Partners for Mathematics Learning

1. 1 PARTNERS forMathematicsLearning FormativeAssessmenttoSupportStudentLearning Module4 Grades3-5 MakingStudents ActivePartners Partners forMathematicsLearning

2. 2 OverviewofModules Module1:LearningTargets Module2:QuestioningandTaskSelection Module3:InferencesandFeedback Module4:MakingStudentsActivePartners Module5:DecisionsAboutNextSteps Module6:CollaborationAroundAssessment Partners forMathematicsLearning

3. 3 Teaching-LearningCycle Clear Learning Targets Decisions About NextSteps Questioning& Instructional Tasks Collaboration Around Assessment Making Inferences &Giving Feedback Partners forMathematicsLearning StudentSelf- Assessment& Responsibility

4. 4 MakingStudentsActivePartners “Involvingstudentsintheirlearningisakey characteristicofformativeassessment.” (BlackandWiliam,1998) “Whenchildrencontinuallyparticipateinthe assessmentprocess,theylearntorecognize theirownexpertise.Asactiveassessors,they necessarilyexerciseamoreautonomousand decision-makingroleintheirlearning. Consequently,insteadofbeingusedtogain poweroverachild,assessmentempowersthe child.” (Anderson,1993) Partners forMathematicsLearning

5. 5 LearningTargetsforModule4 Understandandusestrategiesfor establishingalearningenvironmentthat empowersstudentstobecomeresponsible fortheirownlearning Understandandusestrategiestohelp studentsgrowintheabilitytoself-assess Understandandusestrategiesfor promotingstudentcollaboration,including peerassessment Partners forMathematicsLearning

6. 6 MakingStudentsActivePartners EstablishingtheLearning Environment TeacherResponsibility Learningwithinthe Environment StudentResponsibility SelfAssessment PeerAssessment Partners forMathematicsLearning

7. 7 EstablishingtheEnvironment Theclassroomshouldbeaplacewhere studentsfeelcomfortable,secure,and accepted Studentsknowthatitisokaytotakerisks andmakemistakes Studentsareencouraged tosharetheir strategiesandideas Partners forMathematicsLearning

8. 8 EncouragingStudentResponsibility “Thedialoguebetweenteacherand studentshouldbethoughtful,reflective, focusedtoevokeandexplore understanding,andconductedsothatall pupilshaveanopportunity tothinkandexpress theirideas.” Partners forMathematicsLearning

9. 9 AssessmentForLearning (modifiedfromWilliamandThompson,2007) Partners forMathematicsLearning

10. 10 MakingStudentsActivePartners Formativeassessmentstrategies emphasizestudentself-assessmentand responsibility Clearlearningtargetsandcriteriafor successallowstudentstokeeptrackof theirprogress “Actionable”feedbacktellsstudentswhat theyaredoingrightandsuggestswaysto improve Partners forMathematicsLearning

11. 11 EstablishingtheEnvironment Impedevs.EmpowerStudentResponsibility Readthescenariocardswithyourgroup Decidewhichscenariosimpedestudentsand whichscenariosempowerstudents Listonchartpaperactionsthatempowerand actionsthatimpedestudentresponsibility Bereadytoshareyourthoughtswiththe wholegroup Addyourowngroup’sadditionalexamples Partners forMathematicsLearning

12. 12 EstablishingtheEnvironment Weretheresomescenariosthatthegroup couldnotagreeon? Whatothercharacteristicsthatempower studentresponsibilitydidyourgrouplist? Whatothercharacteristicsthatimpede studentresponsibilitydidyourgrouplist? Partners forMathematicsLearning

13. 13 EstablishingtheEnvironment “Whentheclassroomculturefocuseson rewards,“goldstars,”grades,orclass ranking,thenpupilslookforwaystoobtain thebestmarksratherthantoimprovetheir learning.” (BlackandWiliam,1998) Partners forMathematicsLearning

14. 14 EstablishingtheEnvironment Researchsays:Aclassroomfocusedon rewards,grades,orranksleadstoaculturein which: Studentschooseeasiertasksratherthan difficulttaskssothattheycanearnareward (BlackandWiliam,1998) Partners forMathematicsLearning

