulatingpeople’sconduct.
Thisunderstandingforegroundstherelationsbetweendiscourse,knowledgeand
power(Foucault,1972;Hall,2001a).Inandthroughdiscourse,knowledgeislinked
topracticeandpower (N.Fairclough,2001;Foucault,1972;Hall, 2001a;vanDijk,
2003)anditsapplicationcanleadtotheacquisitionofpower insociety(Foucault,
1972;Hall,2001a).Itassumestheauthorityof“thetruth”(Hall,2001a,p.76)andhas
thepowerto“makeitselftrue”(p.76).Thatis,onceknowledgeisappliedinsocial
contexts,Hall(2001a)arguesithaseffects,andconsequently“becomestrue”(p.76).
Knowledgeinthissensehasthepowertoregulatetheconductofothersandindoing
soinvolves“constraint,regulationandthediscipliningofpractices”(Hall,2001a,p.
76).Discursivepracticesarecentralto“theproduction,distributionandconsump‐
tion”ofdiscourse(Fairclough,1995,p.75).
2.2.DiscursivePractices
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The Discursivepracticesaretheelementsofdiscoursethatareusedbyindividualstogivestructureandcoherencetodailypracticesandroutines(MartinRojo&Gomez
Esteban,2005).Theycanbesaid tobeagroupofrules thatare inherent insocial
practice(Foucault,1972);theyguidepeopleandorderdiscourse(Fairclough,2001).
Practicesaredescribedaspartofthebeliefininstitutionsthatareadrivingforcebe‐
hindsocialorder(Bourdieu,1977).Inmathematicsclassrooms,suchpracticescanbe
identifiedasholdingparticularviewsabouthowmathematicsshouldbetaughtand
learned(Ewing,2017).However,whatmakessuchpracticesdiscursiveisthefocus
ontalkinsocialcontexts,oranactionoractionsdonebyanindividualoragroupin
socialcontexts.Hence,discursivepracticesdonotexistoutsideofdiscourse—they
areassociatedwithparticularareasofsociallife(Hall,2001a),forexample,theclass‐
room.Theyarecarriedoutwithinbroadersocialpracticessuchasteaching.Indoing
so,theycontributetotheongoingprocessoforganisingandconstitutingsocialreality
(Hardy,Palmer&Phillips,2000).
Ifdiscursivepracticesarewaysofinteractingsociallyitfollowsthattolearnsuch
practicesisaprocessofappropriatingthevoicesoftherelevantcommunities(Hirst,
2004).Throughcommunication,suchvoices,thatis,thepersonalandthesocial,con‐
structthepersonandsociety.Theconstructionofanidentityemergesthrough“the
pointofarticulationandsuturebetweendiscoursesandpractices”(p.40).
Therecanbemanycomplexandoftenfine‐grainedlayersofdiscursivepractices
thatcanbefine‐grained.Theycanbesaidtobebeneaththesurfaceofwords,ideas,
andimagesthatareproducedsocially(Baker,2000).Themorenaturalandtaken‐for‐
grantedthediscursivepracticesare,themorepowerfultheyareinsocialandinstitu‐
tional life (Baker, 2000; Bourdieu, 1977). They guidepeople and order discourse.
However,itiswhatpeopledoduringtalk,theirdiscursivepractices,thatcanbesub‐
tle.Forexample,thediscursivepracticesofadiscoursemaintainparticularassump‐
tions thatdirectlyand indirectly “legitimizepowerrelations” (Fairclough,2001,p.
27).Thispowerresidesintheireverydayapplicationandreinforcementofroutine
tasksthatareviewedaspracticalandcommonsensebutwhichatthesametimecre‐
ateaparticularimageofthesubjectintheclassroom(Selander,2003).
Fromallofthisitfollowsthatdiscursivepracticesarenotonlytheproduct/sofa
discourse; they are equally constitutive of the discourse itself (Fairclough, 1992).
Considerforexample,thewaysteachersandstudentsproducethesocialintheclass‐
roomasoutlinedabove.Throughsuchsocialinteraction,teachersandstudentspro‐
ducesocialrelationsand identities.Discursivepracticesmediate theirexperiences
and offer possibilities or constrain their learning in classrooms. They include the
practicesthatfollowwithadiscourse,suchasmethodsforcarryingouttasks.
Therefore,themannerthatthediscursivepracticesofadiscourseofmathematics
aredrawnonwillhavesubstantialimplicationsforthewaysinwhichstudentsshape
an identity as a learner inmathematics classrooms and the types of discourse in
whichtheyengage.Whatisexplicitlylearnedbecomesopportunitiesforfurtherdis‐
cussion,makingsenseofthemathematicspresentedandparticipatinginmathemat‐
icsdiscourse (Cobb,Boufi,McClain&Whitenack,1997;Brown&Renshaw,2004).
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However,howdiscursivepracticesdefineacommunityandwhodeterminesandhas
thepowertograntalearneraccesstoacommunity,isinpartdependentuponthe
exerciseofpowerthroughdiscourse(Fairclough,1995).Herecriticalattentioncan
be directed to the assumptionof the naturalness, indeed the inevitability, of such
“asymmetricalrelationsofpower”(Fairclough,1995,p.16)inclassrooms.Suchan
assumptionisideological.
3.Ideologies,PowerandDiscourses
Ideologiesare“the‘common‐sense’assumptionswhichareimplicitintheconventions
accordingtowhichpeopleinteract”(Fairclough,2001,p.2).Thomas’s(2006)work
describes ideologies as “frameworks of thought, manifested in material practices,
which constitute or shape human subjects and the socialworld in differentways”
(Thomas,2006,p.59;cf.Hall,1982;2001a).They“producedifferentformsofsocial
consciousness,ratherthanbeingproducedbythem”(Hall,2006,p.397).Ideological
structuresaremosteffectivewhenthosewhousethemareunawaretheyinformtheir
claimsandviewsabouttheworld,believingratherthattheyare“simplydescriptive
statements about how things are (that is, must be) or of ‘what we can take‐for‐
granted’”(Hall,2006,p.397).Theyworkbyconstructing“fortheirsubjects(individual
andcollective)positionsofidentificationandknowledgewhichallowthemto‘utter’
ideologicaltruthsasiftheyweretheirauthenticauthors”(Hall,2006,p.397).“How
we‘see’ourselvesandoursocialrelationsmatters,becauseitentersintoandinforms
ouractionsandpractices”(Hall,2006,p.397).
Sinceideologiesareframesofthoughtmanifestedindiscursivepractices,thesig‐
nificanceofideologyforestablishingandcontributingtothemaintenanceofunequal
powerrelationsmustbestressed(Fairclough,2001).Theeffectsofideologyareevi‐
dencedindiscursivepracticesthatarethesiteofsocialstruggle(Thomas,2006).Ide‐
ologythen,asasiteofstruggle,potentiallyallows“forthepossibilityofmultipleand
competingideologies,rejectingonedominantandonesubordinateideologyasinade‐
quate”(Thomas,2006,p.58).Henceideologiesarediscursiveandplural—theyoper‐
ateindiscursiveformations(Thomas,2006).
Whenindividualsorgroupsspeak,theydonotcreatetheirownlanguage,rather,
theyuselanguageandtermsthatareavailableculturally,historicallyandideologically
(Billig,2001;Volosinov,1973).Theydrawonwaysofthinkingandactinginagiven
societywhichmake thoseways seemnatural and commonsense (Billig, 2001) and
whicharecaughtupintheinterplayofknowledgeandpowerinandthroughdiscourse
(Hall,2001a).
However,aswillbeelaboratedlaterinthispaper,thisprocessisdependenton
those inmore powerful positions in institutions or groups to definewhat is com‐
monsensical,andwhichideologiesanddiscoursetypesareatissue(Fairclough,2001).
