building on what students already know

(c)CentreforResearchinMathematicsEducation,UniversityofNottingham2010 1

BUILDINGONWHATSTUDENTSALREADYKNOW

HowcanIrespondtostudentsinwaysthatimprovetheirlearning?

Introduction

Inquiry-basedteachingassumesthatstudentsdonotarriveatsessionsas‘blankslates’,butasactivelythinkingpeoplewithawidevarietyofskillsandconceptions.Researchshowsthatteachingismoreeffectivewhenitassessesandusespriorlearningsothattheteachingmaybeadaptedtotheneedsofstudents(Black&Wiliam,1998).Priorlearningmaybeuncoveredthroughanyactivitythatoffersstudentsopportunitiestoexpresstheirunderstandingandreasoning.Itdoesnotrequiremoretesting.Forexample,itcantaketheformofasinglewrittenquestiongivenatthebeginningofasessiontoelicitarangeofexplanationsthatmaythenbediscussed.Thisprocess,oftenreferredtoasformativeassessment,maybedefinedas:

"…allthoseactivitiesundertakenbyteachers,andbytheirstudentsinassessingthemselves,whichprovideinformationtobeusedasfeedbacktomodifytheteachingandlearningactivitiesinwhichtheyareengaged.Suchassessmentbecomes‘formativeassessment’whentheevidenceisactuallyusedtoadapttheteachingworktomeettheneeds."(Black&Wiliam,1998para,91)

Thismoduleconsidersthedifferentwaysthiscanbedoneandfocusesonthefollowingquestions:

• Howcanproblemsbeusedtoassessperformance?• Howcanthisassessmentbeusedtopromotelearning?• Whatkindsoffeedbackaremosthelpfulforstudentsandwhichareunhelpful?• Howcanstudentsbecomeengagedintheassessmentprocess?

ActivitiesActivityA: Introducingformativeassessment....................................................................................3ActivityB: Teachers'ownexperiencesofformativeassessment.......................................................4ActivityC: Principlesforformativeassessment..................................................................................6ActivityD: Analysestudents’responsestoproblem-solvingtasks.....................................................8ActivityE: Analysestudents’responsestoconcept-focusedtasks...................................................10ActivityF: Observeformativeassessmentinaction.........................................................................12ActivityG: Planandreportbackonanassessmentlesson...............................................................13ActivityH: Considertheeffectsoffeedbackonstudentlearning....................................................14Acknowledgement:Inpreparingthismaterial,weacknowledgethepermissionsgivenbytheBowlandCharitableTrusttoadapttheprofessionaldevelopmentresources,BowlandMaths,thattheyhadpreviouslyfundedustoproducefortheUK.Thisincludesmanyofthehandoutsandmostofthevideoextracts.AdditionalresourceswerealsoadaptedfromImprovingLearninginMathematics,agovernmentfundedprogramintheUK.Theoriginalsourcesare:Swan,M;Pead,D(2008).Professionaldevelopmentresources.BowlandMathsKeyStage3,BowlandTrust/DepartmentforChildren,SchoolsandFamilies.ObtainableintheUKfrom:http://www.bowlandmaths.org.uk.Swan,M;(2005).ImprovingLearninginMathematics,challengesandstrategies,DepartmentforEducationandSkillsStandardsUnit.ObtainableintheUKfromhttp://tlp.excellencegateway.org.uk/pdf/Improving_learning_in_maths.pdf


Relatedresearchtohelpyourplanningforthismodule.Black,P.,&Wiliam,D.(1998).Insidetheblackbox:raising

standardsthroughclassroomassessment.King'sCollegeLondonSchoolofEducation.NowpublishedbyGLAssessment:

http://shop.gl-assessment.co.uk

Thisshortbookletoffersasummaryoftheextensiveresearchliteratureintoformativeassessment.Itshowsthatthereisclearevidencethatimprovingformativeassessmentraisesstandards,andoffersevidenceshowinghowformativeassessmentmaybeimproved.Thisbookletisessentialreadingforallteachers.

