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Partners for Mathematics Learning

This module focuses on the importance of selecting effective mathematical tasks and asking higher-level questions to support student learning. It explores how tasks impact student engagement and understanding. Participants will examine different tasks, compare their characteristics, and learn to select tasks aligned with learning targets.

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Partners for Mathematics Learning

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  1. 1 PARTNERS forMathematicsLearning FormativeAssessmenttoSupportStudentLearning Module2 Grades6–8 Questioning and TaskSelection Partners forMathematicsLearning

  2. 2 PuttingItToPractice Onthepaperprovided,list… Thelesson(s)andlearningtargetsshared Themethodsofsharingwithstudentsand parents Anyimpactyounoticedwithinyourstudents, yourself,and/oryourclassroomfromthis sharing Besuretolookatyourcolleagues pagesatthebreak Partners forMathematicsLearning

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

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

  5. 5 WhyFocusonTasks? Classroominstructionshouldbeorganized aroundmathematicaltasks Thetasksinwhichstudentsengage determinewhattheylearnabout mathematicsandhowtheylearnit “Notalltasksarecreatedequal,and differenttasksprovokedifferentlevelsand kindsofstudentthinking.” (Stein,Smith,Henningsen&Silver,2000) Partners forMathematicsLearning

  6. 6 WhyFocusonTasks? Howdoyouusemathematicaltasksin yourclass? Currently,howdoyou decideonthetasks foryourclass? Partners forMathematicsLearning

  7. 7 TaskSelection “Oneofthemostimportantandyetdifficult aspectsofdesigningalessonischoosingor creatingtheworthwhilemathematicaltaska teacherwantsstudentstoengagein.” Lappan&Friel,1993 Partners forMathematicsLearning

  8. 8 ModuleLearningTargets Tolearnhowtoselecttasksthatallowfor thegreatestopportunityforstudentlearning, whilebeingalignedwithlessonlearning targets Toaskquestionsathigherlevelstosupport thosetasksinordertoengage,deepen,and assessmathematicalunderstandinginour students Partners forMathematicsLearning

  9. 9 CharacteristicsofMathematicalTasks Lookatthetwotasksonthe nextslidesandthinkabout: Howwouldyougoaboutsolvingthem? Whatwouldbeapossiblelearningtargetyou wouldhaveforselectingthesetasks? Whichofthetwotasksrequiresstudentsto domorein-depththinkingandcausesthem tobemoreintellectuallyengaged? Partners forMathematicsLearning

  10. 10 Task1 Youarecarpetingaroomthatis3yards longand4yardswide.Howmanysquare yardsofcarpetingdoyouneedto purchase? Partners forMathematicsLearning

  11. 11 Task2 Ourclasswillraisechickensforthe sciencefairandcanuse24feetoffencing tobuildarectangularpen Howlongarethesidesthatgivethechickens asmuchroomaspossible? Howlongarethesidesifonly16feetof fencingisused? Howwouldyoudeterminethepenwiththe mostroomforanyamountoffencing? Partners forMathematicsLearning

  12. 12 Comparisons Howarethetwotasksalike? Howaretheydifferent? Foreachtask… How/whenwouldyouimplementthistask? Whatistheroleoftheteacherandstudents? Whatskillswereemployedduringthetask? Whatkindsofinformationaboutastudent’s thinkingcanbegatheredthrougheachtask? Partners forMathematicsLearning

  13. 13 Difficultyvs.IntellectualEngagement 12 += 45 Thisproblemwouldbedifficultforafirst gradertosolvebutnotforasixthgraderthat hasthemathematicalunderstanding Themathisthesameandtheintellectual engagementisthesameforanygradelevel Thelevelofdifficultychangesdependingon thestudent’smathematicalunderstanding Partners forMathematicsLearning

  14. 14 NAEPLevelsOfComplexity LowComplexity-recall,recognition,calls forsomeprocedureoralgorithm ModerateComplexity-moreflexibilityof thinkingthanthelow-complexity,beyondthe habitual,morethanasinglestep,methods ofreasoningandproblem-solvingstrategies HighComplexity-moreabstractreasoning, planning,analysis,judgment,andcreative thought Partners forMathematicsLearning

  15. 15 TaskSort Sortthetaskcardsintopiles Onepileyouconsidertocontainlow complexitytasks Onepileyouconsidertocontainmoderate complexitytasks Onepileyouconsidertocontainhigh complexitytasks Remember: Difficulty≠intellectualengagement! Partners forMathematicsLearning

  16. 16 TurnandTalk Whenistheappropriatetimeandplacefor lowercomplexitytasks? Howshouldtasksrelatetolearningtargets? Partners forMathematicsLearning

