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Partners for Mathematics Learning

1. PARTNERS for Mathematics Learning Formative Assessment to Support Student Learning Module 5 Grades 6-8 Decisions about Next Steps. Partners for Mathematics Learning. 2. Putting it to Practice.  Turn and talk  Describe the strategy you used to increase

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Partners for Mathematics Learning

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  1. 1 PARTNERS forMathematicsLearning FormativeAssessmenttoSupportStudentLearning Module5 Grades6-8 Decisions about NextSteps Partners forMathematicsLearning

  2. 2 PuttingittoPractice Turnandtalk Describethestrategyyouusedtoincrease studentresponsibilityinyourclassroom Describewhatworkedandwhatdidn’t Discusspossiblewaysofalteringthispracticeand howyouimplementthestrategyasecondtime Partners forMathematicsLearning

  3. 3 OverviewofModules Module1:LearningTargets Module2:QuestioningandTaskSelection Module3:InferencesandFeedback Module4:MakingStudentsActivePartners Module5:DecisionsaboutNextSteps Module6:CollaborationAroundAssessment Partners forMathematicsLearning

  4. 4 MakingDecisions:NextSteps Learningtargetsforthismodule Identifynextstepsfor meetingstudent’sneeds Practicewithvarious strategies,inorderto implementthemin theclassroom Partners forMathematicsLearning

  5. 5 Teaching-LearningCycle Clear Learning Targets Decisions About NextSteps Questioning& Instructional Tasks Collaboration Around Assessment Making Inferences &Giving Feedback Partners forMathematicsLearning StudentSelf- Assessment& Responsibility

  6. 6 MakingDecisions:NextSteps Thequalityanddepthofstudent learningisinfluencedbythedecisions teachersmake Partners forMathematicsLearning

  7. 7 MakingDecisions:NextSteps Thus,formativeassessmentshould Giveinformationaboutstudents’understanding Guideteachersinchoosinginterventionsfor individualstudents Assistinplanningnextstepsforthewholeclass Formativeassessmentdatahasvalue accordingtohowwellweuseittoplan Partners forMathematicsLearning

  8. 8 InformationAboutStudents Wegatherinformationaboutstudents’ understandinginmanyways… Students’writtenwork Conversationsorinterviews withindividuals Classdiscussions Pre-assessmentsfor learningtargets Partners forMathematicsLearning

  9. 9 MakingDecisions:NextSteps WholeClassInstruction Instructionforalllevels–designing instructiontomeetneedsofallstudents acrossthespectrumofmastery Withinthecontextofwholeclassinstruction Instructionforallneeds–specificstrategies tomeetidentifiedneedsofstudents Individualized/smallgroupinstruction Inthismodule,wefocusonstudentswhohave yettomeetthelearningtargets Partners forMathematicsLearning

  10. 10 ThreeStarsandaWish Inyourjournal… Listwaysyouareusingformativeassessment toinformyourinstructionalplanning Listthewaysyouarecurrentlyaddressing differinglevelsofmasteryinyourclassroom Listthewaysyouarecurrentlyaddressing differingneedsinyourclassroom Starthe3mosteffectiveofthese Writeonespecificwishforideasrelated tothese Partners forMathematicsLearning

  11. 11 ResearchSuggestedStrategies Toeffectivelymeetallstudents’needs… Keepfocusonconceptsandsense-making Useformativeassessmentstrategiesto understandstudents’thinking Maintainhighexpectationsforachievementof learningtargetsforallstudents Useongoingassessmentstoidentifystudents whoneedadditionalsupportorextensions Involvestudentsmoreinself-assessment Useassessmenttomakeflexiblegroupings Partners forMathematicsLearning

  12. 12 NextStep:FlexibleGroups Flexiblegroupingisapowerfulstrategy thatcanbeusedtomeetstudentsneeds Groupsarenotstaticbutareever- changingbasedonavarietyofcriteria Responsestotasks Readiness Workhabits Performance StudentInterestsandchoices Partners forMathematicsLearning

  13. 13 TypesofGroups Wholeclass  Workasindividuals  Teacherdesignated  Randomgroups  Readinessfortasks  Likereadiness Differentlevelsof readiness Learningstyles Similar Random Studentinterests Studentchoice Whatotherwaysdo yougroupstudents? Partners forMathematicsLearning

  14. 14 LookingatStudentWork Dailypracticemaybeusedtomake decisionsabouttheneedsofstudents Lookatthestudentworkandtalkatyour tableaboutwhatyouknowaboutthese studentsandtheirknowledge Whatwouldyoudonextinawholeclasslesson? Howmightyougroupstudentsbasedonthe work? Bepreparedtoshareyourideas Partners forMathematicsLearning

