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https://doi.org/10.4236/ce.2017.813140

https://eprints.qut.edu.au/view/person/Ewing,_Bronwyn.html

https://eprints.qut.edu.au/113066/

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

Author, Author

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).

Author, Author


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

Author, Author


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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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

Author, Author


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

Author, Author


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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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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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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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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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.

Author, Author


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

Author, Author


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‐

Author, Author


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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