Black,P.,&Harrison,C.(2002).Workinginsidetheblackbox:Assessmentforlearningintheclassroom.King'sCollegeLondonSchoolofEducation.NowpublishedbyGLAssessment:

http://shop.gl-assessment.co.uk

Inthisbooklet,theauthorsdescribeaprojectwithteachersinwhichtheystudiedpracticalwaysofimplementingformativeassessmentstrategiesandtheeffectthishadonlearning.Thesectiononfeedbackandmarking(pages8-9)areparticularlyrelevanttothismodule.

Black,P.,Harrison,C.,Lee,C.,Marshall,B.,&Wiliam,D.(2003).Assessmentforlearning:Puttingitintopractice.Buckingham:OpenUniversityPress.

ThisbookgivesafulleraccountoftheearlierbookletsInsidetheblackboxandWorkinginsidetheblackbox.Itdiscussesfourtypesofaction:questioning,feedbackbymarking,peer-andself-assessmentandtheformativeuseofsummativetests.Thesectiononfeedbackandmarking(pages42-49)isparticularlyrelevanttothismodule,whilethesectiononpeerandself-assessment(pp49-53)isrelevantforthenextCPDmodule.

Hodgen,J.,&Wiliam,D.(2006).Mathematicsinsidetheblackbox.

King'sCollegeLondonSchoolofEducation.NowpublishedbyGLAssessment:

http://shop.gl-assessment.co.uk Thisbookletappliestheabovefindingsspecificallyto

Mathematics.ItconsiderssomeprinciplesforMathematicslearning,choiceofactivitiesthatpromotechallengeanddialogue,questioningandlistening,peerdiscussion,feedbackandmarking,andselfandpeerassessment.Thisbookletisessentialreadingforallmathematicsteachers.


ACTIVITYA:INTRODUCINGFORMATIVEASSESSMENT

Minimumtimeneeded:10minutes.

Thedifferenttypesandpurposesofassessment.Inviteparticipantstodiscussthefollowingissues:

• Whydoyouassessstudents?• Whatdifferentpurposesdoyourassessmentsserve?Makealist.

Theirlistofreasonsmightinclude:diagnosingdifficulties;celebratingachievement;motivatingstudents;selectingstudentsforclasses;maintainingrecordstokeepteachersandparentsinformedofprogress;toassessteachingmethods.Tosummarize,therearetwomainpurposesofassessment:

• Summativeassessment-tosummariseandrecordoverallachievementattheendofacourse,forpromotionandcertification.Most‘highstakes’testsandexternalexaminationsaredesignedforthispurpose.Summativeassessmentisalsousedtoevaluatetherelativeeffectivenessofaparticularcourse,teachingmethod,orevenaninstitution.

• Formativeassessment–torecogniseachievementsanddifficultiesatthebeginningorduringacourse,sothatteachersandstudentscantakeappropriateaction.Thistypeofassessmentformsanintegralpartofalllearning.

Thepotentialofformativeassessmenttoimprovelearning.Brieflymentiontheresearchevidencethatsetsoutthecaseforformativeassessment.ThisissummarizedbyBlackandWiliaminseveralaccessiblepublicationsforteachers(seeopposite),mostofwhicharefreelydownloadableontheinternet.Theseresearcherssetouttofindoutwhetherornotimprovingformativeassessmentimproveslearning.“Wecheckedmanybooksandnineyears'worthofmorethan160journals,andearlierreviewsofresearch.Thisprocessyielded580articlesorchapterstostudy.Wepreparedareviewusingmaterialfrom250ofthesesources.All…studiesshowthat…strengthening…formativeassessmentproducessignificant,andoftensubstantial,learninggains.Thesestudiesrangeoverages,acrossseveralschoolsubjects,andoverseveralcountries…”(BlackandWiliam,1998).1Thismodulewillexaminetheimplementationofformativeassessment,basedonthisandotherresearch.Asecondmodulewillexploretheroleofselfandpeerassessment.

1PaulBlackandDylanWiliam,"AssessmentandClassroomLearning,"AssessmentinEducation,March1998,pp.7-74.


ACTIVITYB:TEACHERS'OWNEXPERIENCESOFFORMATIVEASSESSMENT


Whatdoteachersknowabouttheirstudentsandwhatconsequentialactiondotheytake?Askparticipantstoworkinpairs,consideringthefollowingquestions.