Thisexerciseofpoweriswhathasthepossibilityofconstructingandsupportingsocial
inequality (Hall, 2001a; vanDijk, 2001).What comes tobe commonsense isdeter‐
minedinlargemeasurebythelanguageusedbythosegroupswhoexercisepowerin
asocietyorsocialinstitution(Fairclough,2001).Aspartoftheirpower,theyarelikely
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toimposeadiscoursetypeanditsdiscursivepracticesonothers,pressuringthemto
occupyaparticularpositionandtobehaveinacertainway(Fairclough,2001;Hall,
2001a).
Powertheninvolvescontrol(vanDijk,2001)—thepowerofonegroupoverthose
ofothergroupsmaylimittheirfreedomofactionandinfluencetheirthinking.Theac‐
tions of others are controlled through legitimate authority—for example, that of a
schoolprincipal—however,moreeffectivepowercanbecognitive.Thistypeofpower
isenactedthroughpersuasion,dissimulationandmanipulationtochangethemindsof
otherstosuittheinterestsofthoseotherthanthoseonwhomitisexercised(vanDijk,
2001).Itcanalsobeenactedthroughroutinesandday‐to‐daytextandtalkthatappear
naturalandacceptable(N.Fairclough,2001;vanDijk,2001;Wodak,2001).Toexercise
poweristocontrolthecontextandtorestrict,censororignorethetalkofthosegroups
inlesspowerfulpositions.Indoingso,theirdiscoursalrightsaresaidtoberestricted.
Powerisnotonlynegativeanddoesnotalwaysrepresswhatitseekstocontrol.It
canbeproductive (Hall,2001a;Foucault,1980).Forexample, thosewhochallenge
morepowerinsocialstructurescandosobycontrollingitsconsumptionorthewayit
isused,whilstacknowledgingtheinterestsofthemorepowerfulgroup(deCerteau,
1984).Thiscanbesubversive,withmembersofgroups“makingover”(p.xx)whata
powerfulgroupoffers.Subversionoperatesthroughthediscursivepracticesofsocial
structures. Indoingso,groupsseekways tooperateandserve theirown interests.
Whilstsocialstructuresareorganisedstrategicallytocontrolthemeaningsproduced,
theycanalsobeusedtoproducesubversionandorstrugglethroughnetworkssuchas
theordersofdiscourse.
3.1.OrdersofDiscourse
Ordersofdiscourseare “setsof conventionsassociatedwith social institutions”
(Fairclough,2001,p.14;cf.Foucault,1972,1980)suchasschoolsorfamilies.They
provide “a particular social orderingof relationships amongstdifferentwaysof
makingmeaning”(Fairclough,2001,p.2).Anorderofdiscoursestructuresrele‐
vantdiscoursesinwaysshapedbythe“changingrelationshipsofpoweratthelevel
of thesocial institutionorof thesociety” (Fairclough,2001,p.25).Here,power
involvesthecapacitytocontroltheordersofdiscourse,ensuringthattheyare“ide‐
ologicallyharmonizedinternallyor(atthesocietallevel)witheachother”(Fair‐
clough,2001,p.25).
Aschoolforexample,hasanorderofdiscoursethatstructuresitssocialspace
intospecificcontextswherediscourseoccurs(Fairclough,2001).Contextsinclude
assembly,class,staffmeetingsandrecess.Inthesecontexts,peoplesuchashead
teachers,teachersandstudentsparticipateinasetofapprovedpurposes—teach‐
ingandlearning—withintheschool’sorderofdiscourse.Insuchcontextshowever,
participantsarenotequal.Inthisorderofdiscourseheadteachersandteachers
exerciselegitimateauthoritytodirectorcontrolthepracticesofthatdiscourse(cf.
Fairclough,2001).
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Howtheordersofdiscourseareshapedbythosewhohavepowerismostpro‐
ductivelythoughtofasamatterofideology(Fairclough,2001).Thatis,theorders
thatpositionteachersandstudentsinrelationtoeachothercanbeconsideredas
representingtheideologiesofthosewhocontroleducation.Learningadiscourse
becomesamatterof“acquiringthenecessaryskillsortechniquestooperateinthe
institution”(Fairclough,2001,p.76).Discourseestablishesthe“interactionalrou‐
tines” (p. 81), that is, the ways and forms in which people—teachers and stu‐
dents—interactwitheachother.However,itisthroughtheseroutinesthatstrug‐
gleoccurs.Thatis,struggleemergesfrominteractionsbetweendifferentgroups.
Conflictisevidentbecauseofthewaydiscourseisusedtoexercisepowerandcon‐
trolasmentionedearlierinthispaper.
3.2.Discursivestruggle
“Discourseisthesiteofpowerstruggles”(Fairclough,2001,p.61).Atanyonetime,a
discoursemay simultaneously be a part of a situational struggle, an institutional
struggle,orasocietalstruggle(Fairclough,2001).Struggleisevidentinthewaysdis‐
course is used to interpret experience,meaning and evaluate ormake judgments
aboutwhatwords and phrases are referring to (Maybin, 2001; Volosinov, 1973).
Hencetherecanbeideologicallycompetingdiscoursetypesthatcorrespondtopar‐
ticularsituations(Fairclough,2001),andpoweriswon,sustainedandorlostinthe
courseofstrugglebetweenthem.Inthisstruggle,thosewhoholdpoweratagiven
timemustreassertthatpower,andthosewhodonotholdpowermustbidforit(Fair‐
clough,2001).
Issuesofstrugglebetweendiscoursetypesoccurbecauseofthe“establishment
andmaintenanceofonetypeasthedominantoneinagivensocialdomain,andthere‐
foretheestablishmentandmaintenanceofcertainideologicalassumptionsascom‐
monsensical”(Fairclough,2001,p.75).Individualsareconstrainedtooperatewithin
thesubjectpositionssetupinsuchdiscoursetypes.However,whilesuchpositioning
impliesconstraint,itisthroughthetensionsconsequentonsuchconstraintthatpar‐
ticipantsareenabledtoactassocialagentsandcanbecreative(Fairclough,2001).
Here,creativityemergesthroughthecombinationsofwaysthatdiscoursetypesare
used tomeet changing demands and the contradictions of social situations (Fair‐
clough,2001).ThiscreativityissimilartodeCerteau’s(1984)argumentthatindivid‐
ualscansubvertormakeoverwhatpowerfulgroupscando,tosuittheirowninter‐
ests.Powerindiscoursethencanconstrainorenablethecontributionsnotonlyof
thoseinlesspowerfulpositionsbutalsoofthoseinpowerfulpositions.
Theissuessurroundingthepositioningofparticulargroupsofstudentscangive
risetoproblemsassociatedwithacquiringtheknowledgethatistiedtoadiscourse.
Howstudentsarerepresentedinclassroomcontextsisamatterofsocialsignificance
(Fairclough,2001).Ifthestudentsarerepresentedassubjecttotheactionsofothers,
“theimplicationisthattheyareincapableofagency”(Fairclough,2001,p.222).Then,
giventhediscussiontothispoint,theclassroombecomesasiteofdiscursivestruggle.
However,thisstruggleisdiverse,competingandconflictingbecauseofthemanyand
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DOI: 10.4236/***.2017.***** 7 Creative Education
varieddiscoursetypes.Forexample,teachersarenottheonlyparticipantstohavean
authoritativeposition;studentscanalsoacceptandorrejectthatauthority.Thisissue
wasfoundtobethecaseinZevenbergen’s(2004)studyofinteractionsintwomath‐
ematicsclassrooms.Inthatstudy,studentsatAngahookwerefoundtochallengethe
teacher’sauthorityandthecontentofthelesson.Thestudyfoundthat“thelinguistic
habitusof thestudent impliesapropensity tospeak inparticularwayswhich, . . .
workstoexcludestudentsfromthemathematicalcontent”p.126).Becausethestu‐
dentwereidentifiedasnotaslinguisticallycompetentastheir“middle‐classpeers”
(p.126),theyweremarginalisedintheirattemptstolearn.Hence,itisthecombina‐
tionsofdiscoursetypesandtheirrelateddiscursivepracticesusedinsocialsituations
suchasmathematicsclassroomstomeetthedemandsandcontradictionsthatcon‐
tributetodiversityandstruggle.
