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PARTNERS for Mathematics Learning Formative Assessment to Support Student Learning Module 6 K-2

1. PARTNERS for Mathematics Learning Formative Assessment to Support Student Learning Module 6 K-2 Decisions and Collaboration Around Assessment Partners for Mathematics Learning. 2. Overview of Modules.     . Module 1: Module 2: Module 3: Module 4: Module 5:.

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PARTNERS for Mathematics Learning Formative Assessment to Support Student Learning Module 6 K-2

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  1. 1 PARTNERS forMathematicsLearning FormativeAssessmenttoSupportStudentLearning Module6 K-2 Decisionsand Collaboration Around Assessment Partners forMathematicsLearning

  2. 2 OverviewofModules      Module1: Module2: Module3: Module4: Module5: LearningTargets QuestioningandTaskSelection InferencesandFeedback MakingStudentsActivePartners StudentSelf-Assessmentand Responsibility Module6:DecisionsandCollaboration AroundAssessment 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 CollaborationForTeaching-Learning Clear Learning Targets Decisions About NextSteps Questioning& Instructional Tasks Partners forMathematicsLearning Collaboration Around Assessment Making Inferences &Giving Feedback

  5. 5 GoalsforModule6 StructuresforTeacherCollaboration Designinginstructiontomeet theneedsofgroupsof students(differentiation) Usingspecificstrategies tomeetidentifiedneeds ofindividualchildren (interventions) Partners forMathematicsLearning

  6. 6 WhatAreTeacherCollaborations? Groupsofeducatorsworkingtogetherto improveteachingandlearning Gradelevelteachersplanninginstruction Departmentmeetingsforprogramplanning Teachersinvolvedinlessonstudies ProfessionalLearningCommunities(PLCs) Pairsareusuallyunstructured,butgroups usuallyhaveastructureforcollaboration Partners forMathematicsLearning

  7. 7 HowShouldTeachersCollaborate? Withagoalinmind-groupsaremost productivewhenthereisaclearpurpose tothemeeting Inacollegialandsupportiveenvironment- asafeplacetoshare Notforevaluationofoneanother,butfor thesakeofinquiry-thisistheformative aspectoftheteachingprofession Partners forMathematicsLearning

  8. 8 TeacherCollaborations Shouldhaveanagenda Includinggoalsforthemeeting Includingguidelinesforhow themeetingisrun Shouldberunbyafacilitator Implementsandassuresadherencetothe agenda;keepsthegroup“ontask” Managesdiscussionsanddebriefing Actsasa“neutralbody” Partners forMathematicsLearning

  9. 9 UtilizingColleagues’Ideas Collaborationscanbeformativewhenthey studyteaching: Aplanisdevelopedtowardachievingagoal Resultsofimplementingtheplanareshared Discussionoccursaboutwhatcanhappennext Collaborationshavepotentialtoincrease studentachievementwhenplanning, teachingstrategies,andstudentworkare thefocusofthemeetings Partners forMathematicsLearning

  10. 10 ProcessofFormativeCollaboration LookingatStudentWork Theteacherintroducesthework Participantsaskclarifyingquestions Everyoneexaminesthestudentwork providingcomments Theteacherreflectsandrespondstothe commentsasheorshechooses Thefacilitatorleadsadebriefingdiscussion aboutthesession Partners forMathematicsLearning

  11. 11 ProcessofFormativeCollaboration ACollegialEnvironment Answerthefollowingtwoquestions inyourjournals: Whattypeofmeetingstructurewouldbe importanttoensureyourparticipation? Whattypeofmeetingstructurewouldbe importanttoensuremeaningfuldialogue? Partners forMathematicsLearning

  12. 12 OperationalizingCollaboration TurntoyournotesfromModule1andthe PlanningearningGoalsandTargets handout Discusstheassessmenttaskscreatedfor selectedlearningtargets Selectonetaskthatallcollaborating teacherswouldgivetostudentsafteraunit ofinstructiononthetopic Partners forMathematicsLearning

  13. 13 OperationalizingCollaboration Discusshowwillyoutaketheseideasbackto yourschoolandfacilitatecollaborationamong teachersatK-2onthesetopics Makeaplanforcomingtogetherbygrade levelstoexaminestudentwork Whatdoyouexpecta“goodresponse”tobe? Whatmisconceptionsortypicalmistakeswill youlookfor? Ifstudentsdonot“master”thecontent,what mightbethedifferentiationorinterventions? Partners forMathematicsLearning

