Partners for Mathematics Learning

1. 1 PARTNERS forMathematicsLearning FormativeAssessmenttoSupportStudentLearning Module5 Grades3-5 Decisions about NextSteps Partners forMathematicsLearning

2. 2 Overview 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 MakingDecisionsaboutNextSteps Learningtargetsforthismodule Understandanduseinformationabout learningneedsofindividualstudentsto makedecisionsaboutnextinstructional steps Identifystrategies forinterventionand differentiation Partners forMathematicsLearning

5. 5 MakingDecisionsaboutNextSteps Thequalityanddepthofstudentlearningis influencedbythedecisionsteachersmake Thus,formativeassessmentshould Giveinformationaboutstudents’understanding Guideteachersinchoosinginterventionsfor individualstudents Assistinplanningnextstepsforthewholeclass Formativeassessmentdatahasvalue accordingtohowwellweuseittoplan Partners forMathematicsLearning

6. 6 InformationAboutStudents Wegatherinformationaboutstudents’ understandinginmanyways… Students’writtenwork Conversationsorinterviews withindividuals Classdiscussions Pre-assessmentsfor learningtargets Partners forMathematicsLearning

7. 7 MakingDecisionsaboutNextSteps WholeClassInstruction DifferentiatedInstruction–designing instructiontomeetneedsofallstudents acrossthespectrumofmastery Withinthecontextofwholeclassinstruction Interventions–specificstrategiestomeet identifiedneedsofchildren Individualized/smallgroupinstruction Inthismodule,wefocusonchildrenatrisk Partners forMathematicsLearning

8. 8 ThreeStarsandaWish Inyourjournal… Listwaysyouareusingformativeassessment toinformyourinstructionalplanning Listthewaysyouarecurrentlydifferentiating instructioninyourclassroom Listtheinterventionsyoucurrentlyuse Starthe3mosteffectiveofthese Writeonespecificwishforideasrelated tothese Partners forMathematicsLearning

9. 9 ResearchSuggestsStrategies Toeffectivelymeetallstudents’needs… Keepfocusonconceptsandsense-making Useformativeassessmentstrategiesto understandstudents’thinking Maintainhighexpectationsforachievementof learningtargetsforallstudents Useongoingassessmentstoidentifystudents whoneedadditionalsupportorextensions Involvestudentsmoreinself-assessment Useassessmenttomakeflexiblegroupings Partners forMathematicsLearning

10. 10 FlexibleGroups Flexiblegroupingisahallmarkofa classroomthatmeetsstudentsneeds Groupsarenotstaticbutareever- changingbasedonavarietyofcriteria Responsestotasks Readiness Workhabits Performance StudentInterests andchoices Partners forMathematicsLearning

11. 11 TypesofGroups Wholeclass Individualwork Teacherdesignated groups Randomgroups Readinessfortasks Likereadiness Differentlevelsof readiness Learningstyles Similar Random Studentinterests Studentchoice Whatotherwaysdo yougroupstudents? Partners forMathematicsLearning

12. 12 LookingatStudentWork Dailypracticemaybeusedtomake decisionsabouttheneedsofstudents Lookatthestudentworkandtalkatyour tableaboutwhatyouknowaboutthese studentsandtheirknowledge Whatwouldyoudoinawholeclasslesson? Howmightyougroupstudentsbasedonthe work? Bepreparedtoshareyourideas Partners forMathematicsLearning

13. 13 WholeGroupLessons Wholegrouplessons Providecommonexperiences Exposestudentstoavarietyofthinking Cansupportindividualneedsandstrengths • • • • Usethink/pair/sharestrategy Allowwaittimebeforeresponses Encourageresponsesfromseveralchildren Connectcommentstopreviousspeakers Welearnmuchmoretogetherthanwe canalone Partners forMathematicsLearning