15. 15 EstablishingtheEnvironment Researchsays:Aclassroomfocusedon rewards,grades,orranksleadstoaculturein which: Studentschooseeasiertasksratherthan difficulttaskssothattheycanearnareward Studentsspendtimelookingfortheright answersversustakingthetimetounderstand Partners forMathematicsLearning

16. 16 EstablishingtheEnvironment Researchsays:Aclassroomfocusedon rewards,grades,orranksleadstoaculturein which: Studentschooseeasiertasksratherthan difficulttaskssothattheycanearnareward Studentsspendtimelookingfortheright answersversustakingthetimetounderstand Studentsdon’taskquestionsoutoffearof failure Partners forMathematicsLearning

17. 17 EstablishingtheEnvironment Researchsays:Aclassroomfocusedon rewards,grades,orranksleadstoaculturein which: Studentschooseeasiertasksratherthandifficult taskssothattheycanearnareward Studentsspendtimelookingfortherightanswers versustakingthetimetounderstand Studentsdon’taskquestionsoutoffearoffailure Studentswhohavedifficultytendtobelievethey lackabilityandblameitonthemselvesandin returnputlittleeffortinlearning Partners forMathematicsLearning

18. 18 EstablishingtheEnvironment Whatshouldbethefocus oftheclassroomculture? Partners forMathematicsLearning

19. 19 EstablishingtheEnvironment Classroomenvironmentaffectshow studentsfeelaboutthemselvesand howwelltheylearnmathematics Discuss:Inastudent-friendlyclassroom Whatistheteacherdoing? Whatarethestudentsdoing? Howwouldyoudescribethe environmentasawhole? Partners forMathematicsLearning

20. 20 EstablishingtheEnvironment Studentsmustbelievethat… Successinmathiswithintheirreach Theyknowwhatsuccesslookslike Assessmentsupportstheirlearning Feedbackisuseful Theywillhavechancesforimproving Monitoringtheirprogresstowardachieving learningtargetshelpsthemmoveforward (BrightandJoyner,DynamicClassroomAssessment,2005) Partners forMathematicsLearning

21. 21 EstablishingtheEnvironment Theclassroomenvironmentprovidesfor groupworkandgroupgoals Studentsworkasagroupinsteadofinagroup Studentsareresponsibleforcontributingto thegroup Anystudentinthegroupshouldbeableto explainorpresentsolutionstrategies Studentsareinstructionalresourcesfor oneanother Teacherbecomesfacilitator Partners forMathematicsLearning

22. 22 “ThinkingAboutThinking” Teacherssupportstudentlearning whentheycommunicatetotheirclassthat theyvaluetheirstudents’thinking (metacognition),ideas,andresponses Caution:Actionsspeaklouderthanwords! Whyisitimportantthatstudents payattentiontohowtheythink? Partners forMathematicsLearning

23. 23 “ThinkingAboutThinking” Metacognitioninoneshortphraseis “thinkingaboutthinking” Utilizingmetacognitionmeansstudentscan Monitortheirownprogress Reflectontheirwork Takeresponsibilityandinitiativefordoing goodwork Adaptstrategiestoimproveperformance Setgoalsformakingprogress Partners forMathematicsLearning

24. 24 “ThinkingaboutThinking” Whatdoesmetacognitionlooklikeinthe 3rd–5thgrademathematicsclassroom? Listinyourjournalsomethingsyoucan dotobegindevelopingmetacognition inyourstudents Discusswithyourgroup Bereadytoshareyourthoughts withthewholegroup Partners forMathematicsLearning

25. 25 EstablishingtheEnvironment Makea2-columnchartinyourjournal EmpoweringStudentResponsibility Partners forMathematicsLearning

26. 26 MakingStudentsActivePartners EstablishingtheLearning Environment TeacherResponsibility Learningwithinthe Environment StudentResponsibility SelfAssessment PeerAssessment Partners forMathematicsLearning