  15. 15 Remember Groupsshouldchange If,inreactiontostudentwork,thegroups arealwaysthesame,anotherstrategyfor groupingoraddressingstudentneedsis required Groupingshouldhaveapurposeand enhancethelesson Studentswillneedstructureandpractice withintheirgroups Partners forMathematicsLearning

  16. 16 NextStep:WholeClassLesson Wholegrouplessons Providecommonexperiences Exposestudentstoavarietyofthinking Cansupportindividualneedsandstrengths • • • • Usethink/pair/sharestrategy Allowwaittimebeforeresponses Encourageresponsesfromseveralstudents Connectcommentstopreviousspeakers Welearnmuchmoretogetherthanwe canalone Partners forMathematicsLearning

  17. 17 NextStep:WholeClassLesson Havestudentslookatexamplesanddiscuss whicharecorrect,whicharenotandwhy Putsamplesonanoverhead,documentcamera, orwriteontheboard Besurenostudentnamesareattached Letstudents-notteacher-discusserrors Teacherchooses3or4problemstodiscuss withtheclassandthengivesstudentsan opportunitytosolve3or4similarproblems Partners forMathematicsLearning

  18. 18 ClassroomDiscussionTools Teacherre-voicesstudent’sstatement “Soyou’resayingthat…” Studentsrestateanother’sreasoning “Canyouputherideaintoyourownwords?” Studentssharedifferentstrategies “Whosolvedtheprobleminadifferentway?” Applyownreasoningtoanother’sreasoning “Doyouagreeordisagree?Why?” Partners forMathematicsLearning

  19. 19 ClassroomDiscussionsTools Promptingfurtherparticipation “Wouldanyoneliketoaddtohisidea?” Promptingaresponsefromallstudents “Thumbsupifyouunderstandthesolution.” Promptingmorefromonestudent “Saymoreaboutwhatyouarethinking.” Waitbeforeandafterresponses “Takeyourtime…We’llwaitforyoutothink.” Waitatleast5-10secondsforstudentstothink Partners forMathematicsLearning

  20. 20 WhatNext?MakingPlans “…ourjobistochallengestudents’comfortlevel andthentohelpthemfindtheirnextboundaries. …wetrytoidentifyevidenceforwhatthechild knowsorhasmastered,areaswhereinitialideas areformedbutadditionalexperiencewiththem isneeded,andthoseconceptsandskillsthat requirefurtherscaffoldingoradditionalreadiness development.” DaceyandLynch,MathforAll:DifferentiatingInstruction,2007 Partners forMathematicsLearning

  21. 21 KeepinMind… ZoneofProximalDevelopment Vygotsky(1978),Fleer(1992),Jacobs(2001) Student’s Current achievement http://www.learningandteaching.info/learning/constructivism.htm Partners forMathematicsLearning

  22. 22 NextStep:ScaffoldingLearning Scaffoldsarestructuresputinplaceto allowstudentstobesuccessfullearners ofmathematics Scaffoldinggivesstudentsopportunities toaccomplishtasksthat theywouldbeunableto completealone Partners forMathematicsLearning

  23. 23 ScaffoldingLearning Teacherbecomesacoach– helpingallstudentsreachtheirpotential Scaffoldinglearningisguidingthestudent towardthekindofthinkingthatis necessarytodothetask,nottowardone specificstrategyoranswer Scaffoldinglearningdoesnotmean replacingstudentthinkingwithteacher thinking Partners forMathematicsLearning

  24. 24 ScaffoldingLearning Scaffoldsmay Includequestionsthatleadstudentstobe moresystematicorlogical Encouragestudentstogobeyondtheir levelofcomfortandunderstanding Helpdevelopstrategiesexplicitlyfor workingwithnewmathematicalcontentand activities Connectnewlearningtopriorknowledge Partners forMathematicsLearning

  25. 25 Scaffolding:Questions Task:Findtheareaofthetriangle Teacher:Whatisthis taskaskingyoutodo? Whatdoyoualready 13 knowthatwillhelp? 12 Partners forMathematicsLearning

  26. 26 Scaffolding:Questions Task:Findtheareaofthetriangle Studentrespondsby calculating1"12"13 2 Teacher:Tellmeabout 13 yourcalculation.Howdo Partners forMathematicsLearning 12 youknowwhattodo?