14. TwoStrategies 14 WholeGroupLessons Havestudentslookatexamplesanddiscuss whicharecorrect,whicharenotandwhy Putsamplesonanoverhead,documentcamera, orwritethemontheboard Besurenostudentnamesareattached Letstudents-notteacher-discusserrors Teacherchooses3or4problemstodiscuss withtheclassandthengivesstudentsan opportunitytosolve3or4similarproblems Partners forMathematicsLearning

15. 15 ClassDiscussions Classroomdiscussionsprovideinformationfor teachersandbuildsunderstandingamong students Misconceptionssurfacewhichhelpteachersidentify whatstudentsdoandstilldonotunderstand Studentsrealizetheirownlackofknowledgeor understandingwhentheyareaskedtotalkorwrite aboutaconcept Discussionshelpmeetindividualneedswithin wholeclasslessons Partners forMathematicsLearning

16. 16 ToolsforClassroomDiscussions Teacherre-voiceschild’sstatement “Soyou’resayingthat…” Studentsrestateanother’sreasoning “Canyouputherideaintoyourownwords?” Studentssharedifferentstrategies “Whosolvedtheprobleminadifferentway?” Applyownreasoningtoanother’sreasoning “Doyouagreeordisagree?Why?” Partners forMathematicsLearning

17. 17 ToolsforClassroomDiscussions Promptingfurtherexplanation “Saymoreaboutthat” Promptingfurtherparticipation “Wouldanyoneliketoaddtohisidea?” Promptingaresponsefromallstudents “Thumbsupifyouunderstandthesolution” Waitbeforeandafterresponses “Takeyourtime…We’llwaitforyoutothink” Waitatleast5-10secondsforstudentstothink Partners forMathematicsLearning

18. 18 Pre-AssessmentofLearningTargets Pre-tests,pre-assessments,diagnostic assessments Needtobenarrowlyfocusedoncontentin nextinstructionalunit Resultshighlightneedsofstudentswho appearateitherextreme(knowcontentor missalmosteverything) Resultsidentifyareasthatneedmoreorless timefortheclassasawhole Partners forMathematicsLearning

19. 19 Pre-AssessmentofLearningTargets Pre-Assessmentshelpyouknow: Howfamiliararemystudentswiththisconcept? Whatknowledge,skillsandstrategiesdothey alreadyhavetosupportlearninginthisarea? Whatmisconceptionsdotheyhave? Aretheycomfortablewiththevocabularywithin thistopic? DaceyandLynch,MathForAll:DifferentiatingInstruction,2007 Partners forMathematicsLearning

20. 20 Pre-AssessmentofLearningTargets Partners forMathematicsLearning

21. 21 CreatingaPre-Assessment Inyourgradelevelgroupsdeterminea potentiallearningtargetforyourstudentsthat youwilladdressinthecomingweeks Togetherwritea3-4questionpre-assessment forthelearningtargetthatwillallowyouto “takethepulse”ofyourclass Thinkaboutthedifferentkindsofknowledge studentswillusetorespondtothequestions Partners forMathematicsLearning

22. 22 WhatNext?MakingPlans Pre-Assessmentsmaycauseustochange LearningTargets InstructionalPlans Questionstoaskyourself: Wherearewegoing? Wherearewenow? Howcanwegetthere? ? ? ? ? ? Partners forMathematicsLearning

23. 23 WhatNext?MakingPlans Learningtargetsforthis pre-assessmentinclude Identificationofangles Comparingandcontrastingpolygons Usingpre-assessments Examinetheresultsofathirdgradepre- assessmentforageometryunit Identifycommonmisconceptionsandgaps inunderstanding Partners forMathematicsLearning

24. 24 WhatNext?MakingPlans Whatdoyounotice? Isthereawholegrouplessonthatwillbenefit allstudents? Aretherestudentswhoneedspecific interventions? Aretherestudentswhoalreadydemonstrate masteryofthelearningtargets? Howcanalessonbedifferentiatedtomeet theneedsofthesestudents? Partners forMathematicsLearning