27. 27 StudentSelf-Assessment Whatdoesitmeanforstudentstobe “ownersoftheirownlearning?” Theycantellyouwhattheyarelearning (learningtargets) Theycantellyouwhattheyunderstandand whattheydon’tunderstand Theycantellyouwhattheywanttolearn Whatotherattributeswouldyouadd? Partners forMathematicsLearning

28. 28 StudentSelf-Assessment Studentswhoself-assess… Monitorandevaluatethequalityoftheir thinkingandbehaviorwhenlearning Identifystrategiesthatimprovetheir understandingandskills Judgetheirownworktoimproveperformance astheyidentifydiscrepanciesbetweencurrent anddesiredperformance (McMillanandHearn,StudentSelf-Assessment:TheKeytoStrongerStudent MotivationandHigherAchievement,2008) Partners forMathematicsLearning

29. 29 StudentSelf-Assessment Forstudentstoidentifydiscrepancies betweencurrentanddesiredperformance, teachersneedto Showchildrenwhat“goodwork”lookslike Havestudentsexamineaworksampleand suggestwaystoimprovethesamples Provide“student-friendly”rubrics Comparewhereownworkisrelatedtowork samplesortoageneralrubric Partners forMathematicsLearning

30. 30 StudentSelf-Assessment Ifthewholesquare costs$4.00,howmuch wouldeachpieceofthe puzzlecost? Explainhowyouknow Whatinformationwillagoodanswerinclude? Partners forMathematicsLearning

31. 31 StudentSelf-Assessment Ifthewholesquarecosts$4.00, howmuchwouldeachpieceofthe puzzlecost? Explainhowyouknow Asagroupdiscuss… Whatisgoodaboutthisanswer?(usesample1) Howdothesesamplescomparetotheanchor paper?(usesamples2&3) Howdowemakethesesamplesbetter?(use samples2&3) Partners forMathematicsLearning

32. 32 StudentSample1-AnchorPaper Ifthewholesquarecosts $4.00,howmuchwouldeach pieceofthepuzzlecost? Whatis good aboutthis answer? Partners forMathematicsLearning

33. 33 StudentSample2 Ifthewholesquarecosts $4.00,howmuchwouldeach pieceofthepuzzlecost? Howdoes thissample compareto theanchor paper? Partners forMathematicsLearning

34. 34 StudentSample3 Ifthewholesquarecosts $4.00,howmuchwouldeach pieceofthepuzzlecost? Howdoes thissample compareto theanchor paper? Partners forMathematicsLearning

35. 35 “Good”Responses Howdostudentsknowwhentheyhave provideda“good”responsetoaquestion? Thinkabout:Whathave Ithink… youdoneinyour classroomtohelp studentsrecognizea “good”response? Partners forMathematicsLearning

36. 36 Processfor“Good”Responses Wehelpstudentsidentifywhatconstitutes agoodresponsebyprovidingthemwith opportunitiesto… Evaluatesampleresponses Suggestimprovementstoweakresponses Createandusechecklistsorrubricsgiving criteriaforgoodresponses Talkwithabuddyabouthowtoimprovean explanationbeforeturningitin Partners forMathematicsLearning

37. 37 StudentSelf-Assessment Inyourgradegroup… Analyzethestudentsamplesandchoose onetobeananchorpaper Whichothertwoorthreepaperswouldyou usewiththeclass? Talkabouthowtomodeldiscussionsusing anchorpapersandworksampleswith studentsatyourgradelevel Partners forMathematicsLearning

38. 38 Processfor“Good”Responses Whatdowedonext? Providestudentswithanopportunity torevisetheirwork Havestudentssolveasimilarproblem Studentshavetobeabletoapplywhat theylearnedabouttheirresponsesto improvetheirperformance! Partners forMathematicsLearning

39. 39 Processfor“Good”Responses NextStep-anopportunitytosolvea similarproblem Ifthewholesquare costs$12.00,howmuch wouldeachpieceofthe puzzlecost? Explainhowyouknow Partners forMathematicsLearning

40. 40 Describing“Good”Responses Studentslearntocomposegood responseswhenteachers Showthemmodelsandletstudentslistcriteria Havethemcritiqueresponsesandsuggest improvements Encouragestudentpartnerstocritique responsespriortoturninginpapers Conversationsarebothteaching opportunitiesandassessmentstrategies Partners forMathematicsLearning

