PROCEEDINGS OF THE FIFTH ANNUAL MATHEMATICS TEACHER EDUCATION PARTNERSHIP CONFERENCE · PROCEEDINGS...

PROCEEDINGSOFTHEFIFTHANNUALMATHEMATICSTEACHEREDUCATION

PARTNERSHIPCONFERENCE

FROMIMPROVEMENTTOTRANSFORMATION

BrianR.LawlerRobertN.Ronau

andMargaretJ.Mohr-Schroeder

(Editors)

June26-28,2016Atlanta,GA

UnitedStates

ii

ProceedingsoftheFifthAnnualMathematicsTeacherEducationPartnershipConferenceEditedbyBrianR.Lawler,RobertN.Ronau,andMargaretJ.Mohr-SchroederFirstpublishedJune,2016PublishedbytheAssociationofPublicLand-grantUniversities(APLU)Proceedingsavailableatwww.mte-partnership.org/mtep5ArticlespublishedintheProceedingsarecopyrightedbytheauthor.Permissiontoreproduceanarticle

orportionsfromanarticlemustbeobtainedfromtheauthor.ISBN:978-1-5323-2267-9

CiteProceedingsVolumeas:Lawler,B.R.,Ronau,R.N.,&Mohr-Schroeder,M.J.(Eds.).(2016).Proceedingsofthefifthannual

MathematicsTeacherEducationPartnershipconference.Washington,DC:AssociationofPublicLand-grantUniversities.

CiteProceedingsChapteras:Author.(2016).Titleofchapter.InB.R.Lawler,Ronau,R.N.,&M.J.Mohr-Schroeder(Eds.),Proceedingsof

thefifthannualMathematicsTeacherEducationPartnershipconference.Washington,DC:AssociationofPublicLand-grantUniversities.

MathematicsTeacherEducationPartnershipCo-DirectorsHowardGobstein,AssociationofPublicLand-grantUniversitiesW. GaryMartin,AuburnUniversity

MathematicsTeacherEducationPartnership5PlanningCommittee1HowardGobstein,AssociationofPublicandLand-

grantUniversities,co-chairW. GaryMartin,AuburnUniversity,co-chairEminaAlibegovic,UtahStateUniversityEdDickey,UniversityofSouthCarolinaMarkEllis,CaliforniaStateUniversity,FullertonMariaFernandez,FloridaInternationalUniversity

BrianR.Lawler,KennesawStateUniversityW. JamesLewis,UniversityofNebraska,LincolnMargaretJ.Mohr-Schroeder,UniversityofKentuckyRobertN.Ronau,UniversityofLouisvilleMarilynStrutchens,AuburnUniversityDianaSuddreth,UtahStateDepartmentofEducationDavidWebb,UniversityofColoradoatBoulder

AcknowledgementsFundingfortheMTE-Partnership,includingthe2016Conference,wasprovidedbytheLeonaM.andHarryB.

HelmsleyCharitableTrust.SpecialthankstoMaryLeskoskyandKacyReddofAPLUfortheirassistanceinplanningandexecutingthe

logisticsforthe2016MTE-PartnershipConference.

PrefaceTheseproceedingsareawrittenrecordofthepresentationsandpaperspresentedattheFifthAnnualMathematicsTeacherEducationPartnershipConferenceheldinAtlanta,Georgia,June26-28,2016.Thethemefortheconferencewas“FromImprovementtoTransformation.”WearepleasedtopresenttheseProceedingsasaresourceforthemathematicsandmathematicseducationcommunity.

www.mte-partnership.org

1W.JamesLewisandRobertN.RonauparticipatedasmembersoftheMTE-PartnershipPlanningTeamwhileservingattheNationalScienceFoundation.Anyopinion,findings,andconclusionsorrecommendationsexpressedinthismaterialarethoseoftheauthorsanddonotnecessarilyreflecttheviewsoftheNationalScienceFoundation.

iii

CONTENTS

INTRODUCTIONTheMTE-PartnershipStoryasRevealedthroughItsConferences:AnOverviewofthe

PartnershipandIts2016Conference.......................................................................................2W. GaryMartin&HowardGobstein

OverviewoftheConference........................................................................................................10BrianR.Lawler,RobertN.Ronau,&MargaretJ.Mohr-Schroeder

OPENINGADDRESSKeepingtheCourse:TransformingMathematicsTeacherPreparationinResponsive,ResponsibleWays........................................................................................................................19

RobertN.RonauforSuzanneWilson

PANELTALKSPre-SessiononEquityandSocialJustice......................................................................................25

BrianR.Lawler&MarilynStrutchens

ADeeperDiveintoPlan-Do-Study-ActCyclesandMeasures......................................................30MarilynStrutchens,MicheleIiams,RuthmaeSears,&MarkEllis

PathwaystoProgramImprovement............................................................................................37MargaretJ.Mohr-Schroeder,MarkEllis,WendyM.Smith,DeVonneSmalls,&RobinHill

MTE-PartnershipConferenceReactants.....................................................................................45BrianR.LawlerforKarenKing,DianaSuddreth,&W.JamesLewis

RESEARCHACTIONCLUSTERREPORTSClinicalExperiences......................................................................................................................51

MarilynStrutchens,MicheleIiams,&RuthmaeSears

ActivelyLearningMathematics(ALM).........................................................................................61DavidC.Webb

TheMathematicsofDoing,Understanding,Learning,andEducatingforSecondarySchools(MODULES2).................................................................................................................................70

AlysonLischka&EminaAlibegovic

iv

MarketingtoAttractTeacherHopefuls(MATH)..........................................................................77EdDickey

SecondaryTeacherRetention&InductioninDiverseEducationalSettings(STRIDES)................86MeganTaylor,JamesMartinez,&LisaAmick

RESEARCHPRESENTATIONSBuildingacommonvisionand/orpartnershipsacrossstakeholders

ExistingMathematicsTeachingPracticesatanHBCU:FoundationsforTeacherPreparation............................................................................................................................96

LaurettaGarrett&AnaTameru

DevelopingMiddleSchoolPreserviceTeachersKnowledgeofNumberandOperations....102RuthmaeSears&FernandoBurgos

MobilizingEffortsoftheMTE-PHui.....................................................................................103LindaVenenciano&DanDoerger

Mathematicalcontentknowledge(includingmathematicalknowledgeforteaching)ADeeperLookataCalculusIActivity..................................................................................104

LanceBurger

TeachingCollegeGeometryusingGeometryMODULE(S2)..................................................114LipikaDeka

GeometryTeachingKnowledge:AComparisonBetweenPre-ServiceandHighSchoolGeometryTeachers..............................................................................................................115

ShawndaSmith

KnowledgeanduseofeducationalpracticesGettingCollegeReadyfor“CollegeReady”Students...........................................................116

JanetBowers&WendyM.Smith

ActiveLearningMathematicsattheUniversityofNebraska...............................................121WendyM.Smith

UsingtheMCOP2asaGradeBearingAssessmentofClinicalFieldObservations................129JeremyZelkowski&JimGleason

Clinicalexperiences(includingsupportformentorteachers)VariabilityinClinicalExperiencesacrosstheCaliforniaStateUniversities..........................139

StephanieBiagetti&JenniferOloff-Lewis

UsingImprovementSciencetoIncreaseMathematicalLearningthroughCo-PlanningandCo-Teaching..........................................................................................................................143

PattiBrosnan&RuthmaeSears

v

Co-PlanningStrategiestoSupportInternDevelopment......................................................150CharityCayton&MaureenGrady

RecruitmentandretentionofteachercandidatesSupportSystemsofEarlyCareerSecondaryMathematicsTeachers...................................156

JamesMartinez,MeganTaylor,&LisaAmick

CSUChicoProgramRISE:AnalysisoftheFirstRecruitmentCycle.......................................157CherylOrdorica

ComparingNoyceScholars’DecisionstoTeachandPerspectivesonTeachingtonon-NoyceScholars................................................................................................................................161

JenniferWhitfield

CLOSINGREMARKSFromImprovementtoTransformation......................................................................................168

BrianR.Lawler,RobertN.Ronau,&MargaretJ.Mohr-Schroeder

1

INTRODUCTION

Lawler,B.R.,Ronau,R.N.,&Mohr-Schroeder,M.J.(Eds.).(2016).ProceedingsofthefifthannualMathematicsTeacherEducationPartnershipconference.Washington,DC:AssociationofPublicLand-grantUniversities.

2

TheMTE-PartnershipStoryasRevealedthroughItsConferences:AnOverviewofthePartnership

andIts2016Conference

W.GaryMartinAuburnUniversity

[email protected]

HowardGobsteinAssociationofPublic&Land-grantUniversities

[email protected]

TheMTE-PartnershipwasformedbytheAssociationofPublicandLand-grantUniversities(APLU)in2012toaddressamajorprobleminsecondarymathematicsteacherpreparation,anundersupplyofnewsecondarymathematicsteacherswhoarewellpreparedtohelptheirstudentsattainthegoalsoftheCommonCoreStateStandardsforMathematics(CCSSM)(NationalGovernorsAssociationCenterforBestPractices&CouncilofChiefStateSchoolOfficers,2010)andotherrigorousstatemathematicsstandards.Thisconsortiumofover90universitiesandover100schoolsystemshasacommongoaloftransformingsecondarymathematicsteacherpreparationusingtheNetworkedImprovementCommunitydesign(Bryketal.,2015).ThisessaywillprovideabriefoverviewofhowthePartnershiphasevolved,toldthroughthelensofthepastfourMTE-PartnershipAnnualConferences,outlinethegoalsandaccomplishmentsofthefifthconferenceheldin2016,andconcludebylookingatfuturedirectionsfortheMTE-Partnership.

TheDevelopmentofMTE-PartnershipthroughtheLensofPastConferences

WhiletheworkoftheMTE-Partnershipcarriesonthroughouttheyear,theannualconferenceshaveservedasimportantlandmarkswheremanyofthoseactivewiththePartnershipgathertogethertoreflectontheprogressthathasbeenmadeandsetforthplansforthecomingyear.Indeed,theinitialconceptfortheMTE-Partnershipwasformulatedbyparticipantsatthe2011conferenceofAPLU’sScienceandMathematicsTeachingImperative(SMTI),whichfocusesmoregenerallyonimprovingmathematicsandscienceteaching.ThefocusofthatconferencewasonchangesneededinhighereducationtoeffectivelyrespondtotheCCSSM,whichhadjustbeenreleased.Severalspeakers,aswellasaworkingpaperreleasedpriortotheconference(Wilson&Martin,2011),discussedtheneedforsignificantchangesinmathematicsteacherpreparation.Severalmathematicseducatorsattendingthemeetingdiscussedthespecificneedsatthesecondarylevel,andawhitepaperwassubmittedtothe


3

SMTIExecutiveCommitteeproposingtheformationofanewprojectfocusingonpreparingsecondarymathematicsteacherstohelptheirstudentsmeetthesenew,morerigorousstandards.

Overthecomingmonths,aplanningteamwasformedtoorganizewhatbecametheMTE-Partnership.Inresponsetoaninvitationtouniversitiestoapplyformembershiptothepartnership,38teamsrepresenting30statesbecamethefoundingmembers.(Sincethattime,anadditionalteamhasjoinedthepartnership,andseveralteamshaveexpandedtoincludeadditionalcampuses,bringingthetotalnumberofcampusestoover90.)Additionally,eachteamwasrequiredtoincludeatleastoneschooldistrictpartner.Astheinvitationstoapplytojointhepartnershipwentout,applicantswereaskedtoplantoattendthefirstconference,heldinApril2012inAtlanta.

2012Conference

AsapartoftheapplicationprocesstojointheMTE-Partnership,applicantscompletedaneedsanalysisbasedonaninitialframeworkdesignedbySMTI(Coble,2012),includingboththeircorevaluesforsecondarymathematicsteacherpreparationaswellastheirprogressinmeetingthosecorevalues.TheirresponseswereusedtocreateaninitialdraftofguidingprinciplesfortheMTE-Partnershipthatbecamethefocusofdiscussionatthe2012conference.Followingtheconference,theGuidingPrinciplesforSecondaryMathematicsTeacherPreparation(MathematicsTeacherEducationPartnership,2012),sinceupdatedin2014,werereleasedasto“describeasharedvisiontobeexploredandrefinedbytheMTE-Partnershipandothersinvolvedinpreparingsecondarymathematicsteachers”(p.1),thusservingasthecentralorganizingdocumentforthePartnership.

Atthe2012conference,participantswerealsoaskedtoidentifypotentialchallengesinmeetingthoseprinciples.ThisbecamethefirststepindevelopingtheproblemspaceforthePartnership;afollow-upsurveyofconferenceattendeeswasusedtofurtherdefinethislistofchallenges,andasubsequentsurveywassenttorepresentativesofallthepartnershipteams,askingtheirjudgmentofboththeimportanceofeachitemonthelisttotheirteam,aswellastheirteam’sinterestinattemptingtoaddresseachitem.Theresultsfromthissurveywereusedtoidentifyasetofprioritychallengestobeaddressedbythepartnership.Thisemergingsetofhigh-prioritychallengeswaspresentedtothepartnershipforfurtherreaction,whichledtotheformationofworkinggroupstoaddressasetoffourhighestprioritychallenges(Martin&Strutchens,2014).Overthecomingmonths,membersoftheworkinggroupswrotedraftwhitepapersprovidingareviewofrelevantliteratureandinitialrecommendationsforactions.

Asmembersoftheplanningteamreflectedonthe2012conference,theyrecognizedthatastrongerdesignwasneededforthePartnershiptoaddressseveralneeds,including(a)theneedtomaintaintheengagementoftheteamsintheworkofthePartnership,sothat


4

everyonefeltthathadaroletoplay,and(b)theneedtomaintainafocusondisciplinedinquiryconsistentwiththemissionofuniversities(Martin&Gobstein,2016).Onedesignthatwasinvestigated,basedinpartontherecommendationofareactantatthe2012conference,wastheNetworkedImprovementCommunity(NIC)modelbeingdevelopedbytheCarnegieFoundationfortheAdvancementofTeaching(cf.Bryketal.,2015).ThedecisiontoreconstitutethePartnershipasaNICwasratifiedbythemembershipinSpring2013,leadinguptothe2013AnnualConference.Thehigh-prioritychallengesbeingaddressedbytheworkinggroupswerereconstitutedas“primarydrivers”thatwouldhelpthePartnershipreachitsaimofproducingmorewell-preparedsecondarymathematicsteachers;seedetailsinthefirsttwo(leftmost)columnsofFigure1.

Figure1.TheMTE-Partnershipdriverdiagram.

2013Conference

The2013Conference,heldinearlyJuneinSt.Louis,focusedonlearningmoreaboutthenewly-adoptedNICdesignanddevelopingtheproblemspaceforthePartnershipinalignmentwiththatdesign.Closeto90participantsgatheredintofourbreakoutgroupsorganizedbythefourprimarydrivers;eachparticipantwasaskedtoselectoneoftheworkinggroups.Overthecourseoftheconference,thebreakoutgroupsprovidedfeedbackontherespectivewhite


5

paperfortheirchosenprimarydriver,identifiedpossibleaimsandsecondarydriversrelevanttothataim,anddiscussedpossiblemeasuresthatmightbeusedtotrackprogresstowardstheaim.

Theworkofthebreakoutgroupsculminatedwiththeidentificationofpotentialinterventionsthatwerethenpresentedtotheconferenceparticipants.Acrossthefourgroups,thirteenpotentialinterventionswerepresentedinafinalsessionoftheconferenceinwhichparticipantswereaskedtophysicallygatheraroundthepostersoftheirhighestprioritypotentialareasofactionasafirstindicationofinterest.Followingthemeeting,theMTE-PPlanningTeameliminatedorconsolidatedseveraloftheareasbasedonthatinitialfeedback,andasubsequentsurveysenttoallteamleadersfurthernarrowedthelisttofiveinterventionsasbeingofthemostimportanceandinteresttoMTE-Partnership.

Infall2013,partnershipteamswereinvitedtoapplytojoin“researchactionclusters”(RACs)organizedtodevelopeachofthesefiveinterventions.TheseRACshavebecometheprimarystructureforparticipationintheMTE-Partnership.A“bootcamp”washeldinNovember2013withRACleaderstolaunchtheirwork.PlenarysessionsontenetsofNICdesignwereinterspersedwithbreakoutsessionsinwhichparticipantsmetbyRACtoapplythosetenetstodefiningmorespecificdriverdiagrams,aimstatements,measurestotrackprogress,andaninitialactionplanfortheRAC.NotethatoneRACwaslaterdisbandedasconsensuswasnotreachedonaplanofaction,andanadditionalRACwasformedsummer2015toaddressanemergentareaofconcern,inductionofcandidatesintotheprofession.ThecurrentlistofRACs,alongwiththeirconnectionstotheprimarydriversisshowninFigure1.EachRACincorporatestheNICdesign,usingimprovementcyclestodevelopinterventionsaddressingitsidentifiedaim.

2014Conference

The2014conference,againheldinearlyJuneinSt.Louis,wasfocusedaroundtheworkoftheRACs.RACmembersmetinsmallgroupstoreviewtheirinitialworkinforminganaimanddriverdiagramsandtobeginplanningspecificimprovementeffortstobeundertakeninthecomingyearusing“Plan-Do-Study-Act”(PDSA)cyclesasamodel;seeFigure2.PDSAcyclesdescribeaprocessofplanning,implementing,collectingdata,andrevisinginalignmentwiththeNICdesign.AdditionalsessionsfocusedonincreasingunderstandingoftheNICdesignandexploringissuesrelatedtosecondarymathematicsteacherpreparation.AfinalposterwalkallowedRACstosharetheirprogresswithmembersofotherRACs.

Followingtheconference,theworkofthePartnershipwaslargelyfocusedonRAC-levelwork,asRACsbuiltontheirprogressattheconferencethroughoutthefollowingacademicyear,usingacombinationofvirtual,on-line,andface-to-facecommunications.Additionally,theplanningteamcontinuedtomeetperiodicallytoensurecollaborationacrosstheRACsandto


6

maintainfocusonthePartnershipaim.AworkinggroupbeganmeetingtodevelopcommonmeasuresacrossPartnershipteamstotrackprogresstowardstheaim.Severalsurveysweredevelopedaddressingkeyvariables,includingcandidateproductionandtargets,aself-assessmenttobecompletedbyteamleaders,andaself-assessmenttobecompletedbyprogramcompleters.Theseinstrumentswererefinedandpilotedoverthefollowingacademicyear.

Figure2.ThePlan-Do-Study-Act(PDSA)Cycle.(AdaptedfromLangleyetal.,2009)

2015Conference

The2015ConferencewasheldinFullerton,CAinlateJunewithacontinuingfocusontheRACs.Followingfeedbacktothe2014conference,theworktimespentmeetinginRACswasexpanded.TheaforementionednewRAConimprovingtheretentionofprogramgraduatesintheprofessionwasalsolaunched.However,oneofthemajordevelopmentsatthisconferencewastheincreasedparticipationbymembersoftheCaliforniaStateUniversitysystem,whichexpandeditsparticipationtoincludeall22campusesthatprovideteacherpreparation.Thiscreatedaninfluxofnewparticipants,andaspecialsessionwasheldtointroducethemtothePartnershipandtheNICmodel.TheRACseachproducedone-page“promotionalsheets”designedtoencouragethesenewparticipantstojoinintheiractivities.

The2015conferencealsointroducedanemergingemphasisonprogramtransformation,reflectingthechallengesprogramsfaceinmovingbeyondmakingchangesbasedontheoneortwoRACsinwhichtheyareactivelyengagedtoaggregatingthefindingsofmultipleRACstoundertakethebroad-scalechangesneededtoensureboththenecessaryquantityandqualityofsecondarymathematicsteachercandidates.Issuesincludeensuringthat


7

thehumancapitalisavailabletoparticipateintheimprovementeffort,thatsecondarymathematicsteacherpreparationisapriorityacrossstakeholdergroups,andthatinstitutionalresourcesandsupportstructuresareprovided.Theproposedsolutionistoprovidetoolsandtechniquestosupportinstitutionsincreating“strategicpathwaysfortransformation”inwhichtheyscaleuptheiruseoftheapproachesdesignedbytheRACs.

ThissummaryofprogressoftheprogressoftheMTE-Partnershipoverthecourseofitsfirstfiveconferencesnowsetsthestageforadiscussionofthe2016conference.

Goalsofthe2016Conference

The2016MTE-PartnershipConference,heldlateJuneinAtlanta,GA,hadfourprimarygoalsbuildingontheworkdoneinpreviousyears.Eachgoalisdiscussedinturn,alongwithhowthestructureoftheconferencesupportedthatgoal.

1.Tobuildfocusonthetransformationalchangeneededforteamsandprogramstoachievethepartnershipaim.Followingthe2015conference,aworkinggroupwasformedtobegindevelopmentofstrategiessupportingtransformationalchange,asdiscussedabove,possiblyculminatinginthecreationofanewRAC.Membersoftheworkinggrouppresentedapaneldiscussionofissuesrelatedtotransformationalchangeattheconference,andaseriesofbriefresearchreportswasdesignedtoshareon-goingworkacrossthepartnership.

2.Tomakeequityandsocialjusticemoreexplicitasanessentialcomponentofthepartnershipaim.WhileattentiontoequityandsocialjusticeisembeddedintheGuidingPrinciplesandintheworkofmanyoftheRACs,membersoftheplanningteamnotedthatthisisnotvisiblyapartofthePartnershipaimordrivers.Thus,adecisionwasmadetobegintomakethefocusonequityandsocialjusticemoreexplicit,withdiscussionsattheconferenceservingasastartingpoint.Aworksessionwasheldattheconferencetobeginthosediscussions.Moreover,duringtheirworktimeattheconference,eachRACwaschargedwithconsideringhowissuesrelatedtoequityandsocialjusticecouldbemademorevisibleintheirgoalsandwork,andtothenreportingontheirprogressinthisareaintheclosingsession.

3.Tobuildasenseofjointpurposeandidentityacrossthepartnership.GiventhatmuchoftheworkoftheMTE-PartnershipisnowfocusedontheRACs,insomecasesithasbecomechallengingtomaintainasenseofcommonpurposeandidentityforthePartnership;participantsmaytendtofocusmoreontheproblemsthatinterestthem,particularlytheworkoftheRACsinwhichtheyareinvolved(Martin&Gobstein,2015).WhiletheRACsmaybetheirspecificfocusforparticipation,thereismuchtobegainedbyemphasizingthebroaderstructureofthePartnership,includinglearningfromandwiththeotherRACsandconsideringthemoregeneralcontextfortheworkoftheRACs.

Attheconference,generalsessionsincludedtoemphasizethesenseofjointpurposeandidentity.AkeynoteaddressbySuzanneWilsonprovidednationalcontextinwhichto


8

considertheworkofthePartnership.OverviewsessionsbytheprojectleadersemphasizedtheoverallaimandpurposeofthePartnership,aswellasitsaccomplishments.Intheopeningandclosingsessionstotheconference,theRACssharedprogressmadeinachievingtheirgoals.Finally,threereactantsprovidedinsightsgleanedfromobservingtheworkofthePartnershipacrosstheRACs.

4.ToacceleratetheworkofthefiveResearchActionClusters(RACs)towardstheiraims.ArguablythemajorgoaloftheconferencewastosupporttheworkoftheRACs.Havinganextendedperiod(morethan8hours)overseveraldaysinwhichtocollaborateface-to-facecanprovideanimportantstimulustotheirwork.TheRACsspenttimereflectingontheirpastprogressandmakingplansforthecomingacademicyear.Inaddition,apanelontheNICdesignandimprovementsciencesharedinsightsfrommembersoftheClinicalExperiencesRACwhoattendedaseriesofworkshopsofferedbytheCarnegieFoundationtosupportgroupsusingtheNICmodel.

ConclusionsandNextSteps

Theactivitiesforthecomingacademicyearandbeyondbuildfirmlyonthefoundationoftheworkdoneatthe2016AnnualConference.Thetransformationchangeworkinggroupmetaftertheconferenceandwillcontinuetodevelopplanstocreateaformalresearchactionclusterfocusingonsupportinginstitutionalchange.Discussionsrelatedtoequityandsocialjusticewillcontinueaftertheconference,withamajorfocusonhowtobestorganizecontinuingworkinthisarea.Whileadistributedapproachisessentialinfurtheringthework,anewworkinggrouponequityandsocialjusticeisbeingconsideredtobuildcross-RACfocus.ThesenseofjointpurposeandidentityofPartnershipparticipantscontinuestobenurturedthrougheffortsoftheplanningteamtocoordinateandfocustheworkandthroughPartnership-widecommunications,suchasthePartnershipPipeline,anewly-launchedquarterlynewsletter.Finally,theRACscontinuetomeetbothvirtuallyandface-to-facetomeettheiraims.

WhilemuchoftheactivityoftheMTE-PartnershipnowoccurswithintheRACs,overtheyearstheconferenceshaveservedanimportantroleinestablishingandcatalyzingthePartnership’svisionanddirection.Moreover,theyhavecontinuedtoserveanimportantrolebeyondsupportingtheworkconductedinRACs,astheyhavebroughttogetherparticipantsacrosstheRACstosharetheiron-goingwork.Thishasbothprovidedopportunitiestocross-pollinateeffortsacrosstheRACsbutalsotodevelopasenseofsharedidentityandcommitmenttothebroaderMTE-Partnershipeffort,beyondparticipationinoneaspectofitswork.


9

References

Bryk,A.,Gomez,L.M.,Grunow,A.,&LeMahieu,P.(2015).Learningtoimprove:HowAmerica’sschoolscangetbetteratgettingbetter.Cambridge,MA:HarvardEducationPress.

Coble,C.(2012).Theanalyticframework:Atoolforassessinginnovationandqualitydesigninscienceandmathematicsteacherpreparation.Washington,DC:AssociationofPublicandLand-grantUniversities,ScienceandMathematicsTeacherImperative.

LangleyG.L.,Moen,R.,Nolan,K.M.,Nolan,T.W.,Norman,C.L.,&ProvostL.P.(2009).TheImprovementguide:Apracticalapproachtoenhancingorganizationalperformance(2nded.).SanFrancisco,CA:Jossey-BassPublishers.

Martin,W.G.,&Gobstein,H.(2015).Generatinganetworkedimprovementcommunitytoimprovesecondarymathematicsteacherpreparation:Networkleadership,organization,andoperation.JournalofTeacherEducation,66(5),482-493.

Martin,W.G.&Strutchens,M.E.(2014).PrioritiesfortheimprovementofsecondarymathematicsteacherpreparationfortheCommonCoreera.PaperpresentedattheAERAAnnualMeeting.Retrievedfromwww.aera.net/Publications/OnlinePaperRepository/AERAOnlinePaperRepository/tabid/12720/Owner/314509

MathematicsTeacherEducationPartnership.(2012).Guidingprinciplesforsecondarymathematicsteacherpreparation.Washington,DC:AssociationofPublicLandGrantUniversities.Retrievedfromwww.aplu.org/projects-and-initiatives/stem-education/SMTI_Library/mte-partnership-guiding-principles-for-secondary-mathematics-teacher-preparation-programs/File

NationalGovernorsAssociationCenterforBestPractices&CouncilofChiefStateSchoolOfficers.(2010).Commoncorestatestandardsformathematics.Washington,DC:Author.

Wilson,S.,&Martin,W.G.(2011).TheCommonCoreStateStandardsandteacherpreparation:Theroleofhighereducation.Washington,DC:AssociationofPublicandLand-grantUniversities.


10

OverviewoftheConference

BrianR.LawlerKennesawStateUniversity

[email protected]

[email protected]

[email protected]

TheMTE-Partnershipemergedbecausetheworkofchangingsecondarymathematicsteacherpreparationisverydifficult,particularlybecauseofthelackofvalidandreliablemeasuresavailabletoguidetheprocess.Thisgroupstandsapartfrompreviouseffortsbecauseoftheemphasisonconnectinglocaleffortstonetworkunderstandingsandnetworkunderstandingstolocalefforts.Thatisbuildingacommunityoflearners,learningtogether.Throughwell-connectedeffortswithinthenetwork,localexperimentsareleveragedtorevealpowerfulresultsinwhichthefocusistransformation.Transformationismorethanjusttakingtoscale,butstrengtheningtherelationshipsbetweenthoseinvolved.

MTE-PusestheNetworkedImprovementCommunity(NIC)model,developedbytheCarnegieFoundationfortheAdvancementofTeaching(Bryk,Gomez,&Grunow,2011;Bryk,Gomez,Grunow,&LeMahieu,2015),toguidethenumerousandcomplexactivitiesofthememberpartners,andtohelpthemtotransformtheireffortsintomeaningfulresults.NICsareintentionallydesignedsocialorganizationsthatare:(1)focusedonacommonaim,(2)guidedbyadeepunderstandingoftheproblemandasharedapproachtosolveit,(3)disciplinedbythemethodsofimprovementresearchtodevelop,test,andrefineinterventions;and(4)organizedtoaccelerateinterventionsintothefieldandtoeffectivelyintegratethemintothefield.

TheseproceedingsareofthefifthMTE-Pconference.Wehavemovedpasttheinitialorganizationalstartupissuesandarerapidlylearninghowtotranslateindividualpartnershipeffortsintonation-wideresults(Martin&Gobstein,2015).Consequently,thethemeforthisconferenceis“FromImprovementtoTransformation.”Inthiscase,Transformationismorethanjusttakingtoscale,butstrengtheningtherelationshipsbetweenthoseinvolved;thatisstrengtheningtheNICtobettersupportandsharethework.Asyouwilldiscoverintheseproceedingswehavefiveresearchcommunities—ResearchActionClusters(RACs)—thathavedevelopedandimplementedstrategiesthatspanuniversitiesandstagesandnowarebeginningtoshareresults.

1

RonaucontributedtothispaperwhileservingattheNationalScienceFoundation.ThecommentsexpressedherearethoseoftheauthoranddonotnecessarilyreflecttheviewsoftheNationalScienceFoundation.


11

Thisfifthconferencewasdesignedtoachievefourgoals:(1)tobuildfocusonthetransformationalchangeneededforteamsandprogramstoachievethepartnershipaim;(2)tomakeequityandsocialjusticemoreexplicitasanessentialcomponentofthepartnershipaim;(3)tobuildasenseofjointpurposeandidentityacrossthepartnership;and(4)toacceleratetheworkofthefiveResearchActionClusters(RACs)towardstheiraims.Toprovideindividualconsiderationandsupporttogoal4,thetimeoftheconferencewasorganizedtoprovidesubstantiveworktimefortheRACs.Also,severalplenaryandsocialeventswerescheduledtoachievethefirstthreegoals.Further,theplenarysessionsweredesignedtoprovoketheworkwithintheRACstoexplicitlyaddressissuesofequity,underdevelopedtothispointbytheMTE-Partnership.Participantswereespeciallychallengedtomovebeyondindividualworkandseekwaystoelicitsystemicchange,thatis,tomovefromimprovementtotransformationgoals.ThisexecutivesummarywillservetoidentifythesectionsoftheProceedingsandprovideabriefoverviewofeachentry.

PlenarySession

AfterattendeeswerewelcomedandtheconferenceopenedbyMTE-Partnershipco-directorsDr.GaryMartinandMr.HowardGobstein,Dr.SuzanneWilsondeliveredatalkinthefirstoftheplenarysessions,“Stayingthecourse:Transformingmathematicsteacherpreparationinresponsive,responsibleways.”ShechallengedMTE-Ptofaceourcriticsbyusingresearch,meaningfulmeasures,coordinatedcross-institutionalefforts,andpersuasiveanecdotestoguidethepublicfaceofmathematicsteacherpreparation.Dr.Wilsonrelatedhowlackofacommonvisionandmeaningfulmeasuresplaceusatadisadvantageasweattempttorevisemathematicsteachereducationprograms.Proxymeasuresmaynotbeusefulmeasurestohelpguidechangeinteacherpreparation.O’Neil(2016)inherwork“WeaponsofMathDestruction”detailshowsimpleproxymeasurescommonlyusedtoevaluateteacherworkcancausegreatharm.O’Neilshowshowsimple,indirectandproxymeasurescancreatesystemsthatdonotmeasurewhattheyclaim,inappropriatelypunishthetargets(teachersandschools)ofthosemeasures,contributelittletoimprovingqualityofthosesystems,andresisttransparencythatmightleadtomeaningfulchange.Dr.Wilsonstressedthatweshouldcontinueworktogethertomakesmall,well-documentedinterventionstoincrementallymovethefieldforward.Wecantransformteacherpreparationbytweakingwhatwedobasedoncurrenttheoryandguidedbyvalidandreliablemeasures.MTE-P’scurrenteffortsRACsareaveryappropriatetooltotakeonthistask.Dr.Wilson’stalkisreportedintheseproceedingsbyRobertRonau.

AfterDr.Wilson’stalk,eachRACprovidedabriefupdateontheirprogressoverthepastyear.TheremainderofthisfirstafternoonoftheconferencewasdedicatedtoRACworktime.


12

PanelTalks

Thedayconcludedwithapaneltalkthatchieflyservedtofosterconversationabouttheintersectionofissuesofequity,diversity,andsocialjusticeandtheworkoftheMTE-Partnership.Approximatelyone-halftheconferenceattendeesjoinedthisearlyeveningdiscussion.Manyquestionsandneedsemergedduringthediscussions,andstrongsupportforthedevelopmentofaworkinggrouponequity,diversity,andsocialjusticewasexpressed.

Themorningoftheseconddaybeganwiththesecondpaneltalk,“ADeeperDiveintoPlan-Do-Study-ActCyclesandMeasures,”adiscussionthatfocusedontheapplicationofPDSAcyclesandthemeasures,toolsandstrategiesdevelopedtosupporttheimprovementscienceprocess.Thisplenarywasdesignedtocontinuetoincreasethecommunity’sunderstandingoftheNICresearchdesign.Thepresenters,MicheleIiams,RuthmaeSears,MarkEllis,andMarilynStrutchenshadrecentlyattendedaNICworkshopbyCarnegie.Here,theysharedbothsomeimportantelementsofthePDSAresearchcyclesandtheirstrugglesandsuccessesastheirteamsimplementedtheresearchcyclesintheirlocalesandsharedtheresultsacrosssites.

Addressingconferencegoalone,tobuildfocusontransformationalchange,anotherpaneltalkfocusedonlocaleffortstotransformteacherpreparationattheirinstitutions.The“PathwaystoProgramImprovement”plenaryincludedMarkEllis,MargaretMohr-Schroeder,DeVonneSmalls,andWendySmith,withdiscussionbyRobinHill.Eachmemberofthispanelsharedtheirexperienceswithrespectofchangingtheirsecondarymathematicsteacherpreparationprograms.Someofthechallengesthattheyfacedweresimilar;however,panelmembersdescribedverydifferentstrategiesandactivitiesthatdrovechangeintheirsituation.Allpanelmembersindicatedthattheworkhasjustbegunandmuchmoreeffortwillbeneededtoreachtheirgoals.

Afterlunchonthefinaldayoftheconference,threemembersofthenationalcommunityconcernedwiththepreparationofsecondarymathematicsteacherssharedtheirexperiencesandreactionstotheconferenceinafinalpaneltalk,KarenKing,DianaSuddreth,andJimLewis.ThesethreeindividualswereinvitedtofreelyparticipateintheconferenceactivitiestoassesstheprogressofMTE-Pandtosharetheirperspectiveswiththeparticipants.AlthoughthereactantspraisedtheprogressmadebyMTE-P,eachwasabletosuggestadditionalperspectivesand/oractionsthattheinitiativemightconsider.Forexample,Dr.KingsuggestedthatMTE-Pgroupsinvestigateresearchoutsideofmathematicseducationtolearnaboutstrategiesandtheirpotentialunintendedconsequenceswithrespecttodiversitytraining.Ms.SuddrethencouragedMTE-Pteamstobroadentheirengagementwiththeircommunities.Finally,Dr.LewissuggestedthatthetimemayhavearrivedforMTE-Pasanorganizationtoreflectonthegoalsinitiallyestablishedbythepartnershipandontheworkthathasbeenaccomplishedtoevaluateandre-assessthenaturetheofthetaskathand,thefatigueoftheparticipantsafterfiveyearsofcontinualstruggle,andthetransformativeworkthatlies


13

aheadtostrategicallyidentifyandpursuepotentialleversofevolutionthatcouldacceleratetheeffectivenessoftheeffort.ThecommentsofthesereactantsarereportedintheseproceedingsbyBrianR.Lawler.

ResearchActionCluster(RAC)Reports

EarlyinthegrowthoftheMTE-Partnership,RACswereformedtoaddressspecificproblemsidentifiedinthedriverdiagrams.RACsweredesignedtobetheactiveagentsofMTE-P,movingtheeffortfromdiscussiontoaction.RACsprovidethefocusandimpetustotaketheinitiativefromorganizingtotheorizingtotransforming.

Inadvanceoftheconference,eachRACsubmitteda“promosheet”designedtoorientnewconferenceparticipantstotheworkoftheRAC,andupdatelong-timeMTE-Pmembers.ThesepromosheetsareavailableonlineattheAPLUMTE-Pwebsite,linkedintheseproceedingsatthetopoftheRACReports.Duringtheconference,theRACshadapproximately8hoursofstructuredworktime.TheRACssubmittedreportsfortheseproceedingsthatidentifiedtheworkoftheRACtodate,whatwasaccomplishedduringtheconference,andtheirnextstepsmovingforward.

TheClinicalExperienceRAC(CERAC)consistsof24partnershipsorganizedintothreesub-RACs:Methods,PairedPlacement,andCo-PlanningandCo-teaching(CPCT).TheMethodssub-RACisnextfocusingoncreatingaLessonDesignmodules.PairedPlacementisrevisingtheirworkshopforteachersandpreserviceteachers,aswellasdevelopingmanuscriptsandseekingfunding.AndCPCTisworkingtoscaleuptheirmeasureswork.AllmembersoftheRACintendtopayexplicitattentiontoequityandsocialjusticeissuesinthenextiterationsoftheirmodules.EachSub-RACdevelopeditsownresearchquestionsandPDSAcycles;however,overlappinginterests,suchastheMathematicsTeachingPractices,andmeasures,suchastheMCOP2,areusedtodriveacommonfocusacrossallpartnersinCERAC.

TheActivelyLearningMathematics(ALM)RACfocusesonimprovingundergraduatemathematicsinPre-calculusthroughCalculus2(P2C2).ALMhasdevelopedclassmaterialsandastudentsurveythatisavailabletoallMTE-Ppartners.Currently,14partnerinstitutionsareparticipatinginALM.TheALMRACreorganizedtohelpmanagegrowth,intocourse-andtopic-specificgroupssuchasCalculusIandLessonStudyinCalculus.Inthecomingyear,oneimportantelementoftheirworkwillbetoorganizesitevisits.

TheMathematicsofDoing,Understanding,Learning,andEducatingforSecondarySchoolsMODULE(S2)RACisfocusedonthedevelopmentofprospectivesecondarymathematicsteachers’knowledgeofmathematicscontentneededtosupportstudentlearning.TheMODULE(S2)RAChasdevelopedmodulesinGeometry(3),Modeling(3),andAlgebra(3inprogress)andStatistics(1).Thesemodulesarebeingpilotedandareavailableforpartnerinstitutionstopilot.


14

TheMarketingtoAttractTeacherHopefuls(MATH)RAChascompletedthedevelopmentofitsrecruitingmaterialswhichareavailableontheirwebsiteatbit.ly/MATHImplGuide.ElevenpartnerinstitutionshavedevelopedPDSAcyclesforrecruitmentattheirlocalsitesandsharedtheirresultsatwholegroupmeetings.Inadditiontosharingout,theRACdiscussednewinitiativesandnextstepsfortheRACwithattentiontobothidentifyingfundingtosupportrecruitmentworkandresearchandtoaddresstheMTE-Pcommitmenttoequityandsocialjustice.

TheSecondaryTeacherRetention&InductioninDiverseEducationalSettings(STRIDES)RACwasrecentlyformedandisofftoafaststart.AtthisconferencetheSTRIDESanalyzedtheresultsfromapilotsurvey(n=66)andusedthoseresultstoreviseasurveytobesenttostudentsinallpartnerinstitutions.TheSTRIDESRACdividedintosubgroupsbasedonachangeideafocus:(1)Long-TermCollaborativeGroupsforEarlyCareerTeachers,(2)RoleofAdministratorsandSite-BasedColleagues,and(3)Training&SupportingTeacherMentors.CurrentlyPDSAcyclesarebeingdevelopedwithineachofthesethreegroupsforimplementationinthecomingmonths.

ResearchPresentations

ResearchinitiativeshaveemergedfromtheworkoftheRACsasteammembersdesignedandimplementedstudiesabouttheirwork.AspartoftheannouncementforthefifthMTE-Pconference,forthefirsttime,weincludedacallforresearchpapers.Thesepaperswerereviewedandpresentedattheconferencebytheauthors.Somepresentersonlyelectedtosubmitabstractsoftheirtalkfortheproceedings,otherssubmittedacompleteandrevisedpaperforpublication.Theproceedingshavegroupedallthetalks,abstractsandpapers,astheywereorganizedbythemesfortheconference.Herewereportonlyonthefullpaperspublishedintheproceedings,organizedbythemesastheyweregroupedforpresentationattheconference.Thepapersarebrieflymentionedbelow,groupedbythesethemes,andcanbefoundintheirentiretyintheproceedings.

Buildingacommonvisionand/orpartnershipsacrossstakeholders

GarrettandTamerureporttheresultsofastudyexaminingtheexistingmathematicsteachingpracticesattheirinstitution.Theycategorizedexamitemsfromprecalculusandcalculuscoursesonfivetypesofthinkingnecessarytorespond.Studentswereinfrequentlyexpectedtothinkbeyondrecallorapplicationofknownprocedures.

SearsandBurgosinvestigatedtheprocessofcollaborationamongfacultymembersintheCollegeofEducationandtheDepartmentofMathematicsandStatisticsinthedevelopmentofmiddleschoolteacher’smathematicalcontentknowledgeforteaching.AndVenecianoandDoergerreportonathirdefforttobuildcommonvisionamongthenewlyestablishedMTE-PHuiteam.Theyfocusedonrecognizingcommonaltiesandestablishedsharedgoals.


15

Mathematicalcontentknowledge(includingmathematicalknowledgeforteaching)

Threepapersinthiscollectionfocusedonunderstandingdevelopingmathematicalunderstandingoffuturemathematicsteachers.BurgerandMarkinreportonapilotstudythatexploredconceptualapproachestolearningCalculusI.Theymoderatedtheirlessonstoleadstudentstodeeperunderstandingoftargetedconceptsbyactivatingfamiliarprerequisiteknowledge.DekareportedontheimplementationoftheGeometryModulesthatwerereadyforpilotfromtheMODULE(S2)RAC.Shesharedhowstudentsreactedtothemodules,thechallengesexperiencedteachingthecourse,anddiscussedwhethertheapproachseemedtomakeadifferenceinthepreparationofmathematicsteachers.Smithexaminedthemathematicalcontentknowledge—specificallyofgeometry—ofpre-serviceandhighschoolmathematicsteachers.HerfindingssuggesteddomainsofGeometryTeachingKnowledgethatcouldbeemphasizedinpre-serviceandprofessionaldevelopment.

Knowledgeanduseofeducationalpractices

BowersandSmithreportonhowtheymodifiedtheMCOP2observationprotocoltoexaminetheimplementationoftheproductsoftheActiveLearningMathematicsRACattheuniversitylevel.TheirstudysuggestedthattheMCOP2studentsurveytheycreatedappearstobereliable.Secondly,thestudentsurveyappearstobeusefulforidentifyingwhatstudentsbelievearespecificvalue-addedaspectsofactivelearning.

AsecondreportbySmithprovidedadetaileddescriptionandtheresultsoftheimplementationofALMinthepre-calculusclassesatUniversityofNebraska–Lincoln(UNL).ActivelearninghasbecomewellestablishedatUNL,andthemathdepartmentwillextendthisworktoCalculusIandIIclassesduring2016-17.RecentlytheyreceivedanNSFgranttostudymathematicsdepartmenttransformationusingNICsasalens.

UsingtheMCOP2asthePrimaryObservationProtocolforAssessingTeacherCandidatesinMethodsCoursesandStudentTeachingPracticabyZelkowskiandGleasondescribestheprocessusedattheirinstitutiontomovefromageneralobservationprotocol(usedforallsubjects)tousingMCOP2fortheirmathematicsteachercandidates.HereportsthatMCOP2providedaconsistentratingwiththeothergeneralobservationtoolusedintheirprogram.

Clinicalexperiences(includingsupportformentorteachers)

Biagetti&Oloff-LewisinvestigatedtheVariabilityinClinicalExperiencesacrosstheCaliforniaStateUniversities(CSUs).Theyreportthesimilaritiesanddifferencesofmathematicsteacherpreparationprogramsamong18CSUcampuses.Theylearnedofsurprisinglyhighvariabilityacrossthecampuses.Forexample,thenumberoftimesteachercandidateswereobservedduringtheirfirstsemestervariedfromonetotentimes.Theyidentifiedthesegreatvariationsinprogrampracticesposechallengestomeasurementeffortsaswellastransferofeffectivepractices,notonlyamongtheCSUS,butlikelyacrosstheMTE-Partnership.


16

Brosnan&SearsreportontheirPDSAcyclesfortheirCo-PlanningandCo-TeachingSubRAC.Specifically,theyinvestigatethewaysinwhichco-planningandco-teachingstrategiesassistthementorteachersandteachercandidatestofocustheirworkonstudents’learningofmathematics?Inadditiontopositiveresultsbeyondwhatwasexpected,theyfoundthatthestructuresofimprovementsciencehelpedthemengageinresearchwiththeirpartnersaspartoftheireffortstotransformthefieldexperiencesoftheircandidates.

Athirdreportregardingclinicalexperiences,byCaytonandGrady,sharedstrategiestosupportco-teachingendeavorsintheirclinicalexperiences.Inthiscontextco-teachingissharedteachingbetweenmentorteacherandstudentteacher.TheyusedPDSAcyclestoimplementandstudytheseco-teachingstrategies.Theirdatacollectiontoolsincludepre-surveys,aco-teachingobservationprotocol,asurveyofstrategiesused,justintimesurveys,andexitsurveys.Preliminaryresultsshowthatclinicalteachersandinternsreportedthebenefitsoftheco-teachingstrategies.