  17. 17 MaintainingHigherComplexityTasks Sufficienttimeallowedforexploration–not toomuchortoolittle Highlevelperformancemodeledbyteacher orcapablestudents Taskbuildsonpriorknowledge Teacherdrawsonfrequentconnections Teacherpressesforjustifications,explanations, andmeaningthroughquestioning,comments, andfeedback Partners forMathematicsLearning

  18. 18 GoodMathQuestions Goodmathquestionsengagestudents Studentsdomorethanrecallknownfacts Studentshaveopportunitiestomake connections Goodmathquestionspromote developmentofhigherlevelsofthinking andreasoninginstudents Partners forMathematicsLearning

  19. 19 GoodMathQuestions Requiresmorethanrememberingafactor reproducingaskill Studentscanlearnfromansweringthe questionandteacherslearnabouteach studentfromtheirattemptsatsolutions Theremaybeseveralpossibleanswers Relategoodquestionstotasksthat requiregreaterintellectualengagement Partners forMathematicsLearning

  20. 20 MathTask,Question,orProblem? Thesetermsarebeingused interchangeablythroughoutourmodules, thoughdifferentauthorsmayusedifferent definitions Sometimesataskhasonlyonequestion, andothertimes,it’sascenariowith multiplequestions Partners forMathematicsLearning

  21. 21 Recognizing“Good”Questions Explainwhythefirstquestionisroutine Whatisthemeanof6,7,5,8,and4? Theaverageoffivedifferentnumbersis6.What mightthenumbersbe? Afterfivegames,thegoaliehadaveraged blocking6goalspergame.Whatmightbethe numberofgoalsheblockedineachgame? Howdothe2ndand3rdquestionschallenge studentthinkingofthesamelearningtarget? Partners forMathematicsLearning

  22. 22 TransformingaRoutineQuestion LearningTarget:Solvemulti-step inequalities RoutineQuestion:Solve3x+1<28 NOW… Writeapossiblenon-routinequestion thatislikelytostimulatestudent interestandencourageagreaterdepth ofunderstanding Partners forMathematicsLearning

  23. 23 TransformingaRoutineQuestion LearningTarget1:Addandsubtractintegers LearningTarget2:Useratiostosolveaproblem Writearoutinequestion Write2newnon-routinequestions Recordyourexamplesinyourjournals andbereadytosharewithothers Partners forMathematicsLearning

  24. 24 TalkatYourTables Whyisitokayforstudentstostrugglewith ataskoragoodquestion? Writeyourresponsein yourjournal Partners forMathematicsLearning

  25. 25 TheRoleofQuestioning “Duringthecourseofaschoolday, teachersaskmanyquestions.Infact, somethinglike60%ofthethingssaidby teachersarequestionsandmostofthese arenotplanned.” GoodQuestionsforMathTeaching,Sullivan&Lilburn,2002 Discusswithapartnerkindsofquestions youroutinelyaskandwriteexamplesin yourjournal Partners forMathematicsLearning

  26. 26 WaysTeachersUseQuestions EngagingQuestions RefocusingQuestions ClarifyingQuestions DynamicClassroomAssessment,BrightandJoyner,2005 Partners forMathematicsLearning

  27. 27 EngagingQuestions Invitestudentsintoadiscussion, Keepstudentsengagedinconversations Invitethemtosharetheirworkorget answers“onthetable” Examples: Whatstrategiesmightweusetosolvethis problem? Whatdoyouknowthatwillhelpyouanswer thisquestion? Partners forMathematicsLearning

  28. 28 FindThePerimeter Engaging questionsare questionsthat invitestudentsinto aconversation 3cm 4cm 3cm “Howcanwefind themissing measurements?” 1cm ModifiedfromDynamicClassroomAssessment,BrightandJoyner,2005 Partners forMathematicsLearning

  29. 29 RefocusingQuestions Helpsstudentsgetbackontrackorwalk awayfrom“deadend”strategies Reopensconversationtothegroupifonly oneortwostudentsareanswering Examples: Howisthisproblemsimilartotheone wejustdid? Whatquantitiesareyoucomparing? Partners forMathematicsLearning

  30. 30 FindThePerimeter Refocusingquestions helpstudentsgetback ontrackormoveaway fromadead-end strategy 3cm 4cm 3cm “Ifthefigureisalarge rectanglewithapiece cutout,whatdoyou knowaboutthelarge rectangle?” Partners forMathematicsLearning 1cm

  31. 31 ClarifyingandProbingQuestions Helpstudentsclarifytheirownthinking Helpteachersunderstandstudents’ thinking Helpstudentsunderstandeachother’s ideas ExampleQuestions Howdidyoufigureoutyouranswer? Whydidyoustartwiththatnumber? Nika,canyouexplain,inownwordswhat Mariajustshared? Partners forMathematicsLearning