41. 41 StudentSelf-Assessment MyselfasaMathematician WhatdidIlearnnewthis week? WhatdidIlearnwellenough toteachafriend? Ismyworkgettingbetter? Doesmathmakesenseto me? LookingatMyWork DoIcompletemywork carefully? DoIaskforhelpwhen Ineedit? DoIcheckmyanswers? Ismyworkclearso someoneelsecan understandwhatIknow? Partners forMathematicsLearning

42. 42 StudentSelf-Assessment Forstudentstoidentifydiscrepancies betweencurrentanddesiredperformance, teachersneedto Showchildrenwhat“goodwork”lookslike Havestudentsexamineaworksampleand suggestwaystoimprovethesamples Provide“student-friendly”rubrics Comparewhereownworkisrelatedto worksamplesortoageneralrubric Partners forMathematicsLearning

43. 43 RubricsDefineLevelsofPerformance Differentiateinperformance Distinguishhigh-qualitywork Clearlydescribeexpectations Identifybelow-qualitywork Communicateexpectationstostudents andparents Helpstudentsimprovetheirwork DescribetheperformanceNOTthechild Partners forMathematicsLearning

44. 44 ExaminingSampleRubrics ProblemSolvingRubric RUBRICTEMPLATE 3–Correctanswerwithappropriatestrategyused andcompleted,and Correctsolutionclearlystated,and Clearandcorrectexplanationofprocess 2–Correctanswerbutincompleteorunclear explanation,or Correctanswer,butminorerrorsinwork 1–Incorrectanswerbutusesanappropriate strategy,or Onlycompletesonestepoftheproblem,or Correctanswerwithinaccurateexplanation, notrelatedtotheproblem NA–Noanswer,or Wronganswerbasedoninappropriateplan Partners forMathematicsLearning

45. 45 GeneraltoSpecificRubrics Forspecificrubricstobeausefultool… Theyneedtobeappliedtorichtasksthat askforexplanationofhowtaskwassolved Theyoftenneedtoberefined(clarified) usingstudentworksamples Theyshouldgivestudentsideasthatwill helpthemgivegoodexplanationstosimilar problems Partners forMathematicsLearning

46. 46 GeneraltoSpecificRubrics Advantagesofspecificrubrics Easiertouseforevaluatingspecifictasks Canbeappliedmoreconsistently Lesslikelytobeopentodifferentinterpretations Ingradelevelgroups,modifythegeneral rubricforyourgradelevel’stask Howcanthisbedoneefficiently? Partners forMathematicsLearning

47. 47 “Good”Responses Howcanwehelpstudentsidentifywhat constitutesagoodresponse? Haveexplicitdiscussionsaboutwhatquality worklookslike Providestudentswithopportunitiestoevaluate responses Providestudentswithopportunitiestocreate checklistsorrubricsforgoodresponses Providestudentswithopportunitiestosuggest improvementstoweakresponses Partners forMathematicsLearning

48. 48 WhatDoWeDoNext? Providestudentswithanopportunityto revisetheirwork Havestudentssolveasimilarproblem Studentshavetobeabletoapplywhat theylearnedabouttheirresponsesto improvetheirperformance Thesearewhatmakeactivitiesformative Partners forMathematicsLearning

49. 49 QuickStudentSelf-Assessments Studentsidentifytheirownstrengthsand weaknessesinquickways Reflections QuickWrites Pause&Think RecallCards ExitCards MarginSymbols ColorAlerts Partners forMathematicsLearning

50. 50 AMethodforSelf-Assessment Asyoutrytosolvetheproblemonthenextslide, indicateyourlevelofcomfortordifficultyby displayingared,yelloworgreencupusingthiscode Green:on“go”–neednohelp Yellow:“caution”–notsure,mayneedhelp •Otherstudentsmayhelpgroup/studentshowingyellow Red:“stop”–stuck,don’tknowwhattodonext, needhelpimmediately •Teachergoestogroup/studentshowingred Partners forMathematicsLearning