reading to learn maths: a teacher professional development ... · reading to learn maths: a teacher...

ReadingtoLearnMaths Lövstedt&Rose

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ReadingtoLearnMaths:AteacherprofessionaldevelopmentprojectinStockholmAnn-ChristinLövstedt1&DavidRose2

AbstractAstudywasconductedin2010in20StockholmprimaryschoolsofmathsteachingstrategiesknownasReadingtoLearn.Thestrategiesinvolvecloseanalysisofclassroomdiscourseinteachingmathsoperations,andcarefulplanningofteacher-classinteractionsbasedontheseanalyses.Classroomimplementationinvolvesrepeatedguidedpracticeusingtheselessonplans,culminatinginindependentproblemsolving.Resultsofthestudyshowthatlowerandmiddleperformingstudentsimprovedanaverageof~20%intwomonthsbetweenpreandposttests.Higherperformingstudentsalsoimprovedandwerebetterabletoexplaintheirmathematicalworking.Teachersalsoreportedincreasedstudentengagementinmaths,increasedparticipationandconfidenceinlessons,andhigherlevelunderstandingofmathsconcepts.

IntroductionThispaperreportsontheresultsofanevaluativestudyofaninnovativeapproachtoteachingthelanguageofmathematics,knownasReadingtoLearn.ReadingtoLearnisaprogramdesignedtointegratetheteachingofliteracywithsubjectteachinginallareasoftheschoolcurriculum,includingmathematics.TheprogramoriginatesinAustralia,whereitiswidelyusedinprimary,secondaryandtertiaryeducation(Koop&Rose2008,Rose2010,2012),andisgrowinginternationally,forexampleinSouthAfrica(Childs2008,Dell2011),eastAfrica(AfricanPopulationandHealthResearchCenter2011),China(Chen2010,Liu2010)andLatinAmerica.Since2009ithasbeenimplementedinSwedenbytheMultilingualResearchInstituteasateacherprofessionallearningprogram(Acevedo2011).In2010theInstitutedecidedtotrialtheReadingtoLearnstrategiesformathswithapilotstudy,andmeasuretheoutcomesintermsofstudents’improvementsinmathslearning.

SydneySchoolpedagogy

ReadingtoLearnappliesresearchintothelanguageofeducationconductedbytheSydneySchooloflinguisticresearch(Martin2000,Rose2008,2011).TheSydneySchoolresearchprogramfocusesparticularlyonthegenres,ortypesoftexts,thatstudentsneedtoreadandwriteacrossthecurriculum(Cope&Kalantzis1993,Christie&Martin1997,Martin&Rose2008),togetherwiththegenresofclassroomdiscoursethroughwhichtheyarelearnt(Christie2002,Martin2006,Martin&Rose2005,Rose&Martin2012).OneoutcomeofthisresearchisthegenrebasedwritingpedagogythatisnowpartoftheschoolcurriculumacrossAustraliaandincreasinglyinternationally(e.g.Indonesia).Ingenrewritingpedagogy,teachersprovidestudentswithexplicitmodelsofthetypesoftextstheyareexpectedtowrite,andexplicitguidanceindoingso.AkeyactivityinthispedagogyisJointConstruction,inwhichtheclassjointlyconstructsatext,withtheguidanceoftheteacher,thatfollowsthesamestructureasamodeltextinthetargetgenre.

1MultilingualResearchInstitute,Stockholm2UniversityofSydney


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Acentralprincipleofgenrepedagogyis‘guidancethroughinteractioninthecontextofsharedexperience’.ReadingtoLearnextendsthisprincipletosupportstudentstosuccessfullyreadandwriteacrossthecurriculum.OneaimofReadingtoLearnisto‘democratisetheclassroom’(Rose2005),byprovidingteacherswithstrategiestoenableeverystudenttosucceedwiththelearningtasksexpectedoftheirgradeandsubjectarea.Thefundamentaltoolthatfacilitatesthesestrategiesiscloseanalysisofthetextsthatteacherswanttheirstudentstoreadandwrite,andtheclassroominteractionsthroughwhichtheyteachthem.

Genresinmathslearning

SydneySchoolresearchinthelanguageofmathshasidentifiedfoursignificantgenresthatareassociatedwithlearningthesubject–procedures,explanations,definitionsandproblems(Rose2012).Mathsproblemsareoftenidentifiedasawrittengenreuniquetothesubject,thatmanystudentsstrugglewith.Theseso-called‘mathswordproblems’areintendedtocontextualisemathsoperationsbyrelatingthemtostudents’everydayexperience,butteachersoftenreportthattheirwordingstendtoobscureandcomplicatethemathematicaltask.ReadingtoLearnusesastrategyknownasDetailedReadingtoguidestudentstoidentifythreeconsistentelementsofthesewordproblems,includingthedataprovided,thetypeofsolutionrequired,andtheoperationneededtosolveit.Theseelementsarecorrelatedwiththreelevelsofreadingcomprehension,i)identifyingdatathatisliterallyprovidedinwordsandnumbers,ii)inferringconnectionsacrossthetexttofindtherequiredsolution,andiii)interpretingconnectionsbeyondthetexttotheoperationsneededtosolvetheproblem.Howevertheaimofsolvingproblemsinmathspedagogyisprimarilytopractiseoperations(oralgorithms)thathavepreviouslybeendemonstratedtostudents,andthentoevaluatehowwelleachstudenthaslearnttheoperation.Thepedagogicprincipleimplicitinthisactivityissimplythat‘practicemakesperfect’.Ofcourseitdemonstrablydoesnotdosoformanystudents,asevaluationtypicallyshowsawidegapbetweenstudentswhoaremostandleastsuccessfulatmaths.Crucially,thereisnodistinctionintheseactivitiesbetweenalearningtaskandanassessmenttask.Eachstudentmustpractisetheproblemsindependentlysothattheirlearningcanbeevaluated.Thequestioniswhatisbeingevaluated.Beforeattemptingtheseproblems,itisassumedstudentshavefirstlearnthowtoperformtherelevantmathsoperations.Classroomobservationsandextensiveinterviewswithteacherssuggestthatthesearetaughtinaremarkablyconsistentfashionacrossgradesandclassesintheschool.Thatis,theteacherdemonstratestheoperationwithoneormoreworkedexamplesontheclassboard,explainingeachsteporallyasitisdemonstrated.Thiswidespreadpracticeappearstobeindependentofanyideologyorpreferencefortraditionalorprogressivepedagogies.Intermsofgenre,theoraltextprovidedbytheteacherwhiledemonstratingtheexampleisaprocedure.Beyondverybasicalgorithmssuchassimpleaddition,theseoralproceduresbecomeincreasinglycomplexaschoicesmustbemadeatvariouspoints,suchaswhetherto‘carry’or‘trade’numbersifasumismoreorlessthan10.Ingenretheory,suchcomplextextsareknownasconditionalprocedures(Martin&Rose2008,Rose1997,Rose,McInnes&Korner1992).