  32. 32 FindThePerimeter Clarifyingquestionshelp 3cm studentsexplain& teachersunderstandtheir thinking Bobsaidthatthemissing measurementsare1cm and2cm,andtheteacher asks,“Bob,canyou explaintoMaryhowyou gotthoseanswers?” Partners forMathematicsLearning 4cm 3cm 1cm

  33. 33 IntegratingPurposesofQuestions Engagingquestionscanhelpthreada discussionbyinvolvingmanystudentsin theconversation Refocusingquestionscanhelpkeepa discussionfromgoingoffonatangent Clarifyingorprobingquestionscanhelp othersunderstandstudentresponsesand canhelpstudentsself-checktherelevance oftheircontributions Partners forMathematicsLearning

  34. 34 HowtoAskGoodQuestions Fromresearchonquestioningweknow Waitingforanswersisimportant Questionsmayneedtoberephrasedfor clarity Moreprobingquestionsneedtobeasked,not justfactualquestions Askonlyonequestionatatime Beflexiblewithexpectedanswers Somuchofquestioningiscontextual Partners forMathematicsLearning

  35. 35 MakingItAHabit Onceyourlearningtargetshavebeen determinedandtheappropriatetaskshave beenchosen,thinkaboutimportant questionstoaskstudentsduringthelesson Engaging,Refocusing,ClarifyingandProbing • • • • Specifictothecontent Forstudentswhoarestruggling Forstudentswhoareontrack Forstudentsreadyformore Copythemonindexcardstokeepwithyou throughoutthelesson Partners forMathematicsLearning

  36. 36 InSummary Whenselectingtasks,thinkabout… Whatareyourlearningtargets? Whatbackgroundknowledgeisneededforthe task? Whatarewaysthetaskcanbesolved? (misconceptions/errorsstudentsmayhave) Whatareyourexpectationsforstudents? Howwillyoucommunicateandassessyour expectations? ArethereanychallengesforEC/ELLstudents? Partners forMathematicsLearning

  37. 37 SelectingandSupportingTasks Whatquestionswillyouask–engaging, refocusing,andclarifying? Howwillyouorchestratea classroom/groupdiscussionarounda task? Howwillyouassessstudentmasteryof thelearningtarget? Whatwillyoudotomorrowtobuildonthis lesson? Partners forMathematicsLearning

  38. 38 WhyFocusonTasks? Revisitingjournalquestions: Whatquestionsdoyoustillneedanswered onmathematicaltasksfromyourlistfrom earlierinthismodule? Insummary,whatmakesagood mathematicaltask? Partners forMathematicsLearning

  39. 39 Homework:PuttingItToPractice Takeataskyouhaveusedfrequentlyin classandchangeittoincreasethelevelof complexityassociatedwiththattask Createalistofquestions-engaging, refocusing,andclarifyingandprobing- youmightaskaboutthisalteredtask Partners forMathematicsLearning

  40. 40 DPIMathematicsStaff ChiefConsultant ReneeCunninghamKittyRutherford RobinBarbourMaryH.Russell CarmellaFairJohannahMaynor AmyScrinzi PartnersforMathematicsLearningisaMathematics-Science PartnershipProjectfundedbytheNCDepartmentofPublic Instruction.Permissionisgrantedfortheuseofthesematerialsin professionaldevelopmentinNorthCarolinaPartnerschooldistricts. Partners forMathematicsLearning

  41. 41 PMLDisseminationConsultants JuliaCazin RuafikaCobb AnnaCorbett GailCotton JeanetteCox LisaDavis RyanDougherty TriciaEssick TeryGunter BarbaraHardy KathyHarris RendyKing ReneLemons-Matney TinaMcSwain MarilynMichue KayonnaPitchford RonPowell SusanRiddle AlisanRoyster JudithRucker PennyShockley PatSickles NancyTeague JanWessell DanWicks CarolWilliams StacyWozny Partners forMathematicsLearning

  42. 42 PartnersStaff JeaneM.Joyner,Co-PI&ProjectDirector FredaBallard,Webmaster AnitaBowman,OutsideEvaluator MeghanGriffith,AdministrativeAssistant TimHendrix,Co-PIandHigherEd BenKlein,HigherEducation KatieMawhinney,Co-PIandHigherEd CatherineSchwartz,HigherEducation 2010Writers AnaFloyd KatieMawhinney KayonnaPitchford WendyRich NancyTeague StacyWozny PleasegiveappropriatecredittothePartnersforMathematicsLearningprojectwhen usingthematerials.Permissionisgrantedfortheiruseinprofessionaldevelopmentin NorthCarolinaPartnerschooldistricts. Partners forMathematicsLearning

  43. 43 PARTNERS forMathematicsLearning FormativeAssessmenttoSupportStudentLearning Module2 Grades6–8 Questioning and TaskSelection Partners forMathematicsLearning

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