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regarding conjecture regarding lesson planning

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1 The Value of Pairing Pedagogical Hooks with Meaningful Learning NCTM 2016 Regional Conference Frank S. Marfai Phoenix College October 28, 2016 Research reported in this presentation was supported by National Science Foundation Grant No. 1050721. Additional Jindings were made possible through the support of the National Science Foundation Grant No. 1103080. Any conclusions or recommendations stated here are those of the author and do not necessarily reJlect ofJicial positions of NSF. QuesAon How might student conjecture be used to engage students and advance mathematics learning in a lesson? Question was part of a larger study that explored the relationship between teachers’ mathematical goals for teaching and their understandings of the key mathematical ideas of lessons they taught. Conjecture An educated guess, based on previous experience or learning. Regarding conjecture An Example (Dan Meyer’s Three Acts Math) (Source: http://mrmeyer.com/threeacts/watertank/ ) Regarding Lesson Planning Lesson Planning and Debrief Protocols Developed InJluenced by Thinking through a Lesson Protocol (Smith, Bill, Hughes) Professional Developmental Spiral (Thompson) Pathways Professional Development Workshops (Carlson, Oehrtman, Moore; Carlson, O’Bryan, Joyner) Methods ProJile of this study Carolyn at Atlas High School (Fall 2014) Experienced teacher (20 years) Used a conceptual Precalculus curriculum (Pathways) Teaching third time with conceptual curriculum Attended professional development trainings Study Lesson planning sessions Lesson PreJlection Questionnaire Classroom Observations Lesson debrief sessions Lesson Debrief Questionnaire Post Study Interview Methods

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Page 1: Regarding conjecture Regarding Lesson Planning

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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

Page 2: Regarding conjecture Regarding Lesson Planning

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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.

Page 3: Regarding conjecture Regarding Lesson Planning

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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?

[email protected]


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