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Inequalityofaccesstomathsgenres

ObservationsofclassesinSydneySchoolresearchshowedanotherpatternthatisalsohighlyconsistent(RobertVeel,perscomm1999).Somestudentsareableto,i)clearlyfollowwhattheteacherissayingateachstepoftheworkedexample,ii)understandthevarioustermsthatareusedtodenotethemathematicaloperation,iii)relatewhatissaidtothemathematicalprocessbeingwrittenontheboard,andiv)rememberthewholeprocedure.Thisgroupofstudentsmaythensuccessfullysolvemostoftheproblemsthroughwhichtheypractisetheoperation,andthusbenefitfromthepractice.Wheretheydomakeerrorstheycanreadilyidentifythemandthuslearnfromtheirmistakes.Theyalsotendtobeabletoexplainhowtheysolveeachproblemwhenasked.Otherstudentsmaymiss,misunderstandormisremembercertainelementsoftheprocedure,thetermsbeingused,orrelationswiththeworkedexampleontheboard.Thisgroupofstudentsmaythensolvefeweroftheirindependentproblemscorrectly,andexperiencetheirmistakesmoreasfailuresthanasopportunitiesforlearning.Theymaythusreceivelessbenefitfromthepracticethatproblemsareintendedtoprovide.Otherstudentsmayunderstandandrememberverylittleoftheprocedure,beunabletosolvemostoftheirproblemscorrectly,andperceivethemselves(andbeperceived)asunableto‘domaths’.ThroughoutadecadeofReadingtoLearnprofessionallearningprograms,bothprimaryandsecondarymathsteachershaveconsistentlyconcurredwiththeseobservations,althoughtheproportionsofstudentsineachgroupvaryfromclasstoclass.Teachersalsocommentthattheyspendalotoftimeattemptingtosupportstrugglingstudents,astheykeepmakingerrorsandcannotarticulatetheirworkings.Theissueherehastodowiththeemotionalconsequencesofrepeatedfailure,whichconstrainslearners’capacityforprocessinginformation(vanMerrienboer&Sweller2005),rendering‘learningfrommistakes’anineffectivestrategyforstrugglingstudents.Ouranalysisoftheproblemisthatthesestudentshavenotbeengivensufficientguidancetoperformtheoperationsuccessfully,beforetheyarerequiredtoperformitindependently.Theguidancethatisprovidedbystandardmathsactivitiesissufficientforsomestudentstoperformsuccessfully,butisinadequateforothers.

Thelinguisticbasisoflearningmathsconcepts

Contemporarymathslearningtheorieshaveanalternativeexplanationforvariationsinstudents’abilitiestoperformoperations.Thatisthattheymustbeabletounderstandthe‘concept’behinditbeforetheyareabletodotheoperation(Devlin2007).Mathsconceptsmustfirstbelearntthroughavarietyofactivities,whichmayinvolvemanualmanipulationandvisualperceptionofobjects,coins,shapesorsymbols.Aswithdemonstratingworkedexamples,whatremainsunnoticedinthesepracticesistheteacher’soraltextthataccompaniesthem.Likewise,inordertodemonstratethattheyunderstandamathematicalconcept,studentsarerequiredtoproduceanoraltext.Forexample,thepopularNewman’sErrorAnalysis(Newman1983)asksstudentsto“Tellmehowyouaregoingtoworkitout”and“Trydoingitandasyouaredoingittellmewhatyouarethinking”.Ingenrepedagogy,twoquestionswewouldaskhereare‘whatisthetextthatstudentsareaskedtoproduce’,and‘wheredidtheygetitfrom’.Theanswertothefirstquestionisanexplanationofamathsconceptora


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procedureforworkingoutaproblem.Theanswertowherestudentsgettheseoraltextsisfromtheirteachers.ThislattercontentionissupportedbyVygotsky’sobservationthat,

Anyfunctioninthechild’sculturaldevelopmentappearstwice...Firstitappearsbetweenpeopleasaninter-psychologicalcategory,andthenwithinthechildasanintra-psychologicalcategory”(1981:163).

An‘inter-psychologicalcategory’isofcourseaconceptthatisexchangedthroughlanguage,morespecificallygivenverballybyateachertoalearner.Mathematicalconceptsarenotspontaneouslygeneratedinthelearner’smindthroughnon-verbalactivities,theyalwaysinvolvealinguistictext.Thatis,mathematicalconceptsandoperationsdonotexistbeyondlanguage,butareconsititutedinlanguageandarelearnedthroughlanguage.Mathsconceptsarerealisedlinguisticallyasdefinitions.Forexample,onebasicdefinitionthatchildrenareexpectedtolearninthefirstyearsofschoolisaddition:

Additionisfindingthetotal,orsum,bycombiningtwoormorenumbers.3Alreadythisdefinitioninvolvessevengeneral,abstractortechnicalterms,variouslyrelatedtoeachotherinasinglesentence,addition,finding,total,sum,combining,twoormore,numbers.Thesetermscannotbeunderstoodbyyoungchildrenwithoutconcretelyexperiencingtheactitivitestheyrepresent.Thisistheintuitivebasisforthehands-onactivitiespromotedinprogressivemathspedagogy,withoutrecognisingthemediatingroleofteachers’accompanyingoraltexts.Noamountofmovingobjectsfromonegrouptoanothercanteachchildrenhowtointerpretthedefinitionofaddition,withoutunderstandingthelanguagethataccompaniestheseactivities.Infact,theconceptofadditionisdefinedherebytheoperationinwhichitisperformed,intwosteps.Firstitisdefinedasageneralmathematicalprocess‘findingthetotalorsum’,whichsummarisesthepurposeoftheoperation,andthenasamorespecificmathematicalprocess‘bycombiningtwoormorenumbers’,whichsummarisesthestepsintheoperation.Thus,theconceptofadditionisinseparablefromtheprocedureforaddingtwoormorenumbers.Theprocedureisprimaryandthedefinitionflowsfromit.Inordertounderstandthedefinition,learnersmustfirstunderstandtheprocedureitrefersto.Thislearningsequencecontradictstheacceptedmaximincontemporarymathslearningtheory,thatchildrenmustfirstlearntheconceptbeforetheycanperformtheoperation.Thismaximderivesfromtheprogressive/constructivistobjectionto‘rotelearning’.Rotelearningisconstruedinthisframeworkasmeaninglessrepetitivebehaviourswithoutanydepthofunderstanding.Thustraditionalmathsactivitiesthatweredesignedtomemoriseelementsofnumeracy,suchaschantingtimestables,havebeenabandonedinprogressivemathspedagogy,withinevitableconsequencesforskillsthatdependonmemorysuchasmentalarithmetic.