Recruitmentandretentionofteachercandidates

Martinez,Taylor,andAmickreporttheresultsofasurveyofmathematicsteachersinateacherpreparationprogramorservingintheirfirstthreeyearsofteachingregardinghowearlycareerteachersarebeingsupported.ThispreliminarydatacollectioneffortservestolaunchtheworkofthenewlyemergingSTRIDESRAC,resultsofwhichwereanalyzedattheconferenceandusedtoinformnextstepsforthecommunity.

OrdoricareportedonherrecruitingeffortsatCSUChico,andinparticularhowshedrewupontherecruitingmodulesoftheMATHRAC.SheconcludesthattheImplementationGuideproducedbytheMATHRACprovidedtheinfrastructuretomakerecruitmenttasksfeelmoremanageableandalsoprovidedasystemfortrackingtheefforts.Whitfieldalsowasconcernedwithrecruitmentissues,curioustounderstanddecisionstoteach—especiallywithregardstotheimpactofcompetitivescholarshipstheareusedtodrawinmathematicsteachers.ShelearnedthatmanystudentswhohadobtainedaNoycescholarshipmadetheirdecisiontoteachfarearlierthanothers,whilenon-scholarsweremoreinfluencedbyexternalfactors.Whitfield’ssurveystudyprovidedsomeinsightsonrecruitmentfactorsthatdifferedbetweenNoyceandnon-Noycescholars.

Summary

TheMTE-Partnershiphastakenthetime(fiveyears)forparticipantstoselect,study,andownproblemsasdescribedinGomez,Russell,Bryk,LeMahieu,andMejia(2016).AtthisfifthconferenceRACswereabletooffermorecompleteideasandmorefullyvalidatedmaterials.MostRACmaterialshavebeentestedandvalidatedatmultiplesitesandtheseproductsremainavailableforotherpartnerships.


17

RACshavebeenabletocreateusefulstrategiesandmaterialsbytargetingspecificchallengesinthepreparationofsecondarymathematicsteachers.Thenewchallengefacingpartnershipsistorefocusattentiononthechangeeffortsofprogramtransformation.Notonlytore-engagethemanydifferentconstituentsinvolvedinsecondarymathematicsteacherpreparation,butmoreimmediatelydeterminingwhichmaterials,fromwhichRACs,shouldtheyincorporateintheirprograms.PartnershipteamsreportedthatpartoftheproblemisfindingadditionalparticipantsintheirlocalgroupstoassumeleadershiproleswithrespecttoincorporatingnewRACideasandmaterialsintheirprograms.Althoughmuchhasbeendone,moreeffortisneededanditisneededfaster.

TheelementsoftheseproceedingsoftheFifthAnnualMathematicsTeacherEducationPartnershipdocumentthematurationoftheresearchcommunitiesandtheimplementationoftheNICresearchdesignoverall.Thismaturationhasmadeapparenttheneedtoreturntothelargergoalofprogramtransformationtowardthe“goldstandard”identifiedinthecommunity’sguidingprinciples(MathematicsTeacherEducationPartnership,2012).Further,elementsofprogramtransformationthatarepresentintheguidingPrinciplesthatarenotexplicitbeingaddressedbyaRACorinthepresentRACsarebecomingapparent,suchasthecomplexchallengesofequityandsocialjustice.Theopportunitytoreturntothesebroaderissuesattheconferencehasre-energizedandthejointpurposeandidentityacrossthepartnership.Webelieveyouwillfindevidenceintheproceedingsthatfollowthatthefourgoalsoftheconferenceweresuccessfullyachieved.

References

Bryk,A.S.,Gomez,L.M.,&Grunow,A.(2011).Gettingideasintoaction:Buildingnetworkedimprovementcommunitiesineducation.InM.Hallinan(Ed.),FrontiersinSociologyofEducation(pp.127-162).NewYork:SpringerPublishing.

Bryk,A.S.,LeMahieu,P.G.,Gomez,L.M.,&Grunow,A.(2015).Learningtoimprove:HowAmerica’sschoolscangetbetteratgettingbetter.HarvardEducationPress.

Gomez,L.M.,Russell,J.L.,Bryk,A.S.,LeMahieu,P.G.,&Meija,E.M.(2016)Therightnetworkfortherightproblem.PhiDeltaKappan,98(3),8-15.

Martin,W.G.,&Gobstein,H.(2015).Generatinganetworkedimprovementcommunitytoimprovesecondarymathematicsteacherpreparation:Networkleadership,organization,andoperation.JournalofTeacherEducation,66(5),482-493.

MathematicsTeacherEducationPartnership.(2014).Guidingprinciplesforsecondarymathematicsteacherpreparation.(RevisedDraft).Washington,DC:AssociationofPublicLandGrantUniversities.Retrievedfromhttp://www.aplu.org/projects-and-initiatives/stem-education/SMTI_Library/mte-partnership-guiding-principles-for-secondary-mathematics-teacher-preparation-programs/File

O’Neill,C.(2016).Weaponsofmathdestruction:Howbigdataincreasesinequalityandthreatensdemocracy.NewYork:Crown.

18

OPENINGADDRESS


19

KeepingtheCourse:TransformingMathematicsTeacherPreparation

inResponsive,ResponsibleWays

[email protected]

SuzanneWilsonUniversityofConnecticut

[email protected]

Effortstoimproveteachereducationprogramstoensurethattheyhavetheknowledgeandskillstobesuccessfulintoday’sschoolsiscomplicatednotonlybythelayersofscrutinybyawidevarietyofstakeholderssuchas:governmentagencies,privateorganizations,politicians,andindividualcitizens,butalsowiththemyththatteachingabilityisaninnategift.Attemptstoensurethateveryteachercanteacharehobbledbythismyththatteachersareborn,notmade.Forexample,actionstakeninrespondtogovernmentpoliciesreflectthismythwhenthepolicyfocusisonraisingteachingstandards,buttheactionsmutateintoeffortstorecruithigh-flyinggraduatestotheprofessionandencourage‘bad’teacherstoleave.Rarelydosuchpoliciesemphasizeprovidingthestructuralandfinancialsupportsthatteachersneedwithinthecontextofwheretheywork.

Teacherpreparationisasprawlingenterprise,andhasonlygrownlargerandmorediverse.Theemergenceofavarietyofcertificationpathshasincreasedthecomplexityandinconsistencyofhowteachersentertheclassrooms.Withinthisenvironment,alonglistofcriticismsofteacherpreparationappearinthepublicdiscussionsaboutteacherpreparation,including:

• Dividebetweentheoryandpractice• Teacherpreparationcoursesareanti-intellectual(MickeyMousecourses)• Unnecessarybarriers• Notenoughteachersofcolor• Notenoughintellectuallyeliteteachers• Notenoughcontentknowledge• Notenoughclinicalexperience• Notenoughattentiontoissuesofequityandsocialjustice

Thesecriticismsmaybelegitimateforsomepartsofthatlandscape;however,hyperbole,oversimplification,andovergeneralizationarerampant.Nevertheless,this1



20

seeminglyconstantdincontainsrealmessagesaboutimprovingteachereducation.Wemustfindeffectivewaystoberesponsivetothesecallsforchange.Howshouldwemoveforwardamidthisstormofnegativediscourseandcallsforchange?Whichissuesshouldweprioritize?Whichaudiencesshouldweaddress?

Thesequestionsareparticularlyimportanttothisgroup,theMathematicsTeacherEducationPartnership(MTE-P)becauseofitsoverarchinggoal:Totransformsecondarymathematicsteacherpreparationinordertoensureanadequatesupplyofnewteachercandidatespreparedtosupporttheirstudents’college-andcareer-readiness.MTE-Precognizedthenationalneedformoreandbettermathematicsteachersandinitiatedeffortstoaddressthatneed.

Beforeattemptingtoanswerthequestionsabove,weshouldrecognizesomeadditionalrealitiesassociatedwithchangingeducationalpracticeinclassrooms.Changingteachingpracticeisexpensive;sometimesintermsofdollars,sometimesintermsoftimecommitmentforpreserviceandinserviceteachers,andsometimesintermsofstudentopportunitiestolearn.Wemustusetheseresourceswiselybyfocusingoneffectivestrategiesforchange.Thus,weneedtofind,develop,anduseresearch-basedwaystosupportpreserviceandinserviceteachers.Inshort,theoryisimportant,researchiscritical.

Figure1.AModeltoSupportConsistent,ContinuousClassroomChange

Wealsoneedinstrumentsthataddressmeaningfulandagreed-uponoutcomesbeforechangestoeducationalpreserviceandinserviceprogramsarelaunched.Finally,theprocessoftransformingclassroomsneedstotakeplaceinwaysthatareasleastdisruptivetotheeducationalenterpriseaspossible.Wecandothisbytakingsmallstepsandproducingincremental,butconsistentchange.Figure1showsonewaytothinkaboutthisidea.Innovationinclassroomsshouldonlybeattemptedwiththeoreticalsupportandwithmeasuresthatwilldemonstratedifferencesinthedesiredoutcome.Thepointistomakesmallchanges,tweaks,consistentandcontinuousovertime,whichallowsformidcoursecorrectionsandprovidesrealchangeinthecontextofthework.Inthisway,wecanapproachclassroomchangeresponsiblywithteachersasactiveleadersintheresearch.


21

Giventhisbackground,shereturnedtothetwopuzzlessuggestedearlier:

Puzzle1:Whenandhowtorespondtocriticism/newideas?

Puzzle2:Whatkindofevidence,arguments,andwarrantsdoweneedtomuster?

Puzzle1:Whenandhowtorespondtocriticism/newideas?

Teacherpreparationprogramshavebeencriticizedforlackofrigor,lowproductivity,lackofdiversity,andasineffectiveforpreparingcandidatestodothejobofteaching.Fewdisagreethatpreserviceteachersneedrobustandqualityclinicalpractice,coursework,contentknowledgeforteaching,andknowledgeandskillsforculturallyresponsive/relevantteachingandtoimplementhighleveragepractices.Ontheotherhand,manyofthesecriticismsarebasedonanecdotaldata,whichworkswellforstirringuppublicsentimentbutoftenfailstoidentifytruechallenges.Tomakeprogressinimprovingteachereducationprogramsweneedvalidandreliablemeasuresofmathematicsteachingeffectivenessandwaystoimplementthosemeasuresconsistentlyandubiquitouslyforcomparisonswithinandacrossmultiplegroups.Otherwisewestumbleblindlyinourattemptsatteachereducationimprovementaswereacttosymptomsnotcauses;exasperatingthelivesoftheeducatorscaughtinthemix.

Recentresearchcanprovidehelpininstructionalimprovement,andtoguidehowtorespondtosuchcriticisms,overtime,inresponsibleways.Wilsondrewfromexperienceswithprogramssuchas:ComprehensiveSchoolReform,ChicagoSchoolReform,TheSiliconValleyMathematicsInitiative(SVMI),LongBeachTeacherPrepAlliance,andReadingFirst.Teachereducationprogramsthatseemtobesuccessfulusemetricsspecifictothecontext,suchas:diversityofcandidatepool,locationofgraduatesacrossthestate/country,retentionrates,diversityofstudentstaughtbygraduates,measuresofcontentknowledgeforteaching,progresschartsonmasteringhighleveragepractices,principalorsupervisingteacherratings,andperseverance.Fromtheseresearchactivities,we’vecompiledalistofeffectivestrategiesforinstructionalimprovement:

• Mobilizeandsustainsupport:Strongsupportmatters.theabsenceofwillleadstowitheringofreforms;

• Identifyanddeployasetofpolicyinstruments/institutions:Coordinatedpolicyinstrumentsmatter;

• Implementationrequiresthebalanceofcapabilitybuildingandaccountability;• Provideteachers/teachereducatorswithopportunitiestodevelopadaptiveexpertise:

Policiesmustmotivateandengageteacherswhilealsobuildingcapability;• Buildandenableculturalandcommunitysupport:Policyimplementationdependson

socialrelationsamongteachereducators,teachers,schools,statedepartments,andcommunities;and


22

• Produceoutcomeswithdemonstrableeffects:Persuasivedemonstratedeffectsareneededforbothteachersandothergroupsessentialtopolicyimplementation.

• p.s.Noneofthishappenswithoutrelationaltrust….

Puzzle2:Whatkindofevidence,arguments,andwarrantsdoweneedtomuster?

Weneedvalidandreliablesourcesofevidence/warrants/argumentsforindividualcandidatesaswellasforourprograms.Weneedtodevelopadatabase,aninfrastructure,andaculturetomanage,share,andinterpretthatdata.Wealsoneedtoidentifythoseissuesareaboutvaluesandarenotaboutevidence.Evidenceisimportantwhenenteringthepublicdiscussion,butevidenceisnotALLimportant.Wealsoneedstories.Wemustlearntopersuadewithdata,stories,trust,andengagementwithstakeholders.Finally,weshouldcollaboratewithothersbysharingactivities,measures,results,anddatawithinandacrosseducationalinstitutions.Wecannotchangewhatwecannotmeasure,butourmeasuresresultsaremorevalidandconvincingiftheyspanmultiplepopulationsandcontexts.Inresearch,(sample)sizematters.

Onewaytoengagestakeholdersisthroughthedevelopmentofstrategiestopresentcomplexandnumerousdata(andstories)inattractiveandunderstandableways,thatdemonstrateourjourneytowardsteacherpreparationimprovement.Wemustbeclearaboutourapproachtoimprovementbysharingourmodelofsmall,research-based,well-documented,teacher-led,reliably-measuredtrialsinclassrooms.

Weneedcommonmetricsforteachereducationprogramsthatspecificallyaddresstheconcernsofthestakeholderssuchas:diversityofcandidatepool,locationofgraduatesacrossthestate/country,retentionrates,diversityofstudentstaughtbygraduates,measuresofcontentknowledgeforteaching,progresschartsonmasteringhighleveragepractices,principalorsupervisingteacherratings,andperseverance.

Puttingitalltogether

Ifwearetokeepingthecourse,thatistransformmathematicsteacherpreparationinresponsive,responsiblewaysinthecurrentturbulentenvironment,wemustbetransparent,systematic,andpersistentinourefforts.Asacommunity,wemustagreeonavisionthatisneithertoonarrownortoorigid,butnonethelessfocused,democraticallyrobust,mathematically-sound,andambitious(bothintermsofthemathematicsandreachingtheneedsofallstudents).Wealsomustunderstandthatenablingthatvisionwilltakelong-term,collectiveworkinprotectedspacewithadequateresources(includingtimeandtrust).Weneedtotakelessonsfromthepastbothwithinteachereducationandmoregenerallyineducationreform.Wemustaddressteachereducatorcapacity,will,andenergytodevelop,guide,andevaluateimprovement-basedprograms.Infrastructurethatenablestheuseofvariedexpertiseandengagement,andacultureoftrustandcritiquemustbebuiltandnurtured.Mathematics


23

teachereducationprogramsneedwaystogatherinformationthatallowforaccurateaccountsofprogressandproblems,includingrobustassessmentsthatprovidehelpfulinformationaboutbothwhatstudentsunderstandandwhatteachersdo.

Toapproachteachereducationinthiswayweneedto:

• Conceptualizereformsasexperimentsthatneedsoundresearchthatunfoldsovertimeandgoeshand-in-handwithclassroompractice,

• Createnormsandvaluesthatembrace“steadywork,”• Investinthedevelopmentofsocialtrust,• Maintainthewillandfocusinanoisy,conflict-fullenvironment,• Includethebroadestsetofcriticalstakeholderspossible,• Investinthedevelopmentofabroadsetofindicatorsthatspeaktomultiple

stakeholders.

MTE-Phasagoodstartinthisprocessasweareworkingtowardacommonvisionformathematicsteacherpreparationthatspans101universitiesand142K-12schoolsanddistrictsacross30states.Nowinitsfifthyear,thecommunityhaslearnedtoworktogether,topersistinthisprocess,tolookpastthenoiseaswedevelopmeaningfulmeasures,andtocontinuetobuildpartnershipsandrecruitcollaborators.Thereismuchatstakeinthecurrentpoliticallychargedenvironmentinwhichweengageinmathematicsteacherpreparation.Aseducators,wecannolongerworkaloneinourlocaldistrictorcommunitytocreatetheimpactneededformeaningfulchange.Wemustworktogethertopooloureffortsandmagnifyourresults.MTE-Pisagoodstartforthisendeavor.

24

PANELTALKS


25

Pre-SessiononEquityandSocialJustice


[email protected]

MarilynStrutchensAuburnUniversity

[email protected]

OnegoaloftheFifthAnnualMathematicsTeacherEducatorsPartnershipConferencewasto,“makeequityandsocialjusticemoreexplicitasanessentialcomponentofthepartnershipaim.”Onthefirsteveningoftheconference,alooselystructuredgatheringwasorganizedtodiscusstheroleofequityandsocialjusticeintheMTE-Pwork.TogainaperspectiveastohowMTE-Phasfocusedontheissues,participantsexaminedtheMathematicsTeacherEducationPartnership(2012),whichincludesseveralstatementsthatindirectlysupportequityissuessuchasaccessandachievement.Twooftheprinciplesspeakmoredirectlytotheseissues.First,GuidingPrinciple5:Candidates’KnowledgeandUseofEducationalPractices,SectionEcallsforAttentiontoDiversity:

Theteacherpreparationprogramensuresthatteachercandidatesrecognizethatallstudentsintheirclasses—includinglow-performingstudents;giftedstudents;studentsofdifferentracial,ethnic,sociolinguistic,andsocio-economicbackgrounds;Englishlanguagelearners;studentswithdifferentsexualorientations;andstudentswithdisabilities—havethepotentialtomakeimportantcontributions,andthattheymaintainhighexpectationsforallstudents.

Secondly,GuidingPrinciple6:Professionalism,Advocacy,andLeadershipcallsforteacherpreparationprogramstoensurefutureteachersholdthemselvesandcolleaguesresponsibleforthemathematicalsuccessofallstudents.Inparticular,SectionC:SenseofJusticestates:

Theteacherpreparationprogramfostersasenseofagencyinitsteachercandidatessothatthroughtheiractions,behaviors,andadvocacy,candidatesdemonstrateadedicationtoequitablepedagogythatpromotesdemocraticprinciplesbyholdinghighexpectationsforallstudents,whilerecognizingandhonoringtheirdiversity.

TheinterestsunderlyingthecallfortheMTE-PEquityandSocialJusticeworkinggroupwastoconsiderifthesetwoguidingprinciplesweresufficienttoguideeffortsonthistopicfortheMTE-Pproject,andalsotoinitiatediscussionsregardingthebreadthofissuesrelatedtoequityandsocialjusticetobeconsideredinrelationtosecondarymathematicsteacherpreparation.

From6:30to7:15PMonthefirstnightoftheconference,approximately50MTE-Pmembers,slightlyoverhalfofthoseattendingtheconference,satinsmallgroupsattableswhileDrs.LawlerandStrutchensledthediscussion.Toprepareforthis


26

conferencepre-session,eachRACwaschargedtoidentifywaystheirworkaddressedissuesofequityandsocialjustice,orincorporatedspecificMTE-PGuidingPrinciples.TheRACspresentedtheirreportsduringthisopeningpre-session.Theirreportsareincludedintheappendixofthispaper.

Theworksessionsattendeeswereaskedtobrainstormadditionalissuesrelatedtoequityandsocialjusticethatareimportantforthepreparationofsecondarymathematicsteachers.Rich,intenseconversationswereheldateachtableandafewoftheideasgeneratedinthosediscussionswerereportedtothefullgroup.Groupresponseswereorganizedintocategories:children’smathematicalidentities,mathematicsteachers’identities,biasesandstereotypesinthediscourseaboutpeopleandmathematics,biasesinthestructuresaroundmathematicseducation,andchallengestorecruitment.ParticipantresponsessharedthatillustrateeachofthesecategoriesappearinTable1.

Table1Responsestotablediscussionsaboutissuesrelatedtoequityandsocialjusticethatareimportantforthepreparationofsecondarymathematicsteachers.

CategorywithresponsesfromtheworkinggroupChildren’smathematicalidentities Mathematicalidentity(e.g.Dochildrenseethemselvesincurriculum?) Whatteacheractionscausepositiveornegativemathematicsidentities? Betterwaystoassessmathematicalpotential,suchasinearlycollegeexperienceMathematicsteacheridentities Teachingmathematicsisasociopoliticalact Empowercandidatestobeagentsofchange Maintaincandidates’confidenceinmathematicalabilitiesastheytakehighermathematicsBiasesinthediscourseaboutpeopleandmathematics Discourse(howpeopleinteractandtheexpectationstheyhaveforoneanother) Preserviceteacherawarenessofdeficitlanguage,discourses,andpractices DeficitlanguageamongourselvesasMathematicsTeacherEducators(MTE) MTEbiasesandbeliefs,suchashowweperceivestudents,orwhoshouldhaveaccess Stereotypethreat,forbothfacultyandpreserviceteachersBiasesinthestructuresaroundmathematicseducation Tracking Integrationofdiversity,equity,andsocialjusticespecificallytomathematicsandspecificdomains InstitutionalracismChallengestorecruitment Discouragingmessagesagainstbecomingateacher Clinicalexperiencescouldattendtoequityandsocialjusticewithequalimportanceto

mathematicsinstruction Structuralchallengestorecruitmentthateliminatepotentiallygoodcandidates,suchasadvising

andsomestandardizedtests(relatedtoculturalcapital) Broadenedparticipationtomatchlocalpopulation(mayberecruitingearliercanhelp)


27

TablediscussiongroupswerealsoaskedtoconsiderwhatsortsofactionsmightMTE-Ptaketoaddressthedirectandindirectchallengesofequityandsocialjustice.Onetopicfrequentlymentionedwastheneedforprofessionaldevelopment(PD)withintheMTE-Pcommunity;manyoftheparticipantsindicatedthattheyfeltinadequatelypreparedtoachievegoalsrelatedtoequityandsocialjusticeassetforthintheGuidingPrinciples.SubsequentdiscussiononPDrevealedthatstructureslikeawebinarwouldbeinsufficientforthecomplexityoftheissues,forexamplethepossibleneedtovisitbeliefsorvalues.Oneideaemergedrecommendingthedevelopmentofmodulesincludingtalkingpointsforsharingwithcolleaguesatourhomeinstitutions,aswellaswithdistrictpartners.Anothersuggestioncalledforthedevelopmentofspecificactivitiesthatcouldbeusednotonlywithpreservicemathematicsteachers,butalsowithothermembersofourlocalteams.AdditionaldiscussioncenteredonhowMTE-PmightprovideasupportsystemfortheeffortsonindividualRACstoincorporateequityandsocialjusticeintotheirwork.

AsecondelementofthisdiscussionwasfocusedmoreonthecontentofpotentialsupportsystemsandPD.Onesuggestionpromotedincreasingawarenessofhowprivilegeworks,andtoidentifythevarietyofwayspeopleareprivilegedinthissociety.TheHarvardProjectImplicit(implicit.harvard.edu/implicit/index.jsp)wasidentifiedasaspecificexamplethatcanhelpanindividualidentifyhisorherbiases.Dr.KarenKingcautionedthiseffort,pointingtoabodyofresearchthathasdemonstratedthatofteninanattempttoteachdiversityclass,peoplecomeawaywithpreviousbeliefsandbiaseshardened.Thus,itisimportantthatweexamineprofessionaldevelopmentprogramsaroundequityandsocialjusticeissueswellbeforeweimplementthemwithinthepartnership.

Astheworkinggroupwrappedup,severalparticipantssuggestedthatMTE-PmightsupportanEquityandSocialJusticeWorkingGroup.Dr.Kingraisedchallengestokeepinmindasthegroupmovedtowardplanningactivities.Forexample,sheremindedthegroupthatequity,diversity,andsocialjusticearenotthesamethingsandthatthetermsoftengetusedinterchangeably.Topreventconfusionaboutthesetermsinthegroup’sactivities,sheadvisedtofirstteaseoutdistinctionforeach.Dr.Kingposedaquestionthatspeakstothenuancesoftheterms,recognizingthatoureducationalsystemismoresegregatednow(Rothstein,2013)thanatthetimeofBrownvs.BoardofEducation:Canschoolingbeseparateandequitable?Dr.Kingalsocautionedagainstthedrawtoessentializechildren(andpeople)duetomembershipofaparticulargroup.Anothercommonissuerelatedtoequityandsocialjusticeinmathematicseducationisthatataskonitsowndoesnotmakeforequity,butalsotheenactment—theteaching—ofthattaskiscriticaltohowitisperceivedbylearners.Herfinaladvicewastostudyresearchoutsidemathematicseducationtomorefullyunderstandthesechallenges.Forexample,thereisaconsiderableliteratureonhowdiversitytrainingisoftenineffective.Similarly,thereisrobustliteratureinthebusinesscommunityaboutrecruitment,especiallyrelatedtorecruitingpeopleforsomethingtheymaynotknowtheywanttodo--suchasbecomeahighschoolmathematicsteacher.

Dr.GaryMartinreiteratedthatchallengeforus,membersofMTE-P,toconsiderandlearnhowwecaneducateourselvesandourinstitutions.Specifically,whatmightorshouldourteachereducationprogramsdotodevelopskills,knowledge,anddispositionsalignedwiththechargesofequityandsocialjustice;whatisitwehopeourpreserviceteacherswillleaveus


28

preparedtodoashighschoolmathematicsteachers.Dr.MarilynStrutchenschallengedusmorebroadlytoconsiderhowtoweraiseconsciousnessinthecommunityofthecomplexityofthesechallenges.Howcanwecreatechangeagents?AndhowcanMTE-Pleverageitsroletomakechange?

TheEquityandSocialJusticeworksessionconcludedwithaverystrongexpressionofinteresttocreatesomestructurewithinMTE-Ptopursuethesechallenges.Ascomplexastheseissuesare,theyarecertainlycoretopreparinghighschoolmathematicsteachers.Afirststepmaybetoheightentherecognitionthattheseissuesarecoretotheworkofmathematicseducation.

References


Rothstein,R.(2013,August27).Forpublicschools,segregationthen,segregationsince.EducationPolicyInstitute.Retrievedfromwww.epi.org/publication/unfinished-march-public-school-segregation

Appendix:RACReportsonConnectionstoEquity&SocialJustice

ActiveLearningMathematics—ALM

• ALMinundergraduatemathematicscontributestoimprovedengagement,accessandsuccessofallstudents(e.g.Freemanetal.,Laursenetal.,etc.)

• Explicitattentionbeinggiventoproblematicfeaturesofinstructioninundergraduatemathematicsthathavebeeninstitutionalizedindepartments&university

• StudentEngagementinMathematicsthroughanInstitutionalNetworkforActiveLearning(SEMINAL):Explicitfocusoncharacteristicsofproductivemathdepartmentsandstudyingtheprocessofinstitutionalchange

ClinicalPractices

• OneoftheprimarydriversoftheRACis:Focusonaccessandequity• Organizementorselectionandsupportarounddeepeningexpertisewithmathcontent,math

standards,MTPs,andmentoringstrategies• Thepreparationofeachnewteacherofsecondarymathematicsrepresentsanopportunityto

disruptlong-standingteachingpracticesthatcontributetoinequitiesinlearningoutcomes.• Ensurethatrequirementsforstudentteachingandfeedbackduringstudentteachingemphasize

theresponsibilityofTCstoadvancemathematicslearningamongsecondarystudentsthroughcollaborationwithmoreexpertmentorsinuseofMTPs.

• Ensuremutualagreementbetweendistrict(s)anduniversityaboutwhatqualityteachingofsecondarymathematicslookslikeandhowtofurtherskillsofallteachers(includingTCs)andseementorteachingaspartofcareerladder.

• UsetheNCTMPrinciplestoActionseightcoreteachingpracticestopromotedeeplearningofmathematics


29

• ChangeIdeas(How)o ThedevelopmentofaPDprogramrelatedtomentoringmathematicsteacherso ProvideongoingPDandcourseworkrelatedtotheCommonCoreStateStandardsand

NCTM’sMathematicsTeachingPracticeso Conveneeitherface-to-faceoronlinemeetingstoplanfieldexperiences,articulate

expectations,andreflectonnormsandcultureswithintheclasssettings.MODULE(S2)

• Providerepresentationsofteachingpracticeandteachingscenarioswhichincorporateresearch-basedknowledgeaboutculturallyandmathematicallydiversestudents’learningandtheirconceptionsofthespecificcontenttopics.

• Includehistoricalnoteswhichincludecontributionsofallpeoplestothedevelopmentofmathematicalideas

• DevelopPreserviceMathematicsTeachers’professionalnoticingskillsMarketingtoAttractTeacherHopefuls—MATH

• Pastactivity:Implicitstrategiestotargetunderrepresentedpopulations• Possibledirections:Moreovert,direct,andtargetedstrategiestiedtolocalcommunitiesand

institutiontoincreasenumbersounderrepresentedpopulations


30

ADeeperDiveintoPlan-Do-Study-ActCyclesandMeasures


[email protected]

[email protected]

[email protected]

MarkEllis

[email protected]

ThistalkexploresmoredeeplythestructuresandmeasuresofthePlan-Do-Study-Act(PDSA),acoreprincipleofimprovementscience.Webeganthisdiscussionwiththechallengesthatwefacedinmovingfromatraditionalresearchparadigmtousingimprovementscience,specificallythestrugglesweexperiencedintermsofstartingsmallwiththegoaltorampuprapidly.Lewis(2015)sumsupthetransitionsthatwehadtomake:

Improvementscience…treatsvariationinimplementationandsettingasimportantsourcesofinformationandprovidestoolstograspandlearnfromvariation(inbothpositiveandnegativedirections)inordertoredesignboththeinterventionandthesystem.(p.55)

And,

Improvementscienceassumesscale-upoccursthroughintegrationofbasicknowledgewiththe“systemofprofoundknowledge,”suchasknowledgeabouthowtobuildsharedownershipofimprovement,todetectandlearnfromvariationsinpractice,tobuildandshareknowledgeamongpractitioners,tomotivatefrontlineinnovators,andsoforth.(p.55)

ThePDSAcycle(Lewis,2015),Figure1,isanessentialtoolofimprovementscience,

aprocessforrapidcyclesoflearningfrompractice,coupledwiththreefundamentalquestionsthatdriveimprovementwork:(1)Whatarewetryingtoaccomplish?(2)Howwillweknowthatachangeisanimprovement?and(3)Whatchangecanwemakethatwillresultinimprovement?(pp.54-55)


31

Figure1.Plan-Do-Study-Actmodel.

Inthe“Plan”stagewearticulatethechangeweintendtoimplementandrecordpredictionsaboutwhatweexpectwillhappen.As,“Do’suggests,inthisstage,weattemptthechangeanddocumentwhathappens.The“Study”stageiswherewecomparetheactualresultstothepredictionswemade.Next,we“Act”,decidingwhattodonext.Doweadapt,adopt,expand,orabandonthechangeidea?InimprovementsciencePDSAsareused(Kawar,Mejia,Bennett,&Dolle,2015)as

• thekeymechanismbywhichwelearn,• awaytotestandrevisetheoriesatanappropriatescale,• awaytogaininformationbydoingSOMETHING(evenifit’ssmall)ratherthanobsessing

overgettingit“right”fromthestart,• acommonapproachthatdisciplinesoureffortssoweareefficient.

ThepredictionsmadeinthePlanphasemakeexplicitourunderstandingofthesystemweareworkingwithinandhowwethinkourchangeideawillimpactthatsystem.Thegapbetweenourpredictionsandtheactualresultsiswhereourlearninghappens.Whenwhatwepredictcomestrue,weonlyhaveconfirmation—suggestingthatthereisnogapinourunderstandingofhowoursystemoperates.Ifweareunabletoexplainwhyatestsucceeded,thenwemaystillhaveagapinourknowledge,andwemaywishtorepeatthetesttosolidifyourunderstandingofthesystem.Whenourpredictionsarewrong,wehaveexposedagapinourknowledgeprovidinganopportunityandatargettodigintounderstandmoreaboutwhythingsarethewaytheyare.

ThechangeideastobeexaminedinPDSAcyclesaretakenfromthedriverdiagram.Thedriverdiagramisdevelopedbyestablishingaclearaim,aspecificstatementofwhatweare

PLAN • What’s your

change? • What’s your

prediction? • Plan to conduct test

DO • Execute test • Collect data,

document observations

STUDY • Compare results

to prediction • What did you

learn?

ACT • Next steps:

Adapt, expand, adopt, abandon


32

tryingtoaccomplish,andidentifyingprimarydriversorfactorswhichdirectlyimpacttheaim.Thechangeideasaretheactionsidentifiedasappropriateforaffectingtheprimarydriverssothatwemoveclosertoouraim(Bryketal.,2015).Whetherornotourchangeisactuallyanimprovementisdeterminedbycollectingandanalyzingdata.

Thisapproachisdifferentfromthetraditionalapproachoftentakenineducationreform.Thetraditionalapproachinvolveschoosingachangeideatoimplement,delayingimplementationuntiltheideahasbeen“perfected,”andthenenactingtheideasystem-wide.Whenthechangedoesnotimprovethesystemwehaveoftendonemoreharmthangoodtothewholesystemandhavemissedtheopportunitytogainadeeperunderstandingofoursystemandthechangeideafromthefailure(Kawaretal.,2015).Improvementscienceimpliesthattestingchangeideasshouldstartsmallandslowlyexpandtolearnalongtheway.Consequently,whenwefullyimplementachangeidea,wehavegatheredknowledgeaboutnotjusttheeffectivenessofthechangebutalsohowtogetthechangetohappeninvariouscontexts.

IninitialPDSAcyclesthepurposeistodeterminehowtogetthechangeideatowork.Thenextcyclesfocusonlearninghowtogetthechangetoworkacrossmultiplecontextsanddeterminingthesupportprocessneededtoenactthechangesystemwide.Finally,thechangeideaisintegratedintothesystem(Kawaretal.,2015).Although,thisprocessmayseemlongtoaddressonesmallchange,particularlyinacomplexsystem,PDSAsarefocusedcyclesdesignedtomovethroughthetestingofchangeideasrelativelyquickly.Moreover,PDSAscanberuninparallelsoseveralchangescanbetestedondifferentpartsofourdriverdiagramatthesametime.

Thescaleatwhichwechoosetotestachangeideadependsonseveralfactors:(1)Howconfidentarewethatthechangeideawillleadtoimprovement?;(2)Whatisthecostoffailure?;and(3)Howresistanttochangeisoursystem?Lowconfidenceinthechange,withahighcostoffailureandasystemresistanttochangesuggeststhatwerunaverysmallscaletest.Whereas,alarge-scaletestmightbeappropriatewhenthereishighconfidenceinthechange,alowcostoffailureandasystemindifferenttochange(Kawaretal.,2015).AsweprogressthroughPDSAcyclesconfidenceinthechangeideagrowsandthecostoffailuredecreases,consequentlyoursystembecomesmorereadyforchangeandwecanimplementtheideasystemwide.


33


34

ThePDSAform,Figure2,providedtousbytheCarnegieFoundation,isaneffectivetoolforkeepingarecordofourprogressionthroughthetestingprocess.Completionoftheformfocusesourthinking.Weareremindedhowtheplannedcyclefitsintoouroveralldriverdiagram,ourPDSAstepsareclearlyoutlined,andaconciserecordoftheresultsareavailableasthenextcycleisplanned.

Measures

Ideally,datashouldonlybegarneredforaclearpurpose.Datacanbeusedforaccountability,research,andimprovement(Bryketal.,2015).Ifusedforaccountability,thedataisexaminedtoidentifyproblematicorexceptionalperformers,withthepossibilitythattheoutcomemayresultinproblematicperformersbeingterminated.Whendataisusedforresearch,theoriesaredevelopedandrelationshipsamongvariablesmayalsobeexamined.Datausedforimprovementpurposesseektodevelopaswellasevaluatechangeinpractices,withtheoutcomesofdatadocumentingthenatureofchangeandrelevantprocesses.Asanetworkimprovementcommunity,theClinicalExperienceRACuseddatatoimproveclinicalexperiencestoplaceagreaterfocusonthemathematicsteachingpractices(NCTM,2014)

TheClinicalExperienceRACoftheMathematicsTeacherEducationPartnership(MTE-P)usesabalancedsetofmeasures,namely:outcomemeasures,processmeasures,andbalancingmeasures,consistentwithimprovementscience(Bryketal.,2015;Lewis,2015).Outcomemeasuresconsiderhowthesystemperforms,andtheoverallresult.Processmeasuresevaluatewhetherthevariouspartsofthesystemareperformingasanticipated,andthebalancingmeasuresmonitoradverseeffectstootherpartsofthesystemaschangeisimplemented.Onadriverdiagram,theoutcomemeasures,whichareoftenlaggingindicators,provideinsightintotheextenttheaimstatementisachieved;theprocessmeasuresexaminesecondarydrivers,whichareearlyindicatorsastowhethertheproposedchangeisimprovingthesystem;andthebalancingmeasuresconsideritemsthatarenotidentifiedasprimaryorsecondarydriversforthediagramtoensurethechangeisnotresultinginunintendedconsequences.Usingabalancedsetofmeasuresprovidesaholisticviewoftheimplementationandsustainabilityofachangeidea.

ClinicalExperiencesResearchActionCluster’s(CERAC)Measures

TheClinicalExperiencesRACissub-dividedintothreegroups:pair-placement,methods,andco-planningandco-teaching(CPCT).Inthepairplacementgroup,twoteachercandidatesarepairedwithonementorteacherduringthestudentteachingexperience.Themethodsgroupfocusesonpreparingteachercandidateswhiletheyareenrolledinthemathematicseducationmethodscourse,andtheCPCTgroupencouragestheteachercandidateandmentorteachertoteachlessonstogether.TheaimstatementfortheRACindicatesteachercandidatesshouldusetheNCTM(2014)eightteachingpracticesatleastonceaweekforthedurationof


35

theirfieldexperiences.Thesecondarydriversindicatethatthereisaneedto:increasetheamountofmentorteacherswhoareinformedofnationalstandardsandcurrentreforminitiatives;attendtotheteachingpracticeswithinmethodscourses;encourageteachercandidatestoengageinself-assessmentandreflectontheextenttheirenactedlessonembodiestheteachingpractices;facilitatecollaborativemeetingstodiscussbeliefs,complexitiesandchallenges;anddevelopinfrastructurestosupportteachercandidates’needs.

Commoninstruments(MCOP2,MathematicsTeachingPracticesSurvey,andtheMTE-PCompleterSurvey)areusedacrossthethreegroupswithintheRACtogatherdatafortheoutcomemeasures.TheMCOP2measuresK-12classroomsinstructionalpractices’alignmentwithnationalstandardsdocuments(Gleason,Livers,&Zelkowski,2015).TheMathematicsTeachingPracticesSurveyisachecklisttoolusedtoidentifywhetheranyoftheNCTM(2014)eightstandardsareaddressedbyteachercandidatesduringeachdayoftheirfieldexperiences.TheMTE-PCompleterSurveyasksteachercandidatestosharetheirperspectivesabouttheextenttheirteachereducationprogrampreparedthemtobeeffectiveteachers.Therefore,theinstrumentsareusedexplicitlytogatherdatatodeterminewhetherteachercandidatesaretaughttousethemathematicsteachingpracticesintheirteachereducationprogram,andtheextenttowhichtheyactuallyusethepractices.

EachgroupwithintheRACcreatedfocusedinstrumentstoalignwiththegroupobjectivesandtogaininsightintotheprocessmeasures.Forexample,themethodsgroupcreatedmodulesabouttheteachingpracticesandassessestheextenttowhichteachercandidatesdeemedthemodulestobeeffective.Themethodsgroupalsousespre-andpost-methods-coursequestionnaires.Thedatagarneredprovideinsightintothenatureofthemethodscourseandtheextentitpreparesteachercandidatestoaddressnationalstandards.Similarly,thepairedplacementSub-RACusessurveys(ofthementorteacheranduniversitysupervisor)andfocusgroupstomonitorthecomplexitiesofthefieldexperiencesandtorefinetheinfrastructure.TheCPCTgroupusesprofessionaldevelopment,just-in-time,andexitsurveystomonitortheextenttowhichteachercandidatesandmentorsareinformedaboutthenationalstandardsandCPCT,togaininsightintopersonalreflectionsandself-assessments,andtolearnaboutthenatureoftheclinicalexperiences.Hence,theprocessmeasuresprovideactionabledatathatcanbeusedtoreducethelikelihoodthatthechangeeffortsarecultivatingunintendednegativeresults.

Togatherbalancingmeasuresfacultymembersareencouragedtoconversewithmentorteachers,teachercandidatesandsupervisors,todiscussothervariablesthatarealsobeingaffectedduetotheimplementationofchangeideasrelatedtoclinicalexperiences.Consideringthattimeisvaluable,andcanhaveimplicationsonhowareformideaisintroducedandsustained,ourbalancingmeasuresfocusonout-of-classplanningtime.Togarnerthese


36

data,aweeklyonlinesurveycouldbesenttoallconcernedpartiesthatasksabouttheamountofout-of-classtimebeingusedtoprepareforenactedlessons.

EmployingabalancedsetofmeasuresprovidesinsightintotheextenttheclinicalexperiencesRAC’soverallgoalwasachieved,andwhetherthechangesexaminedthroughPDSAcyclesarehavingdesirableeffects.ConsideringthatimprovementsciencereliesonPDSAcyclesasasystematicprocesstogatherdata,changescanbemadetotheideaduringiterationsofthePDSAcyclestoensuretheoverallsystemisimproved.Well-craftedmeasuresandthoughtfulimplementationofPDSAcyclesallowfortherobustresearchdesignofimprovementsciencetoembracevariationinimplementationandsettingasimportantsourcesofinformation,andtolearnfromthisvariationtoimproveboththeinterventionsandhopefullythesystem.

References

Bryk,A.S.,Gomez,L.M.,Grunow,A.,&LeMahieu,P.G.(2015).Learningtoimprove:HowAmerica’sschoolscangetbetteratgettingbetter.HarvardEducationPress:Cambridge,MA.

Gleason,J.,Livers,S.D.,&Zelkowski,J.(2015).Mathematicsclassroomobservationprotocolforpractices:Descriptorsmanual.Retrievedfromjgleason.people.ua.edu/uploads/3/8/3/4/38349129/mcop2_descriptors.pdf

Kawar,A.,Mejia,E.,Bennett,B.&Dolle,J.(2015).Disciplinedinquiry&testingstrategies:LearninglabsessionII[PowerPointdocument].RetrievedfromCarnegieNICDesignLearningLab:sites.google.com/a/carnegiehub.org/learning-labs-2015/home

Lewis,C.(2015).Whatisimprovementscience?Doweneeditineducation?EducationalResearcher,44(1),54-61.

NationalCouncilofTeachersofMathematics(NCTM).(2014).Principlestoactions:Ensuringmathematicalsuccessforall.Reston,VA:Author.


37

PathwaystoProgramImprovement

[email protected]

MarkEllisCaliforniaStateUniversityFullerton

[email protected]

WendyM.SmithUniversityofNebraska-Lincoln

[email protected]

DeVonneSmallsRichlandCountySchoolDistrictOnedevonne.smalls@richlandone.org

RobinHill

AssociationofStateSupervisorsofMathematicsrobin.hill@education.ky.gov

Ifyouthinktransformationislinear,you’lllivetobedisappointed.–GaryMartin

MembersoftheMathematicsTeacherEducationPartnership(MTE-P)whohavebegunworkonthecomplexchallengeofprogramtransformationwereinvitedtosharetheirexperiencesaroundtheseefforts.ThispanelgetstotheheartofMTE-P.Atitsinception,MTE-Palwayshadatransformationgoal–increasethesupplyofsecondarymathematicsteachersaswellasthequalityofbothourprogramsandthefutureteachersweproduce.TheResearchActionClusters(RACs)weremeanttohelpwiththatwork.Butinordertotrulytransform,eachprogrammustdrawupontheworkofmultipleRACstogetherandintegratewhatislearnedfromtheRACsintoourprograms.Enduringandmeaningfulchangeisoftenslowchange.Who’savailabletodothework?What’sthepriorityforimprovement?Whatkindofinstitutionalsupportdowehave?

NowthattheRACshaveestablishedafoundation,MTE-Pisreadytoaddresswhatitmeanstotransform.Whatdoestransformationlooklike?MTE-P’sproposedstrategyistosupportteamsastheycreatestrategicpathwaysfortheirlocalprograms.Noonemodelwillworkforeveryone,butmightaframeworkbecreatedwiththeflexibilitytobeusefulindiverselocalcontexts?MTE-Piscommittedtobuildingthecapacityandinfrastructureneededtohelppartnershipstransformandimprovetheirprograms.Thispanelsetsuptheworkofanewworkinggroup–Transformations–andestablishesafoundationfortheirwork.Thepanelistswereaskedtoaddressthefollowingquestions:

• Whatisthestatusofyourteamwithrespecttooveralltransformationofsecondarymathematicsteacherpreparation?


38

• Wherearetheopportunitiesformakingprogresstowardsthatgoal?

• Whatarethechallengesinmakingprogresstowardsthatgoal?

• WhatmightMTE-Pdotosupportyourprogress?

Theresponsesofeachpanelisttothesequestionsfollowsbelow,withconcludingstatementsfromtheReactant,RobinHill.

MarkEllis–CaliforniaStateUniversityFullerton

CaliforniaStateUniversityatFullerton(CSUF)ispartofthe22-campusteacherpreparationnetworkoftheCSUsystem,whichalsocomprisestheCSUMTE-Pteam.CSUFhasarichlocalcontextwithinthepartnership.Thelocalworkthey’vedonehashelpedinabidirectionalsense–theyhavebeenabletosecureadditionalfundingandthenusethatfunding(e.g.,BechtelFoundation)todevelopmorepartnershipsandcollaborations.Throughthiswork,theyhavebeenabletoenvisionteacherpreparationdevelopmentasacontinuumovertimeinsteadofisolatedincidencesoflearning.ThroughtheBechtelgrant,CSUFdevelopedasharedvisionwithintheirowninstitutionandinpartnershipwithtwolocalschooldistricts.Thatdevelopmentofasharedvisionallowedformoreexplicitconversationsacrossthelocalpartnership,especiallyfocusedonwhatdoesawell-preparedteacherlooklikeandhowcanthatbesupportedsothatlearningforallK12studentscanbesupported.