• Thinkoftwostudentsinyourclass,onewhoisparticularlystrongandonewhoisfindingtheworkverydifficult.Takeitinturnstodescribethestudents'strengthsanddifficultiestoyourpartner,inasmuchdetailaspossible.

• Howdidyoubecomeawareofthesestrengthsanddifficulties?Onwhatevidencedoyoubaseyourjudgements?Testresults?Memoriesoforalresponsesduringlessons?Observationsofthestudentworking?Writtenwork?

• Inwhatwaysdoyourassessmentsofthesestudentsaffectyourlessonplanning?Giveexamples.

Whatdifficultiesdoteacherencounter?IssueparticipantswithcopiesofHandout1:Difficultieswithformativeassessment.

• Howfararethecriticismsonthehandoutvalidinyourcontext?• Ifanyare,thenwhatmaybedoneaboutthem?


Handout1 Difficultieswithformativeassessment

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1 Black, P., & Wiliam, D. (1998). Inside the black box : raising standards through classroom assessment. London: King's College London School of Education 1998.


ACTIVITYC:PRINCIPLESFORFORMATIVEASSESSMENT


IssueparticipantswithacopyofHandout2.Theideaspresentedherearealldrawnfromresearchintoformativeassessment.

• BearinginmindthedifficultiesdiscussedinActivityB,howwouldyousuggestthatyourformativeassessmentpracticesbeimproved?

• DiscusstheprinciplesoutlinedonHandout2.o Whichofthesedoyoucurrentlyuseinyourownteaching?o Whichdoyoufindmostdifficult?Why?

• Whatotherprinciplesdoyouthinkareimportant?

IssuecopiesofHandout3.

"It'sallverywelltellingustoassessourstudents,buthowcanabusyteacherknowwhatisgoingoninside30individualheads?"

• Howwouldyouanswerthisteacher?• Whatstrategiesdoyouhaveforfindingoutwhat

studentsarethinkinginyourlessons?• DiscussthetwosuggestionsshownonHandout3,

andwatchthemoviestoseetheseinaction.• Suggestsomefurtherstrategiesformaking

reasoningmoreevident.

ThetwostrategiesdescribedonHandout3andonthemoviesaccompanyingthisactivitymayhelptomakereasoningmore'visible'.Mini-whiteboardsareanindispensableresourceforthefollowingreasons:

• Whenstudentsholdtheirideasuptotheteacher,itispossibletoseeataglancewhateverystudentthinks.

• Duringwholeclassdiscussions,theyallowtheteachertoasknewkindsofquestion(typicallybeginning:‘Showmeanexampleof....’).

• Theyallowstudentsto,simultaneously,presentarangeofwrittenand/ordrawnresponsestotheteacherandtoeachother.

Postersarealsoapowerfulwayofhelpingstudentstoexternalisetheirthinking.Thisusedoesnotrequire'polished','complete','attractive'productsbutrathertheyshouldbeseenasworkingdocuments.Perhapsthesimplestwayofusingaposterisforstudentstosolveaproblemcollaboratively,explainingthethoughtprocessesinvolvedateverystep.Aseconduseofpostersistofindoutwhattheyalreadyknowaboutagiventopic.InthediagramshownonHandout2,theteacheraskedstudentstowritedownalltheyknewabouty=2x-6.Asaclass,thediagramwasdevelopedonthewhiteboard.Studentswerethengivenavarietyofequations(thelevelofchallengewasvariedappropriately)andwereaskedtoproducetheirownposter.Thediscussionenabledtheteachertoassesshowmuchlearnersknewaboutequationsandhowwelltheywereabletolinktheideastogether.


Handout2:Principlesforformativeassessment

Handout3: Makingreasoningvisible.

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ACTIVITYD:ANALYSESTUDENTS’RESPONSESTOPROBLEM-SOLVINGTASKS

Minimumtimeneeded:20minutesHandout4presentsthreeproblemstogetherwithfourstudentresponsesoneach.Thetasksare:CountingTrees,CatsandKittens,SecurityCameras.

• Readthroughallthreetasksthenchooseonetaskthatwillbemostsuitableforaclassyouwillsoonteach.Ifyouareworkingonthismoduleinagroup,itwillbehelpfulifeachparticipantchoosesthesameproblem,asthiswillfacilitatethefollow-updiscussion.