3fromhttp://www.mathsisfun.com/definitions/addition.html


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Theprogressive/constructivistobjectiontorepetitivepracticeisaphilosophicalpositionratherthananempiricalconclusionbasedonobservation.Theresearchreportedonhereshowsthatunderstandingactuallyemergesfromsuccessfulperformanceofoperations.So-calledmathsconceptsareactuallydistillationsofmathsoperations,asshownforadditionabove.Tounderstandeachconcept,studentsmustfirstlearntodotheoperation.Firstly,thepurposeoftheoperationcanonlybeunderstoodbyexperiencingitsoutcome.Thatis,theconceptof‘totalorsum’canonlybeunderstoodthroughtheactofadding,accompaniedbyaverbalprocedure.Secondly,thetermsusedinthedefinitions,suchasfinding,total,sum,combining,twoormorenumbers,arelearntintheprocessofdoingtheactivitiesthattheyreferto.Theoraltextthataccompaniestheoperationmediatesbetweentheactivityandthecomprehensionoftheseterms,asitpresentsthesetermsincontext,inrelationtothethingsandactivitiestheyrepresent.Thusifstudentsdonotunderstandandremembertheprocedure,theywillnotunderstandthetermsthatrefertoitsstepsandresults.Twodifficultiesformathspedagogyinrecognisingthelinguisticbasisofmathslearningarethati)mathematicsinvolvesawrittensymbolsystemthatappearstobeindependentofverballanguage,andii)theverbaltextsthataccompanymathsoperationsareprimarilyoralandsoappearnottobetextsatall.Infact,themathematicalsymbolsystemisnotindependentofverballanguage,butisalwaysaccompaniedbyanoraltextwhenitistaughtanddiscussed.Theproblemformathspedagogyisthattheseoraltextsareinvisible.

Asocialsemioticsolution

ThesolutiondevelopedinReadingtoLearnisnottoreplacecurrentmathslearningactivities,buttomaketheoraltextsthataccompanythemmoreexplicitandeasierforallstudentstoacquire.Tothisend,wecandrawonHalliday’s1993:112observationthat,

Alllearning-whetherlearninglanguage,learningthroughlanguage,orlearningaboutlanguage-involveslearningtounderstandthingsinmorethanoneway…Teachersoftenhaveapowerfulintuitiveunderstandingthattheirpupilsneedtolearnmultimodally,usingawidevarietyoflinguisticregisters:boththoseofthewrittenlanguage,whichlocatetheminthemetaphoricalworldofthings,andthoseofthespokenlanguage,whichrelatewhattheyarelearningtotheeverydayworldofdoingandhappening.Theoneforegroundsstructureandstasis,theotherforegroundsfunctionandflow.

Withrespecttomathslearning,mathsoperationsforeground‘functionandflow’forwhichoralproceduresarewelladapted,withtheirsequencesofstepsandcontingenciesforsolvingparticularproblems.Incontrast,mathsdefinitionsforeground‘structureandstasis’,astheyequateonemathematicalabstractionwithanother.Withrespecttolearningmultimodally,modesoflanguagevaryintwodimensions,i)inrelationtointeractionasdialogueormonologue,whichmaybespokenorwritten,andii)inrelationtotheactivityconstruedbyatext,eitheraccompanyingtheactivityorconstitutingit.Hallidayreferstotextsthataccompanyanactivityas‘language-in-action’,andtotextsthatcreatetheirownfieldas‘language-as-reflection’.


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Theoralproceduresthataccompanymathsoperationsareexamplesoflanguage-in-action.Suchtextsunfoldcontingently,referringtotheactivitiesandthingsthattheyaccompany,oftenusingreferencewordslikethis,that,here,there.Thesearecharacteristicsofteachers’oraldiscourseasworkedexamplesgoup,step-by-stepontheclassroomboard,oraschildrenmanipulateobjects.Onedifferencefromeverydayoraldiscourseisthetechnicaltermsthatalsopepperteachers’mathsdiscourse.Ontheotherhand,mathsdefinitionsareexamplesoflanguage-as-reflection.Theypresentthedynamicfunctionandflowofmathsoperationssynopticallyasstructureandstasis.Theunfoldingstepsofaprocedurearereconstruedasarelationbetweenatechnicalterm,suchasaddition,andadistillationoftheprocedureasageneralisedactivity‘findingthetotalorsum’.Learningmathsthusinvolvesthecomplementaritybetweenunfoldingoperationsandthestaticdefinitionsthatdistillthem.Intermsofinteraction,theteacher’stextistypicallyanoralmonologue.Studentsmustattendtothewordsofthemonologueandindependentlyrecognisethecomplexrelationsbetweenwhatissaidandtheworkedexamplethatisbeingconstructedontheboard.Iftheoperationisdemonstratedmorethanonce,theaccompanyingdiscoursemaybecomemoredialogic,astheteacheraskstheclasstorememberwhatcomesnext.Howeversuchclassroominteractionsareusuallybetweenteachersandafewstudentswhorespondtotheirquestions.Itisagainlefttomostofclasstoindependentlyrecogniserelationsbetweentheoraldiscourseandtheworkingsontheboard.Bywayofexample,apopularearlyyearsactivityfordemonstratingtheconceptofadditioniswitha‘numberline’,asfollows.Firsttheteacherwritesasumontheboardandreadsitaloud,suchas23+45.Thenahorizontallineisdrawnontheboard,andthelargestnumberiswrittenatthestartoftheline(45).Thedigitsintheothernumberarethenlabelledastens‘T’orones‘O’(T/2andO/3).Alargearcor‘jump’isthendrawnalongthelineforeachofthe‘tens’,andthenumber10iswrittenaboveeachjump.Thenumberoftensisthenaddedtothelargenumberattheendofthelastjump(65).Asmallerarcisthendrawnalongthelineforeachofthe‘ones’,andthenumberofonesisaddedtothenumberoftensattheendofthelastjump(68).Thisansweristhenwrittenforthesumas23+45=68.ThenumberlineisshowninFigure1.Figure1:Numberline

Assimpleasthediagramappears,theactivityofdrawingit,asrecountedabove,isactuallyquitecomplicated,andtheteacher’soraltextthataccompaniesitmaybeevenmorecomplex.Yetthisisoneofthesimplestoperationsintheentiremathscurriculum.Whatisthesolutiontothesetwinproblemsofmultimodalcomplexityandlimitedclassroominteractivity?Tomanagecomplexityofthelarningtask,thegeneralstrategyappliedin


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ReadingtoLearnisknownasguidedrepetition.Theprincipleisthatlearnersgenerallyneedmodellingandguidancebeforetheycansuccessfullycompletealearningtaskindependently.Modellingmeansshowinglearnershowtodoatask,whichiswhatteachersdowithworkedexamplesinmaths.Thedifficultyformoststudentsisthattheyarethenrequiredtoindependentlyperformassociatedmathsproblemswithoutsufficientguidedpractice.Guidedrepetitionmeansrepeatedlyguidinglearnerstopractisethelearningtask,withincreasinghandoverofcontrol,untiltheyarereadyforindependentpractice.Toensurethatalllearnersareequallyengagedintheguidedpractice,teachersdeliberatelydirecttheirinteractionstospecificstudents,oncetheyareconfidentthateachstudentcanrespondsuccessfully.