25. 25 WhatNext?MakingPlans “…ourjobistochallengestudents’comfortlevel andthentohelpthemfindtheirnextboundaries. …wetrytoidentifyevidenceforwhatthechild knowsorhasmastered,areaswhereinitialideas areformedbutadditionalexperiencewiththem isneeded,andthoseconceptsandskillsthat requirefurtherscaffoldingoradditionalreadiness development.” DaceyandLynch,MathforAll:DifferentiatingInstruction,2007 Partners forMathematicsLearning

26. 26 KeepinMind… ZoneofProximalDevelopment Vygotsky(1978),Fleer(1992),Jacobs2001) Student’s Current achievement http://www.learningandteaching.info/learning/constructivism.htm Partners forMathematicsLearning

27. 27 DifferentiatedInstruction “DifferentiatedInstructionisanorganized, yetflexiblewayofproactivelyadjusting teachingandlearningtomeetstudents wheretheyareandhelpallstudents achievemaximumgrowthaslearners.” CarolAnnTomlinson(1999).HowtoDifferentiateInstruction inMixed-abilityClassrooms.Alexandria,VA:ASCD Partners forMathematicsLearning

28. 28 DifferentiatedInstruction        Flexiblegroupings Scaffolding TieredAssignments Choices/Anchors/Menus LearningContracts Compacting Pre-teachingand Mini-lessons Partners forMathematicsLearning

29. 29 ScaffoldingLearning Scaffoldsarestructuresputinplaceto allowstudentstobesuccessfullearners ofmathematics Scaffoldinggiveschildrenopportunities toaccomplishtasksthat theywouldbeunableto completealone Partners forMathematicsLearning

30. 30 ScaffoldingLearning Teacherbecomesacoach– helpingallchildrenreachtheirpotential Scaffoldinglearningisguidingthestudent towardthekindofthinkingthatis necessarytodothetask,nottoward onespecificstrategyoranswer Scaffoldinglearningdoesnotmean replacingstudentthinkingwithteacher thinking Partners forMathematicsLearning

31. 31 ScaffoldingLearning Scaffoldsmay Includequestionsthatleadstudentstobe moresystematicorlogical Encouragestudentstogobeyondtheirlevelof comfortandunderstanding Helpdevelopstrategiesexplicitlyforworking withnewmathematicalcontentandactivities Connectnewlearningtopriorknowledge Partners forMathematicsLearning

32. 32 Scaffolding:Questions 2 Task:Shadeofthisset: 3 Teacher:Whatisthis taskaskingyoutodo? Whatdoyoualready knowthatwillhelp? Partners forMathematicsLearning

33. 33 Partners forMathematicsLearning

34. 34 Scaffolding:Questions 2 Task:Shadeofthisset: 3 Thestudentresponds byshadingasshown Teacher:Showme howwhatyoushaded represents2/3ofthe set Partners forMathematicsLearning

35. 35 Scaffolding:Questions 2 Task:Shadeofthisset: 3 Studentshades secondgroup Teacher:Howdoyou knowthatyouhave 2 3 Partners forMathematicsLearning shadedoftheset?

36. 36 Scaffolding:Questions 2 3 Teacher:Howmany 2 3 Partners forMathematicsLearning Task:Shadeofthisset: circlesareinof theset?