  27. 27 Scaffolding:Questions Task:Findtheareaofthetriangle Thestudentresponds byfindingthelength oftheotherleg 13 Teacher:Showme howyoufoundthe length 12 Partners forMathematicsLearning

  28. 28 Scaffolding:Questions Task:Findtheareaofthetriangle Studentfindsthearea Teacher:Howdoyou knowthatyouhave 13 thecorrectarea? Studentsdescribes thestepssheused 12 Partners forMathematicsLearning

  29. 29 Scaffolding:GraphicOrganizers Canencourageorganizationofwrittenwork forstudentsnotalreadydevelopingtheirown methodsoforganizing Canhelpstudentscommunicatetheir thoughtsandreasoning Lookatthehandoutforsomeexamples Discusstheseideasatyourtablesandshareother graphicorganizersyouhavefoundusefulfor studentsinyourclassroom Partners forMathematicsLearning

  30. 30 Scaffolding:VaryProblemStructures Seaninvested$1,000inamoneymarket account.Howmuchinterestwouldheearn onhismoneyafter2yearsatayearlysimple interestrateof5%? Whatdoweknow? Whatarewetryingtofindout? 1000×.05×2=? Partners forMathematicsLearning

  31. 31 Scaffolding:VaryProblemStructures Seaninvested$1,000inamoneymarket account.Howmuchwouldhehaveinhis account,after2yearsatayearlysimple interestrateof5%? Whatdoweknow? Whatarewetryingtofindout? 1000+1000×.05×2=? Partners forMathematicsLearning

  32. 32 Scaffolding:VaryProblemStructures IfSeanearned$100ininterestonmoney thatheinvestedfor2yearsatasimple yearlyinterestrateof5%,howmuchmoney didSeaninvest? Whatdoweknow? Whatarewetryingtofindout? ?×.05×2=100 Partners forMathematicsLearning

  33. 33 Scaffolding:VaryProblemStructures IfSeanearned$100inintereston$1,000 thatheinvestedatasimpleyearlyinterest rate,whatarepossiblerateandtime combinationsthatwouldhaveearnedhim thisinterest? Whatdoweknow? Whatarewetryingtofindout? 1000×__×__=100 Partners forMathematicsLearning

  34. 34 Scaffolding:VaryProblemStructures Ingrade-levelgroups,write3restructured problemsfromthelistbelow Grade6:Eachtabletinaboxofallergymedicine weighs0.3gram.Findthetotalweightofthe tabletsintheboxifthereare50tablets. Grade7:Aschoolpopulationrosefrom234to 440overaperiodoftwoyears.Whatisthe percentincreaseinstudents,tothenearesttenth ofapercent? Grade8:Onethirdofanumberplusthreetimes thesamenumberissixty.Findthenumber. Partners forMathematicsLearning

  35. 35 Scaffolding:VaryProblemDifficulty Seandrove(60,120,3407)mileslastyear onhisvacation.Hedrove(93,180,2159) milesonthisyear’svacation.Howmany milesdidSeandriveonbothvacations? Teachersmaydirectwhichnumberstouse Studentsmaychoosenumberstouse Whatconversationsmightstudentshave whenyouusethistypeoftask? Partners forMathematicsLearning

  36. 36 ScaffoldingLearning Allstudents-evenourmostadvanced ones-shouldbechallengedtostruggle withtasksthatrequiresomesupportto accomplish Supportthroughteacherquestion Supportbygraphicorganizers Supportbyvaryingproblemstructure Challengesshouldinvolvemeaningful mathematicstodevelopdepthofthinking Partners forMathematicsLearning

  37. 37 ReactingtoStudentResponses Whenweassigntasks,whethertothe classasawholeortogroupsofstudents, weneedtothinkaheadabout Whatarewelookingforinthestudents’ responses Whatmisconceptionsorincomplete understandingsdoweneedtowatchfor Formativeassessmentisaboutstructuring lessonsfordepthofknowledgeandlong- termstudentsuccess Partners forMathematicsLearning

  38. 38 NextStep:TieredAssignments Tieredactivitiesorlessons Aseriesofrelatedtasksofvaryingcomplexity Relatetoessentialunderstandingsandkey skillsthatstudentsneedtoacquire Assignedasalternativewaysofreachingthe samegoalstakingintoaccountindividual studentneeds Teacherscanutilizealternativetasksin textbooks Partners forMathematicsLearning

  39. 39 ProcessofTieredAssignments Identifythelearningtarget(sameforall tiers) Formgroupsbasedonpriorassessments Planameaningfulactivityforeachgroup dependingonthestudents’needs Partners forMathematicsLearning