Aprocedureforguidingmathslearning

Guidedrepetitionwithmathsoperationsbeginswiththeteachercarefullyanalysingandplanningexactlythewordsthatwillbespokenineachstepofaworkedexample.Thesewordsformadetailedlessonplan.HereisanexampleplannedbyateacherofYears1-2,fortheoperationAdditionwithanumberline.

1. Readthesum.2. Drawanumberline.3. Putthebiggestnumberatthestartofthenumberline.4. Splittheothernumberintotensandones.5. Maketensjumpsonthenumberlineandwrite10aboveeachjump.6. Countonintenstofindwhereyouland.7. Makeonesjumpsonthenumberline.8. Countoninonestofindwhereyouland.9. Writeyouranswer.

Thereareseveraltermsinthissimpleprocedurethatexpectpriorlearning,includingsum,biggestnumber,tens,ones,counton,answer.Itassumesthatchildrenhavealreadylearntthedecimalnumbersystem,andtoordernumbersbytheirvaluesasbiggerorsmaller,andtoaddby‘countingon’fromthefirstnumber.Thelessonmaybeginbyreviewingtheseconcepts,inrelationtothefirstsumtobesolved,thatiswrittenontheboard.Forexample,45isbiggerthan23becausethe‘tens’number4isbiggerthan2.Theteacherthendemonstratesaworkedexample,asinordinarypractice,butthistimeusingtheexactplannedwordsforeachstepintheprocedure.Theprocedureisthenrepeatedwithadifferentexample,butnowtheteacherstartsaskingtheclasswhateachstepwillbe,andelaboratesontheirresponseswiththeexactplannedwordings.Bythethirdexample,theteachercandirectthesequestionstoindividualstudents,particularlyweakerstudents,sothatallcanrespondsuccessfullyandbeaffirmed.Thisisthefirststepinhandingovercontroltothestudents.Thenextstepisforstudentstostartscribingtheworkingsontheboardinsteadoftheteacher,astheclasstellsthemwhattodoateachstep,withtheteacher’sguidance.Againtheteacherensuresthatweakerstudentsareactivelyinvolvedinthisactivity,andcontinuallyaffirmed.


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Afterworkingthroughtwoorthreeexamplesontheclassboard,studentsthenpracticefurtherexamplesonindividualboards,applyingthesameprocedure,againwiththeteacher’sguidanceasnecessary.Theadvantageofindividualboardsisthatstudentscanself-correcterrorsastheyworkandtheteacherguidesthem.Markerpensorwater-basedcrayonsareusedthatcanbeeasilyerasedandcorrected.Unlikestandardproblemsolvinginmathsworkbooks,thisactivityisstrictlyaguidedlearningactivity,andisnotconflatedwithanassessmenttask.Aftertwoormoreworkedexamplesonindividualboards,theclassjointlyconstructsawrittenprocedurefortheoperationontheclassboard.Thisjointconstructionrecordsthewordsthathavebeenusedrepeatedlyforeachstepintheprocedure.Studentstaketurnstowritetheprocedureontheboard,astheclasssayseachstep,withtheteacher’sguidance,andstudentswritethetextintheirmathsworkbooks.Atthispointstudentsreturntotheindependenttasksofstandardmathspractice,practisingtheoperationtheyhavelearntbysolvingproblemsonwhichtheywillbeassessed.Nowhoweverallstudentsgetmostoftheirproblemscorrect,benefitfromthepractice,canself-correcttheirerrors,andcanexplainhowtheysolvedeachproblem.Insum,eachrepetitionoftheprocedureinvolvesincreasinghandovertothestudents,beginningwithsayingbackthewordstheteacherhasused,followedbyjointlyscribingexamplesontheboardwithguidance,thenindividualpracticewithguidance,untilallstudentsarereadyforindependentpractice.Figure2showsanexampleofaYear2student’sworking,usinga‘numberline’tocalculateanadditionproblem.

Figure2:Student’sworking(additionwithanumberline)

Followingthestepsintheprocedure,thechildhas

• writtenthesum(23+45=),• drawnanumberline,• writtenthebiggestnumber45atthestart,• splittheothernumber23intotens(T)andones(E),• madetwotensjumpsandwritten10aboveeachjump,• countedonintensandwritten65,• madethreeonesjumps,• countedoninonesandwritten68,• writtentheanswer68inthesumatthetop.


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Thisstudent’ssuccessderivesnotonlyfromrepeatedguidedpracticewiththeprocedure,butalsofromitsrecontextualisationasajointlyconstructedwrittentext.Writingtheproceduredownhasthreeeffects.Firstlytheactofjointconstructiongiveseachstudentmorecontroloverthewordstheyhavelearnttosayandunderstandastheoperationwasperformed.Secondlytheactofwritingandreadingthejointtexthelpsstudentstorememberit.Andthirdly,capturingthedynamicflowoftheoralprocedureasawrittentextallowstheclasstoreflectonitsstructuresandfunctions,todiscusswhatisdoneateachstepandwhy.Notonlycanstudentsuseanddiscussitinclass,buttheycantakeithome,sothattheirparentscanalsounderstandandsupporttheirmathshomework.

ProjectmethodologyTheStockholmprojectwasconductedoverthreemonths(SeptembertoDecember2010).Elevenschools4participatedintheprojectwithatotalof20teachersofgrades1-6,teachingaround500studentsaltogether.

Participatingstudents

Thestudentswhoparticipatedformedamostheterogeneousmixasthestudentpopulationsoftheparticipatingschoolswereverydifferent.Atsomeoftheschoolsover90%ofthestudentsweresecondlanguagelearners,whilestudentsfromotherschoolshadanexclusivelySwedish-speakingbackground.Thesocio-economicstatusoftheneighbourhoodswheretheschoolsweresituatedalsovaried.Thesedifferencesgaverisetonumerousfruitfuldiscussionsamongteacherssincetheyhadtoagreetoworkinasimilarmannerwithstudentgroupsthatdifferedinmanyways.