• Considerthefourstudentresponses.Whatdoeseachstudent’sresponsetellyouabout

hisorhercapacitytouseeachoftheprocesses:represent,analyse,interpretandevaluate,communicateandreflect?

Handout5offerssomecommentsonstudents’responsestoeachofthetasks.

• Ifyouweretheteacherofthesestudents,whatfeedbackwouldyougivethem,tohelpthemimprovetheirresponses?Trytoframethishelpintheformoforalquestionsyoucouldaskintheclassroom.YoumayfindithelpfultorefertothegenericquestionsgivenonHandout6.

• Watchthevideoofthreeteachersdiscussingthefeedbacktheygaveonthethreeproblems.


Handout4: Assessmenttasksandsampleresponses

Handout5: Improvingstudents'responsesthroughquestioning

Handout6: Suggestionsforquestions

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ACTIVITYE: ANALYSESTUDENTS’RESPONSESTOCONCEPT-FOCUSEDTASKS

Minimumtimeneeded:20minutesOnHandout7,wepresentfourmathematicaltopicsandsomesamplestudentworkoneachone.Askparticipantstoassesseachresponseandtrytoidentifythereasoningthatliesbehindeachone.

• Whatdoesthestudentappeartounderstand?Whereisyourevidence?• Listtheerrorsanddifficultiesthatarerevealedbyeachresponse.• Trytoidentifythethinkingthatliesbehindeacherror.• Whatfeedbackwouldyougivetoeachstudent?

Therearetwocommonwaysofreactingtopupils'errorsandmisconceptions:(i)Avoidthemwheneverpossible:"IfIwarnpupilsaboutthemisconceptionsasIteach,theyarelesslikelytohappen.Preventionisbetterthancure."(ii)Usethemaslearningopportunities:"Iactivelyencouragepupilstomakemistakesandlearnfromthem.

• Whatisyourview?

Routinepracticeonstandardproblemsdoeslittletohelpstudentsovercomecommonmistakesandmisconceptionsinmathematics.Thisisparticularlytruewhenteacherstrytoavoiddifficultiesarisingbybeginningeachlessonwithexplanationsanddemonstrationsandfollowingthiswithcarefullygradedquestions.Handout8isaone-pageresearchreviewbyAskewandWiliam.ThisdescribessomeresearchthatwasconductedinBritainoverthepast30yearsondealingwithstudenterrorsanddifficulties.Whatdoteachersfeelaboutthedilemmaspresentedinthispaper?-isitpossibletopresentexampleswhererulesdonotwork?-doteacherssharetheviewthatitiscounter-productivetoteachsimplerexamplesbeforemorecomplexexamples?


Handout7: Assessmenttasksandsampleresponsesforconcepts

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ACTIVITYF: OBSERVEFORMATIVEASSESSMENTINACTION

Timeneeded:15minutes.

Inthisactivity,youareprovidedwithvideoextractsofAndrew,DominicandAmyexploringhowformativeassessmentmaybeusedtopromotestudentslearning.TheyareusingthethreetasksfromActivityD.Inanearlierlesson,theseteachershadaskedstudentstositindifferentplacesandattemptoneofthetasksindividually,withnohelp.Theythencollectedintheirstudents'responses,assessedtheworkqualitativelyandpreparedwrittenfeedbackintheformofquestions.Thefilmclipsyouareabouttoseearetakenfromthefollow-uplesson.Studentshavereturnedtotheirnormalplacesandmosthavesolutionsthataredifferenttothoseoftheirpartners.Watchthevideoandconsider:

• Whatdifferentkindsofassessmentcanyousee?• Whatisthepurposeofeachkindofassessment?• Whatdoboththeteachersandstudentslearn?

Inthevideo,youwillsee:

• Andrewexploringhowstudentsrespondtohisfeedbackonthe"countingtrees"problem;• Amylisteningto,thenquestioningindividualsastheytrytosharetheirideasandproduce

jointsolutionstothe"securitycamera"problem;• Dominiclisteningtopresentationsfromstudentsontheirmethodsandreasoningforthe

"catsandkittens"problem;• Amyconcludingherlessonbyaskingstudentstodescribehowtheyhaveusedherfeedback

toimprovetheirwork.


