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Partners for Mathematics Learning

Learn effective strategies to increase student responsibility in mathematics learning. Explore what works, what doesn't, and ways to modify practices for better results. Partners for Mathematics Learning modules provide guidance and tools for informed decision-making.

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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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