Introducing formative assessment guide
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(c) Centre for Research in Mathematics Education, University of Nottingham 2010 1 INTRODUCING FORMATIVE ASSESSMENT How can I assess students in ways that improve their learning? Introduction Mathematics teaching assumes that students do not arrive at sessions as ‘blank slates’, but as actively thinking people with a wide variety of skills and conceptions. Research shows that teaching is more effective when it assesses and uses prior learning so that the teaching may be adapted to the needs of students (Black & Wiliam, 1998). Prior learning may be uncovered through any activity that offers students opportunities to express their understanding and reasoning. It does not require more testing. For example, it can take the form of a single written question given at the beginning of a session to elicit a range of explanations that may then be discussed. This process, often referred to as formative assessment, may be defined as: "… all those activities undertaken by teachers, and by their students in assessing themselves, which provide information to be used as feedback to modify the teaching and learning activities in which they are engaged. Such assessment becomes ‘formative assessment’ when the evidence is actually used to adapt the teaching work to meet the needs." (Black & Wiliam, 1998, p. 91) This module considers the different ways this can be done and focuses on the following questions: • How can problems be used to assess performance? • How can this assessment be used to promote learning? • What kinds of feedback are most helpful for students and which are unhelpful? • How can students become engaged in the assessment process? Activities Activity A: What is formative assessment? ........................................................................................ 3 Activity B: Teachers' own experiences of formative assessment ....................................................... 4 Activity C: Principles for formative assessment .................................................................................. 6 Activity D: Analyse students’ responses to problem-solving tasks ..................................................... 8 Activity E: Analyse students’ responses to concept-focused tasks ................................................... 10 Activity F: Observe formative assessment in action ......................................................................... 12 Activity G: Plan and report back on an assessment lesson ............................................................... 13 Activity H: Consider the effects of feedback on student learning .................................................... 14 Acknowledgement: In preparing this material, we acknowledge the permissions given by the Bowland Charitable Trust to adapt the professional development resources, Bowland Maths, that they had previously funded us to produce for the UK. This includes many of the handouts and most of the video extracts. Additional resources were also adapted from Improving Learning in Mathematics, a government funded program in the UK. The original sources are: Swan, M; Pead, D (2008). Professional development resources. Bowland Maths Key Stage 3, Bowland Trust/ Department for Children, Schools and Families. Obtainable in the UK from: http://www.bowlandmaths.org.uk. Swan, M; (2005). Improving Learning in Mathematics, challenges and strategies, Department for Education and Skills Standards Unit. Obtainable in the UK from http://tlp.excellencegateway.org.uk/pdf/Improving_learning_in_maths.pdf
Transcript of Introducing formative assessment guide
(c)CentreforResearchinMathematicsEducation,UniversityofNottingham2010 1
INTRODUCINGFORMATIVEASSESSMENT
HowcanIassessstudentsinwaysthatimprovetheirlearning?
Introduction
Mathematicsteachingassumesthatstudentsdonotarriveatsessionsas‘blankslates’,butasactivelythinkingpeoplewithawidevarietyofskillsandconceptions.Researchshowsthatteachingismoreeffectivewhenitassessesandusespriorlearningsothattheteachingmaybeadaptedtotheneedsofstudents(Black&Wiliam,1998).Priorlearningmaybeuncoveredthroughanyactivitythatoffersstudentsopportunitiestoexpresstheirunderstandingandreasoning.Itdoesnotrequiremoretesting.Forexample,itcantaketheformofasinglewrittenquestiongivenatthebeginningofasessiontoelicitarangeofexplanationsthatmaythenbediscussed.Thisprocess,oftenreferredtoasformativeassessment,maybedefinedas:
"…allthoseactivitiesundertakenbyteachers,andbytheirstudentsinassessingthemselves,whichprovideinformationtobeusedasfeedbacktomodifytheteachingandlearningactivitiesinwhichtheyareengaged.Suchassessmentbecomes‘formativeassessment’whentheevidenceisactuallyusedtoadapttheteachingworktomeettheneeds."(Black&Wiliam,1998,p.91)
Thismoduleconsidersthedifferentwaysthiscanbedoneandfocusesonthefollowingquestions:
• Howcanproblemsbeusedtoassessperformance?• Howcanthisassessmentbeusedtopromotelearning?• Whatkindsoffeedbackaremosthelpfulforstudentsandwhichareunhelpful?• Howcanstudentsbecomeengagedintheassessmentprocess?