  14. 14 GoalsforModule6 StructuresforTeacherCollaboration Designinginstructiontomeet theneedsofgroupsof students(differentiation) Usingspecificstrategies tomeetidentifiedneeds ofindividualchildren (interventions) Partners forMathematicsLearning

  15. 15 InstructionalPlans Whenyoubegininstructiononaspecific learningtarget… Isthereawholeclasslessonthatwill benefitallgroups? Aretherestudentswhoneedspecific interventions? Howcanalessonbedifferentiatedtomeet theneedsofthesestudents? Partners forMathematicsLearning

  16. 16 ConversationAboutEquality Studentsareaskedtosolvethisproblem: 8+7=+5  Student:“15” Whatquestioncouldyouasknow thatisNOTdirective? Conversationadaptedfrom ThinkingMathematically Carpenteretal Partners forMathematicsLearning

  17. 17 ConversationAboutEquality Studentsareaskedtosolvethisproblem: 8+7=+5     Teacher:“Howdoyouknowitis15?” Helen:“BecauseIcounted” Teacher:“Whataboutthis5?” Helen:“It’sjustthere” Partners forMathematicsLearning

  18. 18 ConversationAboutEquality Studentsareaskedtosolvethisproblem: 8+7=+5  Nowwhat? Whatisthemathematicsthatthestudent ismissing? Howcouldyoufindoutifthisisa commonmisconception? Whatwouldyouaskifstudentsgave otherincorrectanswers? Partners forMathematicsLearning

  19. 19 WholeGroupLessons Differentiationwithinwholegrouplessons Providescommonexperiences Exposesstudentstoavarietyofthinking Cansupportindividualneedsandstrengths •Usethink/pair/sharestrategy •Allowwaittimebeforeresponses •Encourageresponsesfromseveralchildren •Connectcommentstopreviousspeakers Welearnmuchmoretogetherthanwecanalone Partners forMathematicsLearning

  20. 20 Strategies:FlexibleTasks&Groupings Flexiblegroupingsandassignmentsare hallmarksofadifferentiatedclassroom Differentiationprovidesopportunitiesthat supportstudentachievement Effectiveteachersfocusondifferentiation whenteachingcriticalconcepts Realistically,notalllessonsaredifferentiated Textbooksusuallyofferdifferentiatedtasks Ifdifferentiationisnewtoyou,startsmall Partners forMathematicsLearning

  21. 21 ExamplesofDifferentiationStrategies Pre-teaching/FrontLoading Discussingnewvocabularyforstudentswith languagegaps Pullagroupandpre-teach foundationalideas Unpackwordproblems Partners forMathematicsLearning

  22. 22 ExamplesofDifferentiationStrategies TieredAssignments Allowforavarietyofentrypoints Couldbe2-4different,butparalleltasks Technologydrivenassignments Teacherdirectsstudentstododifferentitems onsameworksheet Partners forMathematicsLearning

  23. 23 TieredAssignments Tieredactivities/lessons Aseriesofrelatedtasksofvaryingcomplexity Relatetoessentialunderstandingsandkey skillsthatstudentsneedtoacquire Assignedasalternativewaysofreachingthe samegoalstakingintoaccountindividual studentneeds Partners forMathematicsLearning

  24. 24 GettingStarted:TieredAssignments Choosethelearningtarget Formgroupsbasedonassessments Planameaningfulactivityandavariation ofthesameactivityforeachgroup dependingonthestudentneeds Partners forMathematicsLearning

  25. TieredAssignments 25 TheDoorbellRang NeedsInstruction Teacherrepeatsstoryas studentsactoutthestory Studentsthenhave12cookies toputintoequalgroupsoftheir choice ReadytoApply Teachergivesstudents18 cookies;theydeterminehow manydifferentwaystheycan bedividedequally Studentsrecordwhatequal groupsarepossible NeedsChallenge Studentsidentifyand record(inwords, picturesornumbers) whatnumbersof cookiescouldbe equallydividedinto 2,3,and4groups Studentsthen exploreifanyoftheir numberswouldwork forgroupsofsix Partners forMathematicsLearning