Duringthistime,thecampuswasbringinginnewmathematicseducationfacultywithintheCollegesofNaturalSciences&MathematicsandEducation.Thenewfacultywereeasilyabletotalkaboutelementsofthetransformedmathematicsteacherpreparationprogram(e.g.,co-plan/co-teach);theybecame“normalized”conversations.Themodesofcollaborationandconversationswerethenormamongthenewfaculty,experiencedmathematiciansandmathematicseducators,andschooldistrictpartners.HavingnewDeansinbothcollegesatthestartofthe2016-17academicyearaidedinsolidifyingtheprogramtransformationastheyunderstoodthetransformedprogramassomethingthatwastypical.

Onesetofchallengeseveryonehasfacedinvolvestime:thetimeforplanning;thetimeforimplementing;thetimeforcollectingdataabouttheimplementation;andtheanalysisofthedataandrevisionstothatthemodel.Forexample,Plan-Do-Study-Actcyclestaketime.Anotherchallengewasthetimerequiredforlong-timefacultytoembracethetransformedprogramasthenewnormal.

Havingthesupportofthestatewidenetworkofthe22-campusCSUteamhashelpedaddressthechallengeoftime,throughpersistenceandvisibility.TheCSUsystemisnowago-topartneracrossthestatebecauseoftheirinvolvementinMTE-P.Infact,theyweresuccessfulinadvocatingtheadditionof16mathematics-specificitemstoastatewideteacherexitsurvey


39

thatwillallowfacultytolookdeeperintotheirprogramsusingdatabothlocallyandacrossinstitutions.

MuchcanbelearnedfromnotonlytheworkatCSUF,butalsoacrosstheCSUteam.Californiaisanexceptionallydiversestate,socontextisespeciallyimportantandmatters.Amongtheinsightsgainedfromconversationsacrossthe22-campusnetworkwastherealizationthatsomecampuscredentialprogramsdidnotrequirecontentspecialiststodosupervisionofteachercandidates.WhenthissurfacedinsurveygeneratedbytheCSUMTE-Pteam,itprovidedfacultywithsubstantivedatatobringtolocalcampusadministratorstoadvocateforprogramchanges.Collectively,it’sessentialthatprogramqualityshouldnotbeaffectedbydifferentcontexts.

MargaretMohr-Schroeder–UniversityofKentucky

ThecurrentstatusofteacherpreparationintheCommonwealthofKentuckyisalittlechaoticandunstable.ThereisadireneedformiddleandsecondarymathematicsteachersacrosstheCommonwealth;boththeurbanandruralregionsarestrugglingtogetqualifiedteachersintoclassroomsandstayinginthoseclassrooms.EvenalternativecertificationprogramssuchasTeachforAmericahavenotsolvedthesetwoissuesofrecruitmentandretentionofmathematicsteachers.Asaresult,mathematicseducatorsfromacrosstheCommonwealthhavecometogether,ontheirownaccord,todiscusshowtocollectivelysolvethechallengesfacingmathematicsteacherpreparation.Onekeychallengeisthatthereislittlestatesupportforthinkingaboutteacherpreparationdifferently;forlookingatteachercredentialingdifferently.

Recruitmentintoteacherpreparationprogramsremainsafundamentalissue,especiallybecausethehighschoolgraduatingpopulationisdecreasingacrossthestate.Amajorityofthepublicinstitutionshavehadtorecruitstudentsfromoutofstate,whichposesdifferentrecruitingchallengesthanfromwithinthestate.Manyoftheprogramshaveundergoneradicaltransformationoverthepastfiveyears.Forexample,WesternKentuckyUniversityandMoreheadStateUniversityareofficialUTeachreplicationsites.UniversityofLouisvilleandtheUniversityofKentuckybothaddedundergraduatecertificationprogramswhentheir5thyear/MATprogramsbegantostrugglewithnumbers.

TheCommonwealthalsohasadramaticallychangingpolicylandscape.WhilethenewgovernorispromotingSTEM,thepromotionisatthecommunitycollegelevel.Meanwhile,therehavebeendeepcuts,includingmid-yearcuts,toinstitutesofhighereducation.Furthermore,pendinglitigationregardingmanyeducation-relatedissuesandthepromotionofprivateeducationoverpubliceducationmaketransformationdifficultandtumultuous.

Theretentionofteachers,notjustinthefirstfiveyears,butespeciallybetweenyears10–15isanunprecedentedproblem.Experiencedteachersareleavingtheclassroombecause


40

theirjobhasbecomeunfulfilling.Astheyleavepubliceducation,theyseekoutdifferentwaystoreachpeople;theystillwishmakeanimpact.Oneexampleisthelossofteacherstomanufacturingcompanies.Thesecompaniesrealizethegreatknowledgeandpedagogicalskillsofsecondarymathematicsteachers,sotheyrecruitandenticeteacherstoleavetheprofessiontocomeanddeliverprofessionaldevelopmenttotheirworkers.Theyofferhighersalaries,amoreflexibleworkschedule,benefitsevenifyouworkparttime,andalltheresourcesandtoolstheyneedtodeliverthetrainingtotheadultlearners.

YetthebiggestchallengeinKentuckyisthatteachersareseenasaprobleminthestate.

DespitethechallengesineducationfacingKentucky,therehavebeenampleopportunitiesfortransformationandimpact,manyofwhichareduetotheMTE-P.ThecurrentfocusontheMATHandSTRIDESRACsareimportant.AlthoughmanyKentuckymathematicsteacherpreparationprogramshavetransformedprograms,theynowneedtoattractmorestudentsandmustfocusonspecificinductionstructurestoretainthemafterthey’vegraduated.

Specifically,attheUniversityofKentucky(UK),therehasbeeninstitutionaltransformation.ThroughtheinvolvementinScienceandMathematicsTeacherImperative(SMTI)andMTE-PandgoingthroughtheSMTIanalyticalframework,UKidentifiedtheneedtocreateaSTEMniche.So,theycreatedaDepartmentofSTEMEducationwhichhelpedtopavethewayforthenewundergraduateprograminwhichastudentearnsadoublemajorinSTEMeducationandmathematics(orwhatevercontentareatheywillbeteaching).

Throughthistransformation,UKlearnedthatinstitutionaltransformationevolvesslowlyandishardwork.Partnershipsmusttakeadeeplookattheirprogramsandinstitutionandoftenthrowoutpreconceivednotionsofwhatsomethingshouldlooklikeorhowitshouldfunction.Butlookingatthingsthiswayishowyoucandramaticallychangewhatyou’redoing.

Movingforward,thebroaderSTEMcommunityinKentuckyisworkingondevelopingastatewideSTEMeducationcenter.Althoughtransformationsarehappeningacrossthestate,thereisnobackbonestructuretohelppullittogether.Acenterwouldhelptoscaletransformationsacrossinstitutions,leverageresources,collectandanalyzecommondata,andgenerallyjusthelpsupporteachotheraschangeagents.

TherearemanychallengesinKentuckymovingforward.Beingahighly-regulatedstateintermsofteacherpreparationisoneofthemostchallengingissues.Therearethreeseparategoverningagenciesforteacherpreparationprograms–thestatedepartmentofeducation,theteachercertificationagency,andthehighereducationgoverningagency.Therearemanytimesregulationsareimplementedoftenwithoutthinkingabouttheimpactonteachereducationprograms,includingstructuresnotdirectlyrelatedtotheregulations.Forexample,theteachercertificationagencyrecentlyreleasedaregulationthatallmiddleandsecondaryteachershad


41

totakeacontentarealiteracycourse.Onthesurfacethisdoesnotappeartobeabadidea.Butadeeperanalysisoftheregulationrevealsthatinsteadofthinkingaboutwaystointegratethoseideasintocurrentcourseworkandteachitincontext,theregulationrequiresanewcoursetaughtbyanaccreditedliteracyfacultymember.Theresult?Thecreationofanisolatedcoursethathasnofieldexperiencecomponentandhadtobesqueezedintoanalreadycredit-heavySTEMmajor.Moreover,thenumberofhoursforanundergraduateprogramarefixed—sotheresultisnotmerelyaddingacourse,butnowacoursemustberemoved.

AstheKentuckypartnershipcontinuesitstransformationendeavors,MTE-Pwillbeabletohelpthinkaboutscalingbeyondlocalchange;theexpansionofpartnershipsisimportant.Localchangeisgreat,buthowdoyougetbeyondlocalchange?Howdoyouscalethatreallygreatideathathasmadeanimpact?Whatdoesscalingevenlooklike?Howdowe,together,betteradvocateforourteachers?

DeVonneSmalls–RichlandCountySchoolDistrictOne,SouthCarolina

TheUniversityofSouthCarolina(UofSC)partnershipfacesmanychallenges,includingsecondarymathematicsteachershortages,poorteacherretention,anddeclininghighschoolenrollment.ThebiggestobstacleintheUofSCpartnershipisfillingalloftheirmathematicsteachingpositionsneededbyschoolsanddistrictsinourstate.Localschoolstoooftenbegintheschoolyearhiringlongtermsubs.

WhilepreserviceteachersatUofSChavefantasticteacherplacements,that’snotalwaystheirrealitywhentheygethiredattheirownschools.Throughanewsummerinductionprogram,theUofSCpartnershipistryingtointroducethemtothesepotentialchallengesandprovidemoresupportmechanismsearlyintheircareer.

WithintheUofSCpartnership,enrollmentlevelsatthelocalhighschoolscontinuetotrenddownward.Thishasespeciallyaffectedtheabilityofschoolstoofferspecializedmathematicscourses.Whilethereisadesiretoofferthesecourses,thelowstudentpopulationwillnotsupportthem.Further,teachersanddistrictpersonnelacrossthepartnershipstruggletofindtimetomeetandtakeactionaroundthechallengessuchastheinabilitytosustainspecializedmathematicscourse.TheUofSCpartnershipishopingthatexpandingthepartnershiptoincludemoreK12schoolsmighthelpleverageresourcesandaidinrecruitingnewteachers.

MTE-PhasbeenagreatsupportfortheUofSCpartnership.TherehavebeenseveralopportunitieswithinthepartnershiptohelpmeetthegoalsofMTE-Pandtheirlocalpartnership.UofSCplanstoaddacapstonecoursethathelpstotietheeducationcourseworkmoreeffectivelytothemathematicsmajor.TheopportunitiesprovidedtonetworkwithandshareresourceswithotherpartnershipsandtolearnfromtheworkofvariousRACshasbeenextremelyhelpful.Additionally,valuableresources(e.g.,MCOP2,RecruitmentGuide)havebeen


42

agreathelpinmakingpartnershiptransformations.AstheUofSCpartnershiplookstothefuture,theywouldliketoseethedevelopmentandofferingofcross-institutionalcourses.

WendySmith–UniversityofNebraskaLincoln

Sometimestinkeringiswhatyouneed.Sometimesgoingalliniswhatyouneed.–WendySmith

TheUniversityofNebraska-Lincoln(UNL)hasgonethroughfiveyearsofinstitutionalchange.Theystartedofftinkeringwithsmallideas,butfoundthatstrategyineffective.Instead,theyneededbiggerchangestowhattheyweredoing—sotheydecidedtogo“allin,”withbringingactivelearningintotheirfirst-yearmathematicscourses.

Two-thirdsofUNLfreshmentakeamathematicscourseintheirfirstsemester;nootherdepartmentgetsclosetoseeingthatmanyfreshmen.Spurredbyanadministrativeemphasisongraduationandretentionrates,themathematicsdepartmenttookadeeperlookattheirlocalandbenchmarkdata.Unsurprisingly,theyfoundthatmathematicsgradescorrelatedveryhighlywithretentionand5-yeargraduationrates.Theirpassratesinthemathematicscoursesrangedfrom40%-70%,dependingontheinstructor.TheyalsonoticedthatstudentspassedCalculusIathigherrateswhentheytookitrightoutofhighschoolcomparedtowhentheytookCollegeAlgebraatUNLpriortoCalculusI.Wantingtogetaheadofanytop-downchanges,themathematicsdepartmentdecidedtoimplement“activelearning,”firstintheirCollegeAlgebracourses.Theytargetedthesehigh-enrollmentcoursesbecausetheywouldhaveamoredramaticeffectonretentionfromfreshmantosophomoreyearandthecoursesweregenerallytaughtbygraduateteachingassistants(GTAs)andadjuncts(e.g.,veryshortinstitutionalmemory).InordertohelppreparetheGTAsforteachingthecourseswiththisnewpedagogicalapproach,themathematicsdepartmentstartedrequiringthemtotakeateachingcourse.Surprisingly,thedepartmentonlyhadtosellthechangethefirstyear;thereafter,theydidn’thavetosellitatall.Themindsetwasalreadyestablishedandnormalized,“Thisishowwedoit.Thisisjusthowyoudoitwhenyou’reatUNL.”

Earlyeffortsaidedinthedramatictransformation:commonsyllabi,commonexams,andcommongradingallhelpedpavethewayforthechange.Therewasalreadyamathematicsresourcecenterfortutoring.Whiletinkeringgenerallydidn’twork,whatreallypavedthewayasanewdepartmentchairwhovocallyadvocatedforactivelearningforallmathematicscourses.

Whiletherewerelotsofstrategies(seeFigure1)thataidedinthetransformation,akeytothesustainedchangewastheFirst-YearMathematicsFacultyTaskforce.Thetaskforcewastheretohelpreviewelementsoftheactivelearningtransformation,forexample,tomakesurethecontentwasstillatanappropriatelychallenginglevel.Thetaskforcereviewedexamsanddeterminedthenewexamswereactuallymorerigorouswithactivelearningthantheyhadbeenpreviously.


43

Figure1.ElementsofacommonvisionforeffectivemathematicsinstructionatUNL.

TherearestillchallengesthatmustbefacedwithinthistransformationprocessatUNL.Issuesremainwithstudentplacementintocourses.Accesstolocalstudentdataisstillunresolved,particularlyfordataneededtocompareprogramsatUNLtothoseofpeerinstitutions.

Thekeystothetransformationsuccessweremany,butoverall,whenyouraisetheexpectationsforthestudents,youhavetoraisethelevelofsupportsostudentscanmeettheseexpectations.PartofthatsupportatUNLwastheimplementationoflearningassistants.Anotherpartwasphysicalresources.UNLrenovatedclassroomstoincludemovableovaltablesandchairs,aswellaswhiteboardsthatwentallthewayaroundtheroom.Additionally,themathematicsdepartmentwasabletoconvincetheuniversitythatActiveLearningwasmorelikeaphysicslabthanatraditionallectureclass,sonowinstructorshavemoreminutesforthesamenumberofcredithours.Thisallowsstudentstheextratimeneededtohelpsupportandprovideanenvironmentthatfostersdeeperconversations.Finally,anewpositionforDirectorofFirstYearMathematicswascreated.

CollegeAlgebraandCalculusIcourseshavebeentransformed.Calculus2isnextandBusinessCalculusisdowntheroad.Throughthisdramatictransformationinthepedagogyofthefirst-yearmathematicscoursesandwithinthemathematicsdepartment,failurerateshavebeencutinhalf.Havingthelocalandnationaldatareallyhelpedtobringthefacultyonboard.


44

RobinHill–KentuckyDepartmentofEducation;PresidentofAssociationofStateSupervisorsofMathematics

Eachofthesefourexamplesindicatetheneedandopportunitytopartnerwithyourstateagenciesinthetransformationprocess.Stateagenciescanhelptoworkstrategically,bringingadditionalpeopletothetableandhelpingtoinfluencepolicy.Bringingtherightpeopletogetherinyourpartnershipscanbethekeytosuccess.ConnectionswithstateagencieswillstrengthenbothpartnershipteamsandtheRACs.Ifyou’renottalkingtotherightpeople,thenit’sdifficulttoenactchange.

Forimplementingtransformation,MTE-Pprovidesatremendousopportunity.Theexamplesgivenheretodayareevidencethattherereallyisandcanbeinstitutionalchange.Gettingpeopletoworktogetherandtobuyintothechangeiskey.Sometipsfortransformationinclude:

1. Don’toversimplifyeverything.Everyonemightnotseethingsasweseeit.Beintentionalaboutyourpartnershipsandbeingintentionalandwhatroleseachmemberplays.

2. Makesureyou’reclearandtransparentaboutwhathappens.Transformationdoesn’thappenmiraculouslyorinstantaneously.

3. Therewillbea“DawnofReasoning”;therealizationthatcertaineffortsaregoingnowhere.Pushingontherightdriversaswellassharingtheloadandtheinformation(see#2)canmakeyoureffortssmoother.Partneringwithstatedepartmentsofeducationcanreallyhelphere.

4. Realizethatyou’renotinthisalone.

Transformationiscomplicated,alittlemessyandhardwork.Someoftheeffortsmayattimeslikeyou’reherdingcats.Managingthecomplexityofmanymovingpartsandpartnershipstotransformyourprogramsmayseemendlessandsluggish.Therewillbesomescratches,bumpsandbruisesalongtheway.Butthisworkisworthdoingbecauseit’sgoingtoleadtostrongermathematicsteachers.ThisgoalthatissoughtissharedbythehundredsofindividualmembersoftheMTE-P,andbroadlybysomanymore.


45

MTE-PartnershipConferenceReactants12


[email protected]

DianaSuddrethUtahStateOfficeofEducation

[email protected]

KarenKingNationalScienceFoundation

[email protected]

W.JamesLewisUniversityofNebraska-Lincoln

[email protected]

ThreefriendsoftheMathematicsTeacherEducationPartnership(MTE-P)wereinvitedtoparticipatethenprovidetheirreactionstotheconference,Dr.KarenKing,Ms.DianaSuddreth,andDr.W.JamesLewis.Thethreewerepetitionedinanefforttoobtainarangeofperspectivesrelatedtomathematicseducation.Dr.KarenKingpresentlyservesasProgramDirectoratNationalScienceFoundation(NSF).Herbackgroundisinmathematicseducation,withastrongfocusonpolicy.Ms.DianaSuddrethisDirectorofTeaching&LearningattheUtahStateOfficeofEducation.Sheofferedabroad,P-12perspective,againparticularlyfocusingonpolicy.Andthethirdreactant,Dr.W.JamesLewis,representsamathematician’sperspective.Dr.LewispresentlyservesasDeputyAssistantDirector,EducationandHumanResourcesattheNationalScienceFoundationonshort-termappointmentfromhispositionasProfessorofMathematicsattheUniversityofNebraska.Eachreactanthadfullyparticipatedintheconference,includingcontributingtotheworkinggroups.Further,eachhasbeenanadvisortooractiveparticipantsincetheMTE-P’sinception.

KarenKing

Dr.Kingbeganhercommentsbyrecognizingthatinherplenary,Dr.SuzanneWilsonframedmathematicsteachereducationinsidelargerconversationsaroundteachereducationandeducationalreform.Dr.Kingindicatedthatherowncommentswouldbeginandthenreturntothesebroaderissues,alongthewaybringingtothetableherpolicyperspective.Shefirstspokebroadlyofmeasuresineducationalresearch,thenturnedtospecificsoftheMTE-Pconference,includingherthoughtsabouttwospecificeventssheattended,theClinical1King,Suddreth,andLewisdeliveredthisfeedbackasareactantpanelattheconclusionoftheconference.Lawlerwrotethispapertosummarizetheircomments,drawingfromtheirslidesandnotes,audiorecordingofthetalks,andnoteskeptastheyspoke.2KingandLewisprovidedreactionswhileservingattheNationalScienceFoundation,andSuddrethwhileservingattheUtahStateOfficeofEducation.ThecommentsorrecommendationsexpressedinthismaterialarethoseoftheauthorsanddonotnecessarilyreflecttheviewsoftheNationalScienceFoundationortheUtahStateOfficeofEducation.


46

ExperiencesRACworksessions,andtheEquityandSocialJusticePre-Session.Sheconcludedwiththebroaderchallengesofequityworkineducation.

Dr.Kingfirstaddressedthechallengesofmeasurement,appreciatingtheplenarypanelonmeasurementinthecontextofworkinginNetworkedImprovementCommunities(NICs).Dr.Kingnotedthatmeasuringtheimpactsofpolicyandteachingpracticeshasnotbeenastrengthofmathematicseducation,ormorebroadly,ofteachereducation.Themeasurementchallengeisexacerbatedbecauseoftensions,suchasthosebetweenvalidityandreliability,ortheneedformeasurestobebothpractical(timely,useful,accessible,do-ableetc.)andconsequential(meaningful,understandable,etc.).Suchqualitiesformeasuresaredifficult,particularlyinschoolsettings.Yetpolicymakers,schooladministrators,andotherstakeholderscalltomeasurewhatiseasy,insteadoffocusingonmeasuringwhatisimportant.

Scienceimproveswhenwefindnewwaystomeasure.Forexample,educationhasanexceptionallystrongqualitativeresearchtradition;however,quantitativemeasuresforthecomplexconstructsunearthedbythesequalitativestudiesarefew.Dr.KingagainechoedDr.Wilson’sopeningplenarycalledformorethoughtfulstrategiestocommunicatewhatwelearnby,forexample,employingnewideasindatavisualization.Finally,Dr.Kingremindedustopreparedoctoralstudentsforthissortofmeasurementworkbyincorporatinginourprogramsnewwaystothinkabout,conduct,andreportdata.Shepointedoutthatunderstandingandusingmeasurementanddataarealsocriticalforprogramsformaster’sstudentsinmathematicsandadministrationbecausetheseprogramsoftenyieldthefutureformalandinformalleadersinthefield.

Duringtheconference,Dr.KingparticipatedintheClinicalExperiencesRAC(CERAC)activitiesandofferedtwosummativethoughtsregardingtheirwork.First,sheremarkedthatthebiggoalsforthegroupseemedtobewell-defined;however,Dr.Kingsuggestedthatthegroupcouldbenefitbyidentifyingmorespecific,actionablelearninggoalsforeachstrategy.Second,sheencouragedtheCERACclarifythedifferencebetweenstructuresfortheClinicalExperience,andstrategiesusedwithpre-serviceteacherswithintheClinicalExperiences.

Dr.KingalsoparticipatedintheEquityandSocialJusticePre-session.Shenotedthattheconstructsequity,socialjustice,anddiversityarenotthesame;however,thesetermsareoftenusedinterchangeablyineducation.Giventhisbackground,sheinquiredabouthowMTE-Papproachesschoolintegrationasanequityissue,asnotedbySecretaryofEducationJohnKing.Forexample,sheaskedwhetheritispossibleforschoolsbeseparateandequitable.Specifically,shenotedthatasettinginwhichallstudentsinaclassroomareminority,butthesameminority,isnotgenerallydefinedasethnicallyorraciallydiverse.Whilethesettingmayprovideculturalexperiencesusefulforpreserviceteachersitdoesnotprovideexperiencewithadiversecontext.Furthermore,understandingdiversityincludesunderstandingthatbeingblack,forexample,isnotthesingulardimensionofone’sidentity.Tofullyaddressissuesof


47

diversity,attentionmustbegiventothefullcharacterofeachchild.Simplechunkingofindividualsintogroupsbysingularcharacteristicsismisdirectedandcounterproductive,andmissesthefactthatthereismorevariationwithingroupsthanbetweenthem.Equityisabouteveryone;apersonmayhaveasetofprivilegesassociatedwitheducationandclass;butalsofacehistoricaldisadvantagesasawomanandanAfrican-American.Broadstrokesareinsufficientinthiswork.Everyoneneedssomedifferentkindofsupport.Dr.Kingremindsusthatequityiscomplicated,andhereshehaspointedmorestronglytoquestionsandchallengesposedbywork,ratherthanintendingtobeprescriptive.

Dr.KingapplaudstheMTE-Pcommunityfortakingontheseissues,buttotakecareaboutessentializingstudentsbasedontheirgroup.Sheencouragedustoinvestigateresearchoutsideofmathematicseducation,echoingthecallsofDr.Wilson’splenary,todiscoverwhatotherfieldshavelearnedaboutthepotentialperilsofwell-intendedeffortsfordiversitytraining.Asasecondexampleofhowresearchoutsideourfieldcanbeinformative,shenotedthatbusinesshaslearnedquiteabitaboutgettingpeopletothingstheymaynotwishtodo,especiallywithregardstoattractingpeopletojobs.

DianaSuddreth

Ms.SuddrethhighlightedthecommonalitiessheobservedacrosstheRACs,includingfundingstructures;highqualityinstruction;afocusonevidence,arguments,andwarrants;workingwithstudents;communityengagementandinstitutionalization.Shenotedtheseelementsseemedtospeaktothecycleofchangedrivenbytheneedtorespondtonewideasandconcerns.

Shenextturnedtotheopportunitiesandchallengesoftheworksuchas:needsofachangingworkforce;timeconstraints;partnershipswithstateagencies,andshortagesofK-12teachers.Ms.Suddrethremindedusthatifwedon’tturnourgreatideasintoactionableinnovationsthataddressstudents,schools,andotherconstituents,alltheseideasbecomenothingmorethandiscussionatameeting.ShehighlightedtheNICresearchdesign,especiallythePDSAcyclesthatallowin-timeinnovationtrialsthatfosteracontinuingcycleofevidence-drivenlearningandimprovement.

Herfinalchallengewastobroadenourengagementwithourcommunities.Peopleinpositionslikehers,thatis,associatedwithstatedepartmentsofeducationorsimilaragencies,needtoknowwhatprojectsarebeingimplementedintheirdomainsinordertobefullysupportive.TheseindividualsneedtounderstandtherolesandgoalsofbothofMTE-Pandtheparticipatingsystems,institutions,teams,andteachersinordertofunctionasanadvocateandusefulpartner.Sheremindsusthatthechangesweseekarenotsolelyaboutmathematics,therearemanyadditionaltheoreticalandpracticalissuesinvolvedinbetterpreparingmoresecondarymathematicsteachers.Althoughmuchotherworkisbeingcarriedoutthatwecan


48

learnfrom,themathematicscommunityhasbeenclearlyimportanttoandaleaderingeneralteacherpreparation.Thishistoryoftheroleofmathematicseducationcanandoughttobeleveraged,bothinfundingandinpractice.

W.JamesLewis

Dr.LewisstressedthathewasofferinghisownviewsassomeonewhohasbeeninvolvedintheMTE-Partnershipfromthebeginning,andnotasanemployeeoftheNationalScienceFoundation(NSF).HeprovidedahistoricalperspectiveontheMTE-Partnershipproject,recallingtheinitialideaforthisprojectemergedataScienceandMathematicsTeacherImperative(SMTI)conferencein2011.Dr.GaryMartinpitchedtheidea,andsoonafterwardswiththesupportofanNSFplanninggrant,thefirstMTE-PmeetingoccurredinMarch2012.Astrengthofthecommunitythathassinceemergedisthelong-termandstablemembershipthatmaintainsacontinuity,bolsteredbynewmembersthataretheresultofgrowthandtransitions.

MTE-Phasambitiousgoals,toseekanationalconsensusonthepreparationofsecondarymathematicsteachers,topromotepartnerships,todeveloparesearchanddevelopmentagenda,andtosetanationalagendafortheissuesrelatedtomathematicsteacherpreparation.Specifically,thisconferencebuildsonthesegoalstobegintoconsiderthechallengesoftransformationalchange.

Dr.Lewisnotedthedesignoftheconferenceasaworkingconferenceissomewhatunique,aworkingconference.Heobservedtheparticipantswereveryengagedandquiteimpressive.AmongthehighlightshenotedweretheupdatesfromRACsofworksincethelastconference,theequityandsocialjusticeworksession,theeveningmixer,theplenarysessionondataandmeasuresintheNICresearchparadigm,andthe15researchpresentations.Becauseoftherichnessoftheresearchpresentations,hecommentedthatitwasunfortunatethateachofuscouldonlyattendthree.

Dr.Lewisasked,“AtthisstageinthegrowthoftheMTE-Partnership,itmaybeagoodtimetotakestock;toaskhowarewedoing?”Hesuggestedthatachallengeistomakeequityandsocialjusticeissuesmoreexplicit,butcommentedthatthecommunityisofftoagoodstart.Asecondchallengeistobuildjointpurposeandidentity.HeofferedtheassessmentthatatthepresenttimetheMTE-PpurposeandidentityoftheseemstobeproductiveandappropriatebutsaidthatthereisasmallchancethattheRACscontributetoacompartmentalization.Hisviewisthecommunityshouldintentionallycreatenetworksandstructuresthatdonotallowthesedivisions.SocialeventslikethemixerandsharedsocialandsharingcommunitieslikeTrellisaregoodapproachestoaddressthischallenge.

Dr.LewissuggestedanotherchallengeisthatthereseemstobeaneedtoacceleratetheworkoftheRACs.Headmittedhemaybeimpatient;butwithoutnoticeablechangeacrossmanyoftheRACs,participantsmayexperiencefatigue.Anotherchallengeisthatwehave


49

reachedadevelopmentalpointinwhichitistimetogivegreaterfocustobuildingtoprogramtransformation.Thereisstillmuchworktobedonetomovefromtweakingtotransforming.

Finally,whileMTE-Pisdoinggoodwork,someconsiderationshouldbegiventohowthatworkcanbestrengthened.RepeatingDianaSuddreth,hearguedthereisaneedtobuildmoretieswithK-12partners.Additionally,thecommunityneedsmoremathematicians(interestedineducation)atthetable;MTE-Pwillnotachieveitsgoalsifitsonlymembersareindepartmentsofteachereducation.Similarly,thecommunityneedsmoredepartmentchairsandothercampusleaderstobeactiveparticipants—especiallytoachieveprogramtransformation.

Summary

EachofthereactantswereverypositiveabouttheworkbeingdonebytheMTE-Partnershipandacknowledgedthestrengthandcommitmentofthecommunity.Commonthemesinthefeedbackfocusedonthechallengesfaced,encouragingfocusforthenextstagesinthework.ThisincludescontinuingtherobuststructureoftheNICresearchdesign,butbeingmorecommittedtodevelopingrobustmeasuresandsharingresultswiththelargercommunityinvolvedinthepreparationofsecondarymathematicsteachers.

ThereactantsalsoadvisedthattherebeincreasedpartnershipswithK-12districts,stateleadership,mathematicians,anduniversitycampusleadership—thechargeofprogramtransformationiscomplexandinvolvesmanyconstituents.Notonlyisprogramtransformationcomplex,soisthepreparationofsecondarymathematicsteachers;particularlytheeffortstochangecurrentpracticesinmathematicseducation.ThechangeeffortsMTE-Pstrivesforreachbeyondmerelythemathematicscontentorcurriculumdesign,butinvolvesteaching,schoolstructures,andsocietalnormsaswell.

AfinalcommonalityamongthereactantscommentswerecommendationstoMTE-Pforitsrobustandproductivehistoryofwork,andforestablishingacommunityfoundedinaresearch-drivenefforttotransformthepreparationofsecondarymathematicsteachers.

50

RESEARCHACTIONCLUSTERREPORTS


51

ClinicalExperiences1


[email protected]

[email protected]

[email protected]

Teacherpreparationprogramsfacesignificantchallengesinprovidingsecondarymathematicsteachercandidateswithqualityclinicalexperiences.Theproblemistwo-fold:

1. Thereisaninadequatesupplyofqualitymentorteacherstooverseeclinicalexperiences.ToofewteachersarewellversedinimplementingtheCCSSandteachersareespeciallyinexperiencedwithembeddingthestandardsformathematicalpracticeintotheirteachingofcontentstandardsonadailybasis.

2. Bidirectionalrelationshipbetweentheteacherpreparationprogramsandschoolpartnersinwhichclinicalexperiencestakeplacearerare.SuchrelationshipsthatreflectacommonvisionandsharedcommitmenttothevisionofCCSSMandotherissuesrelatedtomathematicsteachingandlearningarecriticaltothedevelopmentandmentoringofnewteachers.

TheworkofClinicalExperienceRAC(CERAC)encompassesanumberoftheprinciplesandprincipleindicatorsfromtheMTE-PartnershipGuidingPrinciples,includingfosteringpartnershipsbetweeninstitutionsofhighereducation,schoolsanddistricts,andotherstakeholderssuchasstatedepartmentsofeducationandisfocusedonpreparingteachercandidateswhopromotestudentsuccessinmathematics,asdescribedintheCommonCoreStateStandardsforMathematics(CCSS-M)andothercollege-andcareer-readystandards.IntheCERAChighereducationfacultyandpartnerschooldistrictsandschoolsworktogethertoactivelyrecruit,develop,andsupportinservicemastersecondarymathematicsteacherswhocanserveasmentorsacrosstheteacherdevelopmentcontinuumfrompreservicetobeginningteachers.Moreover,theCERAChelpstoensurethatteachercandidateshavetheknowledge,skills,anddispositionsneededtoimplementeducationalpracticesfoundtobeeffectiveinsupportingallsecondarystudents’successinmathematicsasdefinedintheCCSS-Mandothercollege-andcareer-readystandards.

TheCERACconsistsof24universityledteams,eachconsistingofatleastonemathematicsteachereducator,amathematician,andaschoolpartner.TheCERACisdividedintothreeSub-RACsbasedonthethreetypesoffieldexperiencesthatweareimplementingto

1TheRACPromoSheet,presentedduringtheopeningoftheconferencetoreportoncurrentactivitiesoftheRAC,canbefoundafterthereferencelist.


52

meetthegoalsthatwesetforthinourprimarydriversandouraimstatement.TheSub-RACsare:Methods,PairedPlacement,andCo-planningandCo-teaching.EachSub-RACisimplementingPlan-Do-Study-Act(PDSA)cyclesbasedontheirgoalsandobjectives.Teamsworktogetherviaconferencecalls,email,andtheTrellisplatform.WeuseDropboxandTrellisasawayofsharingfilesandmaterials.Wehaveheldface-to-facemeetingsasawholeRACthatincludedbreakoutmeetingsforSub-RACs.TheSUB-RACShaveoverlapareasthatdriveandfocustheRACasawhole,suchastheemphasisonthemathematicsteachingpractices(NationalCouncilofTeachersofMathematics[NCTM],2014),PDformentorsrelatedtotheCCSSandmentoringmathematicsteachercandidates,andoutcomemeasures.TherearealsospecificgoalstobeattainedwithineachoftheSub-RACs.EachSub-RAChasdevelopedtheirownspecificresearchquestions.

MethodsSub-RAC

TheMathMethodsSub-RACoftheCERACincludesmembersfrom10institutionsofhighereducationandpublicschooldistricts.Ourworkhasfocusedonstrengtheningtheconnectionbetweentheuniversitybasedmethodscoursesandthefieldexperiencecomponentassociatedwiththemethodscourses.Wehavegivenparticularattentiontoincreasinganddeepeningteachercandidates’(TCs’)andmentorteachers’(MTs’)understandingandimplementationoftheCommonCoreStateStandardsforMathematicalPractice(CCSSO,2010).WecreatedaStandardsforMathematicalPractice(SMPs)moduleavailableforuseinmethodscoursesandtheassociatedfieldexperience.ThemoduleincludesthreeactivitiesdesignedtosupportTCsandMTsinmeetingthefollowinggoals:

Activity1

• TCswillrecognizethatforthetypicalstudent,U.S.mathematicsclassroomsleadthemtodevelopunproductivehabitsrelatedtomathematics.

• TCswillbegintoconsiderhowtheiractionsasteachersmightsupportthedevelopmentofadifferent,moreproductivesetofhabits(e.g.,themathematicalpractices).

• TCsknowledgeandunderstandingoftheSMPswillincrease.

Activity2

• TCswillengageintheSMPsas“students”whileexploringhighschoolgeometrycontenttheyarelikelytoteach.

• TCswillapplytheknowledgegainedfromActivity1toidentifyanddiscusstheSMPstheyexperiencedastheyworkedonthePropertiesofQuadrilateralstaskandidentifyhowthefacilitatorsupportedtheirengagementintheSMPs.

• TCsgainadeeperunderstandingofteachermovesthatsupportstudentengagementintheSMPsusingtheParkCityMathInstitute(PCMI)Rubric.


53

Activity3

• TCsandMTswillwatchavideoclipofalessondesignedtoengagestudentsintheSMPsandthendiscusstheirobservationsofthestudentsduringthelesson.

• TCsandMTswillconsiderhowwhattheyobservedinthevideomightimpacttheirteaching.

TheSMPModulehasbeenimplementedbysixmembersoftheMethodsSub-RACandrevisedbasedontheirexperiences.Wearecurrentlyseekingadditionalmethodsinstructorsinterestedinincorporatingthismoduleintotheirmethodscourses.

OurnextstepsincludethedevelopmentofaLessonDesignmodule.ThegoalsofthismoduleareforTCs1)torecognizetheneedtoapproachlessonplanningwithafocusonstudentlearningandengagement;and2)begintointegrateselectMathematicsTeachingPractices(NCTM,2014)intotheirplanningandinstructionpractices.ThismodulewillbepilotedbyMethodsSub-RACmembersstartinginthefallof2016.

Co-PlanningandCo-Teaching(CPCT)Sub-RAC

TheCo-PlanningandCo-Teaching(CPCT)Sub-RACincludesmembersfrom10institutions.Ourgoalistoenablementorteachersandteachercandidatestocarefullyplanandsubsequentlyusevariousco-teachingstrategiesduringclinicalexperiences.Wefocusedonsixco-teachingstrategies,namely:oneteach,oneobserve;oneteach-oneassist;parallelteaching;teamteaching;stationteaching;andalternativeteaching(Friendetal.,2010;Murawski&Spencer,2011).CPCTisaparadigmshiftfromtraditionalapproachestoclinicalexperiences.Hence,theSub-RACmembershasplacedanemphasisontraininganddisseminatinginformationabouthowtoimplementCPCTeffectively.Additionally,themembersfacilitatedCPCTactivitiesattheirrespectivesites,andassistedwithdatacollectiontoprovideinsightintothenatureofimplementationofCPCTduringclinicalexperiences.

TodatetheCPCTSub-RAChasengagedinarigorousefforttodisseminateresearchandscholarshiptoawideraudience.Membersofthegrouphavefacilitatedprofessionaldevelopmentworkshops,publishedarticlesinajournalandmultipleconferenceproceedings,andpresentedatnationalandinternationalconferencesaboutpreliminaryfindingsandpracticalmeanstoimplementCPCT.TheCPCTSub-RACplanstosolicitforfundingtohostaworkinggroupmeetingtoproduceadeliverable(i.e.,bookand/orvideo)thatwouldclearlyexplainhowtointegrateCPCTintoclinicalexperiences.Overall,theCPCTSub-RAChasbeenactivelyseekingtoincreasethevisibilityofCPCTintheliteratureandateducationalmeetings.

DuringtheMTE-P2016annualconference,membersoftheCPCTSub-RACengagedinrefiningourAnnualPerspectivesinMathematicsEducation2017manuscriptthatdescribeshowthegroupusesimprovementsciencetotransformclinicalexperiences,presentedthreebriefresearchreports,articulatedthePDSAcyclesforthenextacademicyear,revisedmultiple


54

instrumentsusedtogatherdataabouttheprocessmeasures,reflectedonchallengesatvariousinstitutionsthathindereddatacollectionefforts,plannedtoembedequityandsocialjusticeintoourCPCTactivities,suggestedthatCPCTtrainingbadgesoughttobeused,andexploredfundingpossibilitiestoproduceapublishabledeliverableandsupportthegroup’sresearchefforts.

Lookingahead,theCPCTsub-RACwillcontinuetoimplementCPCTattheirrespectiveinstitutions,garnerdataandengageinPDSAcycles,inanefforttotransformclinicalexperiences.Withcarefulplanning,andallocationoftimetogatherdata,theteamintendsonscalinguptheirresearchactivities.

PairedPlacementSub-RAC

ThePairedPlacementSub-RACiscomprisedofmembersrepresentingfiveinstitutions.TheSub-RACfocusesonthepairedplacementmodelforstudentteachinginwhichtwoprospectiveteachersarepairedwithasinglecooperatingteacher.Thecooperatingteacherprovidespurposefulcoachingandmentoring,andthetwopre-serviceteachersoffereachotherfeedback,mentoring,andsupport(Mau,2013,Leatham&Peterson,2010b).AsaSub-RAC,wereadarticles(Goodnough,etal.2009;Leatham&Peterson,2010a&2010b;Mau,2013)tolearnaboutthemodel.Oneteamimplementedthemodelfall2013andreportedtotheotherteamsaboutitsfindings.ThetwoteamsusedthisinformationalongwithinformationfromtheliteraturetopreparementorteachersandcandidatesfortheexperienceSpring2014.TeamsalsoworkedwiththeirparticipantstoadjustthemodelwithintheircontextutilizingPDSAcycles.Teamsmonitoredtheprocessthroughoutthesemester.Teamsmetviaconferencecalltodiscusstheresultsoftheimplementationsandwhattheywoulddodifferently.Teamscreatedprofessionaldevelopmentmodules,syllabi,andmeasuresFall2014.TeamsimplementedthemodelagainSpring2015utilizingsuggestedimprovementsfrompreviousiterations.Onepairwasimplementedinthefallof2015,andsixpairswereimplementedspringsemester2016.

ThroughPDSAcyclesanddatacollectedfromparticipants,wearelearningmuchaboutthemodel.Wehavefoundthatitallowsteachercandidatestoreallyfocusonstudentlearningandthecraftofteaching.Teachercandidatesandmentorteacherswhohaveexperiencedthismodelbelievethatitbenefitsalloftheirgrowthinteachingaswellasthestudents’growthinlearningmathematics.Theyalsostatedthatthemodelhashelpedthemtobecomemorecollaborative.

Duringtheconference,weacclimatednewmembersandrevisedandstreamlinedourmeasures.Wealsomadeplanstoimplementtherevisedworkshopsandsyllabiinthespringsemesterof2017.Weintendtosubmitproposalstospeakatappropriatevenuesandsubmita


55

manuscriptrelatedtoourwork.WewillalsoworkinconcertwiththeotherSub-RACstoseekfundingtosupportthework.

Wehavegivenpresentationsaboutthemodelatconferencesandareworkingonsubmittingpaperstojournals.Ourgoalistorefinetheworkshopsandsyllabisothattheycanbeadaptedtodifferentcontexts.

CERAC

TheCERACasawholehasmadegoodprogresstowardourgoals.Wehavecreatedmeasures(MathematicsTeachingPracticeSurveyandothers)tohelpwithgaugingthegrowthofteachercandidatesinvolvedinourprograms,andwearealsousingmeasuresdevelopedbyothers.MeasuresusedacrossthethreeSub-RACSincludethefollowing:

• MCOP2–TheMathematicsClassroomObservationProtocolforPracticesinaK-16mathematicsclassroominstrument(Gleason,Livers,&Zelkowski,2015).

• MTE-PCompleterSurveywillshowhowwellpreparedtheteachercandidatesfeelbasedontheexperiencesthattheyhadintheirprograms.

• MathematicsTeachingPracticesSurveyusedtodeterminethelevelatwhichprospectivesecondaryteachersareengagedwithNCTM’s(2014)Mathematicsteachingpractices.

AsaRAC,weplantopayexplicitattentiontoequityandsocialjusticeissuesinthenextiterationsofourmodules.Eventhoughwehaveincludedissuesofequityinourdriver’sdiagram,wefeelthatitisimportanttomakeitknowninourproductsthataccess,equity,andempowermentforeachandeverystudentisimportanttoourwork.

References

CouncilofChiefStateSchoolOfficers(CCSSO).(2010).CommonCoreStateStandardsforMathematics.Washington,DC:Authors.

Friend,M.,Cook,L.,Hurley-Chamberlain,D.,&Shamberger,C.(2010).Co-teaching:Anillustrationofthecomplexityofcollaborationinspecialeducation.JournalofEducationalandPsychologicalConsultation,20(1),9-27.

Gleason,J.,Livers,S.D.,&Zelkowski,J.(2015).Mathematicsclassroomobservationprotocolforpractices:Descriptorsmanual.jgleason.people.ua.edu/uploads/3/8/3/4/38349129/mcop2_descriptors.pdf

Goodnough,K.,Osmond,P.,Dibbon,D.,Glassman,M.,&Stevens,K.(2009).Exploringatriadmodelofstudentteaching:Pre-serviceteacherandcooperatingteacherperceptions.TeachingandTeacherEducation,25,285-296.

Leatham,K.R.,&Peterson,B.E.(2010a).Secondarymathematicsmentorteachers’perceptionsofthepurposeofstudentteaching.JournalofMathematicsTeacherEducation,13(2),99-119.


56

Leatham,K.R.,&Peterson,B.E.(2010b).Purposefullydesigningstudentteachingtofocusonstudents’mathematicalthinking.InJ.W.LottandJ.Luebeck(Eds.)AssociationofMathematicsTeacherEducatorsMonograph7,Mathematics(AMTE)teaching:Puttingresearchintopracticeatalllevels(pp.225-239).SanDiego,CA:AMTE.

Mau,S.(2013).Letterfromtheeditor:Bettertogether?Consideringpaired-placementsforstudentteaching.SchoolScienceandMathematics,113(2),53-55.

Murawski,W.W.,&Spencer,S.(2011).Collaborate,communicate,anddifferentiate!:Howtoincreasestudentlearningintoday’sdiverseschools.CorwinPress.

NationalCouncilofTeachersofMathematics.(2014).Principlestoactions:Ensuringmathematicalsuccessforallstudents.Reston,VA.

MTE-Partnership Solicitation for Participation in the Clinical Experiences RAC

April, 2016

Problem Addressed

Teacher preparation programs face significant challenges in providing secondary mathematics teacher candidates with quality clinical experiences. The problem is two-fold:

1. There is an inadequate supply of quality mentor teachers to oversee the experiences. This is related to the quantity of teachers who are well versed in implementing the CCSS, especially embedding the standards for mathematical practice into their teaching of content standards on a daily basis.

2. There needs to exist a bidirectional relationship between the teacher preparation programs and school partners in which clinical experiences take place. This relationship should reflect a common vision and shared commitment to the vision of CCSSM and other issues related to mathematics teaching and learning.