ActivitiesActivityA: Whatisformativeassessment?........................................................................................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
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Relatedresearchtohelpyourplanningforthismodule.Black,P.,&Wiliam,D.(1998).Insidetheblackbox:raisingstandards
throughclassroomassessment.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 ThisbookletappliestheabovefindingsspecificallytoMathematics.
ItconsiderssomeprinciplesforMathematicslearning,choiceofactivitiesthatpromotechallengeanddialogue,questioningandlistening,peerdiscussion,feedbackandmarking,andselfandpeerassessment.Thisbookletisessentialreadingforallmathematicsteachers.
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ACTIVITYA:WHATISFORMATIVEASSESSMENT?
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(seep.2),mostofwhicharefreelydownloadableontheinternet.Theseresearcherssetouttofindoutwhetherornotimprovingformativeassessmentimproveslearning.
“Wecheckedmanybooksandnineyears'worthofmorethan160journals,andearlierreviewsofresearch.Thisprocessyielded580articlesorchapterstostudy.Wepreparedareviewusingmaterialfrom250ofthesesources.All…studiesshowthat…strengthening…formativeassessmentproducessignificant,andoftensubstantial,learninggains.Thesestudiesrangeoverages,acrossseveralschoolsubjects,andoverseveralcountries…”(BlackandWiliam,1998).1
Thismodulewillexaminetheimplementationofformativeassessment,basedonthisandotherresearch.
1PaulBlackandDylanWiliam,"AssessmentandClassroomLearning,"AssessmentinEducation,March1998,pp.7-74.
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ACTIVITYB:TEACHERS'OWNEXPERIENCESOFFORMATIVEASSESSMENT
Minimumtimeneeded:10minutes.
Whatdoteachersknowabouttheirstudentsandwhatconsequentialactiondotheytake?Askparticipantstoworkinpairs,consideringthefollowingquestions.
• Thinkoftwostudentsinyourclass,onewhoisparticularlystrongandonewhoisfindingtheworkverydifficult.Takeitinturnstodescribethestudents'strengthsanddifficultiestoyourpartner,inasmuchdetailaspossible.
• Howdidyoubecomeawareofthesestrengthsanddifficulties?Onwhatevidencedoyoubaseyourjudgments?Testresults?Memoriesoforalresponsesduringlessons?Observationsofthestudentworking?Writtenwork?
• Inwhatwaysdoyourassessmentsofthesestudentsaffectyourlessonplanning?Giveexamples.
Whatdifficultiesdoteacherencounter?IssueparticipantswithcopiesofHandout1:Difficultieswithformativeassessment.
• Howfararethecriticismsonthehandoutvalidinyourcontext?• Ifanyare,thenwhatmaybedoneaboutthem?
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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.
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ACTIVITYC:PRINCIPLESFORFORMATIVEASSESSMENT
Minimumtimeneeded:20minutes.
IssueparticipantswithacopyofHandout2Principlesforformativeassessment.Theideaspresentedherearealldrawnfromresearchintoformativeassessment.
• BearinginmindthedifficultiesdiscussedinActivityB,howwouldyousuggestthatyourformativeassessmentpracticesbeimproved?
• DiscusstheprinciplesoutlinedonHandout2.o Whichofthesedoyoucurrentlyuseinyourownteaching?o Whichdoyoufindmostdifficult?Why?
• Whatotherprinciplesdoyouthinkareimportant?
IssuecopiesofHandout3Makingreasoningvisible.
"It'sallverywelltellingustoassessourstudents,buthowcanabusyteacherknowwhatisgoingoninside30individualheads?"
• Howwouldyouanswerthisteacher?• Whatstrategiesdoyouhaveforfindingoutwhat
studentsarethinkinginyourlessons?• DiscussthesuggestionsshownonHandout3,andwatch
theActivityCvideostoseesomeoftheseinaction.• Suggestsomefurtherstrategiesformakingreasoning
moreevident.
ThestrategiesdescribedonHandout3andonthevideosaccompanyingthisactivitymayhelptomakereasoningmore'visible'.Mini-whiteboards,studentresponsesystemsorapplets(likePlickers,Showme,Socrative,orClassflow)areanindispensableresourceforthefollowingreasons:
• itispossibletoseeataglancewhateverystudentthinks.• Duringwholeclassdiscussions,theyallowtheteachertoasknewkindsofquestion(typically
beginning:‘Showmeanexampleof....’).• Theyallowstudentsto,simultaneously,presentarangeofwrittenand/ordrawnresponses
totheteacherandtoeachother.