ACTIVITYG:PLANANDREPORTBACKONANASSESSMENTLESSON

Minimumtimeneeded: 30minutesbeforethelesson 20minutesforthepre-lessonassessment 30minutestopreparefeedback 60minutesforthelesson 15minutesforreportingback

PlanningthelessonPlanyourownlessonusingoneoftheproblems.

• Planatimeforstudentstotackletheproblemontheirownwithouthelp.

• Planhowyouwillassessthiswork,givefeedbackandconductafollowuplesson.

• Collectsamplesofstudents'worktoshowhowtheirthinkinghaschanged.Thesewillbediscussedatthefollow-upsession.

Tohelpyourplanning,youmaynowliketowatchthe10-minutevideothatshowsAndrewteachingtheCountingTreesproblemfromActivityD.HeisfollowingthelessonplanonHandout9.

Andrew'slesson

Thepatternofactivitiesonhandout9isasfollows:

• Givetheproblembeforethelessonandaskstudentstoattemptit.(20minutes)

• Collectintheworkandpreparesomeconstructive,qualitativefeedback.

• Inthefollow-uplesson,reintroducetheproblemtotheclass.(5minutes)

• Studentsworkalone,respondingtothefeedbackusingminiwhiteboards.(5minutes)

• Studentsworkinpairstoimprovetheirsolutions.(10minutes)• Studentssharetheirapproacheswiththeclass.(15minutes)• Studentscontinuewiththeproblemorextendtheproblem.(20

minutes)

Handout9:Aformativeassessmentlessonplan

ReportingbackonthelessonAfteryouhavetaughtthelesson,reflectonwhathappenedwithagroupofcolleagues.Takeitinturnstosharestoriesoftheassessmentstrategiesyouused.

• Howdidyoucollectandassessevidenceofyourstudents'work?• Whatdidyoulearnfromthisevidence?• Whatdidstudentslearnfromthefollow-uplesson?• Whataretheimplicationsforyoumathematicsteachingmoregenerally?

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ACTIVITYH:CONSIDERTHEEFFECTSOFFEEDBACKONSTUDENTLEARNING

Timeneeded:20minutes.

Sofarwehavefocusedontheteachers’roleinprovidingassessmentfeedbacktostudents.Inthisactivitywewillconsidertheusestudentsmakeofdifferenttypesoffeedbackandtheimpactthishasontheirlearning.WatchthevideoofAndrew'sstudentsastheydiscusstheimpactofassessmentfeedbackontheirlearning.

• Whichoftheircommentsstrikeyouasparticularlyperceptiveandimportant?

• Whataretheimplicationsoftheircomments?

Handout10presentssomeresultsofresearchfromBlackandWiliam(1998)intotherelativemeritsoffeedingbackassessmentinformationtostudentsindifferentforms.Inparticularitcomparestheeffectsoffeedingbackquantitativeinformationintheformofmarks,levelsandrankingswiththeeffectsofofferingqualitativeinformationintheformofspecific,content-focusedfeedback.Comparethestudents'commentswiththeresearchquotesgivenonHandout9.Thedangersofgivingmarks,levels,rewardsandrankings

• Whataretheimplicationsofthisforyourpractice?• Whatwouldhappenifyoustoppedgivingmarksorlevelsonpupils’work?• Whyaresomanyteachersresistanttomakingthischange?

Theadvantagesofgivingclear,specific,content-focusedfeedback

• What are the implications of this for your practice? • Does this kind of feedback necessarily take much longer to give?

Researchshowsthatstudentsbenefitmostfromfeedbackthat:• Focusesonthetask,notongradesorscores.• Isdetailedratherthangeneral.• Explainswhysomethingisrightorwrong.• Isrelatedtoobjectives• Makesclearwhathasbeenachievedandwhathasnot• Suggestswhatthestudentmaydonext• OffersspecificstrategiesforimprovementConcludethismodulebydiscussingsomewaysofapplyingwhatyouhavelearnedinthisPDmoduletotheothermathematicslessonsthatyouteach.

• Howcouldyouinvolvepupilsinimprovingyourassessmentpractices?


Handout10:Theeffectsoffeedbackonstudentlearning

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