Theeffectofadiscoursehasimplicationsforstudents’livesandsocialprospects
(Fairclough, 1995). That is, a discourse constructs particular viewpoints, concepts
andvalues,butindoingso,ithasthepotentialtomarginaliseviewpointsandvalues
consideredimportanttootherdiscourses.Itestablisheswhoisaninsiderandwhois
not(Gee,1996).Aspartofthatpowerandthroughpositioningindiscourse,“strug‐
glesover identities”become“strugglesoverdifference” (Chouliaraki&Fairclough,
1999,p.96).Further,whenadiscourseusesthefirstpersonpluralwe(p.96)tocon‐
structauniversalsubject,thisdiscourseiseffectivelyconstitutinganidentitywhich
repressesdifference(Chouliaraki&Fairclough,1999).Inthisregard,suchdiscourses
andtheensuingsocialstrugglesconstraintheformsofparticipationandidentities
thatcanbeconstructedinclassrooms.
However,inanyinstitution,therearemultiplediscoursesthatprovidesocialpar‐
ticipantswithchoicesconcerningwhichdiscoursestheydrawon.Drawingondiffer‐
entdiscoursecanbeimportantforbringingaboutchange(Hardy,Palmer&Phillips,
2000).Withinasingleinstitutionorprogram,hereforexample,aTAFEYouthRecon‐
nected Program, there aremultiple, alternative, even ideologically competing dis‐
courses(Fairclough,2001).Somediscoursesmaybesimilaroroverlapandsharesim‐
ilar characteristics. Somemay be alternative or oppositional to another discourse
type.
3.3.Hegemonicdiscourse
Thetermhegemonydescribes“howtherelationsofpoweroperate”(Lewis,2002,p.
31).Itindicateshowgroupsmaintaintheirpowerthroughprocessesofnegotiation
withsubordinategroups(Gramsci,1977;Hall,1982).Themaintenanceofconsensus
isachievedbystrategicmanagement.That is,whensubordinategroupshavebeen
includedinthenegotiationprocess,theyaresaidtogoalongwiththeirownoppres‐
sion(Hall,1982)however,thisisnotalwaysthecaseaspointedoutbydeCerteau
(1984).Thisusageofhegemonyneutralisesdissentandinstilsthevalues,beliefsand
culturalpracticesofsocialstructures(Hall,1982).
Ahegemonicdiscourse,then,isonethatestablishesandmaintainsparticularide‐
ologicalassumptionsascommonsensical,maintainingitsdominantpositionoverthe
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ordersofdiscourse.Dominanceinthissensereferstotheexerciseofpowerbyan
institutionoragroupthatproducessocialinequality(vanDijk,2001).Thisdiscourse
includes the products and conventions of social institutions such as secondary
schools,TAFEcollegesandaneducationsystemwhosepractices“embellishinequita‐
blesocialrelations”(Lemke,1995,p.54).Thepowertocontroldiscourseisseenas
“thepowertosustainparticulardiscursivepracticeswithparticular ideological in‐
vestments indominanceoverotheralternative (includingoppositionalpractices)”
(Fairclough,2003,p.2).
Learningahegemonicdiscoursecreatesan imageofreality that takeswhat is
seentobecommonsense(Hall,1982;Kenway,1990).Itsconventionsembodypartic‐
ularknowledge,beliefsandrelationssharedbythosewhoparticipateinadiscourse
(Fairclough,1995;Hall,2001a).Itisaccessible,exercisedandconstrainedbypower‐
holders(Fairclough,2001).Itisreproducedthroughformsofintricatesocialinterac‐
tion,communicationanddiscourse(vanDijk,2001).
Thehegemonicnatureofthediscourseofmathematicseducationisofparticular
concern.Itisthemathematicsteacherwhosespecialisedknowledgeandlegitimate
exerciseofpowercanconstrainorenablestudentaccesstothatdiscourse.Theexer‐
ciseoflegitimacyhereismoreimportantthanteaching.Forexample,whenscience
ormathematics istreatedasatechnicaldiscoursetobetaughtbytheteacherand
practisedfromatextbook,someonemusttranslatethelanguageandsemanticsofthe
technicalthematicformulationsintomorefamiliarterms...(Lemke,1990a)...The
opacityoftechnicaldiscoursetotheuninitiated...obligesthetechnocrats[orhere,
theteachers]totransformtechnicaldiscourseintosomethingthatiscomprehensible
toawideraudience[herestudents].(Lemke,1995,p.65)
Theproblemforstudentsiswhenthetechnicaldiscourseofmathematicsisnot
recontextualisedinsuchawaythattheycanunderstand,learnandapplyit(cf.Bern‐
stein,1990).Fromthestudents’perspectives,thisthenimpliesthat“theycanbeap‐
propriated and transformed in diverse and unpredictable ways, and undesirable
ways”(Chouliaraki&Fairclough,1999,p.45).Theinteractionsbetweentheteacher
andstudentarecrucialtostudentslearningmathematics,shapingwhethertheyin‐
quire and discuss their learning aboutmathematics topics , and relate this to the
worldbeyondtheclassroom(Cobb,Boufi,McClain&Whitenack,1997;Schoenfeld,
1994,2002).Barrierstounderstandingatechnicaldiscourserelatetothenegative
influencesofitsdiscursivepracticesonthesestudents.
Ahegemonicdiscourseanditsdiscursivepracticesarean“effectivemechanism
for sustaining and reproducing cultural and ideological dimensions of hegemony”
(Fairclough, 1995, p. 94). For example, to establish “hegemonic relations” (p. 94)
withinamathematicsclassroom,thehegemonicdiscourseandthediscursiveprac‐
ticeshavetobeconstructedandacceptedascommonsenseandpartofthenatural
orderbythosewhoaresubordinatetoit,thatis,thosewhoholdlesspowerfulposi‐
tions.ThislegitimisingofparticularpowerrelationsiswhatFairclough(2001)calls
“opacity”(p.33).Itistheinvisibleorhiddennatureofthisprocessthatisopaque.In
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DOI: 10.4236/***.2017.***** 9 Creative Education
short,amajor functionofahegemonicdiscourse is tomanufactureconsensus,ac‐
ceptanceandlegitimacyofdominance(vanDijk,2001).
Suchformsofdiscoursecanbeunifyinginthattheyupholdan“infinitecontinuity
ofdiscourse”(Foucault,1972,p.25)thatisolatesanythingnew“againstabackground
of permanence” (p. 21). Permanence in this sense is propagated and transmitted
throughindividuals,notionsandtheories.Itmakespossibletheirlinkingtothesame
“organizingprinciple,tosubjectthemtotheexemplarypoweroflife”(p.22).How‐
ever,Foucault(1972)proposestosuspendtraditionasanexplanationfortheirap‐
parentdurability,arguingthat“it istooeasytosimplifytheproblemofsuccessive
phenomenathroughthe levellingagencyof tradition”(p.21).Theappearanceand
reappearanceofcertainformsofknowledgeistoopersistenttobereducedtotradi‐
tion(Cousins&Hussain,1984).Rather,theconditionswithwhichknowledgeappears
andreappearsrequirereferencetospecificmeaningratherthansimplytotradition.
Traditionandpermanencecanbecontestedas theyare seldomcompleteor total.
Theymaybe contested throughvarious formsof challenge and counter challenge
(vanDijk,2001;deCerteau,1984).Thiscontestationcantaketheformofanalterna‐
tivediscourse.
3.4.Alternativediscourse
Analternativediscoursepresentsdifferentperspectivesoftheworldtothosethat
areimplicitinhegemonicdiscourse(Fairclough,1995).Thesedifferencesarerelated
to thedifferentrelationships thatpeoplehavewithoneanother, theirpositioning,
andtheirsocialidentity.Hence,suchdiscoursesmaycomplementeachother,com‐
petewitheachother,oronemaydominatetheother.