The work of Clinical Experience RAC encompasses a number of the principles and principle indicators from the MTE-Partnership Guiding Principles, including fostering partnerships between institutions of higher education, schools and districts, and other stakeholders such as state departments of education and is focused on preparing teacher candidates who promote student success in mathematics, as described in the Common Core State Standards for Mathematics (CCSS-M) and other college- and career-ready standards. In this RAC higher education faculty and partnering school districts and schools work together to actively recruit, develop, and support inservice master secondary mathematics teachers who can serve as mentors across the teacher development continuum from preservice to beginning teachers. Moreover, the clinical experiences RAC helps to ensure that teacher candidates have the knowledge, skills, and dispositions needed to implement educational practices found to be effective in supporting all secondary students’ success in mathematics as defined in the CCSS-M and other college- and career-ready standards.

General Approach

• The RAC is divided into three Sub-RACs based on the three types of field experiences that we are implementing to meet the goals that we set forth in our primary drivers and our aim statement.

• Each Sub-RAC is implementing PDSA cycles based on their goals and objectives. • Teams work together via conference calls, email, and the Trellis platform. • We utilize Dropbox as a way of sharing files and materials. • Have had face-to-face meetings as a whole RAC with breakout meetings for Sub-RACs. • There are overlap areas that focus the RAC as a whole, such as the emphasis on NCTM’s

mathematics teaching practices, PD for mentors around the CCSS and mentoring mathematics teacher candidates, and outcome measures.

• There are also specific goals to be attained within each of the Sub-RACs. • Each Sub-RAC has specific research questions, which they are addressing.

Who We Are

Methods Paired Placement Co-Plan/Co-Teach University of North Dakota MTEP: Michele Iiams Cathy Williams USC Midlands MTEP: Jan Yow DeVonne "Vonnie" Smalls Beth Oliver Nevermind Chigoba West Alabama Partnership, University of Alabama: Jeremy Zelkowski Jim Gleason John Abby Khalilian Karla Moore Jill England Melinda Williams GSU MTEP: Gregory Chamblee Missy Jenkins Sharon Taylors Pier A. Junor Clarke California State University, Fullerton Mark Ellis California State University, Northridge Ivan Cheng California State University, San Bernardino Su Liang Oregon MTEP: Rebekah Elliott Wendy Aaron

Central Alabama MTEP: Marilyn Strutchens Brooke Barron Peggy Dagley Huajun Huang Montana MTEP: David Erickson Bill Lowney Lee Brown Jim Hirstein East Central Texas MTEP: Jennifer Whitfield Dawn Parker Laura Wilding New Mexico State University MTEP: Lida J. Uribe-Flórez Ted Stanford Silvia Celedón-Pattichis Tom Gruszka

Tampa Bay Area MTEP: Ruthmae Sears Fernando Burgos Gladis Kersaint Julie Wagner North Carolina State University MTEP: Karen Keene Karen Norwood Allison McCulloch Karen Hollebrands East Carolina University MTEP: Charity Cayton Maureen Grady Ron Preston Rose Sinicrope. UCF MTEP: Janet Andreasen Melissa Dagley Amanda Ellis Bryan Zugelder California State University, Chico: Jennifer Oloff-Lewis: Mary-Elizabeth Matthews Kerrie Girt California State University, San Bernardino: Catherine Spencer California State University, Northridge Ivan Cheng Julie Gainsburg California State University, Sacramento: Stephanie Biagetti Elaine Kasimatis OSU MTEP Patti Brosnan Marguerethe Jaede

Current Progress RAC Activities

§ In March 2015 we submitted a Phase 4, Robert Noyce Research Grant to the National Science Foundation. While not recommended for funding, we plan to revise and resubmit for the 2016 Noyce competition.

§ Sub-RAC leaders attended the Carnegie Foundation for the Advancement of Teaching Networked Improvement Community Design Learning Lab in spring and fall 2015.

§ We are disseminating our work through conference venues, such as AMTE’s Annual Meeting and SMTI’s Annual Meeting.

§ Some of our members will be presenting their work at the 13th International Congress on Mathematical Education (ICME-13), July 24 – 31, 2016 in Hamburg.

Early Field Experiences within Methods Sub-RAC

§ Teams revised and implemented a module designed to strengthen teacher candidates’ and their mentor teachers’ understanding of the CCSS Standards for Mathematical Practice (SMP). The opportunity to build a productive teacher candidate and mentor teacher relationship is an additional goal. In addition to increasing teacher candidates’ and mentor teachers’ knowledge of the SMP the module provides an opportunity for the teacher candidates and mentor teachers to develop a relationship and common language around these ideas.

§ Teams developed a survey to measure the possible effects of completing the module activities on teacher candidates’ and mentor teachers’ understanding of the SMP.

§ Teams developed and employed additional measures for the SMP Module: Activity “Exit Slips” for teacher candidates and an implementation survey completed by the methods instructor.

§ Teams created and are piloting a survey on teacher candidates’ knowledge and use of the Mathematics Teaching Practices.

Co-Plan/ Co-Teach Sub-RAC

§ Teams created instruments and professional development training module relevant to CPCT, and received feedback from all members of the group.

§ During the 2014-2015 academic year, the CPCT Sub-RAC conducted a pilot study to examine mentor teachers’ and teacher candidates’ knowledge about the Common Core State Standards for Mathematics – Content Standards and Standards for Mathematical Practice, as well as documented their beliefs and instructional practices.

§ During 2015- 2016 academic year, the team revised the PDSA cycle for Cycle 2, and increased its membership.

Paired Placement Sub-RAC § Teams read about the model. § One team implemented the model fall 2013 and reported to the other teams about its findings. § The other two teams used this information along with information from the literature to prepare

mentor teachers and candidates for the experience Spring 2014. § Teams also worked with their participants to adjust the model within their context. § Teams monitored the process throughout the semester. § Teams met via conference call to discuss the results of the implementations and what they

would do differently. § Teams created professional development modules and measures fall 2014. § Teams implemented the model again Spring 2015 utilizing suggested improvements from

previous iterations. § One pair was implemented in the fall of 2015 and six pairs are being implemented spring

semester.

Opportunities for Engagement

Early Field Experiences within Methods Sub-RAC 1) Implementing SMP module and contributing to data collection; and 2) Collaborating on the development of additional modules and measures of module effects on teacher candidates and mentor teachers

Co-Plan/ Co-Teach Sub-RAC 1) Developing, utilizing, and sharing instruments used to measure the influence of the co-teaching model; 2) Implementing and examining teacher candidates’ experiences throughout their field-based preparation (i.e., practicum and internship); and Studying the influence of professional development on the success of the co-teaching model.

Paired Placement Sub-RAC 1) Developing, utilizing, and sharing instruments used to measure the influence of the paired placement model; (2) Implementing and examining teacher candidates experiences throughout their field-based preparation (i.e., practicum and internship); and (3) Refining and studying the influence of professional development and orientation sessions on the success of the paired placement model.


61

ActivelyLearningMathematics:TowardDepartmentalTransformationofthe

TeachingofUndergraduateCalculus1

DavidC.Webb2UniversityofColoradoBoulder

[email protected]

TheoverarchinggoaloftheActiveLearninginMathematicsResearchActionCluster(ALMRAC)istoimprovestudentsuccesswithundergraduatemathematicsinPre-calculusthroughCalculus2(P2C2).TheALMRACdevelopedcurriculummaterialsthatfocusedoneffectiveteachingpractices,whicharesupportedbylearningenvironmentsthataremoreconducivetostudentinteraction,reasoning,andproblemsolving.Gainingfacultybuy-inandinstitutionalleadershipsupportwasnecessarytoencourageand,insomecases,fundGraduateTeachingAssistanttrainingalignedwiththegoalsoftheproject.Moreover,trainingshouldincludeundergraduatelearningassistants,employedbymanycampusestoenhancestudentexperienceswithgroupactivitiesandengagementinmathematicalactivitiesandexplorations.

StatementofProblemandAim

StudentsuccessinundergraduatemathematicshassignificantimplicationsregardingstudentchoiceofSTEMmajorsandrelatedcareers.EvenstudentswhodonotchoosetomajorinSTEM,successinentry-levelundergraduatemathematicscoursessuchascalculuscanmakeorbreaktheirdecisiontopersistinpostsecondaryeducation(Ferrini-Mundy&Graham,1991;Moreno&Muller,1999;Rasmussen,Ellis,&Bressoud,2015;Subramaniam,Cates&Borislava,2008).StudiesofinstructionalimprovementsinundergraduatecalculusthathavebeencharacterizedasActiveLearningorInquiryBasedLearninghavedemonstratedimprovedDFWrates,improvedstudentdispositionstowardsmathematics,andpersistenceintakingsubsequentcourses.Nevertheless,inspiteoftheaccumulationoffindingssupportingALMthereareinstitutionalchallengesthatprecludeitsadoptionandsustainedsupportinuniversitymathematicsdepartments(Ganter,2001).

1TheRACPromoSheet,presentedduringtheopeningoftheconferencetoreportoncurrentactivitiesoftheRAC,canbefoundafterthereferencelist.2ThisbriefwasdevelopedfromvarioussourceswrittencollaborativelybymultiplemembersoftheALMRAC.Thesesourcesincludeplanningdocuments,meetingminutes,andcircularsdevelopedtohelpcommunicatethegoalsandactivitiesoftheALMRAC.


62

Thechallengesinherentininstitutionalchangeincludepolitical,curricular,andculturalfeaturesofdepartmentsandcollegesthatresistchangeandclingtothestatusquo.Overcomingthesechallengesrequiresacommitmenttowillbuilding,curriculumdevelopment,professionaldevelopment,andseeminglysuperficialfeaturessuchasthewaytablescanbeorganizedinaclassroom.Implementingthesemultiplechangestodepartmentalstructures,processesandcommunicationrequirescomplexskills,knowledge,andresourcesthatuniversityfacultyarenottraditionallymotivatednorincentivizedtoacquireordevelop.Teachingcalculusinamannerthatcouldbecharacterizedasstudent-centeredisnottypicallyfoundintenureandpromotionstatements,norisitimpliedinfacultymeetingsordepartmentalcommunication.However,recentinitiativesbytheWhiteHouseOfficeofScienceandTechnologyPolicyandtheNationalScienceFoundationinsupportofactivelearninginSTEMeducationcouldhavesomeinfluencetheprioritiesofuniversities,mathematicsdepartmentsandcalculusinstructors.

Howwehaveaddressedtheproblemtodate

Overthepastthreeyears,wehaveworkedcollaborativelytoimproveinstructioninintroductorycalculuscourses.Initially,withfundingsupportfromtheHelmsleyCharitableTrust.TheexpansionofourcurriculumdevelopmentanddatacollectioneffortsresultedinanumberofpartnersdiscoveringadepartmentcommitmenttoinfusingALMinundergraduatecalculuscoursescanresultinearlydemonstrableimprovementsintheDFWratesandpersistenceofstudentsinsubsequentcourses.

WhilethecontextsacrossthetwelvepartnerinstitutionsinvolvedintheALMRACarequitedifferent,requiringsomewhatdifferentapproachestoimplementingALM,wehavebeenabletolearnfromeachother’sefforts.Wehaveexchangedandco-developedinstructionalresources,usedcommonmeasurestodocumentstudentdispositions,andhaveregularlydiscussedthelocalmodelsusedtosupportlearningenvironmentsthataremoreconducivetoALM.Atleastfourcampusesadoptedthe“learningassistant”modelthatwasdevelopedbytheUniversityofColoradoBoulder,whileWestVirginiausedGraduateTeachingAssistantsinasimilarrole.DiscussionsacrosscampuseshavehelpedtoclarifytheapproachesusedandhaveidentifiedthecriticalroleofinstitutionalchangeinpromotingALM.

TheALMNetworkedImprovementCommunity.ThemembersoftheALMRACunderstandthatchallengesinherentinchanginginstructionalpracticeare,inpart,duetosystemicnatureofteachinginclassrooms.Thedecisionsmadebyaninstructortoteachinaparticularmannerarederivedfromtheirinterpretationofdepartmentgoals,theresourcesallocatedtotimeandspace,thedesignofinstructionalactivities,theopportunitiesforprofessionallearning,andthedepartment’snormsforassessment.Changingclassroompracticerequiresalignmentandcoordinationofmultiplepartsofthesystemtosupportcommongoalsforstudentlearning.Hence,theneedforanALMNetworkedImprovementCommunity(ALMNIC)sothatoneinstitutionissolelyresponsiblefordevelopingaknowledge


63

basewhiledevelopingresourcesforinstructionandprofessionaldevelopment.OurALMNICcommunicatesanddocumentslessonslearnedaswellasdistributesamultitudeofresourcestoreducetheburdensrelatedtopreparationofIRBprotocolsandinstructionalresources.

Productsdeveloped.TwomajorcontributionstoresourcedevelopmenthaveresultedfromoureffortsininfusingALMintheP2C2sequence.FacultyattheUniversityofNebraskaOmahaandUniversityofColoradoBoulderco-developedinstructionalmaterialsthatcouldbeusedtoreplacelessonsforcalculustopics;andourinterestindocumentshiftsinstudentdispositionsresultedintheadaptation,refinementandvalidationofastudentsurvey.

Tactile+Activities=TACTivities.InspiredbyAngieHodgeatacolloquiumshefacilitatedatUniversityofColoradoBoulder,facultyatUniversityofColoradoBoulderpartneredwithHodgeinthedesignofTACTivities3forcalculus.ThecharacteristicsoftheseTACTivitiesgenerallyincludedtwoormoredifferenttypesofmathematicalrepresentationsprintedoncutcardstockthatcouldbeorganizedtosuggesteitherfulfillmentofacompleteset,oracategorizationschemethatcouldbejustifiedbystudents.Forexample,Figure1showsaportionoftheDefiniteIntegralDominosTACTivity.Asstudentstouchedandmovedcardstopairrepresentations,theywoulddiscusstheirreasonsfordoingso.Oftenthiswouldelicitpeerfeedbackeitheraffirmingorcounteringthedecisiontopairtherepresentationsondifferentsidesofthecards.

Figure1:PartialsolutionoftheDefiniteIntegralDominoTACTivity

TheotherreasontodesigntheseTACTivitieswasthatwefoundtheyrequired“lowinstructionaloverhead.”Often,calculusinstructorsaregraduatestudentswhohavelimitedexperienceopportunitiesforprofessionaldevelopmentinstudentcenteredpedagogy.Evenatuniversitieswherecalculusistaughtinlargelecturesthereareusuallyamultitudeofrecitation

3Manyresourcessimilartothesehavebeenreviewed,fieldtested,andpublishedtoapubliclyavailablewebsite:math.colorado.edu/activecalc


64

sectionswhicharetypicallyledbydoctoralstudents.Calculusinstructorstypicallyhavelittleexperiencelearningthecraftofteachingcomparedtothatsecondarymathematicsteachersexperienceintheirlicensureprogram.Ratherthanbeingabletooffermultiplecoursestocalculusinstructorsthatareconnectedtofieldexperiences,trainingattheuniversitywasnecessarilylimitedtotheweeklyone-hourmeetingsforcalculusinstructors.

Theseactivities,therefore,weredesignedtobeeasytolaunch–i.e.,theyweresomewhatintuitiveforstudentsastohowtoproceedwithminimalguidancefromtheinstructor.AsinstructorsusedtheseTACTivities,andasstudentdiscussionsabouttherepresentationsemerged,instructorswouldhearandobservestudents’ideasandconceptionsandusethatinformationastheyinteractedwithgroupsorfacilitatedawholeclassdebriefoftheactivity.

CALCSinstrument.WhentheALMRACformedwerecognizedoneofourprimarydriverswasstudents’dispositionstowardsmathematics.Tochangestudentpersistenceincalculuscoursesweneededtomonitoranyshiftsinstudents’attitudesandconceptionsofmathematicsandwhatitmeanstoengageinmathematicalactivity.Afterreviewingtheoptionsavailableforstudentmathematicssurveys,wedecidedtousetheColoradoLearningAttitudesaboutScienceSurvey(whichhadamathematicsspecificversionavailable).Overtimeasthissurveywasusedwecollectedenoughdatatorunseveralfactoranalyseswhichinformedtheinclusion,adaptationanddeletionofpromptsandtherebystrengthenedtheassessmentofseveralconstructs.ThisadaptedsurveywasrenamedtheCollegiateActiveLearningCalculusSurvey(CALCS)instrumentandhasfourmaincomponents:

• studentattitudestowardmathematics;• perceptionsofthepervasivenessofactivelearninginclass;• historyofpreviousmathcoursesandintenttotakefuturemathcourses;and• StudentAssessmentofLearningGains,toserveasacommonmeasureofstudent

contentlearningthatcanspandifferentcoursesandinstitutions.

TheCALCSsurveyisnowaprimarydatasourcefortheALMRAC,andallpartnersareexpectedtoadministerthissurveyatthebeginningandtheendofthesemester.TheUniversityofNebraskaLincolnhasbeenconductingongoinganalysisofdatareceivedbypartnerstocontinuetomonitorthequalityofsurveyasitrelatestotheintendedconstructsmeasured.

ImpactsoftheALMRAC

SeveralofourpartnersareshowingsimultaneousimprovementstoDFWratesandpersistenceratesintheP2C2sequence.Todate,theALMRAChasgrownfromitsoriginalfiveuniversitiestoincludethefollowingfourteenpartnerinstitutions:AuburnUniversity,CalStateFullerton,ColoradoStateUniversity,FloridaInternationalUniversity,FresnoStateUniversity,UniversityofColoradoBoulder,UniversityofHawaii-Manoa,UniversityofNebraskaLincoln,


65

UniversityofNebraskaOmaha,UniversityofSouthCarolina,SanDiegoStateUniversity,TuskegeeUniversity,WestVirginiaUniversityandWesternMichiganUniversity.Giventhatourworkfocusesonchangingtheteachingofcalculusbysupportingdepartmentalchange,wefindthescalingofourgroupnearlythreefoldtorepresentasignificantimpactoninstructorsandstudents.SincetheP2C2sequenceinvolveshighenrollmentcourses,theinfusionofALMinjustCalculus1couldimpactover1000studentseachyearforjustoneinstitution.IfallpartnerinstitutionsimplementALMthroughouttheP2C2sequence,thepotentialnumberofstudentswhocouldbeimpactedbytheALMRACexceeds40,000studentseachyear.

WithrespecttotheMathematicsTeacherEducation-Partnership,andthepreparationofsecondarymathematicsteachers,datafromtheCALCSsurveyindicatesapotentialyieldrateof2%ofcalculusstudentswhoareinterestedinpursuingateachinglicense,orapproximately800studentsperyear.Eventhoughtheremaybevariousreasonsthatstudents’intentionsmayshiftastheyproceedfromcompletingcalculustocommittingtoamajor,improvingstudents’persistencerateforcoursecompletionandimprovingthequalityoftheirundergraduatemathematicsexperienceshouldhaveapositiveimpactonmathematicsteacherpreparation.

OtherunexpectedimpactsoftheALMRACincludeinfluenceonotherSTEMdisciplinesasmanystudentswhocompletecalculuseventuallypursuescienceorengineeringmajors,andpossiblylicensurepathwaysrelatedtothosedisciplines.WehavealsolearnedofcasesinwhichALMinstructionalresourceshavebeensharedwithscienceandengineeringfaculty,buildinglocalawarenessofactivelearninginitiativesandtheirpotentialbenefit.Lastly,weknowthathighschoolandcommunitycollegecalculusareawareofourworkandareusingourresourcestosupportALMimplementationintheirclassrooms.

SummaryofConferenceActivities

Atthe2016MTE-PAnnualConferenceweneededtoaccomplishseveralgoals:

1. Todecideonanapproachtoorganizeintosub-RACsgiventhegrowthoftheALMRAC;

2. ToprepareproposalsforhostingandarrangingsitevisitstouseavailableHelmsleyfunding;

3. Todevelopalistofneedstosupportlocalefforts,somewhichrequirefunding;

4. Tosupportdatacollectionandanalysisatnewpartnerinstitutions;and

5. TodiscusstherelationshipbetweentheawardedNSFIUSEgrant,SEMINAL,andtheongoingworkoftheALMRAC.

Organizingintosub-RACs.TohelpmanagethegrowthoftheALMRACandprovidesufficientfeedbackandsupporttotheneedsofspecificinstitutions,weagreedthatitwasnecessarytoorganizeintosmallergroupsassubRACs.Afterdeliberatingvariouswaystoorganizesuchgroupswedecidedthatitwouldbebesttohavethreecoursespecificgroups:


66

pre-calculus,Calculus1andCalculus2.Eventhoughsimilarissuesareencounteredineachcourse,thecurriculumexpectationsandstudentenrollmenttendtobemoresimilarwithineachcourse.Thecoursesub-RACshaveagreedtoconvenevirtuallyeveryothermonthstartingSeptember2016.

Wealsorecognizedthatapermanentsub-RACstructurecouldlimittheinteractionbetweenpartnersandsowealsoagreedthattopicalsub-RACscouldbeconvened.Topicsrelevanttotheneedsoffacultywouldbeproposedandfacilitatorswouldself-nominatetofacilitatevirtualmeetingstodiscusschallengesandstrategiesusedtoaddressthosechallenges.Todatefivetopicalsub-RACshavebeenproposed:

• Understandingstudents’backgroundandintereststosupportlearning• LessonstudyinALMCalculusI/II• ProfessionaldevelopmentforGTA/GRAs• RevisingtheCALCSstudentsurvey• SupportingthecollectionofDFWandpersistencedataw/proposalsforadata

dashboard

Weplantoscheduletopicalsub-RACmeetingseveryothermonthstartingOctober2016.

Organizingsitevisits.TohelptheALMRACmembersbetterunderstandthesimilaritiesanddifferencesamongmathematicsdepartmentsandlocalcontexts,wecommittedtositevisitsinfall2016andspring2017.Duringtheconferencewedevelopedatablethatdescribedforeachpartnerthefacultytheyshouldplanonvisitingandwhattheymightexpecttoobserve.Ourplanistoscheduleatleastfourvisitsinfall2016,andwerecentlyconstructedaGoogleSheetthatfacultymodifyatanytimetosupportsitevisitplanning.

Listoflocalneeds.Knowingthateffortsarecurrentlyunderway,wealsoproposedotheroptionsforallocatingfundstosupportlocalinitiatives–forexample,jumpstartingalearningassistantprogram;partiallyfundacalculuscoordinator;developadditionalinstructionalresources,etc.EventhoughthisisnothowHelmsleyfundswereoriginallyallocatedwefeltthatitwouldbeusefultooutlineotherprioritiesforfunding.

Datacollection.ThecollectionofstudentandinstructordataisimportanttoinformprogressandnecessaryrevisionstoPDSAcycles.However,datacollectionrequiresapprovedIRBprotocolsandagreementonmethodstosupportreliabledatacollectionacrossinstitutions.WediscussedhowparticularmethodsandincentivescouldbeusedtosupporthigherresponseratesandsharedpreviouslyapprovedIRBprotocolsandinstrumentstosupportlocalresearch.

AwardofNSFIUSEgrant.WewereawardedaNSFIUSEgrant,akaSEMINAL,tostudytheprocessofinstitutionalizingactivelearninginPre-calculusthroughCalculus2.Theprojectwilldrawoninstitutionalchangeresearch,researchonproductiveundergraduatemathematicslearningenvironments,andonthesharedexpertiseoffacultytostudytheeffectofinstitutional


67

cultureonmathematicsteachingandlearningintheP2C2sequencewithinandacrosscontexts.ALMRACmemberswillcontributetothisworkinmultipleways.

References

Ferrini-Mundy,J.,&Graham,K.G.(1991).Anoverviewofthecalculuscurriculumreformeffort:Issuesforlearning,teaching,andcurriculumdevelopment.AmericanMathematicalMonthly,98(7),627-635.

Ganter,S.L.(2001).Changingcalculus:Areportonevaluationeffortsandnationalimpactfrom1988–1998.Washington,DC:MathematicalAssociationofAmerica.

Moreno,S.E.,&Muller,C.(1999).Successanddiversity:Thetransitionthroughfirst-yearcalculusintheuniversity.AmericanJournalofEducation,108(1),30-57.

Rasmussen,C.,Ellis,J.,&Bressoud,D.(2015).Whoarethestudentswhoswitchoutofcalculusandwhy?ProceedingsoftheKoreanSocietyofMathematicsEducation:2015InternationalConferenceonMathematicsEducation(pp.1-27).SeoulNationalUniversity,SouthKorea.

Subramaniam,P.K.,Cates,M.,&Borislava,G.(2008).Improvingsuccessratesincalculus.MAAFocus,28(5),20-21.

MTE-Partnership Solicitation for Participation in the

Active Learning in Mathematics RAC April 18, 2016

Problem Addressed

Student success in undergraduate mathematics has significant implications for whether they choose to continue into STEM majors and future related careers. Even for those students who do not choose to major in mathematics, science or engineering, success in entry-level undergraduate mathematics courses such as calculus can make or break their decision to persist in postsecondary education. The Characteristics of Successful Programs in College Calculus (Bressoud, Carlson, Mesa, & Rasmussen, 2013) showed the percentage of students with grades of D, F or Withdraw ranged from an average of 25% at Ph.D.-granting universities to an average of 37% at regional comprehensive universities. We are committed to improving students’ achievement in and dispositions towards mathematics through the use of models for Actively Learning Mathematics. With respect to the MTEP Guiding Principles, the ALM RAC involves Commitments by Institutions of Higher Education through Institutional Focus, Disciplinary Partnerships, and Institutional Support for Faculty. The ALM RAC also addresses the guiding principle of Candidates’ Knowledge and Use of Mathematics through future candidates’ engagement in Mathematical Practices in introductory level undergraduate mathematics courses, to deepen their Knowledge of the Discipline.

General Approach Our working theory of change is articulated in the following diagram: The overarching goal is to improve student success with undergraduate mathematics, starting with the Pre-calculus through Calculus 2 sequence (P2C2). This is accomplished through effective teaching practices, which are supported by learning environments that are more conducive to student interaction, reasoning, and problem solving and the use of instructional resources to support ALM. Faculty buy-in and institutional leadership is developed to support Graduate Teaching Assistant training. Also, for many campuses, undergraduate learning assistants are used to support student work with group activities and enhance student engagement in mathematical activity.

Who We Are Auburn University: Gary Martin, Ulrich Albrecht

Fresno State University: Lance Burger

University of Colorado Boulder: David Webb, Faan Tone Liu, Eric Stade, Robert Tubbs

University of Nebraska Lincoln: Wendy Smith, Judy Walker, Allan Donsig, Yvonne Lai

University of Nebraska Omaha: Angie Hodge, Janice Rech

University of South Carolina: Sean Yee

San Diego State University: Chris Rasmussen, Janet Bowers

Tuskegee University: Lauretta Garrett, Anna Tameru

West Virginia University: Vicki Seeley, Nicole Engelke, Matthew Campbell

Western Michigan University: Tabitha Mingus, Melinda Koelling

Current Progress Over the past three years, we have worked collaboratively to improve instruction in introductory calculus courses. While the contexts across the ten campuses are quite different, requiring somewhat different approaches to implementing ALM, we have been able to learn from each other’s efforts. We have exchanged and co-developed instructional resources, used common measures to document student dispositions, and have regularly discussed the local models used to support learning environments that are more conducive to ALM. At least three campuses adopted the “learning assistant” model used by Colorado, while West Virginia uses Graduate Teaching Assistants in a similar role. Discussions across campuses have helped to clarify the approaches used and have identified the critical role of institutional change in promoting ALM.

Opportunities for Engagement We are currently utilizing resources from the Helmsley Foundation to coordinate planning meetings to share data collection efforts and develop a research agenda focused on understanding the process of institutional change. A collaborative research grant – Student Engagement in Mathematics through an Institutional Network for Active Learning (SEMINAL) – describes how we intend to better understand how to enact and support institutional change in undergraduate mathematics. SEMINAL will also support future efforts focused on increasing student success and persistence in the pre-Calculus to Calculus 2 (P2C2) sequence, and will promote adoption of ALM among MTEP institutions. The Active Learning RAC is currently seeking additional partners who are interested in contributing to future research and products, including the use and revision of instructional resources, professional development materials, documented strategies to support instructional change, and the use and improvement of relevant measures to study the impact of these changes (full partner). We also welcome partners who are interested in field-testing and implementing ALM resources and measures, without the full commitment of contributing to the Active Learning agenda or development of resources (participating partner).


70

TheMathematicsofDoing,Understanding,Learning,andEducatingforSecondarySchools1

AlysonLischkaMiddleTennesseeStateUniversity

[email protected]

EminaAlibegovicUniversityofUtah

[email protected]

TheMathematicsofDoing,Understanding,Learning,andEducatingforSecondarySchools[MODULE(S2)]ResearchActionCluster(RAC)isfocusedonthedevelopmentofprospectivesecondarymathematicsteachers’(PSMTs’)knowledgeofmathematicscontentneededtosupportstudentlearning.ThisfocusaddressesrecommendationssetforthinTheMathematicalEducationofTeachersII(ConferenceBoardoftheMathematicalSciences[CBMS],2012)forcoursesinsecondarymathematicsteacherpreparationprogramstoprovideopportunitiesforprospectiveteachersto“delveintothemathematics…whileengaginginmathematicalpracticeasdescribedbytheCCSS”(CBMS,2012,p.46).TheworkoftheRACaimstoaddresstheidentifiedproblemthatundergraduateprogramsfailtoleadteachercandidatesto:a)deeplyunderstandthemathematicstheywillactuallyteachandb)experiencelearninginamannerconsistentwithwhatwillbeexpectedofthemasprofessionaleducators(Baniloweretal.,2013).

Inresponsetothisproblem,theMODULE(S2)RAChasestablishedthefollowingobjectives:

• CreatetwelvecollaborativelydesignedmodulesaimedtodevelopPSMTs’mathematicalknowledgeforteachingalgebra,geometry,modeling,andstatisticsingrades6-12.

• Pilotandsupporttheimplementationofthemodules.

• Revisethemodulesbasedonimplementationdata,instructorfeedback,andPSMTs’work.

• EvaluatetheeffectivenessofmoduleswithregardstotheirabilitytodevelopPSMTs’mathematicalknowledgeforteaching.

• Disseminatethemodulesacrossmultipleinstitutions,beginningwithMTE-Pinstitutions.

WeadoptedtheMathematicalKnowledgeforTeaching(MKT;Hill,Ball&Schilling,2008)frameworkforourwork.Inthisframework,subjectmatterknowledgeforteaching1TheRACPromoSheet,presentedduringtheopeningoftheconferencetoreportoncurrentactivitiesoftheRAC,canbefoundafterthereferencelist.


71

mathematicsincludesthemathematicsoneteaches(CommonContentKnowledge[CCK]),butitalsoincludesknowingmathematicsinaspecializedwaytomeetthedemandsofteaching(SpecializedContentKnowledge[SCK])andthebroaderlandscapeofmathematicsinwhichthemathematicsoneteachesissituated(HorizonContentKnowledge[HCK]).PedagogicalContentKnowledge(PCK)isalsoincludedinthisframework,becauseitisspecifictoteachingmathematics.PCKincludesthreecomponentsintheMKTmodel:knowledgeofhowstudentsconceiveofparticularcontenttopics(KnowledgeofContentandStudents[KCS]),pedagogicalprinciplesforteachingspecificcontenttopics(KnowledgeofContentandTeaching[KCT]),andknowledgeofthecurriculumresourcesavailablefortheteachingofspecificcontentandhowtosequencetheirusetoenhancestudentlearning(KnowledgeofContentandCurriculum[KCC]).Hill,RowanandBall(2005)showedthatteachers’mathematicalknowledgeforteachingispositivelycorrelatedwithstudentachievement,sogrowthofPSMTs’mathematicalknowledgeforteachingcouldhavepowerfuleffectsonstudents’STEMachievement.

CurrentStateoftheWork

Theproposedmoduleswillbewrittenwithacommonorganizationalstructure.MaterialsforPSMTswillincludeactivities,workbooks,excerptsfromjournalsandsecondarycurricula,representationsofpractice,andhomeworksets.Materialsforinstructorswillincludeinstructorguides,assessmentstrategies,andteachingapplications.Writingofmodulesiscurrentlyinvariousstagesofproductionacrosstheselectedcontentareas.

Inthe2014-2015academicyear,EminaAlibegovicandAlysonLischkacollaboratedonwritingandpilotingthreemodulesingeometry:(1)axiomaticsystems,(2)rigidtransformations,and(3)similarityandarea.ThemodulesincludeopportunitiesforPSMTstoanalyzestudentworkanddepictionsofclassroomeventsthroughtheLessonSketchplatform(Herbst,Aaron,&Chieu,2013).Intheinitialpilotyear,participatingPSMTscompletedapre-andpost-testassessmentofMKT(MKT-Geometry;Herbst&Kosko,2012).Eighteenofthetwenty-onestudentsnotedimprovementinscoresfrompre-testtopost-test.InSpring2016,AlysonLischkapilotedrevisedmaterialsandcollectedqualitativeandquantitativedataassessingtheeffectivenessofthematerialsinimprovingPSMTs’MKT.Pre-andpost-testdatawasgatheredusingtheGeometryAssessmentforSecondaryTeachers(Mohr-Schroeder,Ronau,Peters,Lee,&Bush,underreview)tomeasurePSMTs’mathematicalknowledgeforteaching.TheresultsindicatedastatisticallysignificantgainingeometricknowledgeforteachingforthePSMTs.PreliminaryanalysisofqualitativedatademonstratedashiftinPSMTs’abilitytoaddressspecificmathematicalideaswhenrespondingtostudentthinkinginaLessonSketchprompt.Furtheranalysisiscurrentlybeingconducted.Additionalpilotsareplannedforthe2016-2017schoolyear.

Themodelingwritingteam,BrynjaKohlerandCynthiaAnhalt,hasdraftedthreeplannedmodules:(1)themodelingprocess,(2)classicmodels,and(3)in-depthmodelingexperience.


72

Theproject-basedapproachusedinthemodules,involvingdatagatheringandcreativemodeldesignactivities,wasinspiredbylabsthathavebeendevelopedbyKohlerandcolleaguessuchastheShrimpDiffusionLab(Kohler,Swank,Haefner,&Powell,2010),theLeakyBucketLab(Powell,Kohler,Haefner,&Bodily,2012),andCoffeeToGo(Kohler&Bruder,2015).

JasonAubreyandYvonneLai,haveoutlinedthreeplannedmodulesforAlgebraon:(1)functionsandrelations,(2)complexnumbers,and(3)orderedfields.Aninitialdraftofthemoduleonorderedfieldsfocusesonpropertiesoforderedfieldswhichunderliethealgebracurriculuminsecondarymathematics.

Inthe2014-2015academicyear,AndrewRossandStephanieCaseycollaboratedtowriteastatisticsmoduleaddressingcategoricalassociation(includinganalysisoftwo-waytables,segmentedbargraphs,andchi-squaredrandomizationtests)andpiloteditat5institutions.Analysisofthepre-andpost-assessmentdatashowsthatthematerialswereeffectiveatimprovingtheparticipants’MKTforcategoricalassociation(Casey,Ross,Groth,&Zejnullahi,2015;Casey,Zejnullahi,Wasserman,&Champion,2015).

Inadditiontomovingforwardonwritingandpilotingmodules,theMODULE(S2)RAChassubmittedanNSFproposalforanIUSEgrant.Favorablecommentswerereceivedfromreviewersalthoughtheinitialproposalwasnotfunded.Theteamiscurrentlyworkingtowardaresubmissionofarevisedproposaltofundthewriting,analysis,anddisseminationofthiswork.ThisprojectwillnotonlydevelopmaterialsthatwillincreasePSMTs’MKT,itwillalsogenerateknowledgeaddressingimportantquestionsinthefieldofmathematicsteachereducation.Thefollowingquestionsareencompassedwithintheproposedfutureresearchassessingtheeffectivenessofthedevelopedmodules:

1. HowdotheMODULE(S2)materialshelpPSMTsdevelopmathematicalknowledgeforteaching?

2. Inwhatwaysisthedevelopmentofpre-serviceteachers’MKTrelatedtotheirperceptionofcontentandskillatthatcontent?

3. Inwhatwaysdoespre-serviceteachers’MKTtransferbetweencontentcontextinwhichitwaspreviouslylearnedandnewcontentcontexts?

4. Whatarethenecessaryconditionstosupportimplementationofthemodulesincurrentcourses?

MovingForward

AcrossthepartnersinvolvedintheMODULE(S2)RAC,reflectionsonexistingpilotedcoursematerialshavebeenpositive.WehaveobservedevidencethatPSMTsincreasetheirmathematicalknowledgeforteachingwhilelearningmathematicalcontentusingthematerials.Wecontinuetoreviseandimprovematerialsbasedonresearchfindings.Atmanyinstitutions,PSMTscompleteCollegeGeometrywiththeMODULE(S2)materialspriortotheirSecondary


73

MathematicsMethodscourse.ThisisthecaseatMiddleTennesseeStateUniversity,whereithasbeennotedthatmathematicalknowledgeforteachingthatPSMTsgaininCollegeGeometryservesasavitalfoundationfordiscussionsofpracticeinthemethodscourse;PSMTsrepeatedlypointtotheinstructioninCollegeGeometryasprovidingaconnectiontocontenttheywillteachwhiletheyconcurrentlyengageinadeepexplorationofgeometricconcepts.

NextstepsincludeplannedpilotsofthegeometrymaterialsatadditionalMTEPartnershipinstitutionsandfurtherworkonmaterialsinothercontentareas.ThisongoingworkwillcontinuetocontributetothewaysinwhichmathematicsteachereducatorscanimpactthemathematicalknowledgeforteachingdevelopedamongPSMTsatMTEpartnerinstitutions.ParticipationintheRAC’sactivities(includingpiloting)offersanopportunityforlocalpartnershipstostrengthentiesbetweenmembersandstakeholdersthroughthecollaborationandlocaladaptationofthematerials.WeinviteparticipatinginstitutionstoconnectwiththeRACandexplorepossiblecollaborationsthroughwriting,reviewing,andimplementingthematerials.

ForMoreInformation

• AlysonLischka,MiddleTennesseeStateUniversity,[email protected]

• EminaAlibegovic,RowlandHall-St.Mark’sSchool,[email protected]

References

Banilower,E.R.,Smith,P.S.,Weiss,I.R.,Malzahn,K.A.,Campbell,K.M.,&Weis,A.M.(2013).Reportofthe2012NationalSurveyofScienceandMathematicsEducation.ChapelHill,NC:HorizonResearch,Inc.

Casey,S.,Ross,A.,Groth,R.,&Zejnullahi,R.(2015).Developingteachers’knowledgeofcontentandstudentsforteachingcategoricalassociation.InT.Bartell,K.Bieda,R.Putnam,K.Bradfield,&H.Dominguez(Eds.)Proceedingsofthe37thannualmeetingoftheNorthAmericanChapteroftheInternationalGroupforthePsychologyofMathematicsEducation(pp.872-875).EastLansing,MI.Retrievedfrompmena2015.org/info/proceedings

Casey,S.,Zejnullahi,R.,Wasserman,N.,&Champion,J.(2015).Preparingtoteachstatistics:Connectingsubjectmatterandpedagogicalcontentknowledge.PresentationattheUnitedStatesConferenceonTeachingStatistics,StateCollege,PA.

ConferenceBoardoftheMathematicalSciences.(2012).TheMathematicalEducationofTeachersII.Providence,RI,andWashington,DC:AmericanMathematicalSocietyandMathematicalAssociationofAmerica,Retrievedfromwww.cbmsweb.org/MET2/MET2Draft.pdf

Gleason,J.&Cofer,L.D.(2014).Mathematicsclassroomobservationprotocolforpracticesresultsinundergraduatemathematicsclassrooms.In(Eds.)T.Fukawa-Connelly,G.Karakok,K.Keene,andM.Zandieh,Proceedingsofthe17thAnnualConferenceonResearchinUndergraduateMathematicsEducation(pp.93-103).Denver,CO:MathematicsAssociationofAmerica.


74

Herbst,P.,Aaron,W.,&Chieu,V.M.(2013).LessonSketch:Anenvironmentforteacherstoexaminemathematicalpracticeandlearnaboutitsstandards.InD.Polly(Ed.),Commoncoremathematicsstandardsandimplementingdigitaltechnologies(pp.281-294).Hershey,PA:InformationScienceReference.doi:10.4018/978-1-4666-4086-3.ch019

Herbst,P.&Kosko,K.(2012).Mathematicalknowledgeforteachinghighschoolgeometry.InL.R.VanZoest,J.J.Lo,&J.LKratky(Eds.)Proceedingsofthe34thAnnualMeetingoftheNorthAmericanChapteroftheInternationalGroupforthePsychologyofMathematicsEducation(pp.438-444).Kalamazoo,MI:PME-NA.

Hill,H.C.,Ball,D.L.,&Schilling,S.G.(2008).Unpackingpedagogicalcontentknowledge:Conceptualizingandmeasuringteachers’topic-specificknowledgeofstudents.JournalforResearchinMathematicsEducation,39,372-400.

Hill,H.C.,Rowan,B.,&Ball,D.L.(2005).Effectsofteachers’mathematicalknowledgeforteachingonstudentachievement.AmericanEducationalResearchJournal,42,371-406.

Kohler,B.R.,&Bruder,A.(2015,April).Limnologyandinversionsinmultivariablecalculus.IntegrativeandComparativeBiology,55,pp.e99-e99.

Kohler,B.R.,Swank,R.,Haefner,J.W.,&Powell,J.A.(2010).Leadingstudentstoinvestigatediffusionasamodelofbrineshrimpmovement.BulletinofMathematicalBiology,72,230-257.

Mohr-Schroeder,M.J.,Ronau,R.N.,Peters,S.,Lee,C.W.,&Bush.W.(underreview).Knowledgeforteachinggeometry:Predictingstudentachievementfromteachermeasures.

Powell,J.A.,Kohler,B.R.,Haefner,J.W.,&Bodily,J.(2012).Carryingbiomatheducationinaleakybucket.BulletinofMathematicalBiology,74,2232-2264.

MTE-Partnership Solicitation for Participation in the

MODULE(S)2 RAC April, 2016

Problem Addressed During undergraduate study, prospective secondary mathematics teachers (PSMTs) do not always have the opportunity to build deep understanding of the mathematics they will be asked to teach. MODULE(S)2 is concerned with developing mathematical knowledge and habits of mind for teaching for PSMTs. We address Candidates’ Knowledge and Use of Mathematics within the Teacher Candidate Knowledge, Skills and Dispositions section of the guiding principles as represented by the following indicators:

• Mathematical habits of mind • Knowledge of the discipline • Specialized knowledge of mathematics for teaching • Nature of mathematics

General Approach

Our RAC aims to build communities among mathematicians, mathematics educators, and K-12 collaborators and work together to establish common content courses for mathematics teachers relevant to their professional needs. Because of the variety of needs and structures at different universities and teacher preparation programs, we have chosen to use a flexible format of creating course modules, each 3-5 weeks in length, that could be (a) used as a stand-alone mini course, (b) inserted into an existing course, or (c) combined to create one coherent course with the goal of creating a program in which all courses are carefully crafted to develop mathematical knowledge for teaching. Our objectives are:

• Develop twelve collaboratively designed modules that focus on building a deep understanding of secondary mathematics themes identified in the CCSSM and the new CAEP accreditation standards.

• Investigate the impact of modules on PSMTs’ opportunities to learn and readiness to teach school mathematics

Who We Are

• Geometry: o Emina Alibegovic, Department of Mathematics, University of Utah o Alyson Lischka, Department of Mathematical Sciences, Middle Tennessee State University o Taylor Haslam, Taylorsville High School, Granite District, Utah

• Modeling: o Brynja Kohler, Department of Mathematics and Statistics, Utah State University o Cynthia Anhalt, Department of Mathematics, University of Arizona o Brian Lawler, Mathematics Education, CSU San Marcos

• Statistics: o Stephanie Casey, Department of Mathematics, Eastern Michigan University o Andrew Ross, Department of Mathematics, Eastern Michigan University o Kady Schneiter, Department of Mathematics and Statistics, Utah State University o Joyce Smart, Logan High School, Logan City School District, Logan, Utah

• Algebra: o Jason Aubrey, Department of Mathematics, University of Arizona o Yvonne Lai, Department of Mathematics, University of Nebraska-Lincoln

• Master Editor: o Rachael Kenney, Department of Mathematics, Purdue University

Current Progress • Geometry:

o All modules completed o The course has been piloted at three institutions, two modules piloted separately at other institutions o In the process of editing and revising instructor and course materials o New pilots are scheduled for fall

• Modeling: o First module completed, first pilot scheduled for fall. o Modules 2 and 3 outlined, materials in development, ongoing research

• Statistics: o First module completed, and piloted at several institutions o Modules 2 and 3 outlined, materials in development, ongoing research

• Algebra: o First module completed, and piloted at several institutions o Modules 2 and 3 outlined, materials in development, ongoing research


Geometry Modeling Statistics Algebra Full partner Participating partner

Reviewing, editing, piloting*

Contributing, reviewing, editing, piloting*

Reviewing, editing, piloting*

Contributing, reviewing, editing, piloting*

Exploratory partner

Welcome Welcome Welcome Welcome

* Partners involved with piloting will be asked to communicate frequently with the full partners. In addition, there will be data collection required for the purpose of course material improvement and revision.


77

MarketingtoAttractTeacherHopefuls(MATH)ConferenceWorkingGroupReport1

EdDickey

[email protected]

TheMATHRACconvenedonJune26forthefirstoffourworkingsessionsduringtheMTE-Pannualconference.RACleaderEdDickeyhadjustprovidedthefullaudienceofMTE-PattendeeswithabriefupdateoftheworkoftheRACoverthepastyear.ThisupdateincludedtheRAC’srelationtotheMTE-PGuidingPrinciples,inparticular:

GuidingPrinciple8.StudentRecruitment,Selection,andSupport:TheTeacherPreparationprogramactivelyrecruitshigh-qualityanddiverseteachercandidatesintotheprogramandsupportstheirsuccessincompletingtheprogramaswellasthespecificproblemtheRACisaddressing:

• SecondaryMathematicsTeacherPrograms2(SMTPs)arenotenrollingorgraduatingsecondarymathematicsteacherstosatisfytheneedsofU.S.middleandhighschools

• Salary,stereo-types,job-satisfaction,careerprestige,andthechallengesoflearningmathematicscontributetolowenrollmentsinmathematicsteacherpreparationprograms

TheRAC’sgeneralapproachforaddressingthesecondarymathematicsteacherrecruitmentproblemisbasedonthedriverdiagram,Figure1,thatwasestablishedatthefoundingoftheRAC.