37. 37 Scaffolding:GraphicOrganizers Howareasquareandarectanglealike anddifferent? Alike Different WordBank Partners forMathematicsLearning

38. 38 Scaffolding:GraphicOrganizers TogetherToddandKerriearned28pointsinthe basketballgame.Toddearned3timesasmany pointsasKerri.HowmanypointsdidToddearn? Partners forMathematicsLearning

39. 39 Scaffolding:GraphicOrganizers TogetherToddandKerriearned28pointsinthe basketballgame.Toddearned3timesasmany pointsasKerri.HowmanypointsdidToddearn? 28 Todd Kerri Partners forMathematicsLearning

40. 40 Scaffolding:GraphicOrganizers Timhad$1.00incoins.Hehad15coinswhich wereonlydimesandnickels.Howmanyofeach kindofcoindidhehave? WorkSpace: dimes nickels Partners forMathematicsLearning

41. 41 Scaffolding:VaryProblemStructures Seandrove120milesandstoppedforlunch. Thenhedroveanother180milesbeforehe reachedhisdestination.Howmanymilesdid Seandrive? Whatdoweknow? Whatarewetryingtofindout? 120+180=? Partners forMathematicsLearning

42. 42 Scaffolding:VaryProblemStructures Seandrove120milesandstoppedforlunch. Thenhedrovesomemore.Bythetimehe gottohisdestination,hehaddriven300 miles.Howmanymilesdidhedriveafter lunch? Whatdoweknow? Whatarewetryingtofindout? 120+?=300 Partners forMathematicsLearning

43. 43 Scaffolding:VaryProblemStructures Seandroveforawhilebeforehestoppedfor lunch.Afterlunchhedrove180milesto reachhisdestination.Whenhegottherehe haddriven300miles.Howmanymilesdid Seandrivebeforelunch? Whatdoweknow? Whatarewetryingtofindout? ?+180=300 Partners forMathematicsLearning

44. 44 Scaffolding:VaryProblemStructures Seandrove120milesandstoppedforlunch.Thenhedroveanother 180milesbeforehereachedhisdestination.HowmanymilesdidSean drive? Seandrove120milesandstoppedforlunch.Thenhedrovesome more.Bythetimehegottohisdestination,hehaddriven300miles. Howmanymilesdidhedriveafterlunch? Seandroveforawhilebeforehestoppedforlunch.Afterlunchhedrove 180milestoreachhisdestination.Whenhegottherehehaddriven 300miles.HowmanymilesdidSeandrivebeforelunch? Howdoesvaryingtheorderinwhichyou givestudentsproblemsprovidesupport forstudents? Partners forMathematicsLearning

45. 45 Scaffolding:VaryProblemStructures Set1 Set2 Total Partners forMathematicsLearning

46. 46 Scaffolding:VaryProblemDifficulty Seandrove(60,120,3407)mileslastyear onhisvacation.Hedrove(93,180,2159) milesonthisyear’svacation.Howmany milesdidSeandriveonbothvacations? Teachersmaydirectwhichnumberstouse Studentsmaychoosenumberstouse Whatconversationsmightstudentshave whenyouusethistypeoftask? Partners forMathematicsLearning

47. 47 Scaffolding:UsingModels Modelsandrepresentationshelpstudents Makesenseofmathematics Organizetheirthinking Justifytheirresponses Communicatetheirideas Creatementalimagesofmathematical ideasthattheycanuseinsolvingproblems Partners forMathematicsLearning

48. 48 ScaffoldingLearning Allchildren-evenourmostadvanced students-shouldbechallengedtostruggle withtasksthatrequiresomesupportto accomplish Supportthroughgraphicorganizers Supportbyworkingwithapartner Supportbyworkinginagroup Challengesshouldinvolvemeaningful mathematicstodevelopdepthofthinking Partners forMathematicsLearning

49. 49 TieredAssignments Tieredactivitiesorlessons Aseriesofrelatedtasksofvaryingcomplexity Relatetoessentialunderstandingsandkey skillsthatstudentsneedtoacquire Assignedasalternativewaysofreachingthe samegoalstakingintoaccountindividual studentneeds Canutilizealternativetasksintextbooks Partners forMathematicsLearning

50. 50 ProcessofTieredAssignments Identifythelearningtarget Formgroupsbasedonassessments Planameaningfulactivityforeachgroup dependingonthestudents’needs Partners forMathematicsLearning