Analternativediscoursetakesthehegemonicdiscourseandrestructuresitinthe
“courseofhegemonicstruggle”(Fairclough,1995,p.95).Theremaybeoverlapwith
eachdiscoursehavingitsuniquesetofdiscursivepracticesbutalsopracticesshared
bybothdiscourses.Fairclough’s(2001)descriptionofcreativityisusefulheretoun‐
derstand alternative discourses. It is through their creativity that alternative dis‐
coursesemergeasaconsequenceofchangingdemandsinsocialsituations.Putan‐
otherway,hegemonicdiscoursescouldbesaidtobemadeoverbyindividualstosub‐
vertthemaintenanceoftheirdominantpositionwhilstatthesametimeservingtheir
interests(deCerteau,1984).Indoingso,thediscursivepracticesofahegemonicdis‐
coursearepresentbutmodifiedinparticularwaystosuittheinterestsofindividuals.
3.5.Oppositionaldiscourse
Anoppositionaldiscoursestandsinarelationshipof“opposition”toahegemonicdis‐
course(Fairclough,2001,p.75;cf.Halliday’s(1978)usageofanti‐language).Thatis,
anoppositionaldiscoursemaybeestablishedandusedinoppositiontoahegemonic
discourse (Fairclough, 2001). Its discursive practicesmay be consciously opposi‐
tionalfromthediscursivepracticesofahegemonicandoralternativediscourse.
However,wherediscoursesareoppositional,thereispressuretosuppress,elim‐
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inate, or contain themsince theyopposeor reject thehegemonicdiscourse (Fair‐
clough,2001).Forexample,inthemathematicsclassroomahegemonicdiscoursehas
constructedaparticularversionofrealitythatshapesandpositionsstudents.Hence,
studentswhoconsciouslyengageinoppositionaldiscoursesaremarginalised;they
areeitherexcludedorexcludethemselvesandperforceengageinadiscourseofnon‐
participation.Fromarangeofpossiblewaysofbeingastudent—waysthat“theyare
exposedtopartlythroughlearningtooperatewithinvariousdiscoursetypes”(Fair‐
clough,2001,p.85)andtheirrelateddiscursivepractices—studentscometobepo‐
sitionedassubjects.
3.6.TheSubjectandPositioning
Justasidentitiesaredefinedaswhoandwhatpeoplethinktheyareinparticularso‐
cialcontextsorcommunities,whattheydoinconsequence,andhowtheyinterpret
whattheydo(Wenger,1998),subjectsaresociallyproducedandpositionedwithin
discourse (Foucault, 1972;Hall, 2001a).The subjectdoesnot existoutsideofdis‐
course,thatis,outsidethewayitisrepresentedindiscourse,producedinknowledge
andregulatedbythediscursivepracticesofaparticularsocialcontext(Hall,2001a).
Itissubjectedtotherulesanddispositionsofpowerandknowledgeofthatcontext.
Forexample, institutions construct “their ideologicalanddiscoursal subjects: they
constructtheminthesensethattheyimposeideologicalanddiscoursalconstraints
uponthemasaconditionforqualifyingthemtoactassubjects”(Fairclough,2003,p.
39).
Thepowerof thediscursivepracticesofadiscourseandhowpeopleareposi‐
tionedthroughsuchpracticesisgeneratedthroughtheirlearninganduseofparticu‐
larsocialpractices(Davies&Harré,2001;Henriques,1998).Asubjectpositionin‐
cludes“theconceptualrepertoireandalocationforpersonswithinthestructurefor
thosethatusethatrepertoire”(Davies&Harré,2001,p.262).Ifapersontakesup
thatpositionastheirown,theyviewtheirworldfromthatpositionintermsofthe
knowledgethatismaderelevantwithinthediscourseandthediscursivepracticesin
whichtheyarepositioned(Davies&Harré,2001).Likeparticularidentitiesthatare
insomedegreeafunctionofthesocialcontextinwhichapersonfindsthemselves,
whenindividualsspeakoractfromaparticularpositiontheyarebringingtheirhis‐
toryasonewhohasbeenengagedinmultiplepositionsindifferentdiscourses.How‐
ever,toidentifywithapositionthatadiscourseconstructs,theymustsubjectthem‐
selvestotherulesandbecomesubjectsofitspowerandknowledge(Hall,2001a).
Forexample,subjectpositionsareconstructedwithinadiscoursesuchasmath‐
ematics. Through occupying these positions, teachers and students arewhat they
do—they become teachers and students (Fairclough, 2001). Individuals are con‐
strained to operatewithin the subject positions set up in discourse.While in one
sensetheyarepassive,itisthroughbeingconstrainedthattheyareabletoactasso‐
cialagentsandcanbecreative(Fairclough,2001;cf.Zevenbergen,2004).Thecon‐
straintsofadiscourseincludethesocialrelationsthatteachersandstudentsenter
intothroughdiscourse,andtheirsubjectpositions.Italsoincludesthewaythingsare
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done.Theseconstraintsarederivedfromthepracticesofthediscoursetypedrawn
upon(Fairclough,2001),here,adiscourseofmathematics.Thepracticesutilisedmay
contributetocertainstudentscontestingthediscoursetypeanditsrelatedpractices.
Throughparticipation,experienceanditssocialinterpretationinformeachother.
Asindividualsenactsocialrelationswithoneanotherthroughthediscoursesdrawn
on, theyconstructan identity that “textures” (Fairclough,2003,p.102)and inter‐
weavesparticipativeexperiencewiththenegotiationofmeaning.Indoingso,thethe‐
oryofpracticehighlightsthewaysinwhichdiscourseworksasanidentitykit(Gee,
1996),wherewhatmattersaremeaningfulsocialroles,socialmembership,andan
understandingofknowinghowtoengageandshareintheenterpriseinwhichmem‐
bersparticipate.Toasociallymeaningfulgroup,others, that is, thosewhoarenot
members,arepositionedasbeingoutsidethediscourse.Attainingmembershipthen
translates into the enactment of a particular identity as a form of competence
(Wenger,1998)sothatonecanidentifyoneselfasanindividualorasamemberofa
collectiveorgroup(Chouliaraki&Fairclough,1999).
In summary, CriticalDiscourseTheory offers amethodology for analysing stu‐
dents’accountsof theirexperiences inmathematicsclassrooms.CDtheoryand its
elements,discourse,power,ideology,identities,subjectpositionanddiscursiveprac‐
tice,allowagreaterunderstandingoftheworkingofpoweranditscontestation.It
provides themethodological scaffold for the analysis of research participants’ ac‐
countsoftheirexperiencesinlearningmathematics.Criticaldiscourseanalysis[CDA],
becomesthecentralmethodforthattask.UsingCDAbringstogetherthetheoretical
understandingsofcriticaldiscoursetheorytoanalysethesocialcontextaswellasthe
language of research participants’ accounts. It enables an understanding of how
power,discourse, and ideologyare realised in theseaccounts. It alsoprovides the
meansforredressingtheseissuesastheyhappenwithstudentsandinmathematics
classrooms.
4.CriticalDiscourseAnalysis
CDA isdefinedasamethodderived fromCDtheorytobeapplied in the linguistic
analysisoftheaccounts..Asdescribedinpreviously,CDtheoryconsiderslanguage
associalpractice(Fairclough,2003;Wodak,2001),henceitalsoregardsthecontext
of languageuse tobe significant (Fairclough,2003;Wodak,2001). It is concerned
withtherelationbetweenlanguageandpower(Wodak,2001).Itprovides,through
CDA,apowerfulwaytoexploretheprocessesoforganising,andthefragilityofstrug‐
gleswithin,organisationalandinstitutionallife(Hardy,Palmer&Phillips,2000)such
asschoolsandclassrooms.
ThefieldofCDAisdiverse(Chouliaraki&Fairclough,1999).Includedinthisfield
isSaid’s(1978)analysisofthediscourseoforientalismwhichdrawsonFoucault’s
theoryofdiscourse,butunlikeFoucaultincludes“someanalysisoftexts,thoughwith‐
outdrawingonanylinguistictheory”(Chouliaraki&Fairclough,1999,p.6‐7).There
areotherpoststructuralandpostmodernistcritiquesofdiscoursesuchBillig(2003).