  26. 26 ExamplesofDifferentiationStrategies Choicesamongsimilartasks Multipletaskswithinacenter-student choosesactivitiesorteacherassignsthem Numberchoicesintasks Tic-Tac-Toeandotherdifferentiatedformats Signalsforassistance Usegroupbuddiesforassistance Stoplightidea:Unifixcubes,cups,cards Workingwithapartner Partners forMathematicsLearning

  27. DifferentiationStrategies27 NumberChoices Meghanfound(6,15,34)rocks Shehadaholeinherpocketandlost (3,9,21)ofherrocks Howmanydoesshehavenow? Advantages     Childrenchoosechallengebut“doable”numbers Multipleentrypoints Classdiscussionofthesameproblempossible Goodformulti-ageclassrooms Partners forMathematicsLearning

  28. DifferentiationStrategies 28 Tic-Tac-Toe Students choose Teacher plansfor practice Engaging Partners forMathematicsLearning

  29. 29 Cues:Red,Yellow,Green Asstudentswork,theyusethiscodetoself- assessandcommunicatewiththeteacher: Green:on“go”–doesnotneedhelp Yellow:“caution”–notsure,mayneedhelp •Otherstudentsmayhelpastudentshowingyellow Red:“stop”–stuck,don’tknowwhattodo next,needshelpimmediately •Teachergoestostudentsshowingred Partners forMathematicsLearning

  30. 30 DifferentiatedInstruction “DifferentiatedInstructionisanorganized, yetflexiblewayofproactivelyadjusting teachingandlearningtomeetstudents wheretheyareandhelpallstudents achievemaximumgrowthaslearners” CarolAnnTomlinson,UniversityofVirginia,1999(emphasisours) Partners forMathematicsLearning

  31. 31 GoalsforModule6 StructuresforTeacherCollaboration Designinginstructiontomeet theneedsofgroupsof students(differentiation) Usingspecificstrategies tomeetidentifiedneeds ofindividualchildren (interventions) Partners forMathematicsLearning

  32. 32 OurTask “…ourjobistochallengestudents’comfort levelandthentohelpthemfindtheirnext boundaries.…wetrytoidentifyevidencefor whatthechildknowsorhasmastered,areas whereinitialideasareformedbutadditional experiencewiththemisneeded,andthose conceptsandskillsthatrequirefurther scaffoldingoradditionalreadiness development.”-DaceyandLynch,MathforAll,2007 Partners forMathematicsLearning

  33. 33 KeepinMind… ZoneofProximalDevelopment Vygotsky(1978),Fleer(1992),Jacobs(2001) Student’s Current achievement http://www.learningandteaching.info/learning/constructivism.htm Partners forMathematicsLearning

  34. 34 Interventions… Identifystudentsatrisk Throughteacherobservationsandconversations Throughpretestsandstudentwork Implementhighlyeffectivestrategiesfocused specificallytoaddresstheindividual’sneed Shouldbeimplementedfaithfully Needon-goingprogressmonitoring Shouldbeadjustedthroughoutinstruction Partners forMathematicsLearning

  35. 35 Interventions… Mustbebasedondatathattellswhatthe individualstudentknowsordoesnotknow Likelytoaddressgapsinpriorknowledge Startwherethestudentisinhis/herknowledge and/orunderstanding Arenotmoreofthesame Newstrategies Newrepresentations Mini-lessonsonspecificcontent Partners forMathematicsLearning

  36. 36 Intervention… Requiresamodificationin Modesoftaskpresentation Instructionaltime Groupsize Amountandkindofcuesandprompts Amountofsupportwithintasks Amountofpracticerelevanttothemathematics Supportsstudents’increasedcontent knowledge Partners forMathematicsLearning

  37. 37 WhatIntervention? SecondgradestudentCallieconsistently countsallanddoesnotappeartorecall anysumsabove4+4 Theexpectationisthatshewillbedoing2- digitadditionwithrenamingwithinthenext months Herknowledgeofplacevalueis limitedtosaying34is“3tens and4ones” Partners forMathematicsLearning