1TheRACPromoSheet,presentedduringtheopeningoftheconferencetoreportoncurrentactivitiesoftheRAC,canbefoundafterthereferencelist.2AnSMTPisaprogramthatincludesanationallyaccreditedcourseofstudyhousedataninstitutionofhighereducationthatleadstolicensureforteachingmathematicsingrades6-12.


78

Figure1.DriverdiagramoftheMATHRAC

RACmembersattendingtheconferenceincludedthoselistedinTable1,mostofwhomareseeninFigure2.

Table1.MATHRACMembersThatAttendedtheMTE-P5Conference

Name InstitutionCynthiaAnhalt UniversityofArizonaLindaVenenciano UniversityofHawai’iNancyCaukin MiddleTennesseeStateUniversityLaurieCavey&JanSmith BoiseStateUniversityEdDickey UniversityofSouthCarolinaMariaFernandez FloridaInternationalUniversityDanaFranz MississippiStateUniversityMargaretMohr-Schroeder(andRiley) UniversityofKentuckyRafaelaSantaCruz SanDiegoStateUniversityCarolFryBohlin FresnoStateUniversityJulieMcNamara CSU-EastBayCherylOrdorica CSU-ChicoJoshMales Lincoln(NB)PublicSchoolsAmyNebesniak UniversityofNebraskaatKearney


79

Figure2.ParticipantsintheMATHRACworkgroupsduringtheMTE-P5conference.

GregChamblee(GeorgiaSouthernUniversity),RobinHill(AssociationofStateSupervisorsofMathematics),andDianaSuddreth(UtahStateOfficeofEducation),alsoparticipatedinsomeoftheworksessions.RACmembersnotattendingtheconferenceincludedDianaBarrettandJimMcKown(Hawai`i),JoeChampion(BoiseState),NadineBezukandRandyPhilipp(SanDiegoState),KathyHannandJuliaOlkin(CalStateEastBay),andCherylRoddick(SanJoséState).

TheRACrevieweditsprogresstodatethatincludedthecompletionanddisseminationoftheSecondaryMathematicsTeachersRecruitmentCampaignImplementationGuidethatwasfeaturedanddescribedbyEdDickeyaspartofhisopeningkeynoteaddressattheJanuary2016meetingoftheAssociationofMathematicsTeacherEducators.TheGuideispostedforgeneralusebyteachereducatorsatbit.ly/MATHImplGuide.

Figure3.FormatofthewebsitehostingtheSecondaryMathematicsTeachersRecruitmentCampaignImplementationGuide.

ManyoftheRAC’sPlan,Do,Study,Act(PDSA)cyclesaredocumentedonaPadletsitethatincludesnumerousproductstiedtothedifferentinterventionsconductedoverthepasttwoyearsbyRACmemberinstitutions.ThePadletsiteisavailableatpadlet.com/ed_dickey/vhle4gisbq82.


80

Figure4.FormatofthePadletwebsitereportingproductsoftheMATHRAC.

TheplanfortheconferenceRACworksessionswastofirstreviewthePDSAworkateachsite,thendiscussfuturedirectionsorinitiativesfortheRACwithattentiontobothidentifyingfundingtosupportrecruitmentworkandresearchandtoaddresstheMTE-Pcommitmenttoequityandsocialjustice.

ThesecondandpartofthethirdworkingsessionsonJune27includedbriefpresentationsfromeachRACmemberaboutcurrentandpastPDSAs.TheseweresupportedbyaPowerPointpresentationcompliedanddistributedtoattendingRACmembersandaresummarizedbrieflyasfollows:

• Arizona:AfterSchoolandTutoringprograms,undergraduateTeachingAssistantProgram,NoyceSeminarsandrecruitmenteffortsthatincludehighschoolvisits,orientations,careerfairs,postersbrochures,websitedevelopmentandprogramvideo.Moreinformationincludingvideoatsmep.math.arizona.edu.

• BoiseState:completionofwebsiteandseveralrecruitmentandprogramvideosaspartoftheIDoTeachprogram.Moreinformationincludingvideosatidoteach.boisestate.edu.

• FloridaInternational;Studentorientationsthroughadvisingandresourcesfairs,recruitmentcourses,personalizedemailtoallSTEMmajors,math/sciencecoursevisits,STEMadvisorsbriefings,websitedevelopment,openhouses,EducatorsRisingConferenceandhighschoolevents,internships.Surveyanddatacollectiononallstrategies.Moreinformationatfiuteach.fiu.edu.

• Kentucky:continuedsocialmediaeffortsthroughFacebook,retentioneffortsthrough#IamAWomanInSTEM,NSFShowcasevideo:stemforall2016.videohall.com/presentations/815,workingwithnewlyhiredrecruiterandstatewideSTEMEducationCenter.Moreinformationateducation.uky.edu/stem.


81

• MississippiState:focusedondatagatheringthatdocumentedcriticalshortageofscienceandmathematicsteachersinruralareasofstate.UniversityandCollegeofEducationeffortsaround#STATEPROUDcampaignthataddressesteacherpreparation.

• CaliforniaStateEastBay:developmentofflyersandpostersusedthroughoutcampusandcommunity,withPioneersTeach!Branding,meetingwithundergraduateorganizations,personalmessagetoallapplicants.Moreinformationatcsueastbay.edu/ted.

• ChicoState:completedfirstmarketingcampaign(describedbelow)andbeginningplansforsecondcampaign.Graduatefairsanddiversityforums,partnerwithNewMediaAgencyforvideoproduction,andads.WilluseYouTubeandPandora.ExpandtoSacramentoarea.Developingradio,movietheatrePSAsandflyers.Moreinformationatwww.csuchico.edu/soe/rise

• FresnoState:leadingMathematics&ScienceTeacherInitiative(MSTI)thatincludessupportforentireCaliforniaStateSysteminrecruitment:conferencetravelsupport,earlyfieldexperiences,interactiveworkshops,advisement,feewaiversformethodscourses,stipendsforstudent.WorkwithFresnoTeacherResidencyProgramincludingwebsitedevelopment,socialmedia,openhouses,directemails,andvideousedasPSAinmovietheatersandavailableatvimeo.com/114188236.Moreinformationatwww.fresnostate.edu/kremen/teachmathscience.

• SanDiegoState:SocialmediapresencethroughFacebookatwww.facebook.com/SDSUSTE/?fref=ts.

• MiddleTennesseeState:presentingatfreshmanmathematicsandscienceclasses,openhouse,advertisingoncampusTV,postersinscienceandmathematicsbuildings.Developingrecruitmentvideo.Moreinfoatwww.mtsu.edu/mteach.

• SouthCarolina:completionofmultifacetedrecruitmentcampaignthatincludeTVcommercial,ambassadorsprogram,SocialMediaeffortwithAlltheSTEMTeachersVideoandwebsitedevelopment.Moreinformationatteachscienceandmath.org/homeandBeyoncevideoatyoutu.be/i60KEyHtwgA.Facebooksiteatwww.facebook.com/teachscienceandmath.

Inadditiontotheworksessionpresentations,twoRACmembersprovided30-minuteResearchReportsaspartofasetofbreakoutsessionsonJune27.CherylOrdoricaofChicoStatepresentedherworkontheCSUChicoProgramRiSE:AnalysisoftheFirstRecruitmentCycle.Cheryldescribedherproject’srecruitmenteffortsanddatacollectionforPromotingRuralImprovementinSecondaryMathematicsandScience(PRISMS),whichincludestheResidencyinSecondaryEducationprogram.HerpresentationhighlightedtheanalyticaltoolstiedtotheprojectwebsiteandsocialmediastrategiesdescribedintheImplementationGuide.LindaVenencianospokeontheMobilizingEffortsoftheMTE-PHuiinHawai`idescribingtheinitiative’srecruitmenteffortstiedtheinterestofindigenouspeoplesandwithattentiontoethnomathematicsofinteresttoHawai`ianteacherandlearners.


82

Inthethirdworksession,RACmembersdeterminedthatneweffortsmustbeinitiatedtomeasureanddocumenttheimpactofthedifferentrecruitmentinterventionsemployedbyRACmembers.Thegroupassessedthatsignificantprogresshasbeenachievedinunderstandingandcreatingrecruitmentstrategiesandnowmoreeffortandthoughtmustbegiventotheassessmentofhowandtowhatdegreetheinterventionswork.TothisendandaspartofitsfinalmeetingonJune28,thegroupcommittedtogatheringandanalyzingdatagatheredthroughtheMTE-PHubfromallpartnershipmemberstoassessthecurrentstatusofsecondarymathematicsteacherrecruitmentamongpartnershipteamsandtocreateasummarytableforpastPDSAactivitiesthatexpandsthedocumentationavailablethroughthePadletsite.ThesummarytablewillincludemoredetailsonthePDSAsandalsoincludeanassessmentoftheimpact(greenrepresentingpositivegains,yellowindicatinginconclusive,andredsuggestingtheinterventionwasnoteffective).Thetablewillallowfordocumentationoffutureinterventions.Thedataanalysiswillincludeparticularattentiontoassessingprogresstowardrecruitingdiverseteachercandidates.Table2providesapreliminarydraftofthesummarytable.

Table2.ProposedTemplatetoSummarizepreviousPDSAactivitiesconductedintheMATHRAC

RecruitmentStrategy/Intervention

MATHRACInstitution

BriefDescription LinktoResource(s)

ImpactorResults

CalltoAction:TVCommercialonSTEMTeaching

UniversityofSouthCarolina

30secondcommercialtoinformaboutUofSCcommitmenttoSTEMteachingandtosendviewtowebsiteformoreinformation

youtu.be/oxzEdcFn62E

Significantwebtrafficaftereachbroadcast.

Recruitmentstrategiesorinterventionswillinclude:

• CallstoAction:phone,flyer,mailing,poster,website,onlinevideo,TVcommercialvideo,PSAvideo,radio,billboard,openhouse

• Cultivation:classroomobservation,schoolvisit,tutoring,teachingenactment• Conversion:advisementmeeting,facultyinterview

TheRACmembersdecidedtousetheTrelliscience.orgonlinecommunitytosharerecruitmenttoolsthatareunderdevelopmentwithinthenewlycreatedMATHRACgroup.Astoolsbegintobeused,theywillbemadeavailabletotheMTE-PgroupwithinTrellisaswillthesummarytable.ThiswillallowboththeRACandPartnershipgroupstoprovideappropriatefeedbackandsupport.Asproductsmature,theywillbepostedonPadletforabroaderaudience.


83

FundingthroughtheNationalScienceFoundationNoyceprogramwasdiscussed.SeveralmembersparticipatedintheJuneWebinaronthenewsolicitationbutdeterminedthattheexpectationsforTrack4researchfundingarenowfocusingmorenarrowlyonteachereffectiveness,persistence,orretentioninhigh-neededucationagencies,whichthemembersdeterminedtobeincompatiblewithcurrentRACefforts.TheRACwillnotsubmitaproposalfortheSeptember2016cycleandwillconsiderotherfundingoptionsforthefuture.

TheRACmemberscommittedtoparticipatinginthePurposefulRecruitment,Exploration,andPreparation(PREP)InitiativebegunamongtheCaliforniaStateUniversityMTE-Pmembers.Theinitiativeincludesaprocessofidentifyingpromisingfuturesecondarymathematicsteachersthroughmathematicsandotheruniversityfacultymemberstheninvitingthemtoparticipateina“celebrationofteaching”eventdesignedtoincludebothworkingmathematicsstudentsandsecondaryschoolagestudentssoastoprovidethepromisingfutureteacherwithapositiveexperiencethatmightcultivateacommitmenttoteaching.Particularattentionwillbegiventoidentifyingpromisingteachersofcolorandthemathematicsactivitieswillbeselectedtoaddresshowmathematicsmightservetoimpactorinformsocialjusticeissues.

AttheclosingsessionoftheMTE-Pconference,EdDickeypresentedasummaryoftheworkaccomplishedandplansforthecomingyeartotheattendeesfromallpartnershipteams.

Solicitation for Participation in the

MATH: Marketing to Attract Teacher Hopefuls RAC April, 2016

Problem Addressed

Guiding Principle 8. Student Recruitment, Selection, and Support: The Teacher Preparation program actively recruits high-quality and diverse teacher candidates into the program and supports their success in completing the program. Problem:

• Secondary Mathematics Teacher Programs* (SMTPs) are not enrolling or graduating secondary mathematics teachers to satisfy the needs of U.S. middle and high schools

• Salary, stereo-types, job-satisfaction, career prestige, and the challenges of learning mathematics contribute to low enrollments in mathematics teacher preparation programs

* An SMTP is a program that includes a nationally accredited course of study housed at an institution of higher education that leads to licensure for teaching mathematics in grades 6-12.

General Approach

• Provide models for developing and launching purposeful and sustained marketing campaign

that rebrands teaching to appeal to STEM majors • Include adaptions for programs focusing on undergraduates, UTeach, alternative pathways, and

other models • Identify critical experiences in mathematics and clinical work that impact recruitment and

retention

Who We Are Cynthia Anhalt, University of Arizona, & Maria Fernandez, Florida International University

Jennifer Whitfield, Texas A&M University

Diane Barrett, Jim McKown & Linda Venenciano, University of Hawaii

Nadine Bezuk, Randy Philipp & Rafaela Santa Cruz, San Diego State

Nancy Caukin, Middle Tennessee State Carol Fry Bohlin, Fresno State University Laurie Cavey, Joe Champion & Jan Smith, Boise State

Kathy Hann, Julie McNamara & Julia Olkin, CSU-East Bay & Cheryl Roddick, San Jose State

Ed Dickey, University of South Carolina Cheryl Ordorica, CSU-Chico Dana Franz, Mississippi State University Sofia Vicuna, CSU-Monterey Bay Margaret Mohr-Schroeder, U of Kentucky

Current Progress Each partner is implementing Plan Do Study Act cycles tied to recruitment and using measures of program inquires and enrollments to monitor impact. Boise State, Middle Tennessee State, and FIU are addressing UTeach replication recruitment efforts. Arizona, Kentucky, Mississippi State, Texas A&M, and UofSC as well as the California State System campuses are implementing various strategies and recruitment tactics tied to their own programs. Efforts include website development, class meetings, posters, social media efforts and videos. Sample partner websites are at

• UofArizona:SMEP:http://math.arizona.edu/~smep/• BoiseStateUniv,IDoTeach:http://idoteach.boisestate.edu/• FloridaInternationalUniv,FIUTeach:http://fiuteach.fiu.edu/• UniversityofKentucky,STEMDept:https://education.uky.edu/stem/• MississippiState:CISE:http://www.cise.msstate.edu/• TexasA&MUniv,AggieTeach:http://aggieteach.tamu.edu/index.shtml• UnivofSouthCarolina,TeachScienceandMath:http://teachscienceandmath.org

The RAC has created and disseminates a 9-module Secondary Mathematics Teacher Recruitment Campaign Implementation Guide available within Trellis and athttp://bit.ly/MATHImplGuide .

• Module1TeacherRecruitmentCampaignOverview• Module2CampaignPlanning• Module3CampaignResearch• Module4Branding• Module5SocialMedia• Module6PublicRelations • Module7PaidBroadcastMedia• Module8WebSiteIdentity• Module9LessonsLearned/Evaluation

RAC members share recruitment tools (flyers, posters, videos, websites, etc) at http://padlet.com/ed_dickey/vhle4gisbq82 The RAC is collaborating with the STRIDES RAC to implement the Purposeful Recruitment, Exploration, and Preparation (PREP) Initiative in Fall 2016. The RAC is preparing a proposal to anticipated NSF Noyce Track 4 solicitation.

Opportunities for Engagement Ø Asafullpartnercommittoimplementingmarketingtacticsandsharestrategies,results,

anddatawithRACmembers.Asparticipatingpartners,joininperiodicconferencecallstolearnaboutactivitiesandshareinformationasappropriate.

Ø ReviewandprovidefeedbacktoimprovetheImplementationGuide.Ø ParticipateinthePREPInitiativeplanningandimplementation.Ø CollaborateandconsiderparticipatingintheNSFNoyceProposalthatwillbesubmitted

byinFall2016.Ø Exploreandimplementstrategiestodiversifypoolofteachercandidatesandmore

effectivelyimpactissuesofequityandsocialjusticeinschoolsettings.Ø ParticipateinthebuildingofaRecruitmentResourcesCollectionwiththenewMTEP

onlinecommunicationandcollaborativeworkplatformwiththeAAASTrellissite:http://www.trelliscience.com


86

SecondaryTeacherRetention&InductioninDiverseEducationalSettings1

LinktoPromoSheet

MeganTaylorTrellisEducation

[email protected]

JamesMartinezCaliforniaStateUniversity

[email protected]

[email protected]

OverviewoftheSTRIDESRACWorktoDate

Halfofallteachersleavetheprofessionwithinthefirstfiveyears.Thisrateisevenhigherformathematicspositionsinhighpovertyschools(Fantilli&McDougall,2009;Goldringetal.,2014).Furthermore,withhalfofallcurrentteachersintheU.S.retiringinthenextfiveyears(Foster,2010),enrollmentinteacherpreparationprogramsdeclining,andteacherturnovercostingAmerica$7.3billionannually(NationalMath+ScienceInitiative,2013),themathematicsteachingcrisisisofmajorproportion.Thiscrisisleadstomanyunderpreparedmathematicsteachersandhasaprofoundeffectonhowwellpreparedourstudentsaretobesuccessfulinhighschool,collegeandbeyond.Expertsagreethataddressingthemathematicsteachingcrisismeaningfullywillrequirebuildingamorecohesivesystemofteacherpreparation,support,anddevelopment(Mehta,Theisen-Homer,Braslow,&Lopatin2015).

TheSecondaryTeacherRetention&InductioninDiverseEducationalSettings(STRIDES)ResearchActionCluster(RAC)addressesMathematicsTeacherEducationPartnership(MTE-P)GuidingPrinciple8:StudentRecruitment,Selection,andSupport.Teacherpreparationprogramsactivelyrecruithighqualityanddiverseteachercandidatesandmonitor/supportthemastheycompletetheirprograms.SincetheinceptionofMTE-P,thenationalproblemofretainingsecondarymathematicsteacherswithintheprofessionhasbeenapriority.ThispriorityledtoaproposaltoformaRACfocusedonretentionatthe2013MTE-PAnnualConference,butwasnotacteduponinordertofocusfirstonrecruitment.TheMarketingforAttractingTeacherHopefuls(MATH)RACwasformedwiththischarge.Afewyearslater,therecruitmenteffortwasrekindled,andtheSTRIDESRACbeganitsworkbycreatingthedriver

1TheRACPromoSheet,presentedduringtheopeningoftheconferencetoreportoncurrentactivitiesoftheRAC,canbefoundafterthereferencelist.


87

diagramshowninFigure1,basedonareviewofrecentliteratureonretention.TheaimstatementanddriversincludesupportforearlycareerteachersandProfessionalLearningCommunities,andcallfortheexaminationofschoolstructuresandprofessionalpathwaystosupport/retainteachers.

Figure1.STRIDESdriverdiagram.

MembersofSTRIDESdecidedearlyonthattheworkoftheRACmustfocusonunderstandingandprovidingsupportforbothpre-serviceandearlyin-serviceteachers,giventhesignificanceofacohesivecontinuumofprofessionallearningonteachergrowthandretention.Thus,tolaunchearlyinitiativesaimedatimprovingteacherretentionrates,STRIDESmembersdesignedasurveyinsummer2015togatherpreliminarydataonthenatureandqualityofprofessionalsupportforpre-service,1st,2nd,and3rdyearteachers.Specificresearchquestionsguidingthiseffortwere:Whatistheperceivedscope,natureandimpactofprofessionalsupportforearlycareermathematicsteachers?;andHowdoesthis(a)changeasteachersprogressintheirteachingcareerand(b)relatetohowlikelyitisateacherwillremainteaching?Researchersfromthirteeninstitutionsandsecondarymathematicsteachersfromfourschooldistrictsdesignedthepilotsurvey,called“ReflectiononProfessionalActivities.”Thissurveywascreatedthroughaniterativedesignandvettingprocess,havingstemmedfromadiscussioncenteredonresearch-basedreasonsthatteachersleavethefield.


88

Thesurveyaskedparticipantstospecifyactivitiesthathavehelpedthemgrowprofessionally,andthedegreetowhichtheseactivitieswereworthwhiletothem,allowingSTRIDEStobetterunderstandthedegreetowhichearly-careermathematicsteachersarebeingsupportedbyprofessionallearningopportunities,professionallearningcommunities,andadministrators.Also,instructionalcontext(i.e.public,private,etc.)datawascollected,aswellaswhethertheearlyserviceteachersservestudentsfromspecialpopulations(i.e.specialeducation,EnglishLanguageLearner,gifted).Participantestimationsregardingthedegreethatspecificprofessionaldevelopmentactivitieschangedtheseteachers’practices,aswellasthelevelof“inspiration”theseactivitiesinvoked,weresurveyed,allowingresearcherstodiscernconnectionsbetweenthesetwomeasures.Qualitativeresponsesallowedsurveyparticipantstoprovideadditionaldetailsregardingtheirsupportsystems.Finally,thedegreethattheparticipantsfeltthattheiradministratorssupportthemprofessionallywasmeasured,includingsupportinspecificareas(e.g.assessment,instruction,curriculum,classroommanagement,collegialcollaborationandcourseassignments/loads).

WorkoftheSTRIDESRACatthe2016AnnualMeeting

AttheFifthAnnualMTE-PConferenceinGeorgia,STRIDESmembersanalyzeddatafromthepilotsurveywithtwogoals:(1)Createarevisedsurveythatcouldbesenttoearly-careerteachersacrosstheMTE-Pnetwork3-4timesinthe2017-18yeartounderstandprofessionalsupport,and(2)Todevelopintervention(s)targetingprofessionallearningandsupportforearly-careerteacherstolaunchinAugust2016.Thegroupanalyzedpilotsurveydatawithrespecttorespondents’(N=66)reportsofprofessionallearningandsupport,andtheimpactontheirteaching.Further,asubsetofthosesurveyedrespondedtwice(N=19)allowingforconsiderationofthechangeinthesereportsovertime.

Toanalyzethedata,STRIDESmemberssplitintothreegroups,eachwithadistinctlens:natureandimpactofprofessionallearningactivities,natureandimpactofparticipationinprofessionalcommunities,andthenatureandimpactofsupportfromadministrators.Eachgroupexaminedqualitativeandquantitativeresponses,summarizedkeythemesandquestionsforthegroup,andpostedkeyinferencesonpostersaroundtheroom.Basedoneachinference,individualRACmembersbrainstormedwayswemightrevisethesurveyforfullimplementationinFall2016andwayswemightmakeearlycareerteachers’professionallearningandsupportmoreeffective.Fromthiscollectionofideasthegroupdistilledthree,keychangeideas:(1)theneedforlong-term,collaborativegroupsforearly-careerteacherstoparticipatein,(2)aclearerroleofsite-basedadministratorsandcolleaguesinsupportingthesecollaborativegroups,and(3)theneedtotrainandsupportthementorssupportingtheseearly-careerteachers.

STRIDESRACmembersself-selectedintooneofthesethreegroupstocreatePDSAcyclesthatwouldguideearlyinterventionsinFall2016.ThechangeideaandquestionseachgroupwillbegintoaddressareprovidedinTable1.


89

Table1Changeideaandguidingquestions.

ChangeIdea DescriptionofChangeIdea WhatWeWanttoLearn

1. Long-TermCollaborativeGroupsforEarlyCareerTeachers

Teachercollaborativegroupsthatfocussustainedattentionononeteachingpracticeforearlycareerteacherscansupportasenseofprofessionalismandprofessionalimprovementforearlycareerteachers.

Howcancollaborativeteachergroupsbesupportedtoengageinsustainedattentiontoaparticularteachingpracticethatearlycareerteacherscangrowin?Howdoesparticipationinacollaborativegroupdevelopasenseofaccomplishmentinrelationtotheselectedpractice?Whatstructureofcollaborativegroupcreatesapositiveperceptionabouttheirprofessionandfutureprofessionaltrajectory?

2. RoleofAdministratorsandSite-BasedColleagues

Supportadministratorsbycreatingacommonvisionandusingstrategiestoreinforceretentionofearlycareermathematicseducators.

Whattargetedsupportsforadministrators’impactteacherretention?

3. Training&SupportingTeacherMentors

Doestrainingmentorsaffectteacherretention?

Canmentorteachersusethelearningcycle(seebelow)tofacilitateearlycareer(pre-servicethrough3rd)teachersenactingthe8coreteachingpracticesdefinedbyNCTM?

Conclusion

TwoprimaryconclusionsoftheSTRIDESRACfromthe2016annualmeetingwerethatsupportingearly-careermathematicsteacherretentionwillinvolveacohesiveeffortacrossteachers’entranceintoandearlyyearsintheprofession,andthepreparationandsupportprovidedtonewmathematicsteachersbyteachereducators,mentors,coaches,administrators,andcolleaguesmustbemorecohesive.Thethreechangeideasforbettersupportingearlycareerteachers(seeTable1)distilledfromthepilotdataaresymbiotic;early-careermathematicsteachersneedtoparticipateinprofessionalcommunitiescomposedofothernewteachers(ChangeIdea1),needtargetedsupportfromadministrators,colleagues,andmentors(ChangeIdea2),andthesementorsneedtrainingonmentoringthatsupportsmathematicsteacherdevelopmentandretention(ChangeIdea3).MembersoftheSTRIDESRACwillworkduring2016-17insmallergroupstoimplementPDSAcyclesbasedonthesechangeideasattheirrespectiveinstitutions.Additionally,aRACsubcommitteeisrevisingthesurveyanddisseminatingtoalargerparticipantpoolthreetimesduringthe2016-2017academicyear.TherevisedsurveywillinformSTRIDESmembersastheyengageinthePDSAcyclesthattargetretentioneffortsforsecondarymathematicsteachers.


90

References

Barnes,G.,Crowe,E.,&Schaefer,B.(2007).Thecostofteacherturnoverinfiveschooldistricts:Apilotstudy.NewYork,NY:NationalCommissiononTeachingandAmerica’sFuture.Retrievedfromnctaf.org/wp-content/uploads/CTTFullReportfinal.pdf

Fantilli,R.D.,&McDougall,D.E.(2009).Astudyofnoviceteachers:Challengesandsupportsinthefirstyears.Teachingandteachereducation,25(6),814-825.

Foster,E.(2010).Howboomerscancontributetostudentsuccess:EmergingencorecareeropportunitiesinK-12education.Washington,DC:NationalCommissiononTeachingandAmerica’sFuture.Retrievedfromwww.metlife.com/assets/cao/foundation/JobsEducationPaper3-5-10.pdf

Goldring,R.,Taie,S.,&Riddles,M.(2014).Teacherattritionandmobility:Resultsfromthe2012-13teacherfollow-upsurvey.Firstlook.NCES2014-077.Washington,DC:NationalCenterforEducationStatistics.Retrievedfromnces.ed.gov/pubs2014/2014077.pdf

Mehta,J.,Theisen-Homer,V.,Braslow,D.,&Lopatin,A.(2015).Fromquicksandtosolidground:Buildingafoundationtosupportqualityteaching.Boston,MA:HarvardGraduateSchoolofEducationTransformingTeachingProject.Retrievedfromwww.totransformteaching.org/wp-content/uploads/2015/10/From-Quicksand-to-Solid-Ground-Building-a-Foundation-to-Support-Quality-Teaching.pdf

Watlington,E.,Shockley,R.,Guglielmino,P.,&Felsher,R.(2010).Thehighcostofleaving:Ananalysisofthecostofteacherturnover.JournalofEducationFinance,36(1),22-37.

MTE-Partnership Solicitation for Participation in the planned

STRIDES: Secondary Teacher Retention & Induction in Diverse Educational Settings

April, 2016

Problem Addressed Guiding Principle 8: Student Recruitment, Selection, and Support The teacher preparation program actively recruits high-quality and diverse teacher candidates into the program, and monitors and supports their success in completing the program. Since the inception of MTE-P, the national problem of retaining secondary mathematics teachers within the profession has been a priority. A RAC on retention was proposed at the 2013 Conference, but not implemented because recruitment was determined to be a higher priority at the time. From review of the earlier White Paper, the previous RAC proposal, and more recent literature on retention, the driver diagram below is proposed with an aim statement and drivers that include support for early career teachers, PLCs, and the need to examine school structures and professional pathways.

General Approach

Who We Are (Current Working Group) ➢ APLU

o Howard Gobstein ➢ Auburn University

o Gary Martin ➢ California State University

o Nancy Barker o Eric Hsu o James Martinez (co-leader) o Fred Uy

➢ East Central Texas o Laura Wilding o Jennifer Whitfield

➢ Georgia State University o Pier Junor Clarke

➢ South Dakota o Nicol Reiner o Jami Stone

➢ Trellis Education o Megan W. Taylor (co-leader)

➢ University of Cincinatti o Bob Ranau

➢ University of Kentucky o Lisa Amick (co-leader) o Craig Schroeder

➢ University of South Carolina o Ed Dickey (initial organizer)

Current Progress

After a recent survey of partnership members, a significant interest in teacher retention and

induction was assessed, so a working group made up of partners expressing a strong interest in the topic was formed. The working group reviewed prior literature and recommendations to analyze the retention problem in the context of Secondary Mathematics Teachers, to understand the current problem space, and devise a new driver diagram.

From the driver diagram, a research question was selected, “What is the perceived scope, nature and impact of professional support for early career mathematics teachers, and how does this (a) change as teachers progress in their teaching career and (b) relate to how likely it is a teacher will remain teaching?” With this question in mind, researchers from thirteen institutions nationwide and secondary mathematics teachers from four school districts, all part of the MTE-P, designed a pilot survey called “Reflection on Professional Activities.” This survey was created through an iterative design and vetting process that extended from the fall of 2014 throughout early 2016. The survey stemmed from a discussion centered on research based reasons that teachers leave the field. A brainstorming session followed the discussion, clustering those reasons into categories, and those categories eventually became the main components of the survey (professional activities, support, job satisfaction, etc.). This survey was edited numerous times during face to face discussions of the research group, virtual meetings, and finally feedback from early career teachers who will soon be

completing the survey. The current data collection tool is a 20-item survey asking participants – secondary mathematics teachers in their first, second, or third year of teaching – to reflect on the degree to which the professional learning activities and communities they participate in (e.g., working with a mentor, attending a professional conference, being a Noyce Scholar) increases their enthusiasm for teaching mathematics and influences their ability to facilitate student learning. Additionally, participants are asked to describe the role of administrators, universities, and school structures (e.g., teaching load) on these self-reports, and their satisfaction with teaching and likelihood to continue teaching. The survey was recently distributed nationwide in March of 2016 to begin the pilot study. Changes and refinements will continue to be made after the first round of preliminary data is collected to improve the quality and functionality of the survey.

In order to better understand the degree to which early-career mathematics teachers are being supported by: 1) professional development, 2) professional learning communities and 3) administrators, the survey allows participants to specify activities that have helped them grow professionally, and the degree to which these activities were worthwhile to them. Additionally, since the survey is longitudinal, responses can be measured over time, allowing the researchers to understand how these teachers are supported throughout their early service (preservice, 1st, 2nd, or 3rd) years. This measure will allow for correlations to be explored regarding the level of professional support these teachers receive based on years of teaching experience. Also, instructional context (i.e. public, private, etc.) data will be collected, as well as whether the early service teachers have students from special populations (i.e. special education, English Language Learner, gifted) in their classrooms. Surveyed early-career teachers will provide data regarding the level of support they receive from a range of professional learning communities (PLCs), including on- and off-site groups, professional organizations (e.g. NCTM), and on-line groups. Participant estimations regarding the degree that specific professional development activities changed these teachers’ practices, as well as the level of “inspiration” these activities invoked, will be surveyed, allowing researchers to discern connections between these two measures. Qualitative responses are provided in the survey which allows survey participants to provide additional details regarding their most meaningful PLCs. Finally, the degree that the participants feel that their administrators support them professionally is measured, including specific areas (e.g. assessment, instruction, curriculum, classroom management, collegial collaboration and course assignments/loads). The survey ends with an estimation of: 1) their overall level of satisfaction in their teaching, 2) whether they would choose the profession again knowing what they have learned so far, and 3) how long they plan to remain in the teaching profession.


In spring 2016, each, current member of the STRIDES RAC sent the pilot survey to a few, select early career teachers, with a solicitation to complete it twice: March and June. This pilot data will be analyzed by the STRIDES RAC working group in the summer annual meeting to (a) iterate the survey for longitudinal use, (b) make initial hypotheses about the kinds of professional learning activities early service teachers in our partnership are engaging in and and the impact of these activities on their practice, and (c) design initial interventions to launch in fall 2016. It is the goal of the STRIDES RAC to assure that, by July 1, 2022 at least 85% of the program’s early-service teachers employed in partner school districts begin a third year of employment as mathematics educators. With this goal in mind, it is imperative that data from the STRIDES survey be used to design interventions that support the development of pathways for teachers to enter and thrive in the teaching profession. These pathways will be locally defined by MTE-P schools and their district offices which will support early career teachers in their professional growth. For example, one pathway may provide access to a variety of roles for teachers in the program to provide professional growth opportunities at their

schools, reducing the possibility of early departure. The intent is that all prescribed interventions follow a PDSA (i.e. Plan, Do, Study, Act) cycle, so that measures are recursively re-defined to better suit individual early-career teacher needs. Future ramifications of implementing STRIDES interventions to support the program’s early-career teachers include: 1) establishment of a Network Improvement Community (NIC) model for collaboration-based support of mathematics teachers, 2) documentation of PDSA cycle effectiveness for specific support pathways, and 3) the development of a specific data-gathering instrument for researchers to use/modify for future studies.

95

RESEARCHPRESENTATIONS


96

ExistingMathematicsTeachingPracticesatanHBCU:FoundationsforTeacherPreparation

LaurettaGarrett

[email protected]

AnaTameruTuskegeeUniversity

[email protected]

TheMathematicsTeacherEducationPartnership(MTE-P)seekstotransformthepreparationofsecondarymathematicsteachersthroughseveralavenuesofresearchanddevelopment.OneofthoseavenuesisbeingpursuedbyaresearchcommunitysupportedbyMTE-PthatisknownastheActiveLearningMathematicsResearchActionCluster(ALM-RAC).Activelearninginvolvesastudent-centeredpedagogyinwhichstudentsareencouragedtoreasonaboutthought-provokingproblems(Smith,2015).ThegoalistoraisestudentthinkingtohigherlevelsofBloom’staxonomy(Krathwohl,2002)insettingsthatencouragethemtodiscussmathematicswitheachotherandtocommunicateaboutanddefendtheirmathematicalthinking—tobe“active”mentallyandsociallyinthelessonandintheclassroomlearningcommunityratherthantobepassivelylisteningtoalecture(Diederich,2010;Smith,2015).

Higher-levelofthinkingisthinkingthathappensintheanalysis,synthesis,andevaluationofatopic(TeachForAmerica,2011).Whydowewantstudentsengageinhigher-levelthinking?Wewouldlikestudentstoremembermathematicalideaslongerandmoreclearly.Ifstudentsengageinhigher-levelthinking,theycanhaveanincreasedabilitytoretainandapplymathematicalknowledge(Garrett,2014;NCTM,2009).Considerthedifferencebetweenmemorizingmultiplicationtablesandthedeeperunderstandingthatcomesfromconnectingthoseoperationstodifferentwaysofthinkingsuchasanareamodel(NCTM,2000).Suchconnectionsbuildawebofunderstandingthathelpsstudentsaccessanduseknowledge(VandeWalle,Karp,&BayWilliams,2015).

Thequalitiesofassessmentsusedinmathematicscoursesareconnectedtothetypeoflearningstudentswillexperienceaswellasthetypeofinstruction.Inthetraditionallecture,studentstypicallyselectananswerorrecallinformationtocompleteanassessment.Anassessmentalignedwithhigher-levelthinkingisessentialifstudentsareexpectedtoengageinsuchthinkingindifferentclassroomandassignmenttasks.Aninstructorcanidentifythetaskthatneedstobemasteredandthenacurriculumcanbedevelopedthatwillenablestudentstoperformthosetaskswell(McDonald,1992).


97

TheoreticalFoundation:TheExamCharacterizationFramework

TheExamCharacterizationFramework(ECF)wasdevelopedaspartoftheMathematicalAssociationofAmerica’seffortstoprovideempiricalevidenceforbestpracticesincollegemathematicsinstruction(Tallman,Carlson,Bressoud,&Pearson,2016).IntheireffortstocharacterizethenatureofcollegeCalculus1finalexams,Tallmanetal.formulatedtheirownevaluationframework,theECF,followinganextensivereviewofexistingframeworksandassociatedliterature.Theyconstructedtheirframeworkthrough“12cyclesof...codingexamitems[on5CalculusIfinalexams,]refining[the]characterizationofECFconstructsandrecodingitems”(p.4).

TheFramework.Thisdevelopmentalworkresultedinthree“itemattributes”thatareusedtodescribethequalitiesofexamitemsandtherebydescribethequalitiesoftheexam(Tallmanetal.,2016,p.7).Itemorientationreferstothetypeofthinkingthatisneededforeachexamitem.Itemrepresentationreferstothetypeofrepresentationspresentinthestatementoftheproblemaswellasthetypeofrepresentationsneededtosolvetheproblem.Itemformatreferstowhetherornottheitemismultiplechoice,shortanswer,orabroadopen-endedproblemandwhetherornottheitemrequiresanexplanation.

Itemorientationwasbrokendownintosevenlevels.Intheirstudy,Tallmanetal.(2016)foundthatonlythefirstfivelevelswerepresentintheCalculus1finalexamstheyexamined.Theyprovidedexamitemexamplesintheirreportforeachofthefirstfivelevelstofacilitatetheuseoftheframeworkbythosewishingtocharacterizethelevelofcognitivedemandpresentinexaminations.Thosefirstfivelevels,remember,recallandapplyprocedure,understand,applyunderstanding,andanalyzearedescribedinTable1andexamplesgivenofsomeofthebehaviorsthatwillbeexpectedofstudentsfromthosetypesofexamitems.Levelsix,notfoundintheexamsTallmanetal.,lookedat,wasevaluate,whichinvolves“mak[ing]judgments...checkingandcritiquing”(p.9).Levelseven,alsonotfound,wascreate,whichinvolvesassembling,producing,generatingandplanningusingmathematicalideasinwaysthatcreatenewpatterns.Levelsfive,six,andsevenwereinformedbyKrathwohl’s(2002)discussionofBloom’sTaxonomy.

TheirStudy.Oncetheyhadausefulframework,Tallmanetal.(2016)examinedasampleof150Calculusfinalexamsrandomlydrawnfrom253usedduringthe2010-2011academicyearat253differentuniversities.Thesampleof150wascomprisedofabout62%fromnationaluniversities,23%fromregionaluniversities,9%fromcommunitycolleges,5%fromnationalliberalartscolleges,and1%regionalcolleges.TheselectedexamswerecodedwiththeECFuntiltheresultsstabilized,whichoccurredafterabout100exams.AnalysisshowedthattheCalculus1finalexamshadlowlevelsofcognitivedemandanddidnotaddressthekeyideasofthecourseinawaythatallowedstudentstoshowunderstanding.Ofthe3735


98

individualexamitemstheycoded,about85%wereatthetwolowestlevelsofexamorientation,rememberingorrecallandapplyingprocedures.

Table1LevelsofItemOrientation(Tallman,etal.,2016)

Level Description Examplebehavior

Remember Theonlyrequirementistheretrievalofinformation,nottheuseorunderstandingofit.

Statingatheorem

Recallandapplyprocedure

Whenstudentsareaskedtouseaparticularprocedure,theycanremembertheprocedureanduseit.Theyneednotunderstandwhyitworksorunderwhatconditions.

Useanamedformulatosolveagivenproblem.

Understand Studentsmustprovideexplanations,demonstratetheirreasoning,orinotherwaysshowthattheyunderstand.

Interpretingthemeaningofamathematicalconstructasappliedtoareal-worldcontext.

Applyunderstanding

Studentsarenotprovidedwithinformationastowhatformulaortheoremtoapply.Theymustdecidebaseduponunderstanding.

Areal-lifeapplicationproblemthatmakesclearthesituationandneededresultwithoutstatinganythingaboutthetechniquestousetosolvetheproblem.

Analyze Studentsmustbreakdowncomplexideasand“explainhowcomplexideasareconnected”(p.11).

Anessayinwhichstudentsdescribehowonemathematicalconceptisconnectedtoothers.

Connections.Thisreportprovidesinformationthatwillhelpinstitutionstoevaluatetheassessmentstheyareusingintheircollegecoursesandraisethecognitivelevelofthesummativeassessmentsused.Itisourbeliefthatteachingalignedwithsuchassessmentswillencourageanactivelearningpedagogyinthecollegemathematicsclassroom.Itisourexpectationthatfuturesecondarymathematicsteachersandotherswhotakesuchcourseswilllearntothinkcritically,toseehowteachingforhigherlevelthinkinglooks,andwillbebetterequippedtohelptheiranystudentstheymayhaveengageinhigherlevelthinking.


99

Results

Aspartofanefforttocollectbaselinedataregardingcurrentpractices,weaskedfacultymembersinamathematicsdepartmentataHistoricallyBlackUniversityintheSouthernUnitedStatestoprovidesamplesoftheexamstheyusedinPrecalculusandCalculus.Wewantedtoknowthelevelofthecognitivedemandoftheexamitemsusedinthesecourses.Eightfacultymembersrespondedandprovided15exams:3finalexams,6Precalculusunitexamsand6Calculusunitexams.Ofthe6Calculusexamsprovided,twowereremovedfromouranalysissothatanyindividualfacultymemberwouldnothaveprovidedmorethan2examstothesample.Anindividualcoder,usingthefirstfivelevelsoftheItemOrientationframeworkoftheECF,codedthe6Precalculusunitexamsandthe4Calculusunitexams.TheexamplesprovidedbyTallmanetal.(2016)werecomparedwithitemsonthesampleexams,aswereverbaldefinitionsoftheitemorientationlevels.ThisanalysisprovidedasnapshotofthelevelofcognitivedemandofPre-CalculusandCalculusunitexamsatoneHBCU.

Precalculus.Atotalof102itemson6Precalculusexamswerecoded.Ofthoseitems,3werecodedasremembering,95werecodedasrecallandapplyprocedure,1wascodedasunderstanding,2werecodedasapplyunderstandingand1wascodedasanalyze.Figure1showsthepercentagesofPrecalculusexamitemsineachleveloforientation.Notethat96%oftheitemswereatlowlevelsofcognitivedemand.

Calculus.Atotalof82itemson4Calculus1examswerecoded.Ofthoseitems,nonewerecodedasremembering,73werecodedasrecallandapplyprocedure,3werecodedasunderstanding,6werecodedasapplyunderstanding,andnonewerecodedasanalyzing.Figure1showsthepercentagesofCalculusexamitemsateachleveloforientation.

Figure1:Levelsofitemorientationseenon6Precalculusexams(left)and4Calculusexams(right)providedbyHBCUfaculty.


100

Notethatthepercentageofhigherlevelorientation(HLO)fortheCalculusexamsisbetterthanforthePrecalculusexams(11%HLOCalculusvs.4%HLOPrecalculus),butstilllowerthanthenationalaverageforCalculusfinalexams(15%HLO).

Conclusion

ThelevelofitemorientationforthosefacultymemberswhosubmittedexamswashigherforCalculusby7%thanitwasforPrecalculus.Precalculusstudentswererarelyexpectedtothinkabovethelevelsofrememberingorrecallingandapplyingprocedures.AlthoughPrecalculusmaybeseenprimarilyasaprecursortoCalculusandpreparatoryofthealgebraicskillsCalculusstudentswillneed,thereneedstobemoretothecoursethanbuildingalgebraicproficiency.Anyhigher-levelthinkingaskedofstudentsinPrecalculuswillhelpbuildtheirabilitytoconnectmathematicalideas,retainthoseideasandengageinhigher-levelthinkingskillsinotherareasofstudy.Thisisparticularlyimportantifinstructorswishtoproducecriticalthinkersthatwillbeabletocontributetobeneficialinnovationsintheirprofessionalfields(Tyler&Cruz,2016;Wagner,2011).

Talkingandlistening,oneofthefourbasicelementsofActiveLearning,willchangethepassivelearningfromourstudentsbyhavingmoreparticipationinthelecture,andinteractionwiththeirclassmates.Thesewillimprovethelevelofthinking,ournextstepsincludeincreasingawarenessinthemathematicsdepartmentofthelevelsofthinkingcurrentlybeingexpectedofourstudents,encouragingimplementationsthatseektoraisethelevelofthinkingexpected,andconductingresearchthatprovidesevidenceastotheeffectofthoseimplementations.Oncechangehasbeguninthemathematicsdepartment,itisexpectedthatrecruitmentworkcanbemoreeffectiveasweseektoincreasethenumberofstudentsatourinstitutionmajoringinsecondarymathematicseducation.Trackinginstitutionalchangeattheuniversityofthisstudycanalsoprovideevidenceforthoseseekingtoencouragechangeattheirinstitutions.

References

Diederich,K.B.(2010).Theevolutionaryconformationfromtraditionallecturetoactivelearninginanundergraduatebiologycourseanditseffectsonstudentachievement.PhDDissertation:NorthDakotaStateUniversity.

Garrett,L.(2014).Adultstudents’openinteractionswithtechnology:Mediatinghigher-levelthinking.InternationalJournalofEducationinMathematics,ScienceandTechnology,2(1),1-10.

Krathwohl,D.R.(2002).ArevisionofBloom’staxonomy:Anoverview.TheoryIntoPractice,41(4),212-218.

McDonald,J.P.(1992).Dilemmasofplanningbackwards:Rescuingagoodidea.TeachersCollegeRecord,94,152-169.