  40. 40 LinearExample Dotheexample,thendiscuss Howarethetiersalike/different? Howdotheyrelatetothelearningtargets? Aretheredifferentquestionsthatcouldbe askedateachtier? !"#$#%&' 3"*#/$&4((")*+#*,&-./ 1&7,/*%/$%2&"0( 9<'8$/%#:&' #&5B&1"*,&,6#&+ "*);F#G,,"5*% $/0#0$# 5& )&!/$),& )$/06#%&%#,#$+ $5#&, #&/1#&,5"*&,/;1#&5,6#&1 "#$&&@/$"/;1#(& $5;1#+ C$#/,# 6&5 #*&,/;1#$%#$#% 5G,/(, 5"*,(&D5 A&015,< Howwouldyoudebriefthetasks? Partners forMathematicsLearning -((#*,"/#1/,"5*(6+01#2 5B&(150<=&>&?*,#$0$#&91)#;$/ C1/$"BD#/$&$#1/#/*"*)&/ )"@#*&/&E"@#2&9*(6"0(&@/1A#& &,1#:&)<' 0,(/6:&1<=<H&>(# 5"*;"*&4* #/$&#IA,&(10#& /&55 ,"5*$&,J 3#/$*"* ?&J"11&;#B5$&,6 #&/;1#&,5#&1#((5*&> ?&J"11&;&B+&@/1A#(&"*6#&(150# $#0$#(#;&$#1/,#&/<B&"*#& *,#%&"*&,6#&(15 &/&,/;1#0#&,5&,6# !H&K &/&)0 ,6#&)"@$/B&,6#&5 :&G**#&0"$(&1" "*&,6##&"*& )&0%

  41. LinearExample Whatyoudothenextday? Whatwouldthelearningtargetsbe? Whattasksmightyouplanforeachtier? Ifstudentsinthelowertiersaresuccessful withthetasks,wouldyouassignthemthese problems? Wouldyoubringthegroupsbacktogether, keepthesametiers,orreconfigurethetiers? Partners forMathematicsLearning

  42. 42 FlexibleGroups:TieredAssignments Studentsworkinassignedgroups,sothat twogroupscanworkindependentlywhile theteacherworkswithonegroup Ifstudentshaveaquestion,andarenotin thegroupthattheteacheriscurrently workingwith,thentheymust Askatleasttwootherpeopleintheirgroup beforetheycanasktheteacher Orcompletea“3BeforeMe”;try3things beforetheycanasktheteacher Partners forMathematicsLearning

  43. 43 NextStep:StudentChoice Anchors,ChoiceBoards,andMenus Acollectionofactivitiesfromwhichstudents maychoosewhiletheteacherisworkingwith anotherindividualorgroup(orwhenevera choiceisappropriate) Activitiesareworthyofastudent’stime,focus onessentialskills,andareappropriateto learningneeds Activitiesaremeaningfultasksthatprovide extensionsorreinforcementofmathematics Partners forMathematicsLearning

  44. 44 StudentChoice Think-Tac-Toe Agridofactivitychoicesorproblems Teachertellsstudentshowtochoosetheir activities,ex.chooseonefromeachrow,or completeoneactivityfromeachcolumn,or completealltasksinanyroworcolumn X O Partners forMathematicsLearning

  45. 45 NextStep:Interventions Assumeclassroomstrategiesandstudent experiencesarenotenough… StrategicorInstructionalInterventionsare modificationswithintheclassroom IntensiveInterventionsarestrategies employedbeyondtheclassroom Partners forMathematicsLearning

  46. 46 Interventions:MakingtheTime Sharewiththegroupwaysthatyouhave foundtimetoprovideintensiveinterventions forstudents Asyoulistentoyourcolleagues, listinyourjournalnewwaysthat youwouldliketotry Partners forMathematicsLearning

  47. 47 InstructionalInterventionis… Targetedinstructionbasedonongoing assessments Additionalinstructionadministeredbythe teacheroraresourceperson Pre-teachingormini-lessonsonneeded skills Teachingadditionalstrategies Modificationsincurriculum Changesintypesandmethodsoffeedback Partners forMathematicsLearning

  48. 48 InstructionalInterventionis… Modificationsin Modesoftaskpresentation Instructionaltime Groupsize Amountandkindofcuesandprompts Taskstructure(increase) Taskrelevantpractice(increase) Partners forMathematicsLearning

  49. 49 InstructionalInterventionisNOT…       Preferentialseating* Shortenedassignments* Parentcontacts* Classroomobservations* Suspensionsorretention Doingmoreofthesameassignment *Helpfulstrategiesforimprovedstudent performancebutarenotinterventionstrategies Partners forMathematicsLearning

  50. 50 MeetingStudentNeeds Keepfocusonconcepts,understanding, andsense-making Useongoingassessmentstofindstudents whoneedmoresupportorextensions Makegroupingsflexible Betheguideandfacilitator Assessbasedongrowthandachievement oflearningtargets Partners forMathematicsLearning

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