  38. 38 InterventionsGoBeyondModifications Interventionsarenot…      Preferentialseating Shortenedassignments Parentcontacts Classroomobservations Doingmoreofthesame assignment Retention Partners forMathematicsLearning

  39. 39 Intervention:MakingtheTime Whatareshortblocksoftimesthatarenot well-usedduringtheschooldaythatmight beavailableforworkingwithindividuals? Whataresomewaysthatyouhavefound tofindtimetointervenewithchildren? Whataresomenewwaysthatyouwould liketotry? Whatgradeorschool-widechangeswould supportinterventions? Partners forMathematicsLearning

  40. 40 ConversationsAsAssessments Monitoringstudents’progressisespecially importantifstudentsarebehind Conversationswithstudentsaboutwhat theyarethinkinghelpkeepinterventions “movingforward” Classdiscussionsserveasconversationswhen welistencarefullytostudentsandaskprobing questionswhentheyshareanswers Itiseasiertoaddressproblemsifstudentsdo notspendtime“practicing”theirmisconceptions Partners forMathematicsLearning

  41. 41 Scaffolds Areanystructuresthatallowstudentstobe successfullearnersofmathematics Givechildrenopportunitiestoaccomplishtasks thattheywouldbeunabletocompletealone Include: Questionsthatleadstudentstobemore systematicorlogical Strategiesdevelopedexplicitlyforworkingwith newmathematicalcontentandactivities Newlearningconnectedtopriorknowledge, e.g.,KWLorKWHL Partners forMathematicsLearning

  42. 42 ScaffoldingLearning Caremustbetakennottoreplacestudent thinkingwithteacherthinking Partners forMathematicsLearning

  43. Examples 43 Scaffolding:Organizers Howareasquareandarectanglealike anddifferent? AlikeDifferentWordBank Partners forMathematicsLearning

  44. 44 Scaffolding:Organizers Partners forMathematicsLearning

  45. 45 Scaffolding:IdentifyProblemStructures Seanbiked12milesandstoppedforlunch.Thenhe bikedanother16milesbeforehereachedhome. HowmanymilesdidSeanbike? Seanbiked12milesandstoppedforlunch.Thenhe bikedsomemore.Bythetimehegothome,hehad biked28miles.Howmanymiles didhebikeafterlunch? Seanbikedforawhilebeforehestoppedforlunch.After lunchhebiked16milestoreachhome.Whenhegot therehehadbiked28miles.Howmany milesdidSeandrivebeforelunch? Partners forMathematicsLearning

  46. Examples 46 Scaffolding Problemtosolve Toddscored28pointsinthebasketballgame. Kerriscored13points. HowmanymorepointsdidToddscorethanKerri? Focusingattention:Setupproblemtorevealone sentenceatatime Teacherquestions:Tellmewhatishappeningin thestory.Whatdoyouknow?Whatareyou tryingtofindout? Modification:Changenumbersto8and3 Partners forMathematicsLearning

  47. 47 InterventionTarget Studentsoftenneedassistancewith multiplelearningtargets Teachersmustidentifyneeds,prioritize, andfocusonwhatisfoundational Beclearaboutpurposeofintervention “Scaffold”interventionsinlogicalorder Providemultipleopportunitiestolearnand practicecontentofintervention;buildreview Expectandrespectstudentthinking Monitorprogress Partners forMathematicsLearning

  48. 48 LookingataStudent’sWork Withyourpartner Reviewthestudentworksamples Identifymisconceptionsanderrors(also identifywhatthestudentknows) Prioritizehowyouwouldintervenewiththis student(focusingonmathematicscontent) Listspecificstrategies,activities,“steps” Partners forMathematicsLearning

  49. 49 ToEffectivelyMeetStudentNeeds Keepfocusonmathematicalconcepts, understanding,andsense-making Useon-goingassessmentstofindstudents whoneedmoresupportorextensions Keepgroupingsflexible Betheguideandfacilitator Continually(informally)assesstorecognize growthandachievementofgoals Partners forMathematicsLearning

  50. NCTMAssessmentResearchBrief Inyourownwordsdescribethefivemain pointsmadeinthebrief Inwhatwayscouldimplementationof theseideasimproveteachingandlearning inNorthCarolina? Whatchangesneedtotake placeinyourclassroom/school forthesestrategiestowork? Partners forMathematicsLearning

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