Teachertraininginthestrategies

TobeginwiththeteachersattendedatwodayworkshopwheretheywereintroducedtogenrepedagogyandtheReadingtoLearnstrategiesandcomparedthisapproachwithothermathslearningtheories.Theteachersthenformedgroupsaccordingtotheyearlevelsoftheirstudentsandstartedtoplantheworktheyweregoingtodointheirclassrooms.Inordertobeabletocomparethemethodandresultsbetweendifferentschools,allteacherswhotaughtthesameyearlevelagreedtocoverthesametopicswiththeirstudents.Thereafterfollowedaperiodwhenteacherswereworkingintheirclassroomswiththeirselectedmathematicalareas.Thestudentsweregivenapretestinthechosenmathematicalfield,usingthescreeningtests‘ALP1-8’(Malmer&Gudrun2001).TheALPscreeningtestsarecommonlyusedinSwedishschools.Allteachersineachgroupimplementedthesamelessonplansintheirclasses.Data,lessonplans,videoclips,studentsolutions,andwrittenteacherreflectionswerecollected.Theprojectleadersthenvisitedalltheteachersattheirrespectiveschoolstodiscusstheclassroomimplementation.

4SchoolswereTullgårdsskolan,Husbygårdsskolan,Sturebyskolan,Snösätraskolan,Johannesskola,Vinstaskolan,Knutbyskolan,Bagarmossen/Brotorp,Skönstaholmsskolan,Hökarängsskolan,KatarinaNorraskola


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Afterafewweekstheteachersattendedasecondhalfdayworkshopwheretheydiscussedtheirprogressintheclassroom,decidedhowtoproceedandplannedforthenextstageofparallelclassroomactivity.Followingseveralmoreweeksofclassroomimplementationtheteachersmetforathirdhalfdayworkshop.ThenbeforethefourthandfinalonedayworkshopthestudentsweregiventheALPscreeningtestagain.Intheworkshoptheposttestresultswerecomparedtothepretestresultsfromthebeginningoftheproject.Theoutcomesoftheprojectwerediscussedandthedifferentgroupssummarizedtheworkthathadtakenplaceandwhattheresultshadbeen.Eachgroupthengaveashortpresentationontheirfindingstothewholegroup.

Datacollection

Thefollowingdatawerecollectedduringtheproject:• Resultsofpreandposttests• Video-recordedlessons• Lessonplansformathstopics• Students'writtensolutionstomathematicaltasks• Teachers'reflectionsonthenewpedagogicalstrategies.Eachteacherselectedsixrepresentativestudentsfordatacollection:twothattheyperceivedashighperforming,twoaverageperformingandtwolowperformingstudentswhosetestresultswerecollected.Thepurposewastomeasuretherelativevalueofthestrategiesforeachofthesestudentgroups,andtheeffectsontheachievementgapbetweengroupsineachclass.Teacherswerealsoaskedtopayattentiontohowthestudentsreactedtothenewteachingstrategiesthattheteacherused.

Projectoutcomes

Preandposttestresults

Resultsofpreandposttestsshowedimprovementforallstudentgroups,overthetwotermsofimplementation,asshowninFigure3.Atthestartoftheprojectthelowperformingstudentsattainedanaverage55%onpretests,themiddlegroupsattainedanaverage67.5%andthetopgroupsanaverage86.3%.Intheposttests,thelow-performinggroups’resultsincreasedby22.8%,themedium-performingby20.3%,andthehighperforminggroupby4.1%.


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Figure3:Preandposttestresults(%)

Withrespecttotheachievementgapbetweenstudents,theaveragedifferencebetweenthelowperformingandhighperformingstudentgroupswas31.3%inthepretest,butintheposttestthedifferencewasreducedto12.6%,representingan18.7%reductionintheachievementgap.Theaveragedifferencebetweenthemiddleandhighperforminggroupsdecreasedfrom18.8%tojust2.6%.Furthermore,teachersinthreeclasseswithahighproportionofsecondlanguagelearnersemphasizedthatsecondlanguagelearnersconsistentlyshowedthemostdramaticimprovementinperformance.Forexample,testresultsshowedthatinoneYear3class,secondlanguagelearnersmadegainsofupto35%,withthelowerperformingstudentsmakingthegreatestgains,asshowninTable1andFigure4.

Table1:PreandposttestresultsforsecondlanguagelearnersinYear3 Pretest PosttestStudent1 90 93Student2 85 97Student3 77 78Student4 77 82Student5 73 73Student6 72 87Student7 68 90Student8 65 65Student9 48 68Student10 42 77Student11 35 62Student12 7 37


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Figure4:Trenddatashowinghighergainsforlowerperformingstudents

Whilealmostallstudentsshowedsignificantgains,Figure4showsthatthreestudentsinthemiddleperformingrange(students3,5and8)apparentlymadelittlegainbetweenthepreandposttests.Theseresultsparticularlystandoutagainstthehighgainsmadebystudents6,7,9,10,11and12.Howeveritshouldbenotedthatstudents3,5and8werealreadyachievingwellandhavesustainedthatachievementlevel.Neverthelessthelargeimprovementsdemonstratedbytheotherstudentsindicatesthatstudentswhomakerelativelylittlegainrequirecloserattention.5

Teachers’commentsonstudentlearning

Intheevaluationoftheproject,participatingteachersreportedthatthepedagogyhadmadeagreatimpactonstudentengagement.Thestudentswereengagedinthelearningprocessatamuchdeeperlevelthantheywereusedto.Someteachersexpressedsurprisethatstudentswereabletomaintainfocusoveramuchlongertimethanusualwhentheteacherusedthenewpedagogy.72%ofteachersfeltthatthepedagogyhadledtoincreasedinterestinmathematicsamongtheirstudents.(Theremainingteacherswereworkingwithstudentswhowerenewtothem,andsowereunabletomeasureachangeinstudents’attitudes.)SeveralteacherscommentedthatthegapbetweenthehighandlowperformingstudentsdecreasedwhentheteacherappliedtheReadingtoLearnpedagogy.Oneteachersaiditwas“obviousthatthegapbetweenthefastandtheslowerstudentsdecreases,theslowsucceedquickly,understandmathematicalproblemsandhowtosolvethem.”Allteachersreportedthatthelowperformingstudentsweretheoneswhobenefitedthemostfromthepedagogy,butthatmanystudentsinthemediumperforminggroupalsomadegreatimprovements.Amongthehighperformingstudents,improvementwasnotaspronouncedasintheothergroups,buttheteacherscommentedthatthehighperformingstudentshad

5Thisanomalyhasoftenbeenobservedinotherwholeclassassessments,i.e.2-3studentsinthemiddlerangewhoappeartomakerelativelylittlegrowth.Thesestudents’averagesuccessmaymasktheiractuallearningneeds.Suchassessmentsshowteacherswhichstudentsneedcloserattention.