PostersorDisplayingstudentscreensarealsoapowerfulwayofhelpingstudentstoexternalizetheirthinking.Thisusedoesnotrequire'polished','complete','attractive'productsbutrathertheyshouldbeseenasworkingdocuments.Studentscouldsolveaproblemcollaborativelyorindividuallyandexplainthethoughtprocessesinvolvedineverysteportheycouldexpresswhattheyalreadyknowaboutagiventopic.Bysharingstudentsolutionswiththewholeclass,differentapproachestothesameproblem,commonmistakesanddifferentformsofreasoningcanbediscussed.
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"… all those activities undertaken by teachers, and by their students in assessing themselves, which provide information to be used as feedback to modify the teaching and learning activities in which they are engaged. Such assessment becomes ‘formative assessment’ when the evidence is actually used to adapt the teaching work to meet the needs." (Black & Wiliam, 1998 para, 91)
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Handout3: Makingreasoningvisible.
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ACTIVITYD:ANALYSESTUDENTS’RESPONSESTOPROBLEM-SOLVINGTASKS
Minimumtimeneeded:20minutesHandout4Assessmenttasksandsampleresponsespresentsthreeproblemstogetherwithfourstudentresponsesoneach.Thetasksare:CountingTrees,CatsandKittens,SecurityCameras.Thesetasksuseavarietyofmathematicalcontent,butallfocusonproblemsolvingandmodelingskills.Often,suchtasksprovemoredifficultthantheindividualelementsofmathematicalcontentwouldsuggest,asstudentsarerequiredtochooseandcombinetechniquesinnon-routineways.Traditionalsummativeassessmentsoftenfocusonisolatedcontentstandardsandfailtotestthese‘processskills’.Formativeassessmentisaneffectivewaytoensurethatstudentsaredevelopingthesepractices.Thefollowingphasesofproblemsolvingareausefultooltoanalyzestudents’workonthesetasks:
A. Formulatequestions,chooseappropriaterepresentationsandtechniques.B. Reasonlogically,constructhypothesesandarguments,computeaccurately.C. Interpretandevaluateresultsobtained.D. Communicateandreflect.
• Readthroughallthreetasksthenchooseonetaskthatwillbemostsuitableforaclassyouwillsoonteach.Ifyouareworkingonthismoduleinagroup,itwillbehelpfulifeachparticipantchoosesthesameproblem,asthiswillfacilitatethefollow-updiscussion.
• Considerthefourstudentresponses.Whatdoeseachstudent’sresponsetellyouabouthis
orhercapacitytouseeachoftheprocesses:represent,analyse,interpretandevaluate,communicateandreflect?
Handout5Improvingstudents’responsesthroughquestioningofferssomecommentsonstudents’responsestoeachofthetasks.
• Ifyouweretheteacherofthesestudents,whatfeedbackwouldyougivethem,tohelpthemimprovetheirresponses?Trytoframethishelpintheformoforalquestionsyoucouldaskintheclassroom.YoumayfindithelpfultorefertothegenericquestionsgivenonHandout6.
• Watchthevideoofthreeteachersdiscussingthefeedbacktheygaveonthethreeproblems.
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Handout4: Assessmenttasksandsampleresponses
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Sample response: Jenny
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(c)CentreforResearchinMathematicsEducation,UniversityofNottingham2010 10
ACTIVITYE: ANALYSESTUDENTS’RESPONSESTOCONCEPT-FOCUSEDTASKS
Minimumtimeneeded:20minutesOnHandout7Assessmenttasksandsampleresponsesforconcepts,wepresentfourmathematicaltopicsandsomesamplestudentworkoneachone.Askparticipantstoassesseachresponseandtrytoidentifythereasoningthatliesbehindeachone.
• Whatdoesthestudentappeartounderstand?Whereisyourevidence?• Listtheerrorsanddifficultiesthatarerevealedbyeachresponse.• Trytoidentifythethinkingthatliesbehindeacherror.• Whatfeedbackwouldyougivetoeachstudent?