NCTM.(2000).Principleandstandardforschoolmathematics.Reston,Virginia:NCTM.


101

NCTM.(2009).Focusinhighschoolmathematics:Reasoningandsensemaking.Reston,Virginia:NCTM.

Smith,W.(2015).Transformingprecalculusinstruction:EvidencebasedcoursedesignDBERSpeakerSeries,Paper76.Lincoln,Nebraska:UniversityofNebraska-Lincoln.

Tallman,M.A.,Carlson,M.P.,Bressoud,D.M.,&Pearson,M.(2016).AcharacterizationofCalculusIfinalexamsinU.S.collegesanduniversities.InternationalJournalofResearchinUndergraduateMathematicsEducation,2(1),105-133.doi:10.1007/s40753-015-0023-9

TeachForAmerica(2011).LearningTheory:Chapter5:Teachinghigher-orderthinking.Retrievedfromteachingasleadership.org/sites/default/files/Related-Readings/LT_Ch5_2011.pdf

Tyler,B.D.,&Cruz,L.E.(2016).Competentornot?:Exploringadaptionstotheneo-behavioristparadigminasportmarketingcourse.JournaloftheScholarshipofTeachingandLearning,16(3),23-38.

VandeWalle,J.A.,Karp,K.S.,&Bay-Williams,J.M.(2015).Elementaryandmiddleschoolmathematics:Teachingdevelopmentally(9thed.).Essex,England:PearsonEducationLimited.

Wagner,T.(2011).Teaching,learning,andleadinginthe21stcentury.PaperpresentedattheLearningandtheBrainconference:Preparing21stcenturyminds:Usingbrainresearchtoenhancecognitiveskillsforthefuture,Boston,MA.


102

DevelopingMiddleSchoolPreserviceTeachersKnowledgeofNumberandOperations

RuthmaeSears

[email protected]

FernandoBurgosUniversityofSouthFlorida

[email protected]

Abstract

WewilldescribehowfacultymembersintheCollegeofEducationandtheDepartmentofMathematicsandStatisticscollaboratedtodevelopmiddleschoolpre-serviceteachers’mathematicalknowledgeforteachingrelativetonumberandoperations.Wewillhighlightthenatureofthecollaboration,theactivitiesandassessmentutilized,andimplicationsithadonpreserviceteachers’mathematicaldevelopment.


103

MobilizingEffortsoftheMTE-PHui

LindaVenencianoUniversityofHawai’iatMānoa

[email protected]

DanDoergerAlignmentDirector

Hawai’[email protected]

Abstract

TobuildthenewlyestablishedMTE-PHuiwehavetakenthisfirstyeartolearnaboutthegoalsandactivitiesofeachofourrepresentedgroups.WehaveidentifiedcommonalitiesamongourprogramsthatwillhelpuspromotetheMTE-PHuiasaplatformtomediatecollaborationandfosteractionstowardachievingoursharedvision.Ourinitialenergiesarefocusedintwoareas––increasingaccesstocollegecredit-bearingmathematicscourses,andrampinguprecruitmentininitialteacherlicensureSTEMprograms.InthispresentationwewillshareeffortsunderwayforstatewiderestructuringandaligningcommunitycollegemathcoursesattheMATH100andlowerlevels.WewillalsoshareourrecruitmentplansforrecastingtheimageofmathematicsteachereducationtoanimagethatincludesSTEMteachereducationandethnomathematics.Feedbackfromtheattendeeswillbeencouraged!


104

ADeeperLookataCalculusIActivity

LanceBurgerCaliforniaStateUniversityFresno

[email protected]

MaratMarkinCaliforniaStateUniversityFresno

[email protected]

Abstract

AsaresultofNSF-fundedcourseredesigneffortstoimplement,promoteandresearchactivelearninginintroductorycalculus,thispaperdiscussesaderivativesketchingactivityforCalculusI.Pilotresearchindicatesthatoverly-qualitativeapproachestotheactivityoftenleadtocertainincorrectstudentgraphs.Afterrevealingadeeperlookatthemathematicsbehindtheactivity,thepaperexploresanapproachtomoderatingthelessoninawaythatleadsstudentstoadeeperunderstandingbyactivatingfamiliarpre-requisiteknowledge,withoutrequiringmathematicsbeyondtheirzonesofproximaldevelopment.

Introduction

Thisbriefpaperfocusesononecourseredesignapproachforfirst-yearcalculusresultingfromcollaborationswiththeMathematicsFLOK(FacultyLearningforOutcomesandKnowledge)groupatFresnoState.Keyelementsofthisredesignphilosophyarebasedontwoprinciplesinspiredfrommathematicseducationliteratureaswellaswritingsincognitivepsychologyandresearchonanalogicaltransferinlearning(Harel,2007):

1. TheNecessityPrinciple:“Forstudentstolearnwhatweintendtoteachthem,theymusthaveaneedforit,where‘need’referstointellectualneed,notsocialoreconomicneed.”(pp.275-276)

2. TheRepeatedReasoningPrinciple:“Studentsmustpracticereasoninginordertointernalize,organize,andretainwaysofunderstandingandwaysofthinking.”(pp.275-276)

Theaboveprinciplesinfluencethewhatandhowtopicsarecoveredinthisreformclassroom.Intermsofimplementation,thesetwoprincipleshavetakenforminthefollowingrecommendationsforcourseredesign.

• Reviewofprerequisitematerialshouldbeavoided.

• Importantideasandproblemsolvingshouldcommenceassoonaspossiblesothattheirpracticecaninducerecognitionofpatternstoproblemsolving.


105

• Activelearningisessentialforstudentstoauthenticallyinternalize,apprehendandcommunicatemathematics.

Tounderstandtheredesignrationalefromanotherviewpoint,supposethatanenduringanideasuchasthederivativeconceptisviewedasabicycle.Clearlytherearemanycomponents,yetlookingattheminisolationandaddingmoreandmorecomponentstothepicturedoesnotprovideabicycleuntilthepartslisthasbeencompleted(seeFig.1).

Figure1.Learningtorideabicyclewouldbenearimpossiblefromjusthandlingtheparts(IThinkinPictures,2010).

AWholeceptisacognitivestructure,arrangement,orpatternofmathematicalphenomenasointegratedastoconstituteafunctionalunitwithpropertiesnotderivablebysummationofitsparts.

TheWholeceptdefinitionwasoriginallyinspiredfromTall’s“precept”notionwhichblursthedistinctionbetweenprocessesandconcepts;butasreflectiononteachingwasrefined,FritzPerls’gestalttherapywritingsinformedtheneedforadynamicelementsimilartothegestaltforeground/backgroundprocessofconflictresolution(Grey&Tall,1994;Perls,1973).AccordingtoPerls,ifcognitivedifficultyisintheforeground,thenonecannotproceeduntilthedifficultyisresolvedandmadetoretreattothebackgroundsothatprogressioncanbemadetodeeperconflictresolution(seeFig.2).Inthisrespect,realconflictinstudentlearningisnotduetolackofunderstandingofprerequisitematerial,butrathertotheneedforacoherentpictureofthe“relevance”ofanyparticularmathematicaltopictheyarebeingrequiredtolearn;hence,theaboverecommendations.

Figure2.Rubin’s(2001)famousillustrationoffigure-groundperception.


106

TorestatethisintermsofHarel(2007),violationoftheNecessityPrincipleconstitutesafundamentalroadblocktolearning.Thewholeceptrepresentsmathematicalknowledgethatismore“found”thanconstructedthroughadynamicprocessofgradualconflictresolutionanddiscovery.Inthissense,thephilosophicalunderpinningsofthisemergenttheoryofmathematicallearninghavePlatonistunderpinnings,ratherthanbeingpurelyaconstructivistviewoflearning.Mazur(2008)elegantlycapturesthisviewpointinthefollowingquote:

WhenI’mworkingIsometimeshavethesense—possiblytheillusion—ofgazingonthebareplatonicbeautyofstructureorofmathematicalobjects,andatothertimesI’mahappyKantian,marvelingatthegenerativepoweroftheintuitionsforsettingwhatanAristotelianmightcalltheformalconditionsofanobject.AndsometimesIseemtostraddlethesecamps(andthisrepresentsnocontradictiontome).Ifeelthattheintensityofthisexperience,thevertiginousimaginings,theleapsofintuition,thebreathlessnessthatresultsfrom“seeing”butwherethesightsareofentitiesabidinginsomerealmofideas,andthepassionofitall,iswhatmakesmathematicssosupremelyimportantforme.(p.20)

Figure3describestheconventionalapproachtoapprehendingawholecept,suchasthederivativewholecept,bybuildingupfromthebasics,linearly,untilthederivativecaneventuallybedefinedandexamplescanfinallybeginwhichemployandconnectthepreviouslylearnedmaterialtothemaintopic.Acentralweaknessofthisapproachisthatstudentsoftenhaveverylittletimepracticingproblems,reasoningandcommunicatingideasrelatedtothe“bigpicture,”whichcancontributetopoorexamperformanceandretentionofthematerial.ThisisrepresentedbythefaintnessofthefinallargecircleinFigure3.

Figure3.Unilinearconceptformation—learningtorideabikebybuildingitonepieceatatimeandthentryingtorideonlywhencompleted.

Instarkcontrast,Figure4depictsaveryfaintinitialpictureoftheentirewholeceptwhich,byrepetition,becomesmoreandmorecleartoapointofeventualmastery.NotethattheFinalcircleinFigure4isasdarkasthesmallestlow-levelcircleinFigure3,implyingthatthederivativewholecepthasnowbecomeafunctionalunitapplicabletoamuchlargerpicture.

ToillustratehowtheseideascouldbeappliedtoCalculusI,onecouldbeginwiththederivativewholeceptinitsentiretyonthefirstdayofclass,andthencontinuallypullinthe


107

“necessary”conceptswhichareneededtomakeitwork,sotospeak,sothatrichproblemsarisingfromthederivativewholeceptcanbeginandrepeatedassoonandaslongaspossible.

Figure4.Wholeceptresolution—takingalongertimetorepetitivelylearntorideafunctioningbike.

Throughthisrepetitivemantraofrich-structureproblemsolving,conceptssuchastheone-sidedandtwo-sidedlimit,continuity,graphs,slopes,functionsandtangentlinesstarttohaverenewedmeaning.Further,thisallowsforthestudenttoresolveissuesofcontentrelevancy,whichmaynowretreattothebackground,sothatconnectionscanberecognizedandlarger-scaleproblemsolvingpatternspracticedandlearned.Next,anactivityinderivativesketchingisdiscussedwhichisoneofmanyweeklyactivitiesusedintheinfusionofactiveearningincalculusatFresnoState,incollaborationwiththeBoulder-OmahaActiveLearningAlliance(2015).

ActivityDescription

Theinitialproblem:Coffeeisbeingpouredataconstantratevintocoffeecupsofvariousshapes.Sketchroughgraphsoftherateofchangeofthedepthℎ’(𝑡)andofthedepthℎ(𝑡)asafunctionsoftime𝑡(seeFig.5).

Figure5.Thecylindricalcup.

Thetwocupshapesdiscussedinthispaperarethecylindricalandfrustumshapedcups.Ininformalterms,mostallstudentsoverthreesemestersofimplementationproducequalitativelycorrectgraphsforthestraight-sidedcup(seeFig.6).

Figure6.Cylindricalcupstudentsolutions.

Slant-sidedcup.Incontrast,fortheinvertedfrustumcupmostallstudentsproduceincorrectgraphsfor(𝑡, '('))(seeFig.7).Inthefollowingsection,themathematicsbehindtheserelatedrategraphsisdiscussed;however,itshouldbeemphasizedthatthestudentsparticipatinginthisactivityarenotexpectedtounderstanditatthedepthtobediscussed.An


108

importantaimofthemathematicaltreatmentgiveninthispaper,though,istocautionagainstoverlyqualitativeapproacheswhenadeeperunderstandingofthemathematicsbehindanactivitycangreatlyinformpedagogy.

Figure7.Typicalstudentsolutionsofslant-sidedcup.

ADeeperLook

Lookingmorecloselyatthecylindricalcupwithbaseradius𝑟+,wecansafelyconcludethatsincethevolume𝑉(𝑡)ofcoffeeinthecupincreasesataconstantrate,thensodoesitsdepth.Hence,ℎ′(𝑡) ≡ ℎandℎ(𝑡) = ℎ𝑡(thecupbeingemptyinitially,i.e.,ℎ(0) = 0).

𝑉(𝑡) = 𝜋𝑟+3ℎ(𝑡)

Differentiatingbothsidesrelativeto𝑡

𝑉4 𝑡 = 𝜋𝑟+3ℎ′(𝑡)

andconsideringthat𝑉′(𝑡) = 𝑣,wehave:ℎ’ 𝑡 = 6789

⟶ ℎ 𝑡 = 678;9

𝑡(givenℎ 0 = 0).

AsseeninFigure6,thetypicallycorrectstudentgraphsalignwellwiththemathematics,since(𝑡, ℎ’(𝑡))producesaconstantfunctionhorizontalgraph,and(𝑡, ℎ(𝑡))consistsofalineargraphthroughtheoriginwithpositiveslope.Observethatℎ’(𝑡)isnotthesameas𝑉’ 𝑡 ,althoughthisfactmayeludestudents’attentionwhenonlyaqualitativeapproachisapplied.

Fortheslant-sided(invertedfrustum)cup,let𝑟(𝑡)betheradiusofthesurfaceofcoffee.Then

𝑟(𝑡) = 𝑟0 +𝑚ℎ(𝑡)

withsome𝑚 > 0.

Inthiscase,itappears“natural”tothinkofℎ’(𝑡)asalinearfunctionbasedonthelineardependenceoftheradius𝑟(𝑡)onthedepthℎ(𝑡)whichleadstotheconclusionthatℎ’(𝑡)isalinearfunctionandℎ(𝑡)isquadratic.Butasweshallsee,thisdescribedqualitativeapproachfailsthetestbymathematicssincebytheconicalfrustumvolumeformula,thevolumeofcoffeeinthecupattime𝑡isgivenby:

𝑉(𝑡) = ?@𝜋 𝑟+3 + 𝑟+𝑟 𝑡 + 𝑟3 𝑡 ℎ(𝑡).


109

Insteadofdifferentiatingbothsidesoftheaboveequationrelativeto𝑡,whichwouldmakethingsmoreconvoluted,weconsiderthat𝑉’(𝑡) ≡ 𝑣immediatelyimplies𝑉’ 𝑡 = 𝑣𝑡(with𝑉 0 = 0);hence,ℎ(𝑡)istobefoundfromthecubicequation:

𝑚3ℎ@ 𝑡 + 3𝑚𝑟+ℎ3 𝑡 + 3𝑟+3ℎ 𝑡 − 3𝑣𝑡/𝜋 = 0.

AsrecalledintextssuchasBoyerandMerzbach(1991),thegeneralformulafortherootsofsuchanequationinthiscaseyieldsℎ(𝑡)explicitlyas

ℎ 𝑡 = − ?@D9 3𝑚𝑟+ + −27𝑚@𝑟+@ − 81𝑚I𝑣𝑡/𝜋J .

Hence

ℎ(𝑡) = 𝑎(𝑡 + 𝑏)?/@+c

withsome𝑎; 𝑏 > 0and𝑐 < 0suchthatℎ 0 = 𝑎𝑏?/@ + 𝑐 = 0and

ℎ4 𝑡 = P@(𝑡 + 𝑏)Q3/@.Eq.[1]

Letting𝑎 = 𝑏 = 1and𝑐 = 1satisfiestheinitialconditionsandproducesqualitativelyaccurategraphsforℎ(𝑡)andℎ′(𝑡)(seeFig.8)

Figure8.Frustumcupgraphs.

TheExponential-SidedCup.AsaCalculusIIextensionofthepreviousanalyses,thediskmethodperformedonanexponential-sidedcuphighlightsthemathematicaldepthlyingbehindthisactivitywhenanalyzingvesselswhicharewidening(ornarrowing)(seeFig.9).

Figure9.Flat-bottomexponential-sidedcupgeneratedbyrevolving𝑦 = 𝑒Taroundthe𝑥axis𝑥 → 0toℎ > 0.


110

Usingthedisk-methodfrom0toℎandemployingtheprevioustechniqueletting𝑉′(𝑡) ≡ 𝑣and𝑉(𝑡) = 𝑣𝑡,

𝑉 𝑡 = 𝜋 𝑒TW+ 𝑑ℎ = 7Y9(

3− 7

3= 𝑣𝑡.

wherebysolvingforℎgives

ℎ(𝑡) = ?3𝑙𝑛 36\

7+ 1 .

Forasimplerpicture,let𝑣 = 73whichbecomes

ℎ(𝑡) =12 𝑙𝑛(𝑡 + 1)

andthendifferentiatingbothsidesrelativeto𝑡wehave

ℎ′(𝑡) =1

2(𝑡 + 1)

resultingingraphsqualitativelysimilartotheslant-sidedcupgraphs(seeFigs.8&10).

Figure10.Exponential-sidedcupgraphs.

FacilitatingTransfer:KnowntoUnknown

Afirstplacetostartwhendebriefinggroupsofstudentsonthisactivitycanbeginwithcollaborativediscussionsabouttheirinterpretationsoftheirgraphs.Forexample,lookingbackattheslant-sidedstudentsolutiongraphs(seeFig.7),aftersomegoodquestioningstudentscanarriveattheconclusionthattheincorrectgraphs(𝑡, ℎ′(𝑡))don’tmakesensesincetheyimplythattherateofchangeoftheheighteventuallybecomes0.Afactcontradictingthe

constantfillingofthecup,andmoreoverifcontinued,]W]\becomesnegativeimplyingtheheight

functionisdecreasing.

Onapositivenote,studentscanalsoreflectonthefactthattheir(𝑡, ℎ(𝑡))graphsusuallydomakesense,sincetheystartat0andincrease,yettherateofincreaseslowsdownasseenbythetangentlinestothegraphbecomingmorehorizontalandapproachingzero,consistentwiththeassumptionofconstantfillingofanincreasinglywideningcupofcoffee.So


111

thequestionremains,howcanstudentsarriveatcorrect(𝑡, ℎ’(𝑡))graphsgiventhemathematicstheyknow?Analogicalproblemconstruction(APC)refersto“lettingstudentsconstructtheirownanalogousproblems,…[which]allowstheproblemsolvertousehisorherownknowledgeandexperiencestocreatetheanalogicalproblemelements”(Bernardo,2001,p.138).InamathematicsstudyonAPC,Bernardo(2001)foundthat,

Onecanusearatherstructuredtask,andstillallowstudentstoexploreandengagetheinformationinmathproblemsenoughtoleadthemtodeeperlevelsofunderstandingoftheproblemswhichincreaseanalogicaltransferperformance.(pp.147-148)

ThispaperconcludeswithsomestructuredexamplesforhowAPCcanbeinducedinthecontextofthisactivity.

Conclusion

Promotinganalogicalproblemconstructioninthecontextofthiscalculusactivitycanbeginbyaskingstudentstocollaborativelyproducefamiliarfunctionsthatresembletheir(𝑡, ℎ(𝑡))graphs.Afterdiscussionandconcensus,theycanbeaskedtofindthederivativegraphsofthesefamiliarfunctionsandcomparethemtothosemadeinthecupactivity.Asanexample,thefollowingtwofunctionsarefamiliartomoststudentsandhavegraphsthatmatchtheinitialconditionsandhavethesamequalitativeshapesastheircorrectlyproduced(𝑡, ℎ(𝑡))graphs:

• ℎ(𝑡) = 𝑡

• ℎ(𝑡) = 𝑙𝑛(𝑡 + 1)

Atthispointinthecoursematerial,calculusstudentscaneasilytakethesederivativesandsketchtheirgraphs(seeFigs.11&12),andthencomparethemtotheonestheyproduced.Importanttopicssuchasconcavitycanbediscussedaswellassubtleties,suchasthedifferencebetweenFigures8and11,whereinFigure11the(𝑡, ℎ’(𝑡))graphappearstobeinfiniteat𝑡 =0;illustratingthedegeneratecasewhenthefrustumisacone(seeEq.[1],andconsiderwhen𝑏 = 0).

Figure11.(𝑡, ?3 \)graph.


112

Asthisactivityisdoneattheendofthesemester,whenanti-differentiationhasbeencovered,thepreviouslineofquestioninginvolvinggraphingthederivativeoffamiliarfunctionsof(𝑡, ℎ(𝑡))canbereversedtothecaseoffindingfamiliarfunctionstotheir(𝑡, ℎ’(𝑡))graphs,andexploringproblematicalissuesassociatedwithgraphsoftheiranti-derivatives.

Figure12.(𝑡, ?\^?)graph.

Forexample,thefollowingtwofunctionshavethesamequalitativeshapesastheirtypicallyincorrect(𝑡, ℎ’(𝑡))graphs(seeFig.7):

• ℎ’ 𝑡 = −2𝑡 + 3

• ℎ’ 𝑡 = −𝑡3 + 2

Recallingtheinitialconditionthatℎ(0) = 0thenforbothantiderivatives𝐶 = 0;hence,

−2𝑡 + 3𝑑𝑡 = −𝑡3 + 3𝑡 + 𝐶 = −𝑡3 + 3𝑡

−𝑡3 + 2𝑑𝑡 =𝑡@

3 + 2𝑡 + 𝐶 =𝑡@

3 + 2𝑡

Theanti-derivitivecomputationsproducetheabovenon-sensicalgraphs,whichmaypromoterichdiscussionsastheyareproblematicalforavarietyofreasons,onebeingtheyimplytheheightincreasesthendecreases,againcontradictingtheassumptionofconstantfillingofthecoffeecups,(seeFigs.13,14).

Figure13.Anti-derivativegraphforℎ’ 𝑡 = −2𝑡 + 3.


113

Figure14.Anti-derivativegraphforℎ 𝑡 = −𝑡3 + 2.

Insummary,althoughactivelearningcanandshouldinvolvefun,interactiveandconcretewaystoexploremathematicalconcepts,adeeperunderstandingandexplorationoftheunderlyingmathematicsbytheinstructorshouldnotbeavoided,asitcanholdthekeystounlockinglatentstudentknowledgealreadylyingdormantwithin.

References

Bernardo,A.(2001).Analogicalproblemconstructionandtransferinmathematicalproblemsolving,EducationalPsychology,(21)2,137-150.

Boulder-OmahaActiveLearningAlliance.(2015,December23).Activelearningmaterialsforcalculus.Retrievedfrommath.colorado.edu/activecalc

Boyer,C.B.&Merzbach,U.C.(1991).AHistoryofMathematics.NewYork:Wiley.

Gray,E.&Tall,D.(1994).Duality,ambiguityandflexibility:Aproceptualviewofsimplearithmetic.JournalforResearchinMathematicsEducation,26(2),115-141.

Harel,G.(2007).TheDNRsystemasaconceptualframeworkforcurriculumdevelopmentandinstruction.InR.Lesh,J.Kaput,E.Hamilton(Eds.),FoundationsfortheFutureinMathematicsEducation(pp.263-280).Mahwah,NJ:Erlbaum.

IThinkinPictures.(2010,August15).WhatdoesitmeantobeaGestaltlearner?[Blogpost].Retrievedfromvisuallygifted.wordpress.com/2010/08/15/what-does-it-mean-to-be-a-gestalt-learner

Mazur,B.(2008).MathematicalPlatonismanditsopposites.EuropeanMathematicalSocietyNewsletter,68(June),pp.19-22.

Perls,F.(1973).TheGestaltapproachandeyewitnesstotherapy.PaloAlto,CA:ScienceandBehaviorBooks.

Rubin,E.(2001).Figureandground.InYantis,S.(Ed.),VisualPerception(pp.225-230).Philadelphia,PA:PsychologyPress.


114

TeachingCollegeGeometryusingGeometryMODULE(S2)

LipikaDeka

[email protected]

Abstract

TheGeometrymodulesdevelopedbytheMODULE(S2)ResearchActionClusterwasadoptedandimplementedtoourCollegeGeometrycourse,Math329atCaliforniaStateUniversity,MontereyBayduringFall2015.OurCollegeGeometrycourseisdesignedforMathematicsmajorsinthesubjectmatterpreparation(Teaching)concentration.ThiswasthefirsttimeweadoptedpedagogyforourGeometrycoursethatfocusedonpreparinghigh-qualitymathematicsteacherstoteachthenewgenerationofstudentsinCaliforniaschoolsundertheCommonCorestandards.Earlierourcoursewastaughtasacontent-basedmathematicscourseinatraditionalway.Therewerethreemodulesinthisnewmodels,eachfollowedaninquirybasedlearningapproachthatrequiredagoodamountofreading,writingandself-explorationbystudentsinsideandoutsideofclassroom.Thecoursealsorequiredgroupworkonclassactivitiesandoutsideclassassignmentsalongwithpeerreviewsofeachother’swork.ThiswasaverynewapproachforourGeometrystudents.Inthispresentation,wewilldiscusshowweadoptedandimplementedthemodulesforourstudentsandhowstudentslearnedGeometryinanewwaythatpreparedthemtobeeffectivemathteachers.Wewillsharehowourstudentsreactedtothemodules,ourchallengesteachingthecourseanddiscussifthisapproachmadeanydifferenceinpreparingfuturequalitymathematicsteachers.


115

GeometryTeachingKnowledge:AComparisonBetweenPre-Serviceand

HighSchoolGeometryTeachers

ShawndaSmithCaliforniaStateUniversityBakersfield

[email protected]

Abstract

ThisstudycomparesGeometryTeachingKnowledgebetweenpre-serviceandhighschoolgeometryteachers.DatawascollectedviaanonlineMKT-GassessmentdevelopedbyHerbstandKosko(2014),apost-assessmentsurvey,andinterviewsofthreepre-serviceteachersandfourhighschoolteachers.Furthermore,thisstudyalsoinvestigateswherethisknowledgeisdeveloped.Pre-serviceteachersdidnotperformaswellasthehighschoolgeometryteachersinallofthedomains:GeometryContentKnowledge,SpecializedGeometryKnowledge,KnowledgeofGeometryandStudents,andKnowledgeofGeometryandTeaching.Whencomparisonsweremaderegardingexperiencesinpre-serviceteachereducationcourses,pre-servicegeometrycourses,highschoolteacherprofessionaldevelopmentopportunities,currentgeometryclassrooms,andidealclassroomsofbothpre-serviceandcurrenthighschoolteachers,therewerestatisticallysignificantdifferences.ThisstudyprovidesinsightintothedomainsofGeometryTeachingKnowledgethatcouldbeusedinmakingdecisionsregardingpre-serviceteachereducationprogramsandhighschoolgeometryteacherprofessionaldevelopment.


116

RepurposingtheMCOP2ObservationProtocoltoSurveyStudents’ViewsofanActive

LearningCourseRedesign

[email protected]

WendyM.SmithUniversityofNebraska-Lincoln

[email protected]

ThegoaloftheActiveLearninginMathematicsResearchActionCluster(RAC)istostudytheprocessbywhichlowerdivisionuniversitymathematicscoursescanberedesignedtoengagestudentsinactivelearningpracticessuchasforminghypotheses,creatingmathematicalmodelsanddiscussingtheirideaswithothers.AswithmanyotherMathematicsTeacherEducationPartnership(MTE-P)initiatives,implementingthisvisioninvolvessuccessivePlan-Do-Study-Act(PDSA)cycles(Bryk,Gomez,Grunow,&LeMahieu,2015).Thispaperreportsononesuchcyclethatfocusedondevelopingasurveyinstrumenttomeasurestudents’perceptionsofactivelearningopportunitiesbytransformingtheMathematicsClassObservationPracticesProtocol(MCOP2;Gleason,Livers,&Zelkowski,2015)fromateacherobservationtooltoastudentsurvey.

TheproblemwewereaddressingwasthatwhilewehadaPlanandwerereadytoDothework,wedidn’thaveawaytoStudyourimplementation.OurPlanwastodevelopweeklymodelingprojectsthatwouldhighlightreal-worldapplicationsoftheseeminglyabstractfunctionsstudiedinPre-Calculus.InordertoDothis,wehadtoworkwithouradministrationtoaugmentthelargelecturesectionswithsmallbreakoutsectionscappedat30students,andtodeviseweeklylabsthatwouldincludeopportunitiesforactivelearning.OurStudyofthisworkinvolvedrepurposingtheMCOP2observationprotocol(Gleason,&Cofer,2013)intoastudentsurveysowecouldgetapictureofwhatthestudentsthoughtaboutthelabsandmeasurethedegreetowhichtheselabsactuallyengagedstudentsinactivelearningpractices.TheconclusiontothispaperdescribeshowweplantoActtorefineourredesigneffortsinfuturesemesters.

Background

Oneofthemorefar-reachingandcomprehensivestudiesdocumentingtheeffectivenessofactivelearninginuniversityscience,technology,engineeringandmathematics(STEM)courseswasconductedbyFreemanetal.(2014).Intheirmeta-studyof225researchpapersdescribingactivelearninginvarioussettings,theauthorsconcludethatstudentperformance


117

onfinalexamsandotherconceptualtestsincreasedbyalmost.5standarddeviationsinclasseswithactivelearningversustraditionallecturing.Inaddition,otherstudieshavefoundthatactivelearninghavedemonstrateddecreasedfailurerates(Henry,2010),improvedstudentengagement(Freemanetal.,2014),persistenceintakingsubsequentcoursesinthePrecalculustoCalculusIIsequence(Laursen,2013)andimprovedattitudestowardmathematicsforfemaleandunder-representedpopulations(Laursenetal.,2014).Whileallofthesestudiesuseddifferentmeasuresofsuccess(finalexamgrades,persistence,andstudentattitudes,respectively),noneofthestudiesactuallymeasuredthedegreetowhichthestudentsperceivedtheywereengaginginactivelearning.Ourgoalwastodevelopameasureofthestudents’perceptionofactivelearningandtrytoidentifythe“valueadded”betweenthelectureandactivelearninglabsfromthestudents’pointofview.

Description

TheMCOP2toolwasdevelopedtohelpresearchersmeasurethedegreetowhichclassroompracticesalignwithvariousteachingreformdocumentssuchastheStandardsforMathematicalPractice(NationalGovernorsAssociationCenterforBestPractices&CouncilofChiefStateSchoolOfficers,2010).Wechosethistoolbecauseitfocusesonmanyaspectsofactivelearningandbecauseithasbeenproventobebothreliableandvalid(Gleason,Livers&Zelkowski,2017).However,itsusealsoposessomechallenges.First,itisresource-intensiveduetotheneedtotrainandpayobservers;inourcasetheobserverswouldhavetoobserveatleastfivelecturesand32breakoutsectionsmultipletimesacrossasemester.Second,itonlycapturessnapshotsofthelessonsobserved,andislimitedtotheobserver’sperspective.Inordertocapturethestudents’perspectivesoverthecourseofthesemester,wemodifiedthetooltobeusedasastudentsurvey.Althoughonecouldarguethattrainedobserversmightbemoreastuteatseeingopportunitiesforparticipationthanstudents,ourhypothesiswasthatifstudentsdonotseeanopportunityforengagement(evenifonemayexistintheeyesoftheobserver),thentheyarenotdevelopingthemetacognitiveawarenessneededtoengageinthesepracticesastheyprepareformorechallengingcourses.

Ourmethodinvolvedthreestages:(1)modifyingtheprotocolandadministeringitonlinetoallstudentsenrolledinthecourse,(2)analyzingthemodifiedprotocolbyconductingaconfirmatoryfactoranalysis,and(3)analyzingstudents’surveyresponses,includingtotheopen-endedresponsestoquestionsregardingtheirenjoymentofvariouslabs.Duringthemodificationprocess,weattemptedtolimittheamountoftimestudentsneededtospendansweringitemsbyrewordingtheitemstoaccommodateboththelectureandlabsettings.Wecutthe16MCOP2itemsinhalf,toasktheeightquestionsmostrelevanttostudentexperiences,butthenaskedeachquestiontwice:onceaboutstudents’experiencesinlectures,andoncefortheirexperiencesinthelabs.Thus,forexample,question1wasstatedasfollows,“Duringmylectureclass,studentsengagedinexploration/investigation/problemsolvingabout


118

howmuchofthetime?[regularly,sometimes,seldom,never]”.Question2read,“Duringmylabclass,studentsengagedinexploration/investigation/problemsolvingabouthowmuchofthetime?[regularly,sometimes,seldom,never]”.Thus,allodd-numberedquestionsrefertolecturewhileeven-numberedquestionsrefertolabs.Theeightpairsofitemsaskedstudentsaboutengagementinexploration/investigation/problemsolving,useoftools,timetoworkonquestions,discussionofsolutionstrategies,perseverance,conceptuallinkswithinthemathematics,mathematicalmodeling,andprecisemathematicallanguage.

Duringthesecondphaseofthiswork,weaskedallstudentstotakethesurveyonline.Ofthe706studentsenrolledin6sectionsofthecourse,wereceived504completedsurveys—overa70%responserate.Thisreturnrateissignificantenoughtoclaimthattheresultsarerepresentativeofmoststudents.Weexaminedthestudents’answerstotheopen-endedquestionsbydeterminingthemostcommoncommentsandputtingthemtogetherincategories.

Theanalysisofthestudentresponsesinvolvedconductingaconfirmatoryfactoranalysistogaugethedegreetowhichourstudents’answersalignedwiththeMCOP2factorsthatGleason,LiversandZelkowski(2015)foundwhentheyusedanexploratoryfactoranalysistoestablishthereliabilityoftheMCOP2.Theirinitialfactoranalysisrevealedtwosubscales:TeacherFacilitationandtheStudentEngagement.Theteacherfacilitationsubscale(Cronbachalphaof0.850)measuresthedegreetowhichtheteacherplanslessons,promotesproblemsolving,andfacilitatesclassroomdiscourse.Thestudentengagementsubscale(Cronbachalphaof0.897)measuresthedegreetowhichstudentsengageinthelearningprocess.

Results

TheresultsoftheconfirmatoryfactoranalysisrevealedthattheMCOP2studentsurveydidhavethesamefactorstructureastheoriginalobservationtool(TeacherFacilitationandStudentEngagement).ThefiveitemschosenfromtheTeacherFacilitationscaleandthreeitemsfromtheStudentEngagementscaleloadedontoseparatescalesfortheMCOP2survey.However,withinthetwoexpectedfactors,twoadditionalfactorsalsoemerged:LABandLECTURE.Thus,the16totalitemscouldbesplitintofourfactors:TeacherFacilitation-Lab(5),Teacher-Facilitation-Lecture(5),StudentEngagement-Lab(3),StudentEngagement-Lecture(3).Allfourfactorshadgoodmodelfitaccordingtomodelfitindices(Chi-square,CFI,TLI,RMSEA,andSRMR).Inaddition,allfactorloadingsandR2coefficientswerestatisticallysignificant.

ThemodalresponsesforthelectureandlabareshowninFigure1.Ascanbeseen,thestudentsratedthelabshigherineverycategorythanlectureintermsofofferingopportunitiesforactivelearning.Thetwoareasthatshowedthegreatest“valueadded”wereexploringsolutionpathways(Cohen’sdeffectsizeof.51)anddiscussionofsolutionstrategies(Cohen’sdeffectsizeof.43).


119

Figure1.ModalresponsesonmodifiedMCOP2fromstudentreportsofactivelearninginlectureandlabclasses.

Theopen-endedresultsindicatedthatover70%ofstudentswereeitherhappyorveryhappywiththelabs.Inparticular,manyofthemnotedtheirrelevancetoreallife.Forexample,onewrote“Ienjoytheactivelabswhereyouhavetogetupandcollectdatabyinteractingwithothers.Itactuallymakesmathsemifun.”

Conclusion

Thisstudyrevealedtwokeyfindingsthatwillinformourworkgoingforward.First,theMCOP2studentsurveydoesalignwiththefactorsusedtovalidatetheMCOP2protocol,andhenceappearstobereliable;sincethelargerRAChadalreadydeterminedtheMCOP2observationinstrumenttobeavalidmeasurealignedprojectgoals,asubsetoftheseitemsposedasasurveywouldretainthatvalidity.Second,thesurveyisusefulforidentifyingwhatstudentsbelievearespecificvalue-addedaspectsofactivelearningthatthelabsoffertoaugmentlecture.

ThisworkimpactsourinstitutionbecauseweareintheprocessofredesigningtheentirePrecalculustoCalculus2sequence.Hence,wewillbeabletousetherevisedsurveyinallthreecoursestomeasuregainsinactivelearning.TheworkcontributestoMTE-PbecauseitoffersasecondusefortheMCOP2toolformemberswishingtoreportstudents’perspectivesandperhapscompareresultswiththoseoftrainedobservers.

OurnextstepsforconcludingthisPDSAcyclearetoACTasfollows:(1)revisethewordingofthesurveytomakeitmore“studentfriendly,”(2)comparestudentresultswithoutsideobservers,(3)shiftsomeofthechoicesfromestimationsofpercentofstudentengagementtomeasuresofpersonalengagement,and(4)comparesurveystudentsinlecture-onlyclassesversusthosewhohavebothlectureandlabclasses.Furthermore,otheruniversitiesparticipatingintheActiveLearningMathematicsResearchActionClustermaybegin


120

tousetheMCOP2surveytobetterunderstandtheirstudents’experiencesinreformedmathematicsclassrooms.

ForMoreInformation

• Formoreinformationand/ortoobtainacopyofthesurvey,pleasecontactJanetBowersatSanDiegoStateUniversity–[email protected]

• Formoreinformationabouttheconfirmatoryanalysismethodology,pleasecontactWendySmithatUniversityofNebraska-Lincoln–[email protected]

• TheoriginalMCOP2surveyanddocumentationcanbefoundonline:jgleason.people.ua.edu/mcop2.html

References

Bryk,A.S.,Gomez,L.,Grunow,Al.,&LeMahieu,P.(2015).Learningtoimprove:HowAmerica’sschoolscangetbetteratgettingbetter.Boston:HarvardEducationPublishing.

Freeman,S.,Eddy,S.L.,McDonough,M.,Smith,M.K.,Okoroafor,N.,Jordt,H.,&Wenderoth,M.P.(2014).Activelearningincreasesstudentperformanceinscience,engineering,andmathematics.ProceedingsoftheNationalAcademyofSciencesoftheUnitedStatesofAmerica,111,8410-8415.[Abstractavailableatwww.pnas.org/content/111/23/8410.abstract]

Gleason,J.,&Cofer,L.(2013).Mathematicsclassroomobservationprotocolforpracticesresultsinundergraduatemathematicsclassrooms.InT.Fukawa-Connelly(Ed.),Proceedingsofthe17thAnnualConferenceonResearchinUndergraduateMathematicsEducation,Volume1(RefereedArticles),93-103.

Gleason,J.,Livers,S.D.,&Zelkowski,J.(2015).Mathematicsclassroomobservationprotocolforpractices:Descriptorsmanual.Retrievedfromjgleason.people.ua.edu/mcop2.html

Gleason,J.A.,Livers,S.D.,&Zelkowski,J.(2017).MathematicsClassroomObservationProtocolforPractices(MCOP2):Avalidationstudy.InvestigationsinMathematicsLearning,TBD.

Henry,R.(2010).AnassessmentofSTEMfacultyinvolvementinreformofintroductorycollegecourses.JournalofCollegeScienceTeaching,39,74-81.

Laursen,S.L.(2013).Frominnovationtoimplementation:Multi-institutionpedagogicalreforminundergraduatemathematics.InD.King,B.Loch,&L.Rylands(Eds.),ProceedingsofLighthouseDELTA2013(pp.102-112).Kiama,Australia:UniversityofWesternSydney,SchoolofComputing,EngineeringandMathematics.Retrievedfromdelta2013.net/documents/ConferenceProceedings.pdf

Laursen,S.L.,Hassi,M-L.,Kogan,M.,&Weston,T.J.(2014).Benefitsforwomenandmenofinquiry-basedlearningincollegemathematics:Amulti-institutionstudy.JournalforResearchinMathematicsEducation,45(4),406-418.

NationalGovernorsAssociationCenterforBestPractices&CouncilofChiefStateSchoolOfficers.(2010).CommonCoreStateStandardsforMathematics.Washington,DC:Authors.Retrievedfromwww.corestandards.org/Math


121

ActiveLearningMathematicsattheUniversityofNebraska-Lincoln

WendyM.Smith

[email protected]

OneofthetoptwogoalsoftheMathTeacherEducationPartnership(MTE-P)istoincreasethequantityofsecondarymathematicsteacherspreparedatthepartnerinstitutionsby40%.Suchanincreasenecessarilyinvolvesmoreundergraduatesinterestedinmathematics.Typically,beforeundergraduatesbecomemathematicsmajors,theytakeoneormorefreshman-levelmathematicscourses(precalculustocalculus2).However,in1987mathematiciansreportedthat“asmanyas40%ofundergraduateswerefailingintroductorycalculus,andeventhosewhopasseddidnotappreciatethesubject’srelevance”(Wilson,1997,p.A12).Morerecently,theCharacteristicsofSuccessfulProgramsinCollegeCalculus(Bressoud,Carlson,Mesa,&Rasmussen,2013)showedfailurerates(gradesofD,ForWithdraw)rangedfromanaverageof25%atPh.D.-grantinguniversitiestoanaverageof37%atregionalcomprehensiveuniversities.Thus,improvingstudents’experiencesinfreshman-levelmathematicscoursesisalogicalprerequisitetoincreasingthenumberofundergraduateswhoseektobecomemathematicsteachers.

Inrecentyears,researchoverwhelminglyhasshownthatactivelearningstrategiesareeffectiveatincreasingstudentsuccessinundergraduatescienceandmathematicscourses(e.g.,Bressoud&Rasmussen,2015;Freemanetal.,2013;Laursenetal.,2011;2014),particularlyforunderrepresentedgroupsofstudents.Thus,theMTE-PchosetofocusoneofitsfiveinitialResearchActionClustersaroundActiveLearningMathematics(ALMRAC).TheDepartmentofMathematicsattheUniversityofNebraska-Lincoln(UNL)wasoneofthefoundingmembersofthisALMRAC,havingalreadybeguneffortstoimproveprecalculuscourses.ThemathematicsdepartmentalsoembracedtheMTE-PNetworkedImprovementCommunity(NIC;Bryketal.,2015;Martin&Gobstein,2015)model.WorkingaspartoftheALMRAChasallowedUNLtoacceleratecourseimprovementsbybuildingonthelearningofotherALMRACinstitutions.Further,thepositiveresultsofimplementingactivelearninginprecalculushasinstitutionalizedthesepracticesatUNL.

UNLutilizestheALMRACdefinitionofactivelearning:WedefineALMasteachingmethodsandclassroomnormsthatpromote:(1)students’deepengagementinmathematicalreasoning,(2)peer-to-peerinteraction,and(3)instructorinquiryintostudentthinking.In


122

support,thecurriculumshouldfocusonkeymathematicalideas,includingtheuseoftasksthatpromotesensemakingandproceduralfluency.Studentactivityshouldfavoropportunitiesforthemtoproposequestions,communicatereasoning,andsharesolutionsinprocess.Instructoractivityshouldshowcasepracticesthatpromotestudentengagementandbuildonstudentthinkingtoadvancethemathematicalagenda.ThisclassroomdescriptionisrepresentedinFigure1.

Figure1.Classroom-levelALMfeatures.

Adoptinganactivelearningapproachtoinstructionisonlyonecomponentofalargerinstitutionaltransformationtoimprovestudentsuccessinmathematics.Besidesfacultyleadership,activecampusanddepartmentalleadershiparealsocriticaltosuccessfulinstitutionalizationofALM.Departmentscommittedtoinstitutionaltransformationattendtostudentdata,particularlyplacementdata,studenttrajectoriesthroughcourses,andstudentsuccess.Inadditiontoeffectiveleadershipandintellectualresources,physicalresourcessuchasclassroomfurnitureandclassminutesperweekalsocancontributetoorhinderinstitutionaltransformation—representedinFigure2.UNLhascommittedtoinstitutionalchangeatthedepartmentalandclassroomlevels.TheoverallpurposeofthisbriefreportistosummarizetheUNLeffortstotransformfreshman-levelmathematicscoursesandraisestudentsuccess.

Background

TheresearchteamatUNLcollectsextensivedataeachsemesteraboutthestudentsintheprecalculusandcalculuscourses.ThisbriefreportfocusesondocumentingtheinstitutionalchangesatNebraska,drawingmainlyonthequantitativedatacollectedaboutstudentsandcourses.UNLjoinedtheBigTenin2011,andstartedtofocusonraisingthesix-yeargraduationratesandfreshmanretentionrates.AtUNL,overtwo-thirdsoffreshmentakeamathematicscourseintheirfirstsemester;nootherdepartmentevengarnershalfoffirst-timefreshmen


123

enrollment.Thus,freshmenretentioncorrelatesveryhighlywithpassingprecalculusandcalculusmathematicscourses.

Figure2.Department-levelALMfeatures.

AtUNL,fallenrollmentinmathematicscoursestendstobeapproximatelydoublethatofspringenrollment.InFall2015,approximately1,500studentstookoneoffourtypesofprecalculuscourses,andapproximately2,000studentstookcalculus1or2.PrecalculuscoursesatUNLinclude:IntermediateAlgebra(3credithoursbutdoesnotcountasmathematicscredits),CollegeAlgebra(3credithours),Trigonometry(2credithours),andCollegeAlgebra&Trigonometry(5credithours;theunionoftheprevioustwocourseslisted).

Table1RelevantparametersofActiveLearningMathematicscontextatUNL

UNL–BytheNumbers(Fall2015)AllStudents 25,260Undergrads 20,182FirstTimeFreshmenAverageACTScore 25.2University-wideFreshman/SophomoreRetention 82.5%6-yeargraduation 67.0%MathGTAs 77MathTenure-trackFaculty 29


124

MethodstoImproveFreshmanSuccessinMathematics

Withsubstantialvariationacrosssections,historicalsuccessrates1inCollegeAlgebraandCollegeAlgebra&Trigonometry(2007-2011)hoveredinthelow-60%range.Thefirsteffortstoimprovethesecoursesinvolvedanemporiummodel,inwhichstudentsworkedattheirownpacethroughmaterialsinacomputerlab,withgraduateteachingassistants(GTAs)availabletoanswerquestions.Thatmodelwasquicklyabandonedin2012,atwhichtimethefocusshiftedtoactivelearningapproaches.