There is also a diversity of positions within approaches that are defined as CDA
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(Chouliaraki&Fairclough,Chouliaraki,1999;Fairclough&Wodak,1997).
There has been criticismof CDA (see for example,Hutchby&Wooffitt, 1998;
Schegloff,1997;Widdowson,2000).SuchcriticismssuggestthatCDAappliessocio‐
logicalcategoriestodiscoursewhenitdoesnotneedtodoso,“imposingitsownpre‐
occupations on the discourse” (Chouliaraki & Fairclough, 1999, p. 7). Critical dis‐
courseanalystsaresaidtousethetermsthattheyarepreoccupiedwithtodescribe,
explainandcritiquethetextsthattheyareattendingto(Schegloff,1997).Hence,from
acriticalposition,thedangercouldbethattheanalystmaynotbesurprisedbythe
data(Wetherell,2001).Thatis,“theworldisalreadyknown,andispre‐interpreted
inlightoftheanalyst’sconcerns”(p.385).Ithasalsobeenclaimedthattheyare“not
beingsensitiveenoughtothemorebasicsenseofcontext...thelocal...sequential
contextoftalkinwhichutterancesareproduced”(Hutchby&Wooffitt,1998,p.164).
Inresponse,itisassertedthatCDA“beginsfromsomeperceptionofadiscourse‐
relatedprobleminsomepartofsociallife.Problemsmaybeintheactivitiesofsocial
practice”(Chouliaraki&Fairclough,1999,p.60).Itchoosestheperspectivesofthose
whosuffermost (vanDijk,2001;Wodak,2001). Indoingso, it “criticallyanalyses
thoseinpower,thosewhoareresponsibleandthosewhohavethemeanstosolve
suchproblems”(Wodak,2001,p.1).Itfocusesonissuesofsocialimportance,inpar‐
ticular,thosethatcontributetoreducingharmandpromotingsocialjustice(Wodak,
2001).CDAseekstocriticallyinvestigatesocialinequalityasitisexpressed,consti‐
tutedandlegitimisedbylanguageuseorindiscourse(Wodak,2001).Itisconcerned
withfindingwaysofredressingtheseissues(Martin,2000).Thisapproachisseenas
positiveinthatitgivesvoicetothoseinlesspowerfulpositions(Martin,2003;May‐
bin,2001;Pietikäinen,&Dufva,2006).
Asmentionedabove,thecontextoflanguageuseissignificantforCDAandthis
includesitssocial,psychological,politicalandideologicalcomponents(Meyer,2001).
ItisunderstoodinCDAas“somethingthatrequiresamorecomprehensivetheoreti‐
calexplanationtoallowananalysisofdiscourses”(Weiss&Wodak,2003,p.21).To
do this, an interdisciplinary approach is proposed (Meyer, 2001;Weiss&Wodak,
2003).Thatis,CDAintegratestheoreticalapproaches—hereCDtheory—toproduce
newholisticapproaches(Weiss&Wodak,2003).
Inthisprocess,discoursesarenotinvestigatedfortheirimmediateusealone.Ra‐
ther,theirideologicalhistoryisexaminedtoidentifyhowhistoryshapesandcontin‐
uesthelocalpractices(Billig,2001).CDAseekstoinvestigatewhathasbeentaken‐
for‐grantedascommonsense,notingthat“ideologyembracesthecommon‐senseof
eachsocialperiod” (Billig,2003,p.220).Theanalyst, inseekingto investigate the
patternsofdiscourse,observesnotonlytheissuesbeingchallengedbyspeakersbut
alsohowthosechallengesarediscursivelyaffected,andthosethatare leftunchal‐
lenged(Billig,2003).
Thatsaid,thetaskofCDAistoprovideadetailedanalysisofaccountsfromaso‐
cialcontext,herethemathematicsclassroom,andindoingso,toattempttotheoreti‐
callyandempiricallyconnecttheseaccountstounderstandingsofpoweranddiscur‐
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sivestruggleandtobroadsocialconditions.Thisinvolvesexaminingthesocialcon‐
ditionsoftheproductionandinterpretationofdiscourse.Therearethree levelsof
socialconditions:thelevelofthesocialsituationorimmediateenvironmentinwhich
thediscourseoccurs;thelevelofthesocialinstitutionthatconstitutesawidermatrix
forthediscourse;andthelevelofthesocietyasawhole(Fairclough,2001;Rogers,
2004).Theseconditionsshapewhatpeoplebringtoproductionandinterpretation.
Theyshapethemannerinwhichtheaccountsthatareresourcesforunderstanding
what is going on, are produced and interpreted (Fairclough, 2001, p. 20).
Accountsareconstitutedbytheirsocialcontext(Fairclough,1995,Lazar,2005).
Constitutionappliesinthissensetothemeaning‐makingthroughspokenandwritten
text,andwhichcontributestounderstandingthesocialcontext(Lazar,2005).
4.1.DimensionsofDiscourse
Fairclough’s (2003) three dimensions of discourse, representations, relationships,
andidentitiesprovideausefulframeworkforanalysingaccounts.Thesedimensions
enableabroaddescriptionofthediscoursesofmathematicsastracedinthepartici‐
pants’accounts.Therepresentationdimensionfocusesonthehappeningsandrela‐
tionshipsintheworld;thepeople,animalsandobjects involvedinthehappenings
andorrelationships.Itincludesthewaysthehappeningsoccurandtheir“spatialand
temporalcircumstances”(Smith,1990,p.57).Itconsiderswhatprocessesandpar‐
ticipantspredominate(Fairclough,2001). Indoingso, it focusesonrepresentinga
realorimaginaryaction,event,orrelationshiptextually(Fairclough,2001),thatis,as
aparticularversionofrealityofwhatisoccurring.
Therelationsdimensionofdiscoursefocusesonhowthechoiceofatext’sword‐
ingcreatessocialrelationshipsbetweenparticipants(Fairclough,2001).Itsinterest
is inexaminingparticular ideologiesthatarecommonground for thespeakerand
otherparticipants (Fairclough,2001;Thomas,2006). Inparticular, thisdimension
considerstherelationshipsofpowersetupandenactedinparticularversionsofre‐
ality.
The identitiesdimension involves the “commitment thatpeoplemake in their
textsandtalkwhichcontributetoidentification”(Fairclough,2003,p.162).The“pro‐
cessofIdentification”(Fairclough,2003,p.159)referstohowpeopleidentifythem‐
selvesandhowothersidentifythemintalkandtexts(Fairclough,2003).Itisacom‐
plexprocessbecauseitarisesfromthedistinctionsbetweenpersonalandsocialas‐
pectsofidentity.Theconstructionofanidentityisassociatedwithdiscourseasdis‐
cussedpreviously,however,“peoplearenotonlypre‐positionedinhowtheypartici‐
pateinsocialeventsandtexts,theyarealsosocialagentswhodothings,createthings,
changethings”(p.160).Identityconstructionthenisatextualandsocialprocessand
involvestheconstitutiveeffectsofdiscourse.Suchprocessestherefore,aredialectical,
asdiscoursesareinculcatedinidentities.
Althoughdescribedindividually, inpractice,thethreedimensionsofdiscourse
arenotdiscretetheyco‐occurandoverlap. It isuseful,however,todistinguishbe‐
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tweenthethreeforanalysis.Theyserveasaframeworkforemployingparticulartex‐
tualfeaturestotraceparticularelementsofdiscourse.
4.2.TextualFeatures
Thefollowingtextualfeatureshavebeenidentifiedasusefulforanalysingresearch
participants’accounts.
classificationschemes
modalityandmodalmarkers
deicticcategories
binaryoppositions
presuppositionsand,
declarativemood.
Eachfeaturewillbedescribedinturnandthefocusforanalysisexplained.Thefea‐
tureswillbeselectivelyappliedintheanalysisasnotallthefeatureswillberelevant
toallthedata.