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learnttoexplaintheirsolutionsmorearticulately.Thisappliedparticularlyinthehighergradelevels.Teachersalsoconsideredthatstudents’conceptualunderstandinghadincreased,particularlyamongsecondlanguagelearners.Inaddition,theyfoundthatstudentsusedmathematicalconceptstoagreaterextent.Theyinterpretedthisasaconsequenceofthestrongfocusonlanguageinthepedagogy.Theyalsoexpressedsurpriseathowmuchthestudentsappreciatedrepeating(alltogether)theverbalproceduresofhowaspecificmathematicaloperationshouldbesolved.Teachersreportedthatworkinginthisnewwaygavestudentsopportunitiestounderstandandusemathematicallanguage.Themajorityoftheteachersalsosaidthatthelowperformingstudents'self-confidencegrew.Thiswasnotedwithstudentswhonormallydidnotparticipateactivelyinclassroomdiscussionsaboutmathematicsandsolutionsofmathematicalproblem,butwhonowattendedwithjoyinthecommonconversationsandcommoneffortstosolvethemathematicaldetailsofthetasks.Accordingtooneteacher,astudenthadspontaneouslysaid“Atlastwehaveamodeltofollow!”Otherscommentedthat“Theweakestpupilsfeelthattheyarereallygood!”and“Thosewhopreviouslythoughtmathswasdifficultthoughtthatthiswasfun.”Teachersstatedthatallstudentswereinvolvedintheworkwhenusingthenewapproach.Manyweresurprisedbyhowfocusedthestudentswereduringthejointeffortstosolvemathematicaltasks.Oneteachersaidthatstudentsnowwantedtoparticipatebyprovidingpartofthesolutiontotheproblemandcomingtotheblackboardtowrite.“Sinceeachstudentonlyneedstowriteasmallpartofthesolutionwiththehelpoftheothers,itisnevertoodifficultandallsucceed.”Thiswasanewexperienceformanyteacherswhosaidthatitwasusuallyhardtogetallthestudentstocomeuptotheboardandwritesolutions,especiallythelowerperformingstudents,whooftenusedtoremaininactiveinlessons.Oneteachercommentedthat“Itisgoodthatthereisa‘speed’inthemethodology!Theydonothavetimetogettiredorbored!”Ontheotherhand,someteachersmentionedthatthehighperformingstudentssometimesgotboredwhilejointlyrepeatingthesamekindofproblemontheboard.Teachersagreedthatitwouldbeinterestingtoexplorewhatwouldhappentothesestudentsbyraisingthelevelfurther,whichtheythoughtwouldbepossible,oriftheywouldimplementavarietyof‘peel-offgroups’intheclassroom.6

Teachers'commentsabouttheirownlearning

Teacherreflectionsontheirownpracticewerecollectedbothduringtheprojectandattheend.Arepeatedreflectionwasthattheprojectwouldaffectandchangetheirteaching.Inparticular,teachersmentionedthattheyrealizedtheimportanceofteachingexplicitlyandnottoreferstudentstoindependentworkintheirmathsbookstooquickly.Theyemphasizedthattheynowunderstoodthattheyprobablyhaddemonstratednewarithmetictoofastpreviously,withtheresultthatmanystudentshadnotunderstood.6Peel-offgroupsreferstoamethodofgroupingthatbeginswiththeteacherworkingwiththewholeclassandthenallowinggroupsofstudentswhorequirelessscaffoldingtomoveontocompleteindependenttaskswhiletheteachercontinuestoworkwithotherswhorequiremoresupport.


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Teachersstatedthattheyhadnotunderstoodtheimportanceofjointconstructionbefore,butinthisprojectithadbecomeclearwhatanimpactworkingtogetherhasonstudentlearning.Theyfoundthatstudentslearnedmuchmorewhentheyhaveplannedindetailhowtoexplainmathematicstothemandthendevotedenoughtimetoguideclassestosolvetasks,withallstudentsactivelyparticipating.Severalalsocommentedthatbyusingthisapproachitispossibletoincreasethelevelofdifficultycomparedtowhatwasnormallypossible,becauseofallthescaffoldingthatisbuiltintothepedagogy.InFigure4,aYear2studenthaswrittendowntheprocedureusedtosolvethesuminFigure1above.

Figure5:Jointconstructionofmathsprocedure(studentcopy)

Englishtranslation

Idrawanumberline.Iwritedownthelargestnumber.Idividethesmallestnumberintotensandones.Iadd2tensand3ones.Iwritethesumasthesolutiontotheaddition.Theadditionis68.Ireadtheaddition.

Mostteacherscommentedthatasaresultoftheprojecttheyhavebecomeawareoftheroleoflanguageinthelearningprocess.Oneteachersaidthatshe's“nowthinkinginanalmosttotallydifferentwaythanbeforeandshehaslearnedanewwaytoactivelydevelopstudents’mathematicallanguage”.Examplesofotherreflections(translatedfromSwedish)included:

• IhavegotanewtooltousewhenIteach.• ForthefirsttimeitfeelslikeI’mdoingsomethingreallygood,realteaching.• Ihavelearnedawholenewattitudeandlearnttoclarifythelanguageof

mathematics.• Thepedagogyhasmademehaveagreaterfocusonlanguageandthemeaningof

concepts.• Thiswayofworkingallowedthinkingindetailaboutwordings,thelanguageoneuses

andmakesitclearnotonlyforthestudentsbutfortheteachersaswell.Genrepedagogyaddedanotherdimensiontoavariedway–andaveryeffectivewayitistoadd.


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• Thepedagogyrequiresmorepreparationbytheteacherbutyoucan"recycle"thestructureforothersimilarlessons.

• Youcanincreasethedegreeofdifficultywhenyousupportthisthoroughly.• IwasnegativewhenIsawtheexamplevideotapedlessons,butwhenItrieditmyself

Iwasverypleasantlysurprised!Thestudentswereveryactiveandnowhiningthattheygottired.Wecouldgoonandtogethersolveproblemafterproblemthroughoutthewholelesson.Otherwise,theytendtogetboredaftertenminutes.Ididnothaveto‘beg’themtowork!