UNLinvestedconsiderableresourcesintoimplementingactivelearning,addressingallofthecomponentsinFigure2.Successratesnowaresteadyataround80%.KeyeffortsincludedFirst-YearMathematicsTaskForce,hiringaPrecalculusCoordinator,strongadministrativeleadershipandphysicalresources,theuseofLearningAssistants,acoursereadinessactivity,andanefforttoimprovestudents’onlinehomeworkexperience.Eachisdiscussednext.

TheFirst-YearMathematicsTaskForcewasafacultycommitteededicatedtoimprovingfreshman-levelmathematicscourses;akeyrolewastoevaluatethequalityanddifficultyoftheexams,toprovideassurancethatimprovedsuccessrateswerenotduetoloweringofmathematicalstandards.Thetaskforcealsomarshalledandmadesenseoflocaldata,tohelpinformtheongoingefforts.

UNLhiredafulltimeassistantprofessorofpracticetoserveascoordinatorforthefourprecalculuscoursesandtooverseethetrainingandongoingmentoringofGTAs.Closecoordinationofthecoursesincludesnotjustasyllabusandcommonexams,butalsodetailedlessonplans,toreinforceamodelofclasstimedominatedbystudentsdoingmathematicsingroups,andengaginginsmall-groupandwhole-classdiscussionstomakesenseofthemathematics.Thefirst-yearGTAsareresponsibleforteachingtheirowncourse(insectionsof40students),andtheyarerequiredtotakeayear-longteachingseminar.Tobalancethisdemand,theGTAs’first-yearteachingassignmentisonecourseeachsemester;inlateryears,GTAsteachtwocoursesinthefallandoneinthespring.

Duetostrongadministrativeleadership,multipleclassroomsoncampuswererenovatedtoincludemoveabletablesandchairs,andwhiteboardsallaroundtheroom,andthendedicatedtohousemathcourses.Additionally,understandingthatactivelearningtakesmoretimethanlecture,whilethecredithoursremainedconstant,theminutesperweekinCollegeAlgebrawereincreasedfrom150to225,andtheminutesperweekinCollegeAlgebra&Trigonometrywereincreasedfrom250to300.

AfinaleffortwastheimplementationofLearningAssistantsintotheprecalculusandcalculusmathematicscourses.Thedepartmenthiresundergraduatelearningassistants,initially

1SuccessheremeansthestudentearnedaCorbetterinthecourse(orPassiftakenpass/nopass).


125

grant-funded,tohelpintheprecalculuscoursesandtoserveasanadditionalinstructortofacilitategroupdiscussions.

Inadditiontotheaboveactivities,theDepartmentofMathematicsalsodecidedtoinstituteatestonthefirstdayofclass,coveringprerequisitematerial,andwhichcanserveasacheckoncourseplacement.Thedepartmentquicklylearnedtocallthisa“coursereadinessactivity”ratherthan“prerequisitemasteryexam”;studentswhodidnotpassonthefirstdaywereallowedtoretakethetestonceperdayfortwoweeksinthecollegetestingcenter.StudentscouldgetreviewpacketsandworkontheseintheMathResourceCenter(tutoringroomstaffedbyGTAsandundergradmathmajors)withtheirinstructororlearningassistant.

Thiscoursereadinessactivitysortedstudentsintothreegroups:thosewhopassedonthefirstday(knowthematerial);thosewhoeventuallypassed(investedtimetorelearnmaterial);thosewhoneverpassed(noobvioustimeinvestment).Mostofthe“neverpassed”groupneverattemptedtotakethetestinthetestingcenteratall.Thiscoursereadinessactivityhasprovedtobeincrediblypredictive.Thoseinthefirsttwogroups(pass/eventuallypass)average80%onthecourseexams(threeexams+final),with75%ofstudentsinthosegroupsearninggradesof75%orhigher.Studentsinthe“neverpassed”groupaveragedunder60%oncourseexams,withnearly75%ofthesestudentsearninggradesbelowaC.AmongthestudentswhodonotpassthecoursereadinessactivityonDayOne,thechancestoretakethetestseemtohelpdistinguishstudents’“collegereadiness”skillsofbeingabletoengageinpositivehabitssuchasstudyingandseekinghelp.

Oncethemathematicsdepartmentrealizedthepredictiveabilityofthiscoursereadinessactivity(Fall2014),thedepartmentsoughttoimplementinterventionswiththe“neverpassed”groupinFall2015.Theinterventionstargetedmathskills,andweresuccessfulinraisingstudentexamaverageshigherthanthepreviousyears’“neverpassed”group,butnottothelevelofthosestudentswhodidpassthisinitialtest.Futureinterventionsmayneedtofindawaytoincorporatebroader“collegereadiness”skills.

Finally,aninternalgrantallowedtwofacultymemberstoimprovetheonlinehomeworkexperienceforstudents.UNLusesWeBWorK,anopen-sourceplatform,todeliveronlinehomeworkassignmentstostudents,asawaytoprovidestudentsopportunitiestopracticewhatislearnedinclass.WeBWorKwasadoptedin2013,followingtheprevioususeofMyMathLab.Studentsgetmultipleattemptsperitem;theonlinesystemallowsstudentstoknowimmediatelyiftheiranswersarecorrect.Yet,knowingananswerisincorrectalmostneverhelpsastudentdeterminehowtocorrectlysolveaproblem.

StudentswereinitiallyfrustratedthatWeBWorKlackedthe“hint”featureofMyMathLab,inwhichastudentcouldseethesameproblem(withdifferentnumbers)workedoutinastep-by-stepfashion.However,thistypeofhintemphasizesprocedurememorization,


126

andthedepartmentwantedtoemphasizeconceptualunderstanding.Thus,throughthisinternalgrant,experiencedGTAsandseveralhighschoolteacherswerehiredtocreatemoreconceptualhintstotargetcommonerrorsormisconceptions.Thesenewhintsweredesignedtobethequestionaninstructorwouldask,orareminderaninstructorwouldgivetostudentswhowerestuckonaproblem,suchastheoneshowninFigure3.

Figure3.SampleimprovedhintofferedintheWeBWorkenvironment.

WeBWorKallowsadepartmenttokeeptrackofproblem-leveldata,sotheDepartmentofMathematicscouldtrackthequestionswithandwithouthints.Studentsearnedmorepoints,onaverage,onhomeworkquestionsthatincludedthesenewhints.Inresponsetoanend-of-semestersurvey,84%ofstudentsreportedusingthehintsatleastonce,and87%ofthosestudentsfoundthehintstobeatleastoccasionallyhelpful,demonstratedinFigure4.Incraftinghints,thegoalwastoaddressthemostcommonmisconceptions,knowingthatthehintswouldnotbeabletocomprehensivelyaddresseverypossiblestudenterror.

Figure4.Resultsofstudentsurveyshowingthedifferenceinhomeworkscoresonproblemswithandwithouthints.

0102030405060708090100

OverallHomeworkMean

HomeworkMean:Hintproblems

HomeworkMean:NoHints

Fall2015Percentage


127

Conclusion

TheresearchteamatUNLcontinuestobeinvolvedintheALMRAC.Withactivelearningwell-established(successfully)inprecalculuscourses,thefocusin2016isonextendingactivelearningstrategiesintocalculus1andcalculus2courses.Inthosecourses,taughtinlarge(150)lecturewithsmall(25-30)recitations,thelecturesarenowinfusedwithnumerousclickerquestions,whichtheinstructorcanfollowupbyhavingstudentsdiscusswithstudentsnearby.Therecitationshaveshiftedfrom100to150minutesperweek,andinsteadofservingastimeswhenstudentswatchaGTAsolvehomeworkproblems,nowtheserecitationsserveastimeforstudentstoworkcollaborativelyonnewproblems.

TheWeBWorKhintsareexpandingtoothercourses(initialfundingfocusedonCollegeAlgebra).Afuturegoalistocreatesomeshortvideohints,inwhichaninstructorgivesaverybrief(lessthan3minutes)lectureaboutthetopic,coveringmoreofthecommonmisconceptions.

Finally,theUNLresearchteamispartofanewgrantfromtheNationalScienceFoundation,titledSEMINAL:StudentEngagementinMathematicsthroughanInstitutionalNetworkforActiveLearning.SEMINALseekstostudytransformeddepartmentslikethoseatUNL,UniversityofColorado-Boulder,andSanDiegoStateUniversity,aswellasdepartmentsatearlierstagesoftransformation,bothinsideandoutsidetheALMRAC.ByfocusingontheNetworkedImprovementCommunitymodel,whatSEMINALlearnsaboutdepartmentaltransformationcanberapidlydisseminatedtotherestoftheALMRAC,aswellastotheMTE-Pmorebroadly,tosupportthepropagationofimprovedstudentsuccess.

ForMoreInformation

• URL–www.math.unl.edu

• Contact–WendySmith,UniversityofNebraska-Lincoln,[email protected]

References

Bressoud,D.,Carlson,M.P.,Mesa,V.,&Rasmussen,C.(2013).Thecalculusstudent:InsightsfromtheMathematicalAssociationofAmericanationalstudy.InternationalJournalofMathematicalEducationinScience&Technology,44(5),685-698.

Bressoud,D.,&Rasmussen,C.(2015).Sevencharacteristicsofsuccessfulcalculusprograms.NoticesoftheAmericanMathematicalSociety,62(2),144-146.

Bryk,A.S.,Gomez,L.,Grunow,Al.,&LeMahieu,P.(2015).Learningtoimprove:HowAmerica’sschoolscangetbetteratgettingbetter.Boston:HarvardEducationPublishing.

Freeman,S.,Eddy,S.L.,McDonough,M.,Smith,M.K.,Okoroafor,N.,Jordt,H.,&Wenderoth,M.P.(2014).Activelearningincreasesstudentperformanceinscience,engineering,andmathematics.


128

ProceedingsoftheNationalAcademyofSciencesoftheUnitedStatesofAmerica(PNAS),111(23).Retrievedfromwww.pnas.org/cgi/doi/10.1073/pnas.1319030111

Kezar,A.,&Gehrke,S.(2015).CommunitiesoftransformationandtheirworkscalingSTEMreform.LosAngeles,CA:PulliasCenterforHigherEducation.Retrievedfrom:www.uscrossier.org/pullias/wp-content/uploads/2016/01/communities-of-trans.pdf

Laursen,S.,Hassi,M.L.,Kogan,M.,Hunter,A.B.,&Weston,T.(2011).EvaluationoftheIBLmathematicsproject:Studentandinstructoroutcomesofinquiry-basedlearningincollegemathematics.UniversityofColoradoatBoulder.Retrievedfrom:www.colorado.edu/eer/research/documents/IBLmathReportALL_050211.pdf

Laursen,S.L.,Hassi,M.L.,Kogan,M.,&Weston,T.J.(2014).Benefitsforwomenandmenofinquiry-basedlearningincollegemathematics:Amulti-institutionstudy.JournalforResearchinMathematicsEducation,45(4),405-418.

Martin,W.G.,&Gobstein,H.(2015).Generatinganetworkedimprovementcommunitytoimprovesecondarymathematicsteacherpreparation:Networkleadership,organization,andoperation.JournalofTeacherEducation,66(5),482-493

Wilson,R.(1997).Adecadeofteachingreformcalculushasbeenadisaster,criticscharge.ChronicleofHigherEducation,43(22),A12-A13.


129

UsingtheMCOP2asaGradeBearingAssessmentofClinicalFieldObservations

JeremyZelkowski

[email protected]

JimGleasonTheUniversityofAlabama

[email protected]

Thedevelopmentandvalidationofobservationprotocolsforlessonsimplementedinmathematicsclassroomsisscarce.Thatistosay,protocolsformentorteachersoruniversitysupervisorstousewhenobservingandscoringpreservicemathematicsteachersarevirtuallyabsentinthefieldofmathematicsteacherpreparation.Departmentalorprogramchecklists,alignedtodiscipline-agnosticstateteachingstandards,aremorecommonlyusedforpreserviceteacherobservations(Brown&Crippen,2016;Caughlan&Jiang,2014;Morrell,Flick,&Wainwright,2004).Becausemanysecondarymathematicsteacherpreparationprograms(SEMA-TPP)arehousedindepartmentsofeducation,secondarymathematicseducatorslocatedinaMathematicsdepartmentmayhavelittleflexibilitywithregardstothedocumentationofgeneralistpractices,dispositions,andstandardscommonacrossdisciplines.Further,theaccreditationunitisoftentheSecondaryTeacherPreparationProgramratherthanthemorediscipline-specificSEMA-TPPs.Toaddtothiscomplication,mostSEMA-TPP’saresmall,providinglimitedopportunitytocollectlarge-scaledatainareasonableamountoftimetodorigorousquantitativeanalyses.

Withinasimilarcontext,theUniversityofAlabama(UA)mathematicseducationfacultydevelopedaresearch-basedobservationprotocolforK-16mathematicsclassroomsusableforcooperatingmathematicsmentorteachers,supervisors,andfaculty.TheMathematicsClassroomObservationProtocolforPractices(MCOP2)wasdevelopedduring2012-15toevaluatealarge,grant-fundedprofessionaldevelopmentproject.TheresearchonthedevelopmentofMCOP2,validation,reliability,andfactoranalysesresultedinstrongfindings.Withouttraining,goodinterraterreliabilityonthetwofactorswasdetermined(IRR=0.669onstudentengagement[SE],IRR=0.616onteacherfacilitation[TF]).Onthetwofactors,SEhadanα=0.897andtheTFhadanα=0.850.Finally,thetwonationalsurveysofexpertsinthefieldproducedastrongexternalvalidationoftheMCOP2(Gleason,Livers,&Zelkowski,2017).

Thisbriefresearchpaperpresentstheresultsfromatwo-yearstudyintheUASEMA-TPPtoaligngradingpracticesoftheMCOP2withpreviousun-validatedgeneralistobservationforms.ThegeneralistobservationformshavehistoricallybeenusedatUAtoaddressstateteacherpreparationstandards,aswellastodeterminelettergradesassignedtolessons


130

conductedbygrades6-12preservicemathematicsteachers.Wesetouttodetermine:(1)WhatgradingscalewouldbeappropriateontheMCOP2andcorrelatewelltothegradesreceivedonthegeneralistobservationform?(2)HowdopreserviceteachersperceivetheMCOP2astheirgrade-determiningobservationprotocol,asopposedtothegeneralistobservationform?(3)DoespreparingpreserviceteacherstoconsidertheMCOP2intheirplanningofformalobservationlessonsimprovethequalityofthelessonsthanpriortotheMCOP2implementation?(4)Whataretheimpactsforbothstudentsandprogramtousethegeneralistformasanon-grade-bearing,end-of-semester,summativeform,andtheMCOP2astheexclusivegrade-determiningobservationprotocolforbothmethodsstudentsandstudentteachers?

InstitutionalTransformationofSEMA-TPPtotheCollege

In2008,thefirstauthorarrivedatUAtoleadtheSEMA-TPPandquicklyjoinedforceswiththesecondauthor,amathematicianresponsibleforthecurriculumofthesecondarymathematicsmajortrack.ApartnershipwascreatedandthesecondarymathematicseducationmajortrackwasalignedtotherecommendationsofTheMathematicalEducationofTeachers(ConferenceBoardoftheMathematicalSciences[CBMS],2001),andlaterTheMathematicalEducationofTeachersII(CBMS,2012)ensued.Changesincludeddevelopingasecondcapstonecourse,revisingthefirstcapstonecourse,insertinganalysisanddifferentialequationsasrequirements,andadjustingtheprogrammingancillarycourse.Ontheeducationside,threemethodscourseswerealignedsequentiallyalongsidethecapstonemathcourses,andstructuredtocreateatwo-yearcohortmodeltodevelophabitsofmindandmathematicalpracticesthatrelatetoteachingmathematicswithqualitytasksinamannerthatmaintainshighlevelcognitivedemand(Stein,Smith,Henningsen,&Silver,2009).

Afewyearslater,thedevelopmentanduseoftheMCOP2spurredtheentirecollegetobegintransformingothersecondaryeducationprograms,withSocialStudiesandEnglishprogramsutilizingstructuressimilartomathematics.TheseinitialtransformationsledtodevelopmentofathirdcapstonecoursethathassincebeenpilotedtwiceandwillbecomepermanentintheFallof2017.ThetransformationoftheSEMA-TPPsince2008,andmorerecentlywiththeMCOP2,hasmovedthepreparationprogramtoapointthatthequalityofourgraduatesandtheirabilitytomodelbestpracticesregularlyhasout-performedanoldphilosophyinwhichthequantityofgraduateswasofgreaterconcern.Initially,resistancecameadministratively,buttheprogramrigor,voluntaryNCTMSPAaccreditationreview,andresearch-baseddesignconvincedotherdisciplinestotransform.Bothprogramqualityandquantityhaveincreasedwithoutreductionofrigor.


131

TheoreticalFrameworkfortheMCOP2

TheMCOP2becameanimportantmechanismtotheSEMA-TPPtocommunicateexpectationsformathematicsinstruction,toprovidefeedbacktosecondarymathematicsstudentsastheydesignedandimplementedlessons,andtoevaluatetheresultsoftheprogram.TheMCOP2wasdesignedtoreflecttheimportantqualitiesofmathematicsinstructionasadvisedbytheprofession.Forexample,conceptualunderstandingfocusesonstudentsdrawing,inferring,andultimatelymakingconnectionsbetweenmathematicaloperations,representations,structure,reasoning,andmodelingthroughengagementwithcontentandthroughdiscourse(Brownell,1935;Hiebert&Carpenter,1992;Hiebert&Grouws,2007;NationalResearchCouncil,2003Resnick&Ford,1981;Skemp,1971,1976).Withthatsaid,apreserviceteacher’slessonwouldnotfitwellwithinagoalforconceptualunderstandingifthelessonfocusedsolelyproceduralfluencyandefficiencythroughinstructionalpracticessuchasdrillworksheetsemphasizingprocedurestobelearnedbyrote.Thispracticemaybebeneficialattimeswithinthelargercontextofmathematicsinstruction,thoughshouldbeneithertheprimarymethodofinstruction;itfailstoengagestudentsindoingandunderstandingmathematicsbeyondproceduralfluency.Furthermore,“thereisnoreasontobelieve,basedonempiricalfindingsortheoreticalarguments,thatasinglemethodofteachingisthemosteffectiveforachievingalltypesoflearninggoals”(Hiebert&Grouws;2007,p.374).

Fromthebeginning,Cohen,Raudenbush,&Ball’s(2003)theoreticalmodelofinstructionasinteractionbetweenteachers,students,andmathematicalcontentguidedthedevelopmentoftheMCOP2frameworkofteachingforconceptualunderstandingthroughvariousformsofinstructionalpractices.TheteambeganwithexaminingthecommonlyusedReformedTeachingObservationProtocol(Sawadaetal.,2010)aswellastheStandardsforMathematicalPractice(SMPs)fromtheCommonCoreStateStandards,whichhavebeenshowntoalignwellwiththeNCTMprocessstandards(Koestler,Felton,Bieda,&Otten,2013).WethenconsideredtheUASEMA-TPPprogramstandards,well-alignedtotheNCTMSpecializedProfessionalAssociation(SPA)standards(NCTM,2012),andassignedconnectionsbetweenthesestandardsandtheCohenetal.(2003)model.AsseeninFigure1,theInstructionasInteractionmodeldevelopedatUApresentsthreenodes,orfactors,whichcouldbedenotedasteacherresponsibilities,mathematicalcontentofthelesson,andstudentengagement.

Atthecompletionoftheaforementionedfactoranalysis(Gleasonetal.,2017),atwo-factorstructureoftheMCOP2wasfound,asopposedtotheinitialdesignofthreefactorsseenintheInstructionasInteractionmodel.ThefinalinstrumentmorecloselyalignswithRogoff,Matusov,andWhite(1996),aframeworkcharacterizedbyacommunityoflearnersinwhichauthorityandresponsibilityaresharedamongstudentsandteachers.Thisisevidentinourmodel(Figure1)byvisualizingbothhalvesoftheovalasdenotedwithadottedline.Theteacherprovidesgoalsandobjectivesofthelessonwhiletargetinglearningandproblem


132

solvingthroughdiscourse.Likewise,theroleofstudentstoengageinthemathematicalcontentofthelessonthroughproblemsolvinganddiscourseisasharedresponsibilitytonurturebothsidesofresponsibilitythatwillincreasethelikelihoodofmathematicallearning.TheMCOP2frameworkandmeasurablefactorsemphasizethatbothteacherandstudenthavesharedresponsibilitieswithinthelearningcommunityofthemathematicsclassroom.

Figure1.InstructionasInteractionmodel(BaseduponCohenetal.,2003).

Methodology

TheSEMA-TPPaimedtoreplaceageneralistsecondaryprogramsformforgrade-bearingobservationsofmethodsstudentsandteacherwithaspecificmathematicsobservationprotocoltargetingbothteacherfacilitationandstudentengagementmeasuresofeffectiveinstruction.1Tosupportthisshiftandsubsequentlyaddresstheresearchquestions,theSEMA-TPPcollectedobservationaldataandsurveydatafortwoyears,duringthe2014-15and2015-16academiccalendars.Observationsofthedeliveryofmathematicslessonsin6-12mathematicsclassroomsbymethodsstudentsandstudentteachersusedbothobservationforms,withtheorderofformcompletionalternatingbetweenobservations.Thismethodwasusedtoincreasethereliabilitybetweenscoresonbothforms,aswellasincreasethevalidityofaccuratelyrecordingtheobservationacrossbothforms(Bryman,2012).Thegeneralistformwasusedinthedeterminationofstudentgrades,andalthoughMCOP2datawascollected,itdidnotimpactgrades.AttheconclusionofYear1,datafromthepairedobservationformswaspresentedtothesecondaryprogramsfaculty.SEMA-TPPfacultymovedforwardinusingeachprotocolinYear2witheachformcountingas50%oftheobservationalgrades.

1ThegeneralistforminuseatUAcanbefoundathttp://bit.ly/SecObsForm,andtheMCOP2canbefoundathttp://bit.ly/UA-MCOPP.


133

BriefOverviewoftheResults

Weaddresseachresearchquestionindividually.Thefirstquestionconsidered(1)WhatgradingscalewouldbeappropriateontheMCOP2andcorrelatewelltothegradesreceivedonthegeneralistobservationform?Overthetwo-yearstudy,weexamined59SEMA-TPPcandidatesinmiddleanduppergradesmathematicsclassroomsusingbothobservationforms.Ofthe59candidates,31werestudentsenrolledinamethodscourse,while28werestudentteachersinthesubsequentandfinaltermintheprogram.Analysisofthedatayieldedaverystrongcorrelationbetweenscoresonthetwoforms,showninFigure2.

Figure2.CorrelationalanalysisoftheMCOP2observationformtothegeneralistform.

Sucharesultissufficientevidencetowarrantusingeitherform.Ontheotherhand,thisresultisheavilyreliantononerater;theraterinthiscaseistheleadauthorwhoregularlyscoredlessonsonthegeneralistformintheCoraveragerange(rangeduringstudy72to97).Cooperatingmathematicsteachers,incontrast,rarelyscoredobservationsofstudentteacherslessthanamid-B,mostlyassigningA’s(95%ofthetime).Thus,thestrongcorrelationofthefindingsindicatethatanaccuratelyscoredMCOP2rubricwillaligntoA,B,C,D,Flettergradeseasily,whetherusedbyateacher,supervisor,oruniversityfaculty.NextwastoconsiderwhatMCOP2pointtotalequatestoeachlettergradeA,B,C,D,andF.

InFigure3,weexaminetheuseofthelinearmodelinFigure2,whileinFigure4wepresentanimprovedspreadacrossexcellence,good,average,andbelowaverage(failing)scores.UsingonlythelinearregressionmodelontheMCOP2pointtotals,Figure3revealsgradeswouldconverttoarangeofabout75to95.Thisresultalignstotherangeofscoresthatsupervisingteachersregularlyassigned,80-100,onthegeneralistformsreducedbyfivepoints.Therefore,wedecidedtoexaminetheMCOP2meansperitem(0.0to3.0).

y=0.6667x+64.919R²=0.6761r=0.8223

60

70

80

90

100

10 20 30 40 50

SCTLGen

FormScore(0-100)

MCOPPScore(Max54)

MCOP2 v.SecondaryGeneralForm


134

Figure3.ConversionofMCOP2scoresusingleastsquareslinearmodel.

WeexploredafewoptionsandsettledonaconversionthatisshowninFigure4toobtainthedesireddistribution.Figure4demonstratesthatthespreadoftheconvertedscores,68to100,isverysimilarinnaturetothespreadofgeneralistformscoresbytheleadauthor,72to97.

Figure4.UASEMA-TPPadoptedgradeconversionmodelfortheMCOP2.Notesonconversion:MCOP2meanscoreof2.5isequivalentto100%,anA+;MCOP2meanscoreof1.0isequivalentto70%,aC-.

TherawscoresfromtheMCOP2canrangeintotalpointsfromzeroto54.Itisunreasonabletoexpectperfectthrees,letalonehalftwosandhalfthreesfromnoviceteachers.However,programmaticallyweviewameanof2.5asatopscoreforapreserviceteacherdesignedanddeliveredlessonandameanof1.0asminimallypassing.Therange1.0to2.5ontheMCOP2mapstoadistributionfromthemid-60s(failing)to100(perfect)forconvertingtoagrade.Wehaveadoptedthelinearscoreconversionofgrade=50+10/9*MCOP2(showninFigure4)totranslatetheMCOP2scoretoagradeoutof100points,revealingexcellence,good,average,andinneedofimprovementtopass.

60.0

70.0

80.0

90.0

100.0

ConversionwithLinearRegressionModel

60.0

70.0

80.0

90.0

100.0

50+1.111(MCOP2)Model


135

Oursecondresearchquestionwas,(2)HowdopreserviceteachersperceivetheMCOP2astheirgrade-determiningobservationprotocol,asopposedtothegeneralistobservationform?TheresultingMCOP2gradeswerehigheroralmostequalthanthegeneralformgradesabout2/3ofthetime.Eighty-threepercent(n=49of59)ofpreserviceteachersreported,throughonlineanonymoussurveys,theypreferredtheMCOP2scorebecausetheyknewwhattoimproveonforthenextobservationwhereasthegeneralistformwasnotspecificenoughwithoutwrittenfeedbackordiscussion.Thisfeedbackwasverytelling;theypreferredknowingexactlytheirroleandtheirstudents’rolesinaformallyobservedlessonasitwasoutlinedintheMCOP2.Alargeportion(n=25of28)saidtheypreferredtheMCOP2duringtheirstudentteachingsothatonlymathematicsteacherswouldscoreanddeterminetheirgrades.Abouthalfofstudentteachersareobservedbyout-of-fieldteacherswithinschoolsforupwardsofhalftheirobservationalscoresduringtheirstudentteachinginternship.Thispracticehassincechangedtoonlyformativenon-gradebearingfeedbackbyout-of-fieldteachers.MTE-Ppartnershaveindicatedthisout-of-fieldobservationpracticeiscommoneventhoughitdoesnotprovidefeedbacktothepreserviceteachersorprogramfacultyregardingtheimplementationofhighqualitymathematicslessons.

Wealsosetouttostudy,(3)DoespreparingpreserviceteacherstoconsidertheMCOP2intheirplanningofformalobservationlessonsimprovethequalityofthelessonsthanpriortotheMCOP2implementation?Toanswerthis,weexaminedthelessonplanscoresofallformalobservationsduringthetwoyearsofdatacollectionofallmethodsstudents(studentteacherswerenotscoredonlessonplans).Wethenlookedbacktothepriortwoyearsoflessonplangradesofgeneralistformscoredobservationsofmethodsstudentsoflessonsimplemented.Wefoundthat26of31(84%)methodstudentlessonplansfromtwoyearsofMCOP2werescoredhigherthaninthetwoyearspriortoMCOP2.ThisindicatesahigherqualityinlessonplanningwhentheMCOP2isusedasanobservationprotocol.Whencomparingthepre-MCOP2eraobservationscoresonthegeneralistformtotheobservationswiththegeneralistformduringtheMCOP2use,thesame84%ofobservationsscoredbetter.Hence,weconcludethatbothplanningandenactmentwasclearlybetterwiththeMCOP2useinourprogram.

Conclusion

OurconclusionsofthispreliminaryworktobeginandunderstandtheimplementationoftheMCOP2intheUASEMA-TPPprogramresideinourfourthresearchquestion,(4)Whataretheimpactsforbothstudentsandprogramtousethegeneralistformasanon-grade-bearing,end-of-semester,summativeform,andtheMCOP2astheexclusivegrade-determiningobservationprotocolforbothmethodsstudentsandstudentteachers?Aunit,college,orprogramcanandshouldusegeneralistsummativetoolsforanalyzinglarge-scalefactorsasoveralluniversity/collegepreparation,secondaryprogramspreparation,orstate-levelpreparation.Ontheotherhand,atthelevelinwhichweevaluateandassessourteacher


136

candidatesduringmethodsandstudentteaching,theMCOP2resultsclearlypromotebetterdesignedlessons,andstrongerimplementationofthoselessons.Inaddition,teachercandidatesprefertheMCOP2tohelpbecauseofthedetailedinformationprovidedtoguidetheirprofessionaldevelopmentandthemoreaccuratedeterminetheirgradesforformalobservationsofteaching.

OurinstitutionalcolleagueshaverecognizedthisworkandarenowfollowingontheheelsofthesuccessesoftheSEMA-TPP.Moreimpactedarethelocalcooperatingteacherswhonowfindgreatvalueinawell-definedrubricmeasuringbothsidesoftheirresponsibilities,themathematicsclassroomitself,andsupportingthestudentteachertoachievethistarget.Moreover,thecooperatingteachersdonotfeelpressuredtogivehighergrades.SometeachershavementionedusingtheMCOP2helpsthemnowlookforcertainpracticesofthemselvesandtheirstudentsintheirnormalclassroomdailyoperation.ThisimpactoncooperatingteacherinstructionalpracticesimplicitlyfromclassroomteachersusingtheMCOP2toevaluatepreserviceteachersisanintriguingareaforfutureresearch.

DrawbacksandLimitations

WerecognizenotallprogramscanimplementthepracticesatUAasmanyout-of-fieldteachersevaluatemethodsstudentsorstudentteachers,andsomeprogramsdonothaveayearofstrongpreparatorycontent,pedagogy,andclinicalfieldexperiencesbeforemethodsandstudentteaching.ThesepracticesforpreparationofsecondarymathematicsteachersatUAareourimplementationoftherecommendationsofMETandMETII,structuresintendedtobestservebothpreserviceteachersandthestudentsinsecondaryschoolsinwhichtheywillteach.Weareconcernedthatthepracticeofevaluationdonebyout-of-fieldeducatorsworksagainsttheeffortstotransformmathematicsteacherpreparationintheeyesofthepublicandstakeholders.HighstakestestingliketheedTPAareherebecausethefieldofteacherpreparationhasallowedaperceptiontoemergethatweproduceanunacceptablepercentageofunpreparedandunqualifiedcredentialedteachers.Wequestiontheethicalrationaleofanypracticethatcontributestothepublicperceptionofweakteacherpreparation,aproblemheightenedinmathematicsduetothegenerallynegativeviewsofmathematicsintheU.S.

NextSteps

OurnextstepsonourprogramtransformationatUASEMA-TPPcenteraroundthreeitems.First,weaimtobeginworkontyingstudentachievementmeasurestotheMCOP2.Thisisamassiveendeavorrequiringfundingforalarge-scalestudy.Second,weaimtobeginanalyzingourNCTMSPAdatasettoextractprogrammaticvariablesthatinfluenceMCOP2scoresandmakechanges,additions,anddeletionstotheprogrammaticstructurewhereneeded.Lastly,weaimtobeginworkwithourcooperatingandmentorteacherswiththeMCOP2aspreviouslymentioned.


137

WehopethattheMTE-Pcommunitywelcomesthisinstrumentandfindsitusefulinaidingthesimilartransformationoftheirsecondarymathematicsteacherpreparationprogram,especiallyforevaluatingmethodsstudentsandstudentteachersinthemathematicsclassroom.

References

Brown,J.C.,&Crippen,K.J.(2016).Thegrowingawarenessinventory:Buildingcapacityforculturallyresponsivescienceandmathematicswithastructuredobservationprotocol.SchoolScience&Mathematics,116(3),127-138.

Brownell,W.A.(1935).Psychologicalconsiderationsinthelearningandteachingofarithmetic.InW.D.Reeve(Ed.),Theteachingofarithmetic:TenthyearbookoftheNationalCouncilofTeachersofMathematics(pp.1-31).NewYork:TeachersCollege,ColumbiaUniversity.

Bryman,A.(2012).Socialresearchmethods(4thedition).OxfordUniversityPress:Oxford,UK.

Caughlan,S.,&Jiang,H.(2014).Observationandteacherquality:Criticalanalysisofobservationalinstrumentsinpreserviceteacherperformanceassessment.JournalofTeacherEducation,65(5),375-388.

Cohen,D.K.,Raudenbush,S.W.,&Ball,D.L.(2003).Resources,instruction,andresearch.EducationalEvaluationandPolicyAnalysis,25(2),119-142.

ConferenceBoardoftheMathematicalSciences(2001).Themathematicaleducationofteachers.Providence,RIandWashington,DC:AmericanMathematicalSocietyandtheMathematicalAssociationofAmerica.

ConferenceBoardoftheMathematicalSciences(2012).ThemathematicaleducationofteachersII.Providence,RIandWashington,DC:AmericanMathematicalSocietyandtheMathematicalAssociationofAmerica.

Gleason,J.A.,Livers,S.D.,&Zelkowski,J.(2017).MathematicsClassroomObservationProtocolforPractices(MCOP2):Avalidationstudy.InvestigationsinMathematicsLearning,TBD.

Hiebert,J.,&Carpenter,T.P.(1992).Learningandteachingwithunderstanding.InD.A.Grouws(Ed.),Handbookofresearchonmathematicsteachingandlearning(pp.65-97).NewYork:Macmillan.

Hiebert,J.,&Grouws,D.A.(2007).Theeffectsofclassroommathematicsteachingonstudents’learning.InF.K.Lester(Ed.),Secondhandbookofresearchonmathematicsteachingandlearning(pp.371-404).Reston,VA:NationalCouncilofTeachersofMathematics.

Koestler,C.,Felton,M.D.,Bieda,K.D.,&Otten,S.(2013).ConnectingtheNCTMprocessstandardsandtheCCSSMpractices.Reston,VA:NCTM.

Morrell,P.D.,Flick,L.,&Wainwright,C.(2004).Reformteachingstrategiesusedbystudentteachers.SchoolScience&Mathematics,104(5),199-209.

NationalResearchCouncil.(2003).Evaluatingandimprovingundergraduateteachinginscience,technology,engineering,andmathematics.Washington,DC:TheNationalAcademiesPress.

NationalCouncilofTeachersofMathematics(NCTM).(2012).SpecializedProfessionalAssociation(SPA)2012StandardsfortheCouncilfortheAccreditationofEducatorPreparation(CAEP).Reston,VA:Author.Retrievedonlinefromwww.nctm.org/Standards-and-Positions/CAEP-Standards


138

Resnick,L.B.,&Ford,W.W.(1981).Thepsychologyofmathematicsforinstruction.Hillsdale,NJ:Erlbaum.

Rogoff,B.,Matusov,E.,&White,C.(1996).Modelsofteachingandlearning:Participationinacommunityoflearners.InD.R.Olson&N.Torrance(Eds.),Thehandbookofeducationandhumandevelopment(pp.388-414).Cambridge,MA:BlackwellPublishers.

Sawada,D.,Piburn,M.D.,Judson,E.,Turley,J.,Falconer,K.,Benford,R.,&Bloom,I.(2010,March17).Measuringreformpracticesinscienceandmathematicsclassrooms:Thereformedteachingobservationprotocol.SchoolScienceandMathematics,102(6),245-253.

Skemp,R.R.(1971).Thepsychologyoflearningmathematics.Middlesex,England:Penguin.

Skemp,R.R.(1976).Relationalunderstandingandinstrumentalunderstanding.ArithmeticTeacher,26(3),9-15.

Stein,M.K.,Smith,M.S.,Henningsen,M.A.,&Silver,E.A.(2009).Implementingstandards-basedmathematicsinstruction:Acasebookforprofessionaldevelopment(2ndedition).NewYork,NY:TeachersCollegePress.


139

VariabilityinClinicalExperiencesacrosstheCaliforniaStateUniversities

StephanieBiagetti

[email protected]

JenniferOloff-LewisCaliforniaStateUniversityChico

[email protected]

CaliforniaStateUniversityFullertonhasparticipatedinthenational-levelMathematicsTeacherEducationPartnership(MTE-P)sinceitsinception.However,additionalmembersfromfiveotherCSUcampusesjoinedMTE-PattheAnnualConferenceinMilwaukee,June2014.ThefeedbackfromtheMTE-PconferenceattendeesandtheinnovativeapproachestoresearchonbestpracticesthatMTE-PembodiesledtheCSUOfficeoftheChancellortoopentheinvitationforparticipationofall22CSUcampuseswithteacherpreparationprograms.Inaddition,theChancellor’sOfficebegansponsoringseparateCSUMTE-PeventsinordertofocustheapproachtotheuniquequalitiesoftheCaliforniateacherpreparationcontext.ThiscreatedthelargestteamintheMTE-Porganization.

AspartoftheCSUMTE-Pstructure,aMeasuresGroupwasformedinternaltotheCSUteam.ThepurposeofthegroupwastocollectandorganizedatafromacrosstheCSUsystemanddeterminewhat,ifany,measurescouldbeimplementedacrosstheCSUteacherpreparationprograms.Analysisofthedatacollectedcouldbeusedtoidentifybestpracticesandareasforimprovement.

ThefirststepintheprocesswastoinvestigatehowsimilarordifferentteacherpreparationprogramswerewithintheCSUsystem.TheMeasuresGroupconsideredvariouscomponentsofteacherpreparationprograms(e.g.methodscourses,fieldexperiences)anddevelopedasurveytocollectinformationaboutthespecificcomponents.TheMeasuresGrouppositedthatcommonmeasuresacrossprogramscouldleadtohighlyvariableresultsbasedonprogrammaticstructuresasopposedtodifferencesinfundamentalprogrammaticapproachestoteacherpreparation.Inaddition,themannerinwhichthemeasuresareappliedcouldvarytremendouslybasedonstructuresaswell.

ThesesameissuesrelatedtostructuraldifferencesacrossprogramsarepresentinthelargerMTE-Pcommunityaswell.Californiaissomewhatuniqueinthatteacherpreparationprogramsarepost-baccalaureateprograms,withtheexceptionoftherare“blended”programsinwhichstudentscantakesometeacherpreparationcourseworkduringtheirundergraduateyears.Thevastmajorityofotherstateshaveteacherpreparationprogramsatthe


140

undergraduatelevelsuchthatstudentscangraduatewithadegreeandberecommendedforateachingcredentialsimultaneously.Fieldworkcomponentsaredifferentlengthsandhavedifferentintensities.Contentmethodscourseworkvariesinnumberandcurriculardepthofmathcontent.Consequently,whatevertheCSUMTE-PMeasureGroupscanlearnfromitsinvestigationcanbeapplied,intheory,tothelargerMTE-Pentity.

Description

TocollectinformationaboutthestructuresandpracticesacrossCSUteacherpreparationprogram,theMeasuresGroupcreatedasurveythatwasdistributedtoCSUMTE-Prepresentativesatall22campuses.Thesurveyincludeditemsrelatedtothecampus’ssubjectmatterwaiverprogramforfoundationallevelandfullmathcredentials,whetherthecampusisonasemesterorquartercalendar,detailsaboutthemathmethodscoursework,thefieldexperience,mentorteachers,universitysupervisors,frequencyofobservations,observationprotocols,andstudentteachingevaluations.Thesurveywasdistributedthroughanonlinesiteanddatawasamassedinthesamepassword-protectedonlineenvironment.TherawdatawastranslatedintopiechartsandbargraphsandlaterpresentedtothecampusrepresentativesataCSUMTE-Pmeetingduringwhichadjustmentstotherawdataweremadeduetooriginalmisunderstandingsofthequestionsorsimpleerrorsinresponses.Oncethedatawasaccurate,theMeasuresgroupshareditagainwiththeCSUMTE-PcommunityandplannedtopresentittothelargerMTE-Pmembership.

Results

Ofthe22campusessurveyed,18responded.ThesurveyquestionsandtheirresponsesarereportedinTable1.

Table1SurveyResultsofSecondaryMathematicsTeacherPreparationProgramsintheCSU

Question # Response

1. Doesyourcampushaveanapprovedwaiverprogramforfoundationallevelmathematics?

117

NoYes

2. Doesyourcampususeasemesterschedule? 414

NoYes

3. Howlongisyourstudentteachingexperience? 49121

1Semester2Semesters1quarter2quarters3quarters

4. Doyourteachercandidates(TCs)takeamathmethodscourseconcurrentwiththeirstudentteachingexperience?

414

NoYes


141

Question # Response

5. Howmanyunitsisthemethodscourse,ifyouhaveone? 14841

1.5units2units3units4quarterunits5quarterunits

6. Howmanymentorteachersdoyourteachercandidatesstudentteachwith?

108

1mentorteacher2mentorteachers

7. WhatareyourMaster/MentorTeacherspaidforworkingwithteachercandidatespersemester?Choosetheclosestmatch.

711

Nothing$50–$250

8. Duringtheteachercandidate’sstudentteachingexperience,aretheyrequiredtobesupervisedbysomeonewhois/wasacredentialedteacherofsecondarymath?

612

YesNo

9. Howoftenareyourteachercandidatesformallyobservedduringthefirstsemester?

14171111

OnceasemesterTwiceasem.ThreetimesFourtimesFivetimesSixtimesEighttimesTentimes

10. Howoftenareyourteachercandidatesformallyobservedduringthesecondsemester?

124352

Twiceasem.ThreetimesFourtimesFivetimesSixtimesEighttimes

11. Whentheteachercandidateisobserved,whatsortofobservationprotocolisused?General?Subjectspecific?

944

GeneralBothNeither

Conclusion

FromcollectinginformationfromallCSUcampusesthatofferteacherpreparationprograms,welearnedthattherewashighvariabilityinallaspectsofmathematicsteacherpreparationclinicalexperiences.Keycomponentsincludedthenumberofunitsrequiredinmathematicsmethodscoursework,thenumberofhoursandsemesters/quartersoffieldworkexperiences,thenumberofmentorteachersandsupervisorsacandidatehasthroughouttheteacherpreparationprogram,thequalificationsofmentorteachersandsupervisors,thenumberofformalobservationssupervisorsmakeeachquarter/semester,andtheamountof


142

money(ifany)mentorteachersarepaid.Whilesomecomponentsonthesurfacemayseeminconsequential,forexampletheamountofmoneymentorteachersarepaid,allcomponentsplayaroleinthedevelopmentofateachingcandidatesuchasrecruitmentofmentorteachersinthisexample.Consequently,theresultsofmeasuresutilizedbyMTE-P,ResearchActionClusters(RAC),andsub-RACsmustbecarefullyanalyzedinlightofthisprogrammaticvariability.

AsaCSUlocalpartnership,theChancellor’sOfficeexpressedinterestinidentifyingcommonmeasurestobeusedacrosstheCSUteacherpreparationprogramstodetermineprogrameffectiveness.However,withsuchtremendousvariabilityintheprograms,itwouldbedifficulttomakeprogrambyprogrameffectivenesscomparisonsbeforedetermininghowdifferentprogramconfigurationsimpactmeasuresoutcomes.

However,newCaliforniaCommissiononTeacherCredentialingteacherpreparationprogramstandardsforclinicalexperienceswillreducethevariabilityinmanyprogramelements,butnotall(CommissiononTeacherCredentialing,2016).Forexample,aminimumof600hoursoffieldworkwillberequiredacrossthearcofeachpost-baccalaureateteacherpreparationprogram.Inaddition,eachcandidatemustbeformallyobserved4timeseachquarteror6timeseachsemesterbyasupervisorwhohasexpertiseinthesubjectareathecandidateisteaching.Whilethenewprogramstandardsreducethevarianceinmanyaspectsoftheteacherpreparationprograms,othersremainsuchasthoseassociatedwithmethodscoursework.

Ifsuchlarge-scalevariabilityexistswithintheCSUsystem,imaginethescaleacrosstheMTE-Pparticipatinguniversities.WhileallRACswillbeusingseveralcommonMTE-Pmeasures,wemustbemindfulofwhattheoutcomesindicateandtowhatextenttheyaretheresultof“bestpractices”orprogrammaticdifferences.

References

CommissiononTeacherCredentialing.(2016).CaliforniaTeachingPerformanceExpectations.Retrievedfromwww.ctc.ca.gov/educator-prep/TPA-files/TPEs-adopted-2016.pdf


143

UsingImprovementSciencetoIncreaseMathematicalLearningthroughCo-PlanningandCo-Teaching

PattiBrosnan

[email protected]

[email protected]

Nomatterwhatthescenarioiswithinthefieldofmathematicseducation,onepointthatallteachersshouldagreeuponisthatprovidingopportunitiesforstudents’learningtooccurshouldbeanultimategoalofteaching(Bransford,Brown,&Cocking,2004;Shulman,1999).Therefore,teacherpreparationprogramsarechallengedtoequipteachercandidateswiththeskillsneededtocultivatelearning,whilebeingcognizantofthefactthatteachercandidatesarealsoengagedinthelearningprocess,becausetheyareapprenticesofteaching(Collins,Brown&Newman,1988).Thus,tomodelthedesiredpracticesthatcanpromotelearning,teacherpreparationprogramsarechallengedtomakeexplicitconnectionsbetweencourseworkandfieldexperiencesfortheirteachercandidates(Darling-Hammond&Bransford,2005;Sowder,2007).