ClassificationschemesAclassificationschemeisasystematicmeansoforganising,classifyingandevaluating
people,practicesandthings.Socialgroupsimposemeaningontheirworldbyorder‐
ingthingsintoclassificationschemes(Douglas,1966).Classificationschemesworkto
emphasisethedifferentiationofpeopleandpracticesfromoneanother,howtheyare
placedinoppositiontooneanother,andhowtheyareplacedasequivalenttoone
another(Fairclough,2003;Laclau&Mouffe,1985).Classificationschemesindifferent
discoursetypesallowforanunderstandingofthewordingofparticularversionsof
realityto“differentdegrees,withalargerorsmallernumberofwords”(Fairclough,
2001,p.96).Theyworktoshow“howpeoplethinkandactassocialagents”(Fair‐
clough,2003,p.88).Theyalsoworktoindicate“equivalenceanddifference”(p.88),
that is, the tendency for creating and proliferating particular differences between
groupsofpeopleand“collapsingor‘subverting’differencesbyrepresenting”(p.88)
groupsof people as equivalent toone another. Binaryoppositions,which aredis‐
cussedlater,areconsideredcrucialforclassificationschemesbecauseacleardiffer‐
encebetweenthingsmustbeestablishedinordertoclassifythem(Hall,2001b).The
followingaccountindicateshowsomestudentsareclassifiedinoppositiontoschool.
A lot of these children I think they’ve been in big trouble at main stream schools. A lot of them find great difficulty in sitting still and I can imagine that they’d spend a fair bit of time in isolation in the classroom where they— be-cause they’re disruptive and they talk to each other—which in a classroom
situation is untenable for a teacher. (Interview, Joan, Program Tutor)
ThisaccountisfromatutorintheYouthReconnectedProgram.Ostensibly,thestate‐
mentisaboutaparticulargroupofstudentswhorejectschooling.However,theac‐
countcarriesmanymeanings,allofwhichmaybeplausible,forexample,thestudents
havebeenintroubleatschool,thestudentshavebeenexcludedfromclassbecauseof
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DOI: 10.4236/***.2017.***** 15 Creative Education
theirdisruptivebehaviour,andtheteachermayfindthestudentsdifficulttowork
with.Whatisimportant,though,isthatthisaccountclassifiesaparticulargroupof
studentsasdifferenttoanothergroupwhichisnotincludedintheaccount.Thatis,
themembersofthisgroupareintrouble,havedifficultysittingstill,areplacediniso‐
lation,andaredisruptiveandtalkative.Thisclassificationplacesthestudentsinop‐
positiontoothergroupsofstudents intheclassroomandindoingsogivesriseto
“negativefeelingsandpractices”(Hall,2001b,p.230).
Whatisseentocausenegativityiswhensomethingisinthewrongcategoryor
doesnotfitanycategory(Douglas,1966;Hall,2001b)butfloatsambiguouslyinan
unstablein‐betweenzone,forexample,socialgroupswhoaremixed‐racedandwho
areneither“black”nor“white”(Hall,2001b;Stallybrass&White,1986).Stabilityre‐
quires everything tobeorderedand inplace.However,whatunsettles stability is
whensomethingisoutofplaceandtherulesarebeingbroken.Thingsthatareoutof
place are seenas a “signofpollution, of symbolicboundariesbeing transgressed”
(Hall,2001b,p.330).Thingsthatareoutofplaceareremoved,torestoreorder.Clas‐
sificationsofdifferencecanleadtoaclosureofranksandthestigmatisationandex‐
pulsionofanythingthatisdefinedasimpure(Hall,2001b).However,differencecan
bepowerfulbecauseitisforbiddenandthreateningtosocialorder(Hall,2001b).Dif‐
ferencethencreatessocialdivisions,whilstequivalencesubvertsexistingdifferences
and divisions. In doing so, they continue the process of social classification (Fair‐
clough,2003).
Aclassificationschemecanbeidentifiedthroughtheuseof“overwording—an
unusuallyhighdegreeofwording,ofteninvolvingmanywordswhicharenearsyno‐
nyms”(Fairclough,2001,p.96).Overwordingmaybeusedwhenthereisapreoccu‐
pation with an aspect of reality that may cause ideological struggle (Fairclough,
2001).Whenitoccurs,thatparticularversionofrealityislikelytobe“afocusofide‐
ologicalstruggle”(p.96).
Alternatelyfocusingonthetextandthediscoursetypeenablesabetterunder‐
standingof“meaningrelationships”betweenthewordsusedinthetext,thediscourse
typesunderlyingthewords,andtheideologiesonwhichtheyarebased(p.96).Two
formsofmeaningrelations,synonymyandantonymy,aresignificanthere.Thefirst
term refers towords that sharea similarmeaning. “Generally, suchwordsdonot
overlap,butratherasfarasonemeaninggoes,theymeanthesame”(Halliday&Ha‐
san, 1989, p. 80). The second term relates to “oppositionalwording” (Fairclough,
2001,p.94),aswhenanexistinganddominantwording isreplacedbyanother in
oppositiontoit,forexample,thewords“subversiveandsolidaritybelongrespectively
to‘right’and‘left’ideologicalframeworks”(p.95).Howeitherofthesewordstends
tooccur,will“ideologically‘place’atext”(p.95).Thesetermsareextendedtoinclude
phrasesthatinrepetitionemphasisethesametheme.
ModalityandModalMarkersModalityrefers tothestanceorattitudetaken ina textorstatement,a judgement
madeaboutsomeoneorsomething(Fairclough,2003,p.165).Asatextualfeatureit
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DOI: 10.4236/***.2017.***** 16 Creative Education
identifieswhatpeoplecommitthemselvesto,whatisdesirableorundesirable.Iten‐
ablestheanalysttotracetheprocessesbywhichsuchidentificationproceeds.Here
identificational meanings presuppose representational meanings, that is, “the as‐
sumptionsonwhichpeopleidentifythemselvesastheydo”(p.160).Examiningmo‐
dalityintheanalysismakesapparentwhatpeoplecommitthemselvestothroughdif‐
ferenttypesofexchanges,eitherintermsoftheirauthoritytomakethatstatement,
ortheirevaluationoftheissueinthatstatement(Fairclough,2001).
Modalityisusedintheanalysisbecauseitemphasisesthe“stance”thatpeople
taketowardstheirrepresentations(Hodge&Kress,1988,p.122). Itexpressesthe
speaker’sjudgementontherealityoftherepresentationinastatement(Kress&van
Leeuwen,1990,p.49).Ofimportanceishowsocialparticipants,contextsandrela‐
tionsarecategorisedanddescribed.Descriptionsofparticularversionsofeventsare
descriptionsoftherelationsofsocialparticipantstothesocialcontext.Thedescrip‐
tionsrepresentsocialconstruction,contestationandstruggle.Throughthedescrip‐
tions,discoursesandtheprocessesofpowerthatcontributetosuchconstructionand
contestationcanbetraced.Modalityisrealisedbytheuseofmodalmarkers—verbs
suchasmay,might,must,modaladverbssuchasprobablyandpossibly,andmodal
adjectivessuchaspossibleandprobable.Modalmarkershaveastrategicroleindis‐
course (Baker, Francis&Tognini‐Bonelli, 1993). They areusedby a speakerwho
wantstomaketheirinterpretationofthesituationstandoutfromothers’interpreta‐
tionsormorecommonconsensusviews.It isacommonemphasiserthatservesto
expressthat“whatisbeingsaidistrue”(Quirk,Greenbaum,Leech&Svartik,1985,p.
583)andthatthereisadegreeofunexpectednessandsurprise(Lenk,1998).
Modalityisconcernedwiththespeakerorwriter’sauthorityandthedirectionof
thatauthority.Therearetwodimensionstomodality,relationalmodalityandexpres‐
sivemodality,eachdependingonthedirectioninwhichauthorityisorientated(Fair‐
clough,2001).Relationalmodalityexistsifitisacaseofthe“authorityofonepartici‐
pantinrelationtoothers”(Fairclough,2001,p.105).Expressivemodalityrefersto
the“speaker’sauthoritywithrespecttothetruthorprobabilityofarepresentation
ofreality”(Fairclough,2001,p.105).