Discussion

TheresultsofthissmallscalestudysuggestthattheReadingtoLearnstrategiesforteachingthelanguageofmathscansignificantlyimprovethemathsoutcomesandengagementofstudentsfromavarietyofbackgroundsandachievementlevels.Theaverageimprovementofmiddleandlowerperformingstudentsofaround20%intwomonthsismostencouraging.Althoughtheseresultswereachievedwitharelativelysmallsample(~500studentsintotal),theyareconsistentwiththefindingsofteachersinAustralia(Rose2012).Theyarealsosupportedbytheevaluationsofteachersintheproject,reportedabove,whoconsistentlyfoundthatthegapbetweenlowerandhigherperformingstudentsnarrowed.Theseresultsareparticularlynoteworthywhenviewedagainstmoretypicalgrowthratesinmathsoutcomes.Forexample,inAustraliaaseriesoflargescalestudieshavefoundthattherehasbeennosignificantimprovementinnumeracyoutcomesinrecentdecades(NSWAuditor-General2008,VictorianAuditor-General2009).Onelargestudyfoundthatnumeracyoutcomeshavenotimprovedsincecontemporarymathsteachingmethodswereintroducedinthe1960s(Leigh&Ryan2008).Oneexplanationforthissituation,offeredfromtheperspectiveofgenrepedagogy,isthatcontemporarymathslearningtheoriesmaynotadequatelyaccountfortheoraldiscoursethroughwhichmathsoperationandconceptsareacquiredbystudents.Inparticular,thesetheoriesemergedfromthecognitiviststanceofPiagetianpsychology,whichconstrueslearningasaprocessinternaltotheindividual,incontrasttosocial-psychologicallearningtheoriessuchasVygotsky’s,andsocialsemiotictheoriessuchasgenrepedagogy.Thus,whilethelearningactivitiesadvocatedbycontemporarymathslearningtheorymayenablesomestudentstoacquiremathsconcepts,afailuretoexplicitlyanalyseandplantheoralexchangesthroughwhichtheconceptsaretaughtmayleaveotherstudentswithinadequatesupport.Thegenrebasedstrategiestrialledinthisstudydonotseektochangethelearningactivitiesofcontemporarymathspractice.Theysimplymaketheoraldiscoursethataccompaniestheseactivitiesexplicitforbothteachersandstudents.Thisisachievedbytheteachercarefullyanalysingtheiroraldiscourse,exchangingitwithstudentsthroughacarefullyplannedseriesofrepeatedactivities,andtheclasswritingitdown.Asidefromenablingsignificantlymorestudentstoachievehighersuccesswithmathstasks,thisapproachhasanumberofassociatedadvantagespointedoutbyteachersabove.Firstlyitgivesteachersinsightsintothenatureoftheirownpedagogicdiscourse,notthroughacourseoflinguistics,butbybringingteachers’ownunconsciousknowledgeabout


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languagetoconsciousness.Thestartingpointforthisprocessof‘conscientization’7istonamethegenresofmathsteaching,andsoidentifytheirstructures–suchasthestepsinaprocedure.Fromthispointon,theanalysisandplanningdependsonteachers’knowledgeofthesubjecttheyareteaching,butthecontentofthesubjectandthelanguagethroughwhichitistaughtarenolongerdivorced.Teacherscometorecognisethattheyareoneandthesamething.Secondly,iteffortlesslyengagesallstudentsintheactivitiesofmathslearning,includingthosestudentswhoareotherwisealienatedandperceivethemselvesasunabletodomaths.Thisisachievedbytheprocessof‘guidedrepetition’whichensuresthatallstudentsarealwaysadequatelysupportedineachlearningstep,experiencecontinualsuccess,andarecontinuallyaffirmedbytheteacherandclass.Itisoftenassumedthatstudentsmustbeengagedinanabstractsubjectsuchasmathsbycontinuallyrelatingitbacktotheireverydayexperience.Thusmathsproblemsareconstantlycloakedineverydayscenariossuchasshopping,whichformanystudentsmerelyservestoobscurethemathematics.Butthekeystoengagingstudentsinschoollearningareactuallysuccessandaffirmation.Students’engagementreportedbytheteachersabove,andtheirconsequentgrowinginterestinsubjectmaths,derivefromtheirexperienceofsuccessasaresultoftheexplicitteachingstrategiesofReadingtoLearn.Thismayhaveimplicationsnotonlyforthemathsclassroom,makinglearningandteachingapleasure,butalsoforstudents’educationalandprofessionaltrajectoriesbeyondschool.Thirdly,teachersreportthatitimprovesstudents’understandingofmathsconcepts,andmakesitpossibletoincreasethedifficultyofthemathematicstheystudy.Twoofthecriticismsthathavebeenmadeofthepedagogy,bythosewhohavenotusedit,arethatitseemstoinvolverepetitiverotelearning,andthatstudentsarenotlearningindependently,sotheywouldnotacquirea‘deep’understandingofthemathsconcepts.Yetpractisingteachersfindthattheoppositeoccursasaresultofthestrategies.Theexplanationonceagainreturnstotheindivisibilityofschoolknowledgeandthelanguageinwhichitistaughtandlearnt,andtothesocialnatureoflearningasanexchangebetweenteacherandlearners.Thatis,studentsdeepentheirunderstandingofmathematicalconceptsastheyincreasetheircontrolofthetextsinwhichtheseconceptsareencoded.Thiscontrolincreasesthroughrepeatedexchangesbetweenteacherandstudents,inwhichtheteacherhandsovermorecontrolateachstep,untilstudentsarereadyforindependentpractice.Notonlycantheythensuccessfullyperformthemathematicaltasksexpectedofthem,buttheyhavethelanguageresourcestoexplainhowtheysolveproblemsandtheconceptsthatunderliethem.

Conclusionsandrecommendations

TheanalysisofboththequantitativeandqualitativedataintheStockholmpilotprojectindicatesthatthestrategiesdevelopedinReadingtoLearnfortheteachingofmathematicscanrapidlyreducetheachievementgapbetweenlower,middleandhigherperforming

7ConscientizationistheEnglishapproximationofPortugueseconscientização,meaning‘becomingaware’.InFreireanpedagogyitisgivenanideologicalinterpretation.Ihaveuseditheretodenotebecomingawareoflanguageingeneral.


