Upload
others
View
8
Download
0
Embed Size (px)
Citation preview
ReadingtoLearnMaths Lövstedt&Rose
1
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
ReadingtoLearnMaths Lövstedt&Rose
2
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).
ReadingtoLearnMaths Lövstedt&Rose
3
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
ReadingtoLearnMaths Lövstedt&Rose
4
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
ReadingtoLearnMaths Lövstedt&Rose
5
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’.
ReadingtoLearnMaths Lövstedt&Rose
6
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
ReadingtoLearnMaths Lövstedt&Rose
7
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.
ReadingtoLearnMaths Lövstedt&Rose
8
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.
ReadingtoLearnMaths Lövstedt&Rose
9
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
ReadingtoLearnMaths Lövstedt&Rose
10
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%.
ReadingtoLearnMaths Lövstedt&Rose
11
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
ReadingtoLearnMaths Lövstedt&Rose
12
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.
ReadingtoLearnMaths Lövstedt&Rose
13
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.
ReadingtoLearnMaths Lövstedt&Rose
14
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.
ReadingtoLearnMaths Lövstedt&Rose
15
• 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
ReadingtoLearnMaths Lövstedt&Rose
16
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.
ReadingtoLearnMaths Lövstedt&Rose
17
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/
ReadingtoLearnMaths Lövstedt&Rose
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.