Animportantfeatureofrelationalmodalityisanunderstandingoftheimplicit
authorityandpowerrelationsintheaccounts,authorityandrelationsthatarenot
madeexplicitbutyetimposeobligationsonsubjects.Thefollowingaccountfroma
programtutorillustratesthisaspect:
Well that’s the way I work, others may not work, but I prefer to get to know the student really well, look for their good points and empower them and praise
them wherever I can. (Interview, Joan, Program Tutor)
Inthisaccount,thetextualfeaturerelationalmodalityisidentified.Thisfeatureshows
theauthorityofthetutortospeakabouttheirknowledgeofwhattheywoulddoand
therelationswithothers.Therelationalmodalauxiliaryverb,may,signalsapossibil‐
ity,butwiththenegatingadverbnot,themeaningsuggeststhatthereisthepossibility
thatothersdonotworkinthesamewayasthetutor.Ofinterestinthisaccountare
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DOI: 10.4236/***.2017.***** 17 Creative Education
thespeaker’sauthorityandthepowerrelationstowithholdwhatothersdo,thatis,
notmakeexplicitwhatothersdo.Theimplicitclaimandpowerrelationsareamatter
ofideologicalinterestbecause“ideologyismosteffectivewhenitsworkingsareleast
visible”(Fairclough,2001,p.71).Suchaninvisibilityisachievedwhenitisbroughtto
discourseasbackgroundassumptionsthatleadthespeakerto“textualizetheworld
inaparticularway,...andyetleadstheinterpretertointerpretthetextinaparticular
way”(Fairclough,2001,p.71).
Expressivemodality,thatis,thespeaker’sevaluationofaparticularrepresenta‐
tionofaversionofrealityandthebasisofherauthoritytomakethatevaluation,can
alsobeexpressedusingmodalmarkerssuchasmay,might,must,should,can,can’t,
andothersimilarterms(Fairclough,2001).Evaluationreferstotheexplicitor im‐
plicitwaysthatspeakersorwriterscommitthemselvestovalues(Fairclough,2003).
Claimsaboutexperience,otherpeople,andrelationshipsforexamplearevaluejudg‐
mentsthatareusedinconjunctionwithan“evaluativeaccent”andconveyedusing
expressiveintonation(Volosinov,1973,p.93).Evaluativestatementsareaboutde‐
sirabilityandundesirability,andorwhatisgoodorbad;forexample,mathematicsis
goodormathematicsisbad.Thedesirabilityofanythingissociallyconstructed(Gra‐
ham,2003).Evaluativestatementsarerealisedasrelationalprocesses,withtheeval‐
uativeelementtheattribute,whichcanbeanadjective—good—oranounphrase—
agoodexample.
Explicitevaluativestatementsaboutdesirabilitygenerallycontainwordssuchas
good,bad,hate,andlove.Theperceiveddesirabilityofsomethingissociallymediated
(Graham,2003).Withinadiscourse,theevaluativedimensionsthatpropagatedesir‐
ability for something, suggest significance. Evaluative statements evaluate by im‐
portanceandusefulnesswheredesirabilityisconcerned(Fairclough,2003).Whatis
takenasself‐evidentasimportantorusefulisconsidereddesirable,forexample,the
textbookisuseful.
Oneimplicationofevaluationforanalysingdiscoursesofmathematicslearningis
thatitallowsfortheidentificationofthepossibilitiesforstudentlearning.Anotheris
thatitrevealstheexistingproblemsthatproduceexclusionandisolationfrommath‐
ematicslearning.Evaluationallowsforconsiderationofwhatexiststhatcausesstrug‐
gle inandthroughdiscourse,andthepossibilitiesthatmight leadtosocialchange
whichcoulddecreasethestruggleandenhancestudentaccesstodiscoursesofmath‐
ematicslearning.Forexample,
Well let’s go back and look at this, you can see at a glance that it is not right. I then go back, then take them through, and say to them, you can’t, [you]
must take the bottom number from the top number, and what you do is bor-row from next door. (Interview, Louise, Program Tutor)
Inthisaccountexpressivemodalityisidentified.Thismodalityshowsthespeaker’s
commitment to the“truthof theproposition”(Fairclough,2001,p.107)ofhowto
solveasubtractiontask.Themodalauxiliaryverb,must,marksexpressivemodality
andisassociatedwithcertainty“youmusttakethebottomnumberfromthetopnum‐
ber”. The ideological interest is in the authenticity of the speaker’s claims to
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DOI: 10.4236/***.2017.***** 18 Creative Education
knowledge,withthestepsusedtosolveasubtractiontaskrepresentedasfactwithout
anyintermediatemodalities(Fairclough,2001).
DeicticcategoriesDeicticcategoriesrefertothetermsusedtoorganisesociallywhatandwhoispresent
orabsentinatext(Smith,1990,p.57).Forexample,thetermsnow,then,here,there,
theverbscomeandgo,andthepersonalpronouns,we,I,they,them,usandyou,work
tosociallylocateandorganiseby“timeanddistanceandthepositionsandarrange‐
mentsofparticipantswithreferencetothe‘position’ofthespeaker”ofatext(p.56).
Whatthespeakerreferstocanonlybeidentified“whenthepositionofthespeaker
andthecontextinwhichtheyareusedisknown”(p.56).Usingthesecategoriesena‐
blesanunderstandingofthesocialorganisationofparticipantsinatext.Itsconcern
iswiththeideologicalsignificanceofparticipantsandtheirrelations(Thomas,2006).
Deictic categorieswork to locate howparticipants are included and excluded
fromadiscourse(Thomas,2006).Aparticipantmaybeasocialactor,althoughthisis
notalwaysthecase;aphysicalobject,forexample,atextbook,canbeaparticipant
(Fairclough,2003).Deicticcategoriessuchasthepersonalpronouns,I,we,you,they,
them,andus,canbetiedtorelationsofsolidarity(Fairclough,2001).Becausesocial
actorsareclassifiedandrarelynamed(Fairclough,2003),understandingweasthe
firstpersonpluralpronouniscrucialtotheidentificationofgroupsandhowaccounts
represent communities. Such groups and communities “are elusive, shifting and
vague”(Thomas,2006,p.86).Theuseoftheysuggestsknowledgeofthegroupina
themandusway,ratherthanmakingreferencetothepreviouslyusednoun(Fair‐
clough,2003).Forexample,
The teacher like say they would not explain the whole subject to you. They just explain parts of it. (Interview, Aderley, Program Student)
Deictic categorieswere identified in this account. This textual feature shows two
groupsofpeople,theteacher,identifiedasthepersonalpronoun,they,andthestu‐
dentorstudentsidentifiedasthepersonalpronoun,you.Thesetwogroupsaremu‐
tuallyexclusive.Itisnotpossible,inthisaccount,tobeboth.Thiscategorisationis
constructedaround“thewholesubject”.Theteacher,identifiedasthey,hastheability
toexplainthewholesubject.Thestudent,identifiedasyou,expectsthisresponse,but
itisonlypartiallyfulfilled.Heretheteacherhaspower,andthestudentdoesnot.This
constructionworkstoindicatewhoisincludedandexcludedfromthediscourseof
mathematics.Further,itshowshowsuchaconstructionpositionssomestudentsout‐
sidethatdiscourse.
Inthisexample,deicticcategoriesworktoproduceanoppositionbetweentwo
socialactorsaroundpowerandcontrolandinclusionandexclusion.Therearetwo
types of exclusion of social actors, suppression, and backgrounding (Fairclough,
2003).Suppression iswhentheactor isnotevident intheaccountatall.Whenan
actorismentionedintheaccount,buthastobeinferredinoneormoreplaces,itisa
caseofbackgrounding(Fairclough,2003).Thereasonsforexclusioncanbevaried,
forexample,asirrelevantorpoliticallyorsociallysignificant.