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students.Furthermore,teachersreportthatallstudents’understandingofmathematicsbenefitsfromthesestrategies,albeitindifferingdegrees,andthattheirengagementandinterestinmathsmarkedlyimproves.Accordingly,wesuggestthatmoreteachershavetheopportunitytodevelopskillsinteachingmathematicsusingtheReadingtoLearnstrategies.Ideallythiscouldbeachievedusingcomparableprofessionaldevelopmentactivitiesasthosedescribedforthisproject.Inaddition,furtherprojectscouldexploreandevaluatehowthispedagogymayworkintheuppergradesofprimary,juniorandseniorsecondaryschoolsandinothermathematicalareas,andhowquicklythelevelsofdifficultyandabstractionmaybeincreasedasstudentsacquiremathematicalskills.Oneaspectofsuchprojectsmayalsoexaminehowvariationsofgroupactivitiescouldbeappliedintheclassroomtoextendstudents’learningatdifferentskilllevels.References:Acevedo,C.(2010)WilltheimplementationofReadingtoLearninStockholmschools

accelerateliteracylearningfordisadvantagedstudentsandclosetheachievementgap?AReportonSchool-basedActionResearch,MultilingualResearchInstitute,StockholmEducationAdministration,http://www.pedagogstockholm.se/-/Kunskapsbanken/

AfricanPopulationandHealthResearchCenter(2011).EducationResearch,http://www.aphrc.org/insidepage/page.php

Chen,J2010SydneySchoolGenre-basedLiteracyApproachtoEAPWritinginChina.PhDThesis,DepartmentofLinguistics,UniversityofSydney&SchoolofForeignlanguages,SunYatSenUniversity.

Childs,M.(2008)AreadingbasedtheoryofteachingappropriatefortheSouthAfricancontext.PhDThesis,NelsonMandelaMetropolitanUniversity,PortElizabeth,SouthAfrica

Christie,F.(2002)ClassroomDiscourseAnalysis:afunctionalperspective.London:Continuum

Christie,F.andJ.R.Martin(eds.)(1997)GenreandInstitutions:socialprocessesintheworkplaceandschool.London:Pinter(OpenLinguisticsSeries).

Cope,W&MKalantzis(eds.)(1993)ThePowersofLiteracy:agenreapproachtoteachingliteracy.London:Falmer(CriticalPerspectivesonLiteracyandEducation)&Pittsburg:UniversityofPittsburgPress(PittsburgSeriesinComposition,Literacy,andCulture).

Culican,S.(2006)LearningtoRead:ReadingtoLearn:AMiddleYearsLiteracyInterventionResearchProject,FinalReport2003-4.CatholicEducationOfficeMelbourne,http://www.cecv.melb.catholic.edu.au/ResearchandSeminarPapers

Dell,S2011.Readingrevolution.Mail&GuardianOnline,http://mg.co.za/article/2011-04-03-reading-revolution

Devlin,K2007.Whatisconceptualunderstanding?MAAOnline.TheMathematicalAssociationofAmerica,http://www.maa.org/devlin/devlin_09_07.html

Halliday,M.A.K.(2004)AnIntroductiontoFunctionalGrammar.2ndedn.London:Arnold.(1stedn,1994)

Koop,C.andRose,D.(2008)ReadingtoLearninMurdiPaaki:changingoutcomesforIndigenousstudents.LiteracyLearning:theMiddleYears16:1.41-6,http://www.alea.edu.au/

Leigh,A.andRyan,C.(2008)HowhasschoolproductivitychangedinAustralia?Canberra:AustralianNationalUniversity,http://econrsss.anu.edu.au/~aleigh/


18

Liu,Y2010.CommitmentresourcesasscaffoldingstrategiesintheReadingtoLearnprogram.PhDThesis,UniversityofSydney,SunYatSenUniversity.

Malmer,G.(2001)AnalysavLäsförståelseiProblemlösning,ALP-test1-8,Screeningtestfrånskolår2ochupptillvuxnaelever.Lund:FirmaBok&Bild/GudrunMalmer.

Martin,J.R.(2000)‘GrammarmeetsGenre–Reflectionsonthe‘SydneySchool’,Arts:thejournaloftheSydneyUniversityArtsAssociation.22:47-95

Martin,J.R.(2006)‘Metadiscourse:DesigningInteractioninGenre-basedLiteracyPrograms’,inR.Whittaker,M.O'DonnellandA.McCabe(eds)LanguageandLiteracy:FunctionalApproaches.London:Continuum.pp95-122.

Martin,J.R.&Rose,D.(2008).GenreRelations:MappingCulture.London:EquinoxNewman,M.A.(1983)Strategiesfordiagnosisandremediation.Sydney:Harcourt,Brace

JovanovichNSWAuditor-General(2008)StateofliteracyandnumeracyinNSW,

http://www.audit.nsw.gov.auVictorianAuditor-General(2009)LiteracyandNumeracyAchievement,

http://www.audit.vic.gov.auRose,D1997Science,technologyandtechnicalliteracies.inChristie&Martin.40-72.Rose,D.(2005).DemocratisingtheClassroom:aLiteracyPedagogyfortheNewGeneration.

JournalofEducation,37:127-164,www.ukzn.ac.za/joe/joe_issues.htmRose,D.(2008).Writingaslinguisticmastery:thedevelopmentofgenre-basedliteracy

pedagogy.R.Beard,D.Myhill,J.Riley&M.Nystrand(eds.)HandbookofWritingDevelopment.London:Sage,151-166

Rose,D.(2010).Beyondliteracy:buildinganintegratedpedagogicgenre.AustralianJournalofLanguageandLiteracy,SpecialEdition2010(alsoinProceedingsofASFLAConference,Brisbane,Oct2009www.asfla.org.au)

Rose,D.(2011).GenreintheSydneySchool.InJGee&MHandford(eds)TheRoutledgeHandbookofDiscourseAnalysis.London:Routledge,209-225

Rose,D.(2012).ReadingtoLearn:Acceleratinglearningandclosingthegap.TeachertrainingbooksandDVD.Sydney:ReadingtoLearnhttp://www.readingtolearn.com.au

Rose,D.andAcevedo,C.(2006)‘ClosingtheGapandAcceleratingLearningintheMiddleYearsofSchooling’,AustralianJournalofLanguageandLiteracy.14(2):32-45,http://www.alea.edu.au/llmy0606.htm

Rose,D.,D.McInnes&H.Korner.1992.ScientificLiteracy(WriteitRightLiteracyinIndustryResearchProject-Stage1).Sydney:MetropolitanEastDisadvantagedSchoolsProgram.308pp.[reprintedSydney:NSWAMES2007]

Rose,D.&J.R.Martin(inpress2011).LearningtoWrite,ReadingtoLearn:Genre,knowledgeandpedagogyintheSydneySchool.London:Equinox

vanMerrienboer,J.J.G.&Sweller,J.2005.CognitiveLoadTheoryandComplexLearning:RecentDevelopmentsandFutureDirections.EducationalPsychologyReview,17:2,147-175

Vygotsky,L.S.(1978).MindinSociety:TheDevelopmentofHigherPsychologicalProcesses,M.Cole,V.John-Steiner,S.Scribner&E.Souberman(eds),Cambridge,Mass,HarvardUniversityPress.

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