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TheValueofPairingPedagogicalHookswithMeaningfulLearning
NCTM2016RegionalConference
FrankS.MarfaiPhoenixCollegeOctober28,2016
ResearchreportedinthispresentationwassupportedbyNationalScienceFoundationGrantNo.1050721.AdditionalJindingsweremadepossiblethroughthesupportoftheNationalScienceFoundationGrantNo.1103080.AnyconclusionsorrecommendationsstatedherearethoseoftheauthoranddonotnecessarilyreJlectofJicialpositionsofNSF.
QuesAon� Howmightstudentconjecturebeusedtoengagestudentsandadvancemathematicslearninginalesson?� Questionwaspartofalargerstudythatexploredtherelationshipbetweenteachers’mathematicalgoalsforteachingandtheirunderstandingsofthekeymathematicalideasoflessonstheytaught.
� Conjecture� Aneducatedguess,basedonpreviousexperienceorlearning.
Regardingconjecture� AnExample(DanMeyer’sThreeActsMath)
(Source:http://mrmeyer.com/threeacts/watertank/)
RegardingLessonPlanning� LessonPlanningandDebriefProtocolsDeveloped
� InJluencedby� ThinkingthroughaLessonProtocol(Smith,Bill,Hughes)� ProfessionalDevelopmentalSpiral(Thompson)� PathwaysProfessionalDevelopmentWorkshops(Carlson,Oehrtman,Moore;Carlson,O’Bryan,Joyner)
MethodsProJileofthisstudy� CarolynatAtlasHighSchool(Fall2014)
� Experiencedteacher(20years)� UsedaconceptualPrecalculuscurriculum(Pathways)� Teachingthirdtimewithconceptualcurriculum� Attendedprofessionaldevelopmenttrainings
Study� Lessonplanningsessions
� LessonPreJlectionQuestionnaire� ClassroomObservations� Lessondebriefsessions
� LessonDebriefQuestionnaire
� PostStudyInterview
Methods
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QuesAon� Howmightstudentconjecturebeusedtoengagestudentsandadvancemathematicslearninginalesson?
� Curriculumalreadyestablished.� Conceptualcurriculumcontainedrichtasksthatpromoted
quantitativereasoningandsensemeaning� SupportiveofeightStandardsforMathematicalPractice
� LessonCollaborationresultedinreJinementstoexistinglessons.� OneofthesepossibleavenuesforreJinementincludedamini-task
promotingstudentconjectureusedasasegueintothekeyideasoftheprimarytask.
Anexample� Originalmathematicstaskfromconceptualcurriculum:
� Laterinsamelesson….
Stagingtheconjecture
Thequestionthatwouldbeaskedtothestudents:Ifthispatterncontinues,howmanydaysdoyoupredictitwilltakeforeveryoneintheUnitedStatestoknowthesecret?
ClassimplementaAon
StudentsaskedtoGoogletheinformationofU.S.populationwiththeircellphones.Classconsensusis314millionpeopleintheUnitedStates.
ConjecturescreatesnewopportuniAesfordiscussion
(Postersonbackwall)Meaningof“upthere”duringdiscussion.
Arichdiscussionbeginsincomparing/contrastinglinearandexponentialfunctions.
MainlessononexponenAalfuncAonsconAnues…
StudentsJilledoutatablethatdescribesthepatternofpeoplewholearnthesecretfortheJirst15days.Theyusethepatterntowriteafunctionthatdescribesthepatterninthetable.
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ConjectureResolvedMeaningfullyforclass
Thereasoningusedinthisinteractionwasthatif314millionpeopleknewthesecret,halfofpeople(157million)hadlearnedthesecret.ThenCarolynasksstudentstousethemodeltodeterminethenumbersofdaysittakes.Somestudentsusedguessandcheck,somecontinuedthetable,oneusedagraphingmethod(Jindingwheny1=3�2Xintersectsy2=157,000,000).Morerichdiscussion.
WhatmakesaneffecAvepedagogicalhook?
� Piquesinterestandengagesstudents.
� Createsanintellectualneed.
� Relatestothekeyideasofthemathematicaltask.
� Isresolvedmeaningfully.
AnoteaboutcollaboraAon� Thoughtsoncollaborationandlessonplanning.
Workingandplanningtogetherfosteredadditionalopportunitiesforstudentstoengageinrichmathematicaltasks.Theseopportunitiesemergedasaresultofthiscollaboration.
ReferencesCarlson,M.P.,O'Bryan,A.,&Joyner,K.(2012).PathwaysAlgebraII:Implementingthe
CommonCoreMathematicsStandards(1sted.).Gilbert,AZ:RationalReasoning.Carlson,M.P.,Oehrtman,M.C.,&Moore,K.C.(2013).Precalculus:Pathwaysto
Calculus(4thed.).Gilbert,AZ:RationalReasoning.Clement,J.(2000).Analysisofclinicalinterviews:Foundationsandmodelviability.InR.A.Lesh&A.E.Kelly(Eds.),Handbookofresearchmethodologiesforscienceandmathematicseducation(pp.547-589).Hillsdale,NJ:LawrenceErlbaum.Marfai,F.S.(2016).CharacterizingTeacherChangeThroughThePerturbationOfPedagogicalGoals.UnpublishedDoctoralDissertation,ArizonaStateUniversity,Tempe.Smith,M.S.,Bill,V.,&Hughes,E.K.(2008).ThinkingThroughaLesson:SuccessfullyImplementingHigh-LevelTasks.MathematicsTeachingInTheMiddleSchool,14(3),132-138.Thompson,P.W.(2009).CaseModulesFacilitatorGuide.
Thankyouforcoming!Questions?