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DOI: 10.4236/***.2017.***** 19 Creative Education
Whensocialactorsareconstructedinandbydiscoursetheyareeitherinitiators
orcontrollersofactionsandevents.Therearethosewhodothingsandmakethings
happen,whileothersareconstructedasaffectedorbeneficiaries,theobjectsofaction
orcontrol(Fairclough,2003).Indiscoursetheysaidtobeeither“activated”or“pas‐
sivated”(p.145).
BinaryoppositionsAbinaryoppositioniscomposedoftwomutuallyexclusiveterms(Thomas,2006,p.
91),forexamplegood,bad;white,black;man,woman.Inmakingsenseoflanguage,
thewordchoicesandpatternsofrepetitionusedbyaspeakeraregenerallyorganised
aroundbinaryoppositions(Gee,1996).Anoppositioncanbeacontrastoffeelingand
beliefontheonehandandrationalevidenceontheother.Thatis,onesidewinsout
overor“subordinates”theother(Gee,1996,p.100).Oppositionsarenotalways“ex‐
plicitlystatedintexts”(p.101)butimpliedbythelanguageused.Therefore,theway
anoppositionisfunctioninginatextcanbearguable.Whenanoppositionisnotre‐
solved, paradoxes, and contradictions emerge as a consequence of a speaker’s at‐
temptstomakesenseinthefirstplace.
BinaryoppositionsenabletheidentificationoftheOtherasthesourceofprob‐
lems(Thomas,2006,p.91).Thisidentification,or“meta‐contrastprinciple”(Meyer‐
hoff,2001,p.67)predictsthatagroupofpeoplewillbeclassifiedandtreatedasmem‐
bersofan“outgroup,whenthedifferencebetweenallofthemandallthemembersof
anothergroupisgreaterthanthedifferencebetweenthemselves”(p.67).Themeta‐
contrastprinciplelocatesprominentidentitiesinchangesinthewaytheratiosofin‐
groupandoutgroupdifferencesareevaluated(Meyerhoff,2001).Evaluationscanbe
basedon“anti‐languages(opposedsubcultures)”(Halliday&Hasan,1989,p.40),lan‐
guagesestablishedforaparticularpurpose.Whensuchevaluationsaremade,posi‐
tiveornegativerepresentationsofthegroupsaremade.Here“negation”(Hodge&
Kress,1988,p.263)isusefulforthepositivethatitrejects—signifyingapositiveterm.
Binary oppositionshavebeen criticized as reductionist andover‐simplified in
theirtwopartstructure(Hall,2001b).However,therearefewneutralbinaryopposi‐
tions—onepoleisusuallydominantandthereisalwaysarelationofpowerbetween
thepoles(Derrida,1981;Hall,2001b).Suchdifferentiationsreflectsharpdivisions
withinasociety. Indoingso, theyareusedtoupholdandsustainexistingunequal
relationsofpower“byemphasisingthetypicalityornormalityofthepositivemodel
andthedevianceoftheOthers”(Thomas,2006,p.92).Theyalsoreflectstrugglebe‐
tweendiscoursetypes(Fairclough,2001).Thestruggleiswiththeestablishmentof
onediscoursetypeinasocialcontextandtheestablishmentofparticularideological
assumptionsviewedascommonsense(Fairclough,2001).
PresuppositionsWhatisimplicitinatextisofsocialimportance.Thisisbecausesolidarityinacom‐
munitydependsonsharedmeaningsthataretakenasgivensandthatworktoform
commonground (Fairclough, 2003).However, the capacity to shape this common
groundisequallysignificant.Thatis,theexerciseofpowerandhegemonyincludes
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DOI: 10.4236/***.2017.***** 20 Creative Education
thecapacitytoshapethecontentofwhatisconsideredcommonground.Implicitness
andassumptionsaresignificantwhenconsideringideologies(Fairclough,2003).
Makingjudgmentsaboutthemeaningofwhathasbeensaidvariesdependingon
thesocialgroupsthatpeoplebelongtoandthelanguagesspoken(Gee,1996).Inthis
instance,makingguessesaboutthemeaningaremadeeasierbecauseofsimilarities
inthegroupandorthelanguagespoken.Theguessingprinciple(Gee,1996,p.74)
referstothejudgmentsmadeaboutwhatothersmeanbyawordorwordsusedby
“guessingwhatotherwords theword ismeant toexcludeornotexclude” (p.74).
Making judgments isalsoaboutbuilding theories, testing thembyhow “well they
makesenseofpastandfutureexperience”(p.75)andrevisingthemwhennecessary.
DeclarativemoodTheexpressionofmoodinclausesisdescribedbyHallidayandMatthiessen(2004)
asconsistingofa“SubjectplusFinite”(p.114)whichrealisestheindicativefeature.
Thisfeatureisusedtoexchangeinformation.Associatedwiththisfeatureisthede‐
clarative(Halliday&Matthiessen,2004).Declarativemoodenablesstatementstobe
madethatprovideorgiveinformation(M.A.K.Halliday,1990).Itisthe“orderSubject
beforeFinitethatrealisesdeclarative”(p.115).Adeclarativesentenceisgenerally
instigatedbythepersonwhohastheknowledge,althoughitcanalsobeinitiatedby
apersonwhowantstheknowledge,thatis,theinterviewer(Fairclough,2003).Such
statementsarethemostfrequentlyusedwhenspeakingorwriting.
Insummary,usingCDAbringstogetherthetheoreticalunderstandingsofcritical
discoursetheorytoanalysethesocialcontextaswellasthelanguageofresearchpar‐
ticipants’accounts.Itenablesanunderstandingofhowpower,discourse,andideol‐
ogyarerealised in theseaccounts. Italsoprovidesthemeans forredressing these
issuesastheyhappenwithstudentsandinmathematicsclassrooms.Asamethodfor
analysis,togetherwiththethreedimensionsofdiscourse,representations,relations
andidentities,CDAprovidesawayofascribingmeaningtotheparticipants’experi‐
ences.Theyenablebroaddescriptionsof thediscoursestraced in theparticipants’
accounts. They also serve as a framework for employing the textual features de‐
scribedtotracetheparticularelementsofdiscourse,andidentitiesintheaccounts.
5.FinalWords
ThediscussionofCriticalDiscourseTheoryhighlightedthesignificanceofthesocial
contextandprovidedthemethodologyfromwhichCDAanditselementsdescribed
couldbedrawn.Indeed,“societycan...beunderstoodasavastargumentativetex‐
turethroughwhichpeopleconstructtheirreality”(Laclau,1993,p.341)inparticular
contexts.Thatcontextcanincludefactorssuchasthematerialsetting,thepeoplepre‐
sentandwhattheyknowandbelieve,thelanguagethatisused,thesocialrelation‐
shipsofthepeopleinvolvedandtheiridentities,aswellashistorical,culturalandin‐
stitutional factors (Gee, 2004). This framing of context implies a correspondingly
complexsetoftheoretically‐basedtoolsormethodssuitedforanalysisofdiscourse
(Chouliaraki&Fairclough, 1999; Poynton, 2000;Weiss&Wodak, 2003 ). CDAat‐
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DOI: 10.4236/***.2017.***** 21 Creative Education
temptstotheorisethemediationbetweenthesocialandthelinguisticinaninterdis‐
ciplinaryapproach,andtooperationalisethetheoreticalconstructionsofdiscourse
intosuchtoolsandmethods(Chouliaraki&Fairclough,1999).
The adoption of such an interdisciplinary approach necessitates the acknowl‐
edgementoftheimportanceofthesocialcontextinwhichtheaccountsareproduced.
Suchaccountsareconstitutedinandbythesocialcontext,andthatcontextcanbe
understood throughspokenandwrittenaccounts (Fairclough,1995;Lazar,2005).
CDA,with itscommitment to fine‐grainedanalysesofaccountsconstructedwithin
socialcontexts,hasbeenchosenbytheresearchertomeetthisrequirement.Suchan
analysisensureslinksaremadebetweentheaccountsofparticipantsandtheirsocial
context.Thatis,theresearchneedstobesensitivetotheiraccountswithoutlosing
sightofthecontextsinwhichtheyoccur(Chouliaraki&Fairclough,1999).
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