Therearetwocommonwaysofreactingtopupils'errorsandmisconceptions:
(i)Avoidthemwheneverpossible:"IfIwarnpupilsaboutthemisconceptionsasIteach,theyarelesslikelytohappen.Preventionisbetterthancure."(ii)Usethemaslearningopportunities:"Iactivelyencouragepupilstomakemistakesandlearnfromthem.• Whatisyourview?
Routinepracticeonstandardproblemsdoeslittletohelpstudentsovercomecommonmistakesandmisconceptionsinmathematics.Thisisparticularlytruewhenteacherstrytoavoiddifficultiesarisingbybeginningeachlessonwithexplanationsanddemonstrationsandfollowingthiswithcarefullygradedquestions.Handout8Misconceptionsanderrors:researchfindingsisaone-pageresearchreviewbyAskewandWiliam.ThisdescribessomeresearchthatwasconductedinBritainoverthepast30yearsondealingwithstudenterrorsanddifficulties.Whatdoteachersfeelaboutthedilemmaspresentedinthispaper?
• isitpossibletopresentexampleswhererulesdonotwork?• doteacherssharetheviewthatitiscounter-productivetoteachsimplerexamplesbefore
morecomplexexamples?
(c)CentreforResearchinMathematicsEducation,UniversityofNottingham2010 11
Handout7: Assessmenttasksandsampleresponsesforconcepts
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(c)CentreforResearchinMathematicsEducation,UniversityofNottingham2010 12
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.
(c)CentreforResearchinMathematicsEducation,UniversityofNottingham2010 13
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!! ! !
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! ReportingbackonthelessonAfteryouhavetaughtthelesson,reflectonwhathappenedwithagroupofcolleagues.Takeitinturnstosharestoriesoftheassessmentstrategiesyouused.
• Howdidyoucollectandassessevidenceofyourstudents'work?• Whatdidyoulearnfromthisevidence?• Whichfeedbackdidyou/yourstudentsgive?• Whatdidstudentslearnfromthefollow-uplesson?• Whataretheimplicationsforyourmathematicsteachingmoregenerally?
(c)CentreforResearchinMathematicsEducation,UniversityofNottingham2010 14
ACTIVITYH:CONSIDERTHEEFFECTSOFFEEDBACKONSTUDENTLEARNING
Timeneeded:20minutes.
Sofarwehavefocusedontheteachers’roleinprovidingassessmentfeedbacktostudents.Inthisactivitywewillconsidertheusestudentsmakeofdifferenttypesoffeedbackandtheimpactthishasontheirlearning.WatchthevideoofAndrew'sstudentsastheydiscusstheimpactofassessmentfeedbackontheirlearning.
• Whichoftheircommentsstrikeyouasparticularlyperceptiveandimportant?
• Whataretheimplicationsoftheircomments?
Handout10Theeffectsoffeedbackonstudents’learningpresentssomeresultsofresearchfromBlackandWiliam(1998)intotherelativemeritsoffeedingbackassessmentinformationtostudentsindifferentforms.Inparticular,itcomparestheeffectsoffeedingbackquantitativeinformationintheformofmarks,levelsandrankingswiththeeffectsofofferingqualitativeinformationintheformofspecific,content-focusedfeedback.Comparethestudents'commentswiththeresearchquotesgivenonHandout9.Thedangersofgivingmarks,levels,rewardsandrankings
• Whataretheimplicationsofthisforyourpractice?• Whatwouldhappenifyoustoppedgivingmarksorlevelsonpupils’work?• Whyaresomanyteachersresistanttomakingthischange?
Theadvantagesofgivingclear,specific,content-focusedfeedback
• Whataretheimplicationsofthisforyourpractice?• Doesthiskindoffeedbacknecessarilytakemuchlongertogive?
Researchshowsthatstudentsbenefitmostfromfeedbackthat:• Focusesonthetask,notongradesorscores.• Isdetailedratherthangeneral.• Explainswhysomethingisrightorwrong.• Isrelatedtoobjectives• Makesclearwhathasbeenachievedandwhathasnot• Suggestswhatthestudentmaydonext• OffersspecificstrategiesforimprovementConcludethismodulebydiscussingsomewaysofapplyingwhatyouhavelearnedinthisPDmoduletotheothermathematicslessonsthatyouteach.
• Howcouldyouinvolvepupilsinimprovingyourassessmentpractices?
(c)CentreforResearchinMathematicsEducation,UniversityofNottingham2010 15
Handout10:Theeffectsoffeedbackonstudentlearning
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