Asameanstoplaceafocusonlearninginteachereducationprograms,theuseofco-planningandco-teaching(CPCT)strategiescanbeemployed.Co-teachingisapedagogicalpracticethatencouragescollaborationandcommunicationbetweenteachercandidatesandtheirmentorteacherswhoshareacommonspaceintheorganization,delivery,andassessmentofinstruction(Bacharch,Heck,&Dahlberg,2010).WhenCPCTisemployed,teachercandidatesarevaluedasteachersintheclassroomfromtheinceptionofthefieldexperiences.Therearevariousco-teachingstrategies,including:oneteachoneobserve,oneteachoneassist,stationteaching,parallelteaching,alternativeteaching,andteaming(Friend,Cook,Hurley-Chamberlain,&Shamberger,2010).Duringtheco-planningmeetings,whichoccursbeforetheco-taughtlessons,theteachercandidatesandtheirmentorsreflectonthenatureoftaskstobeused,themathematicaldiscoursethatwouldbeencouraged,meanstomakemathematicalconnections,andinstructionalstrategiesthatcanbeemployed.Thus,employingCPCTduringfieldexperiencescanbeusedtopromoteafocusonstudents’learning,whileprovidinglearningopportunitiesforboththeteachercandidatesandtheirmentors.

Traditionally,inthefieldofmathematicseducationresearch,weobtainresultsfromempiricalstudiesofstudentslearningafterthestudentshaveprogressedtoanothergrade


144

level,sothestudentswhowereactuallystudiedcanneverbenefitfromchangesininstructionalpracticeindicatedbythestudy.Improvementscienceoffersanalternativetoanempiricalresearchdesign,becauseitisdesignedtostudypracticesrapidly,makeappropriatechangesimmediately,andtoengageindividualsinanongoingcycleofimprovement(Bryk,Gomez,Grunow,andLeMahieu,2015).Forexample,duringamedicalsurgery,ifcomplicationsaroseduringthesurgery,thesurgeonsmaymakeimmediatechangestotheirplannedproceduresinordertominimizecomplicationswhileseekingtopreservetheirpatient’slife.Ineducation,timelinessofchangemaynotbelifethreatening,butmakingchangestopracticewhencurrentactionsfallshortofdesiredresultsisthecornerstoneofgoodteaching.Thus,wehypothesizethatteachercandidatesandmentorteacherswillplaceagreaterfocusonlearningbyusingCPCTwhenimprovementscienceresearchdesignisemployed.

Purpose

Thisstudyseekstodescribetheextentteachercandidatesandtheirmentorsplacedafocusonstudents’mathematicslearning,whenCPCTstrategieswereusedandimprovementscienceresearchdesignwasemployed.Therefore,wesoughttoanswerthefollowingquestion:Inwhatwaysdoesco-planningandco-teachingstrategiesassistthementorteachersandteachercandidatestofocustheirworkonstudents’learningofmathematics?

RelatedLiterature

Thecoreresponsibilitiesofteachereducationprogramsaretodevelopteachercandidates’pedagogicalcontentknowledge,andtopromotestrategiesthatcanfacilitatestudentslearning(Feiman-Nemser,2001).Fieldexperiencesareintendedtoservethesepurposes,butmentorteachersoftenviewtheseexperiencesmainlyaswaysforteachercandidatestodeveloptheirclassroommanagementskills,andbecomeacculturatedwithdidacticalnormsandactivities(Leatham&Peterson,2010).Toaddresstheshortcomingsoftraditionalfieldexperiences,co-teachingstrategiescanbeemployed.Co-teachingcanpromoteprofessionalgrowthopportunities,enhanceteachers’understandingofthecurriculum,improvestudentswithdisabilitiesacademicperformance,andincreaseteachers’jobsatisfaction(Bacharch,Heck&Dahlberg,2010;Dieker,1998;Dieker&Murawski,2003;Idol,2006;Rea,McLaughlin&Walter-Thomas,2002;Rice&Zigmond,2000).Nevertheless,professionaldevelopmenttrainingisvitalwhenseekingtoimplementco-teaching(Cardullo&Forsythe,2013).Duringtheprofessionaldevelopmenttraining,mentorteachersandteachercandidateslearnaboutvariousco-teachingstrategies,andreflectonhowrolesandresponsibilitiesmaychangedependingonwhichstrategywillbeutilized.Additionally,teachercandidatesandtheirmentorsareprovidedanopportunitytointeractwitheachother,andaddresschallengesthatmightbeencountered(e.g.,approachestocultivateproductiveconsultations)(Feiman-Nemser,2001).


145

Co-planninglessons,whichareaprimarycomponentofco-teaching,benefittheteachercandidatesandtheirmentorteachers(Mastropieri,Scruggs,Graetz,Norland,Gardizi,&Mcduffie,2005;Scruggs,Mastropieri,&McDuffie,2007).Althoughtherearesomechallengesthatcanhindereffectiveco-planning(e.g.,insufficienttime),ifdonewell,co-planningcanfacilitateproactivediscussionsacrossthecurriculum,andaboutavarietyofinstructionalpracticesthatcanbeusedtofacilitatestudents’learning(Dieker&Murawski,2003).

ConnectionstoInstitutionalTransformation

Since2012,theNetworkImprovementCommunity(NIC)thatfocusedonCPCTduringclinicalexperiences,whichisasub-groupwithintheclinicalexperiencesresearchactioncluster(RAC),hassoughttodesignprofessionaldevelopmentmodulesandinstrumentstomeasurethenatureofimplementationofCPCT.Additionally,theNIChavesoughttouseimprovementsciencesystematicprocess(Plan-Do-Study-Act(PDSA)cycles)toimprovefieldexperiencesandpromotingstudents’success.Overtime,afocusonstudentlearninghasgainedmomentumandwasintensified.CurrentlyourNICiscomprisedof11universitiesfrom6differentstates.MembersoftheNICvaryintheirimplementationofCPCT,someofourparticipatingresearchsitesareinthebeginningstagesofinstitutionalizingthepracticeofCPCT,whileothershavefullyimplementedCPCTintotheirclinicalexperiences.

Method

Inthispilotstudy,weusedthesystematicprocessofimprovementscience(Plan-Do-StudyAct[PDSA])toexaminehowCPCTcanbeusedduringfieldexperiencestoplaceafocusonlearning.Moreparticularly,weimplementedtheCPCTApprenticeshipModelforLearning(Brosnan,Jaede,Brownstein,&Stroot,2014)inwhichmentorteachersinitiallyprovideguidance,andovertimeteachercandidatesandmentorteachersshareinstructionalresponsibilities.Duringthe2014-2016academicyears,wegatheredquantitativeandqualitativedatausingmultipleinstruments(pre-survey,just-in-timesurvey,andfocusgroups).Thequantitativedatawereanalyzedusingdescriptivestatisticsandthequalitativedatawereanalyzedusingthematicanalysis.HighlightsofthevariousPDSAphasesaredescribedbelow.

Plan:FocusonLearning.Inspiredbymantraoft-repeatedbyBrosnan,“Wewillnolongerteachteachershowtoteach.Rather,wewillteachteachershowtogetstudentstolearn,”weplannedtoimplementCPCTduringfieldexperiencesandencouragedboththementorteachersandteachercandidatestoplaceanexplicitfocusonstudents’learning.Tohelpourmentorteachersandteachercandidatesfocusonlearning,weaskedtheinstructionalpairtousethefollowingthreequestionsasaguideduringtheirco-planning:

• Whatdostudentsneedtolearn?• Howwillyouknowiftheylearned?• Inwhattaskswillstudentsengagetoensurelearninghappens?


146

Byfocusingonlearning,thementorteachersandteachercandidateswerealsoaskedtoestablishclearmathematicalgoals,andtoposetasksthatallowedfordiverseapproachestosolvetheproblem,multipleentréepoints,andmultiplesolutionstothetasksprovided.ThementorteachersandteachercandidateswerealsoencouragedtoexhibittheStandardsforMathematicalPractice(NationalGovernorsAssociation,2010)withintheireverydaypractice.

Do:Co-PlanningandCo-Teaching(CPCT)

Duringthedophaseofthecycle,eachmentorteacherandteachercandidatepairwererequiredtoattendaprofessionaldevelopmenttrainingandestablishregularmeetingtimestoconducttheirco-planningsessions.Atopicwasidentifiedfortheseplanningmeetingsandeachparticipantwasaskedtobringideasaboutthetypesoftasksinwhichtheymightengagetheirstudentstoreachthelearningneedsoftheclass.Atthebeginningofthesemester,thementorteacherswereresponsibleformostoftheinstructionaldecisions,buttheywereaskedtoexplaintheirthinkingandinstructionaldecisions.Overtime,usingaguidedapproach,thementorteachersandteachercandidatesstartedtosharetheresponsibilityofcontributingtheirideasaboutinstruction.Duringthelesson,onepersonwasencouragedtotaketheleadtoestablishthetask,andthenbothteachercandidatesandtheirmentorscirculatedtheroomlookingforevidenceofstudentlearning.Continuousassessmentwasapartofallenactedlessons.UsingCPCTprovidedincreasedopportunitiesforbothinstructionalpairstoengageinformativeassessmentmeasures.

UniversityrepresentativesalsocollecteddataaboutthenatureofCPCTfromtheteachercandidatesandtheirmentors.Datawerecollectedviathepre-survey(Oloff-Lewis&Biagetti,2014),just–in-timesurvey(Sears&Maynor,2014),andfocusgroupinterview(Brosnanetal.,2014).Thepre-surveyprovidedinsightsintorespondents’perspectivesaboutCommonCoreContentStandardsandStandardsforMathematicalPractice;strategiesusedtoteachdiverselearnersperspectivesaboutCPCT;andassessmentpracticesthatareutilized.Thejust-in-timesurveyaskedrespondentstoratehowfrequentlytheyusedCPCTduringtheirfieldexperiences,theextentCPCTwasbeneficial,theextentthecommunicationbetweeninstructionalpairswereproductive,andthefrequencyofvariousinstructionalnormsoccurrences.Additionally,thementorteacherswereaskedtoparticipateinafocusgroupinterviewthatdocumentedtheirperspectivesontheCPCTprocess.

Study

Duringthestudyphase,wereviewedteachercandidatesandmentorteacherresponsestothevariousinstruments,andexaminedtheextentthefocusonlearningduringenactedlessonswentasplanned.WealsoexaminedtheirperspectiveabouthowCPCTcontributedtostudentslearning,anddocumentedchangesintheirperspectivesovertime.


147

Basedonthedatagatheredfromthepre-survey,initialconcernsexistedrelativetohowinstructionwillbesharedandtheextentinternshadsufficientexperiencetoworkindependentlyaswellasexhibiteffectiveclassroommanagementpractices.However,theseperceptionschangedovertimebasedontherelationshipbuildingactivitiesthatoccurredduringtheprofessionaldevelopmenttrainingandsubsequentCPCTinteractions.Basedonthedatagarneredfromthejust-in-timesurveyandfocusgroup,mentorsreportedthatusingCPCTtofocusonlearninginfluencedtheteachercandidatestofeelmorepreparedandmoreconfidenttoteach.Furthermore,intheeraofaccountability,thementorteachesfeltmoreateasesincetheywerestillgivenadegreeofcontroloftheirclassprogression,andwasabletohelpteachercandidatesinfacilitatingscaffoldingactivities,andacquiringskillsofthediscipline.

Moreparticularly,thementorteachersfocusgroupinterviewsrevealedfourmajorimplicationsofusingCPCTtofocusonstudentslearning:theirinstructionalpracticesimproved,qualityofmentorshipwasrefined,theteachercandidateswerebetterprepared,andstudents’academicperformancewasimproved.Thementorteachersclaimedthattheybecamebetterteachersandthattheybecamebettermentors.Inaddition,theyfoundthattheteachercandidateshadmoreopportunitiestolearnskillsofthedisciplinetherebyresultinginbetter-preparedteachers.Andfinally,theyclaimedthatthestudentsweretheultimatebenefactorsbecauseofthefocusonlearning(Brosnanetal.,2014).Thus,thefocusoflearningduringCPCTwasperceivedtobebeneficialinmultipleways.

Act:ReflectontheProcess

Basedonourfindings,wereflectedontheresultsandconsideredmeanstofurtherpromotestudentslearning.Wenoticedthattheteachercandidatesandtheirmentorteacherreflectionfocusedmoreondatadrawnfromformativeassessments,andmadestudentslearningamoredominantfocusoftheirreflection.Thiswasindeedashiftfrompreviousnorms,inwhichteachercenteredreflectionswerequiteevident.Wealsonoticedthatthefocusonlearningstrengthenedcommunicationchannelsbetweentheinstructionalpairsbecausetheysoughttocollaboratetosupportstudentlearning,ratherthanconcentratingsolelyonsummativeassessmentmeasuresoftheteachercandidates’actionsduringfieldexperiences.Thevarianceamongteachercandidates’andmentorteachers’conceptionsoflearning,andteachingpractices,weseektoscaleupourfocusonlearningatotherinstitutionsthroughourfuturePDSAcycles,andwillfurtherunpackthefollowingquestions.

• Whatdoestheevidenceoflearningwecollecttellusaboutwhatstudents,teachercandidates,mentorteachers,knowandareabletodo?

• Whatcountsaslearningfromthelensoftheteachercandidatesandmentorteachers?• Howdoteachercandidatesandmentorteachersusedatagatheredonstudentlearning

toplanforfuturelearning?


148

Conclusion

Fromthisstudy,welearnedthatplacingafocusonlearningduringCPCTactivitiesincreasedopportunitiesforthementorteachersandteachercandidatestocollaborateandpromotestudentsuccess.Wealsonoticedthatimplementingachangeconceptcantaketime,sodetailedplanningisvitaltoensuretheideaspresentedareviableandsustainable.Wenoticedmentorteachers’perspectivesaboutCPCTchangedovertime.Theysawvalueinwelcomingteachercandidatesasteachersfromtheonset.Collaborativeefforts,whichareevidentwhenCPCTstrategiesareemployed,canseektomaximizelearningopportunities,andcanbebeneficialforallpartiesinvolved.

Furthermore,thecollaborativepartnershipamongMTE-PNICmembersprovidedanopportunitytoengageinresearch,whilesystematicallyseekingtopositivelytransformfieldexperiencesusingCPCT.Duetothepartnership,theworkloadwasshared;localschoolpartnersbecameawareofthesuccesspatternsandinquiredaboutmeanstoincludeCPCTwithinfieldexperienceswithintheirdistrict.Therefore,thispilotstudyhashelpedourNICmoveclosertomeetingseveralofourgoalstosubstantiateCPCTasaviablestrategytoimproveteacherlearningandstudentmathematicslearning.Inthefuture,weintendtocontinuethisworkandimplementitinagreaternumberofsites.

References

Bacharach,N.,Heck,T.W.,&Dahlberg,K.(2010).Changingthefaceofstudentteachingthroughco-teaching.ActioninTeacherEducation,32(1),3-14.

Bransford,J.D.,Brown,A.L.,&Cocking,R.R.(2004).Howpeoplelearn.NationalAcademyPress,Washington,DC.

Brosnan,P.,Jaede,M.,Brownstein,E.,&Stroot,S.A.(2014,April3-7).Co-planningandco-teachinginanurbancontext.PaperpresentedattheAnnualMeetingoftheAmericanEducationalResearchAssociation,Philadelphia,PA.

Bryk,A.S.,Gomez,L.M.,Grunow,A.,&LeMahieu,P.G.(2015).Learningtoimprove:HowAmerica’sschoolscangetbetteratgettingbetter.HarvardEducationPress,Cambridge,MA.

Cardullo,V.M.,&Forsythe,L.(2013).Co-teachinganewpedagogicalpracticeforteachercandidates.School-UniversityPartnerships,6(2),1-7.

Collins,A.,Brown,J.S.,&Newman,S.E.(1988).Cognitiveapprenticeship.Thinking:TheJournalofPhilosophyforChildren,8(1),2-10.

Darling-Hammond,L.,&Bransford,J.(Eds.).(2005).Preparingteachersforachangingworld:Whatteachersshouldlearnandbeabletodo.Jossey-Bass:SanFrancisco,CA.

Dieker,L.A.(1998).Rationaleforco-teaching.SocialStudiesReview,37(2),62-65.

Dieker,L.A.,&Murawski,W.W.(2003).Co-teachingatthesecondarylevel:Uniqueissues,currenttrends,andsuggestionsforsuccess.TheHighSchoolJournal,86(4),1-13.


149

Feiman-Nemser,S.(2001).Helpingnoviceslearntoteachlessonsfromanexemplarysupportteacher.JournalofTeacherEducation,52(1),17-30.

Friend,M.,Cook,L.,Hurley-Chamberlain,D.,&Shamberger,C.(2010).Co-teaching:Anillustrationofthecomplexityofcollaborationinspecialeducation.JournalofEducationalandPsychologicalConsultation,20(1),9-27.

Idol,L.(2006).Towardinclusionofspecialeducationstudentsingeneraleducation:Aprogramevaluationofeightschools.RemedialandSpecialEducation,27(2),77-94.

Leatham,K.R.,&Peterson,B.E.(2010).Secondarymathematicsmentorteachers’perceptionsofthepurposeofstudentteaching.JournalofMathematicsTeacherEducation,13(2),99-119.

Mastropieri,M.A.,Scruggs,T.E.,Graetz,J.,Norland,J.,Gardizi,W.,&Mcduffie,K.(2005).Casestudiesinco-teachinginthecontentareassuccesses,failures,andchallenges.InterventioninSchoolandClinic,40(5),260-270.

Murawski,W.W.,&Spencer,S.(2011).Collaborate,communicate,anddifferentiate!:Howtoincreasestudentlearningintoday’sdiverseschools.ThousandOaks,CA:CorwinPress.

NationalGovernorsAssociation.(2010).Commoncorestatestandards.Retrievedfromwww.corestandards.org/Math/Practice

Rea,P.J.,McLaughlin,V.L.,&Walther-Thomas,C.(2002).Outcomesforstudentswithlearningdisabilitiesininclusiveandpulloutprograms.ExceptionalChildren,68(2),203-222.

Rice,D.,&Zigmond,N.(2000).Co-teachinginsecondaryschools:TeacherreportsofdevelopmentsinAustralianandAmericanclassrooms.LearningDisabilitiesResearch&Practice,15(4),190-197.

Scruggs,T.E.,Mastropieri,M.A.,&McDuffie,K.A.(2007).Co-teachingininclusiveclassrooms:Ametasynthesisofqualitativeresearch.ExceptionalChildren,73(4),392-416.

Shulman,L.S.(1999).Takinglearningseriously.Change:TheMagazineofHigherLearning,31(4),10-17.

Sowder,J.T.(2007).Themathematicseducationanddevelopmentofteachers.InF.K.LesterJr.(Ed.),Secondhandbookofresearchonmathematicsteachingandlearning(pp.157-223).IAP:Charlotte,NC.

Zigmond,N.,&Magiera,K.(2001).Afocusonco-teaching:Usecaution.CurrentPracticeAlerts,6(6),1-4.Retrievedfromteachingld.org/alerts


150

Co-PlanningStrategiestoSupportInternDevelopment

[email protected]

[email protected]

Researchersconsistentlystatethatco-planningiscriticalwithinaco-teachingcontext(e.g.,Howard&Potts,2009;Magiera,Smith,Zigmond,&Gebauer,2005).Unfortunately,theliteratureprovideslittleguidanceonhowco-teachersshouldco-plantogethereffectively.Inordertoprovidesomedirectionforco-planning,wefirstexploredanadaptationofco-teachingstrategiestoco-planning.Workingwithmentorteachers,wefurtherdefinedco-planningstrategiesandthentestedthestrategieswithmentorteachersandinterns.

Co-planningisparticularlyimportantduringpre-serviceteachers’internshipexperiences.Interns,giventheirlackofteachingexperience,arelikelytohavemoredifficultythanexperiencedteachersbeingflexibleandattentivetostudentneedsastheyplanforinstruction(Borko,Livingston,&Shavelson,1990;Leinhardt&Greeno,1986;Livingston&Borko,1989).Atthesametime,internsmaybecreatingsomeoftheirfirstlessonplansdesignedforactualstudentsinclassroomsratherthanplansforlessonswithhypotheticalstudents.Internsarealsofacingarapidescalationintherateatwhichtheyneedtopreparelessons–oftentransitioningfromwritingseveralinasemestertowritingseveraleachday.Furthercomplicatinganalreadychallengingsituationisthatfactthatinternsareplanningandimplementingtheselessonsinasettinginwhichtheirclinicalteachersetstheclassroomnormsandtheexpectationsforqualityinstruction.Addedtothesechallengesisthefactthatmanyexperiencedteachersmaynotwritedetailedlessonplans,leavinginternslittleaccesstotheplanningdecisionsmadebytheirmentorteachers.Havinginternsandmentorsco-planlessonshasthepotentialtoaidinternsinthetransitionfrommathematicseducationstudentstomathematicseducatorsandhelpensurethatplansreflectnormsacceptabletothementorteacher.

TheoreticalSupport

Ourworkwithco-teachingandco-planningduringpre-serviceteachers’internshipexperiencesisgroundedinLave’s(1991)constructofsituatedlearning.Asinternsgooutintothefield,theirlearningmovesfromapredominatelyacademicexperiencetoanapprenticeshipwithinacommunityofpractice.Insuchasettingtheworkingrelationshipbetweeninternand


151

mentorteacherbecomesamajordeterminingfactorintheintern’sabilitytoparticipateproductivelyandcollaborativelyinthepracticeofclassroomteaching.Inourworkweconsiderwaystoexpandtraditionalvisionsofthisworkingrelationshipbetweeninternandmentor,envisioningmentorandinternascollaboratorsinclassroomplanningandinstruction.

ConnectionstotheMTEPartnership

ThepurposeoftheMathematicsTeacherEducation(MTE)Partnershipistoimprovesecondarymathematicsteachereducation.Internshipexperiencesareacriticalcomponentofteachereducation.Therangeofexperiencesduringtheinternshipmaybedescribedasaniterativecyclethatencompassesobserving,planning,teaching,assessment,andreflection.Inourpastexperiencesworkingwithclinicalplacements,theimplementationofthiscyclehastakenaverytraditionalroutewheretheinternisprovidedwithasetofcoursestandards,apacingguide,andpossiblytheirmentor’sinstructionalresources,andtheyarechargedtocreatealessonplanindependently.Thementorcritiquesthislessonplanonceitiswritten.Frequentlythislessonplandoesnotmeetthementor’sexpectationsforqualityinstruction;theinternthenscramblestorevisethelessonplanbasedonthementor’scritique.Ifthelessonplanisstillnotadequate,theplanningandcritiqueprocessisrepeated.Eventually,thelessonplanisapproved,andtheinternhassurvivedtheplanningcycle.However,theremaynowbeinsufficienttimetoreflectontheplanningcycleandconceptualizequalityinstruction.Thenthecyclebeginsagain.

Inanefforttoproducemoreeffectivesecondarymathematicsteachers,wenowemphasizea1:1co-teachingmodelthatemphasizesfeedbackandreflectionthroughouttheiterativecycledescribedabove.Ratherthanbeingsentofftoplaninisolation,thementorandinternplantogether,eachbringinghisorherindividualknowledgeandskilltotheplanningprocess.Planningdecisionsaremadewiththegoalofoptimizingstudentlearning;instructionalstrategies(includingco-teachingstrategies)areselectedappropriately;and,together,thementorandinternreflectaboutinstructionandtheeffectonstudentlearning.Throughoutthisprocesstheinternassumesanincreasingresponsibilityforplanningandinstructionastheinternshipprogressesbut,unlikethe“sinkorswim”paradigmpresentedabove,internsareprovidedwithcontinualsupport.

DescriptionoftheECUProject

ThemathematicseducationprogramatEastCarolinaUniversityhasbeeninvolvedwithco-teachingsincethefallof2013.ThroughoutthisprocesswehavebeenworkingwiththeMTEPartnershipwithintheClinicalExperiencesResearchActionCluster(RAC).AspartoftheClinicalExperiencesRAC,wehavebeeninvolvedwiththeco-planning/co-teachingsub-RAC.Despiteyearlytrainingsrelatedtoco-teaching,ourclinicalteachersandinternsreportedcontinueddifficultywithexactlyhowtoco-plantogetherandeffectivelyincreasetheinterns’


152

responsibilityforplanningandinstruction.Oursolutiontothisissuewastodrawuponourcombinedexperienceteachinghighschoolmathematicsandsupervisinghighschoolmathematicsinternshipstodraftsixspecificco-planningstrategies.

Bacharach,Heck,&Dahlberg(2010)andMurawski&Spencer(2011)outlinespecificco-teachingpracticesthathavesuccessfullysupportedmentorteachers’inshiftingfromthetraditionalstudentteachingmodeltoaco-teachingmodel.Analogoustotheseco-teachingpractices,ourgoalwastodevelopspecificco-planningpracticesformentorteachersandinternstouseforeffectiveco-planning.Webeganthisprocessbytranslatingseveralco-teachingstrategiesintoasimilarcollaborationprocessforco-planning.Forexample,wethoughtaboutwhattheOneTeach,OneAssistco-teachingstrategywouldlooklikeforco-planning,whichresultedintheOnePlans,OneAssistsco-planningstrategy.Afterdefiningeachstrategyweworkedwithmentorteacherstofurtherrefinethemandpilotthemwithmentorteachersandinterns.Theresultingsixco-teachingstrategiesaredescribedinTable1.

Thesestrategiesparalleltheco-teachingstrategies,butarenotintendedtobepairedwithanyspecificco-teachingstrategy.Theyalsoshouldnotbeviewedashierarchical,althoughsomestrategiesrequireamoreestablishedrelationshipandrapportbetweentheclinicalteacherandinternthanothers.Consequently,somestrategiesarebestusedearlierorlaterintheinternshipexperience.Similartoco-teachingstrategiestheyshouldbeutilizedtobestmeettheneedsoftheclinicalteacherandinternineffectivelydesigninginstructiontosupportstudentlearning.

MethodsUsedtoAddresstheIssue

OurfirstPlan,Do,Study,Act(PDSA)cycle(Bryk,Gomez,Grunow,&LeMahieu,2015)spannedtheacademicyears2014-2015and2015-2016.Wedevelopedtrainingmaterialsforco-planningandco-teaching,andconductedprofessionaldevelopmentwithourclinicalteachersandinterns.Basedonfocusgroupinterviewfeedbackfrom2014-2015,werevisedourmaterialstoincludemoreactivitiesfocusedonimplementationoftheco-planningstrategiesbetweenclinicalteachersandinternsduringtheprofessionaldevelopment.Duringthe2015-2016academicyearwewereabletopilotdatacollectionrelatedtoimplementationofco-planningandco-teachingstrategies.Wewereinterestedtolearnifclinicalteachersandinternswereusingtheco-planningstrategies.

Theseco-planningstrategiesarecurrentlytheoreticalconstructsthatdescribespecificwaysthatclinicalteachersandinternscanoperationalizetheco-planningprocess.WehaveseenpromisinganecdotaldatafromclassroomobservationsandexitsurveyscompletedbyclinicalteachersandinternsduringthefirstPDSAcycle,andweareusingthisinformationtoimplementmorestrategicandfocuseddatacollectionandanalysisforoursecondPDSAcycle.


153

Table1.Co-PlanningStrategies

Co-PlanningStrategy

Description AdaptedCo-TeachingStrategy

OnePlans,OneAssists

Eachco-teacherbringsaportionofthelesson,althoughoneclearlyhasthemainresponsibility.Theteamworksjointlyonfinalplanning.

OneTeach,OneAssist

PartnerPlanning Co-teacherstakeresponsibilityforabouthalfofthecomponentsofthelessonplan.Thentheycompletetheplancollaboratively.

StationTeaching

OneReflects,OnePlans

Oneco-teacherthinksaloudaboutthemainpartsofthelessonandtheinternwritestheplan.

AlternativeTeaching

OnePlans,OneReacts

Oneco-teacherplansandtheotherprovidesfeedbackontheplan.

OneTeach,OneObserve

ParallelPlanning Eachmemberoftheco-teachingteamdevelopsalessonplanandthetwobringthemtogetherfordiscussionandintegration.

ParallelTeaching

TeamPlanning Bothteachersactivelyplanatthesametimeandinthesamespacewithnocleardistinctionofwhotakesleadership.

TeamTeaching

Results

OurfirstPDSAcyclewasconsideredapilotstudy,andwereceivedpositiveindicationsthatclinicalteachersandinternswereusingtheco-planningstrategiestodesigninstruction.Inthewordsofoneclinicalteacher,

Weparticipatedinco-planningactivitieswhereIprovidedthelessonsandtheinternprovidedtheactivities,aswellaswheresheprovidedthelessonandIprovidedtheactivities.Wedevelopedthinkingmapstogetherduringco-planningsessions.ShecreatedfulllessonsthatIprovidedinputon.Wedeterminedtogethertherolesforco-teaching.(PDSAcycle1,MentorExitSurvey,2016)

Thisquotedoesnotciteaspecificco-planningstrategybyname,butwhencomparedtothedefinitionsfromTable1,thereisevidenceofOnePlans,OneAssists/PartnerPlanning,OnePlans,OneReacts,andTeamPlanning.

Internsalsonotedsuccessfuluseoftheco-planningstrategies.Accordingtooneintern,

Atfirstshe[theclinicalteacher]wasthemainplannerandteacher.Shetoldmewhatshedid,howshedidit,andherthoughtprocess.WhenItookover,sheassistedme.Shehelpedmethinkthroughplanningandwhatmystudents


154

neededtoknowandhowIshoulddeliverit.(PDSAcycle1,InternExitSurvey,2016)

ThisquotesuggeststheuseofOnePlans,OneAssistsalongwithOneReflects,OnePlanswiththeroleoftheclinicalteacherandinterntransitioningastheinternshipprogressed.Theinternalsohighlightsthecriticalityoftheclinicalteachermakingexplicitfortheinterntheimplicitdecision-makingprocessduringplanningandinstruction.

Impactonlocalpartnership

Thequotesaboveillustratethatclinicalteachersandinternsnotonlyutilizedspecificco-planningthroughouttheinternship,butalsonotedthebenefitsofco-planningforthemselvesandtheirstudents.AsaresultofourworkwiththeMTEPartnershipandwithinourprogramareaatEastCarolinaUniversity,theco-planningstrategiesarenowembeddedinourCollegeofEducationco-teachingtrainingacrossallprogramareas.Thesestrategieshavealsobeensharedwithoursub-RAC,andwearenowrefiningthetrainingmaterialsforwiderdisseminationwithourRACandtheMTEPartnershipatlarge.

ContributiontoMTEPartnership

Twomemberinstitutionsofoursub-RAChaveinvitedustoconductworkshopsfortheirclinicalteachersandinterns.InOctober2105andJuly2016,Dr.CaytonandDr.GradyvisitedtheUniversityofSouthFloridainTampatoworkwithDr.RuthmaeSearsandtheHeliosSTEMMiddleSchoolResidencyProgram(www.usf.edu/education/research/anchin/teacher-initiatives/preservice-teachers/helios-ms-stem-residency.aspx).WewerejoinedbyDr.PattiBrosnan(OhioStateUniversity)toconductaone-dayworkshopforco-planningandco-teachingwithclinicalteachersandinternsformiddlegradesmathandscience.InAugust2016,weworkedwithDr.JenniferOloff-LewisandtheResidencyinSecondaryEducationprogram(www.csuchico.edu/soe/rise)atCaliforniaStateUniversity-Chico.Hereweworkedwithsecondaryclinicalteachersandresidentsacrosscontentareasonimplementingthesixco-planningstrategiesmentionedabove.AsaresultofourworkatCSU-Chico,wearedevelopinganonlinemoduleforco-planningthatwillcomplementtheonlineco-teachingmodulecurrentlyutilizedintheRiSEprogram.ThegoalisfortheseCPCTtrainingmodulestobemadewidelyavailabletoMTEPartnershipschoolsandbeyond.

Nextsteps

WearecurrentlyinoursecondPDSAcycle(2016-2017)utilizingtheco-planningstrategies.Basedonthefirstcycle,wehaverevisedourdatacollectiontoolstoalignwithourupdatedresearchquestions:

• TowhatextentdoesthetraininginfluenceimplementationofCPCT?• TowhatextentisCPCTbeingimplemented?


155

• WhatareperceptionsaboutCPCTfromvariousstakeholders(administrators,mentors,pre-serviceteachers,universitysupervisors)?

Ourdatacollectiontoolsincludepre-surveys,aco-teachingobservationprotocol,asurveyofstrategiesused,justintimesurveys,andexitsurveys.LookingaheadtothethirdPDSAcycle,wehopetoexamineimplicationsofCPCTonpre-serviceteachers’practices,classroominstruction,agencyanddisposition.Wealsointendcreateadatadashboardacrossinstitutionswithoursub-RACthathavebeenimplementingCPCTthroughoutPDSACycles1and2.WearecurrentlyrefiningourtrainingmodulesforCPCTforwiderdisseminationwithinnotonlyourRAC,butalsotheMTE-Partnershipatlarge.

ForMoreInformation

• CharityCayton,[email protected]

• MaureenGrady,[email protected]

References

Bacharach,N.,Heck,T.W.,&Dahlberg,K.(2010).Changingthefaceofstudentteachingthroughcoteaching.ActioninTeacherEducation,32(1),3-14.doi:10.1080/01626620.2010.10463538

Borko,H.,Livingston,C.,&Shavelson,R.J.(1990).Teachers’thinkingaboutinstruction.RemedialandSpecialEducation,11(6),40-49.doi:10.1177/074193259001100609

Bryk,A.S.,Gomez,L.M.,Grunow,A.,&LeMahieu,P.G.(2015).Learningtoimprove:HowAmerica’sschoolscangetbetteratgettingbetter.Cambridge,MA:HarvardEducationPress.

Howard,L.,&Potts,E.A.(2009).Usingco-planningtime:Strategiesforasuccessfulco-teachingmarriage.TEACHINGExceptionalChildrenPlus,5(4)Article2.Retrievedfromescholarship.bc.edu/education/tecplus/vol5/iss4/art2

Lave,J.(1991).Situatinglearningincommunitiesofpractice.PerspectivesonSociallySharedCognition,2,63-82.

Leinhardt,G.,&Greeno,J.G.(1986).Thecognitiveskillofteaching.JournalofEducationalPsychology,78(2),75-95.doi:10.1037//0022-0663.78.2.75

Livingston,C.,&Borko,H.(1989).Expert-novicedifferencesinteaching:Acognitiveanalysisandimplicationsforteachereducation.JournalofTeacherEducation,40(4),36-42.doi:10.1177/002248718904000407

Magiera,K.,Smith,C.,Zigmond,N.,&Gebauer,K.(2005).Benefitsofco-teachinginsecondarymathematicsclasses.TEACHINGExceptionalChildren,37(3),20-24.

Murawski,W.W.andSpencer,S.(2011).Collaborate,Communicate,andDifferentiate:HowtoIncreaseStudentLearninginToday’sDiverseSchools.ThousandOaks,CA:Corwin.


156

SupportSystemsofEarlyCareerSecondaryMathematicsTeachers

JamesMartinezCaliforniaStateUniversity

[email protected]

MeganTaylorTrellisEducation

[email protected]

[email protected]

Abstract

Thisstudyreportsfindingsfromapreliminarysurveyofmathematicsteacherswhoareinateacherpreparationprogramorservingintheirfirstthreeyearsofteaching.Themainobjectiveofthesurveywastogatherinformationabouthowearlycareerteachersarebeingsupportedthatwouldinforminitiativesaimedatimprovingteacherretentionrates.Thesurveydatafocusedonwhattypesofactivitiesteachersareparticipatingin,theirperceptionsoftheseactivities,andhowtheactivitiesinfluencedtheirteachingpractice.Additionalquestionsfocusedonsupportfromprofessionallearningcommunities,administrators,universities,overalljobsatisfaction,andhowlongteachersplantostayteaching.


157

CSUChicoProgramRiSE:AnalysisoftheFirstRecruitmentCycle

CherylOrdoricaCaliforniaStateUniversityChico

[email protected]

FundedbytheUSDepartmentofEducation,thefocusofPRISMSistopromoteruralimprovementinthesubjectsofmathematicsandscienceforsecondaryschoolsacrossthenation.RiSE,ResidencyinSecondaryEducation,oneoftwoprogramssupportedbyPRISMSatCaliforniaStateUniversity–Chico,isanaccelerated12to18-monthgraduateprogramthatcombinesaMasterofArtsinEducationandateachingcredential.Astherecruiter,myprimaryroleistoutilizeinnovativeandresults-drivenmethodstoattractabroadanddiverseapplicantpool.

Throughmyworkexperience,aswellasmyinvolvementintheMATHResearchActionCluster,I’vehadtheopportunitytoexperimentwithdifferentmarketingstrategiesandrecruitmenttools.HereIsharethetechniquesI’vefoundmostusefulinmypractice,drawnfromthosedetailedintheninemodulesoftheSecondaryMathematicsTeacherRecruitmentCampaignImplementationGuide(Ranta,2015).

Chico’sRecruitmentCampaign

Ideally,asuccessfulrecruitmentcampaignstartswithacomprehensiveapproachthatincorporatestheconceptsoutlinedinModules1-4.However,limitedfundingandanabbreviatedtimelinedon’talwaysallowforextensiveplanningandresearchpriortolaunchingacampaign.Additionally,atthetimeIbeganmyrecruitmentefforts,thegrantalreadyhaditsbrandinginplace.Inotherwords,asisoftenthecasewithprojectmanagement,Ihadtohitthegroundrunningandprioritizeaquicklaunch.Thatbeingsaid,IconcentrateonModules5-9,includingSocialMedia,PublicRelations,PaidBroadcastMedia,WebsiteIdentity,andeventuallyEvaluation.

Module5,whichfocusesonSocialMedia,assertsthatthemostpopularplatformisFacebook.Withitswideningpopularity,socialmediahasseenarapidgrowthinaudiencediversity,makingitanevenmoreviabletoolforrecruitmentandagoodstartingpointformanyorganizations.Conveniently,italsohappenstofeaturesomeofthestrongestanalyticsavailablewhenthetimecomesforevaluation.ThroughtheRiSEFacebookpage,Ireceiveaweeklyreportthatprovidestangiblefeedbackmeasuringthingslikepagevisits,numberoflikes,andinquiries


158

resultinginengagementwithmytargetaudience–allveryusefuldatawhendeterminingtheextenttowhichaparticularadorcampaignmaybegeneratinginterest.

Ofcourse,theultimatebenefitofFacebookandsocialmediaingeneral,isthenetworkingfactor.Module6,whichfocusesonPublicRelations,definesthisinteractionas“astrategiccommunicationprocessthatbuildsmutuallybeneficialrelationshipsbetweenorganizationsandtheirpublics”(Ranta,2015,p.72).Whiledefiningthegroupsofindividualsorpublicsyouwishtoreachiscertainlyanimportantstep,Irealizedthepowerofreachingthemasspublic,andIlearnedtheimportanceofhoninginonthisaudienceasastrategytohelpmedeterminemytargetapplicantpool.

Facebookandmanyothersocialmedianetworksprovidefreeaccounts,butpayingforcertainupgradesoradditionaloroutsourcedassistancecanbeaworthyinvestment.Withcarefuldiscretionaboutavailablegrantfunds,wehaveestablishedcontractswithmultiplemediaagenciesthathavehelpedtoproduceprofessionaladvertisementsforourprogram,includingmovietheatreads,televisionandradiospots,onlinebanners,andFacebook“boosts”usedtogeneratemorecontentexposure.Module7coverseachoftheseoptionsandmore,providinghelpfultipsonproductionand“BuyingaSchedule,”whileemphasizingtheimportanceoftiming.“Themostbrilliantschedulecanberuinedbypoorproductionvaluesandviceversa,agreat-lookingcampaignthatnooneseesisequallyasineffective”(Ranta,2015,p.108).Inotherwords,makeinvestmentsthatcountbytakingacarefullookattheproductionqualityyourbudgetwillallow,andbeequallycriticalwhennegotiatingairtime.

Whilereachingthetargetaudienceistheongoingchallengeforanyrecruiter,Iquicklylearnedjusthowcriticalitwastohaveanestablishedinfrastructureinplace.Module8:WebsiteIdentitydetailsthebasicconstructionandorganizationofasite.Withinthecontextofmyacademicinstitution,therewasalreadyawell-establishedprotocolinplace,somostofthetechnicalworkhadtobeoutsourcedtoourcampusITstaff.Withsometeamworkonthecontent,itdidn’ttakelongtolaunchthemainwebpagefortheRiSEprogram,andthecampuswebdeveloperswerehelpfulinofferingweeklyupdatesonsitetrafficthroughGoogleAnalytics.

Butalmostimmediatelyafterthedetailsofthewebsitefellintoplace,wehadseveraladcampaignsupandrunning.Theburdenofasuccessfulcampaignisalotoftraffic,anditdidn’ttakelongtorealizethatIneededanotherresourceforfollowinguponpublicinquiriesandcandidateleads.WithmoreassistancefromIT,wedecidedtoutilizeGoogleFlowChart,inordertomapoutanew“landingpage,”oronlinedestinationtobeusedasanautomatedtoolfordirectingtheinfluxofinterestedcandidates.Creatingthisinfrastructurewasnotasimpleprocess,butithadabigpayoff.


159

WithinteractivebuttonsandlinkstoGoogleforms,potentialcandidatescouldsubmithelpfulinformation,andalsoaccessneededresources.Riseteachers.orgbecameoureasyandcatchyURL,forquickreferenceinradioandTVads.Asa“destination”forgeneralinterest,itservedtoredirectthosewhoarenotagoodmatchfortheprogramtomoreappropriateresources,butindoingso,alsohelpeddedicatemorestafftimetothemostqualifiedcandidates.

Inotherwords,Iwasnolongerworkingtirelesslyrunningthephonesandaddressingemailstoanswermoregeneralquestionsandredirectmisguidedinquiries.Thismulti-purposedinformationalsystemandscreeningtoolallowedmetoprioritizeandfocusmyeffortsonthemostviablecandidateleads.Infollowingupontheseleads,Iwasabletooffernecessarysupporttoindividualsneedingjustalittleextraboosttobecomequalifiedcandidatesreadytoapplyforandbegintheprogram.Thiscombinationofinfrastructureandoutreachiswhatultimatelytranslatedtosuccessinrecruitment.

EvaluatingtheCampaign

ButhowcouldIdeterminewhatoutreachworkedandperhapsmoreimportantly,whatmightbethebestuseoffutureresources?Module9:Evaluationmentionstheimportanceofmeasuringeffectsasasubsetofresults.Italsoprovidesaguidelinetoevaluateresourceuseandtheeffectivenessofagivenrecruitmentstrategy.

GoogleAnalyticsisahelpfulfreetoolthatcanassistincalculatingtrafficdataandhelpzoneinonthetargetaudienceandwhat’sworkingintermsoffuturerecruitmentcycles.AccordingtoGoogleanalytics,ourlandingpagehadapproximately7,000pageviewsandhasreachedaworldwideaudience,whichhelpedprovethatourlandingpagewasasuccessinreachingthepublicthroughpaidmedia.

Weconductedan8-monthdigitalmarketingcampaignwithActionNewsNow(ourlocalmediaagency),whonotonlyairedaRiSEcommercialforus,butalsoassistedwithmanagingourpaidadsthroughFacebook.ThismediacampaignturnedouttobeasuccessfulpartnershipbasedonourevaluationdatathroughFacebookanalytics.Wereachedover171,000peoplethroughthissocialmediaplatform,andbasedondatasubmittedbyprogramapplicants,wecanalsoconfirmFacebookcontributedto10%ofourapplications.OurFacebookpagealsogeneratedalmost7,000clicksandnearly500likes,helpingbuildour“brand”andcreatingfutureretentiontowardsourprogram.

Uponconclusionofourfirstrecruitmentcampaigncycle,Iwasabletoanalyzeallthedatacollectedandcreatechartsforfuturecampaigninvestmentsanddecisions.IcreatedaspecificchartthatrepresentedtheRiSEProgramleadsbyrecruitmentsource,witheachsourcecategorybrokendownbypercentages.Thedataisbasedon334leadsfromJanuary2015toMarch2016,andpaidmediageneratedaboutonethirdofourleads.


160

SincethestartofrecruitmentfortheRiSEPrograminJanuaryof2015,wehavehadthreeseparatepoolsofapplicants—foratotalof42applicants.Inreferencetothepreviouschart,whatthismeansisthatoutofthose334individualswhoexpressedinterestintheprogram,42(orabout13%)submittedapplications.Sowhileithelpedtoseewhichrecruitmentmethodswereeffectiveingeneratingleads,Iwantedtomorecloselyevaluatethiscritical13%.

Tobegin,weexaminedthepercentageofRiSEapplicationsperleadsource.Ifirstexaminedapplicationssourcedfrommovieads,findingtheywerenon-existent.Thisexpensedidnotproduceagoodreturn,whichiswhywewillbediscontinuingthatcampaign.Second,whiletelevisioncommercialsgeneratedalargeamountofleads,thenumberofapplicantsfromleadsgeneratedbyourSanFranciscoBayAreamediacampaignwereinsignificant,withagreateramountofapplicantscomingfromleadsgeneratedbyourlocalnewsagency.

Ihavefoundthatevaluationisoneofthemostessentialcomponentsinanalyzingasuccessfulcampaign;itcanhelpfacilitatediscussions,determinewhatlessonscanbelearned,andwheretofocusfutureefforts.Thatbeingsaid,asaresultofourevaluationdata,weintendtocontinueourcampaignwithourlocalmediaagency,ActionNews,andtargetmoreofouraudiencebyexpandingtothe(morelocal)Sacramentoarea.Weareworkingonproductionwithanewmediaagencytodiscussourfuturemarketingcampaignandpartnershipforoursecondrecruitmentcycle.

Havingtherighttools,includingtheImplementationGuide(Ranta,2015)producedbytheMATHResearchActionCluster,andinfrastructureinplacehasnotonlyhelpedmakemyrecruitmenttasksfeelmoremanageable,butalsoprovidedasystemfortrackingmyefforts.Ilookforwardtodeterminingtheoutcomesoffuturerecruitmentstrategiesandadcampaignsinrelationtothegrant’sbudget,andmoreimportantly,discoveringwhereimprovementscanbemadeaswecontinueoureffortstorecruitfuturesecondarymathematicsteachers.

ForMoreInformation

• URL–www.csuchico.edu/soe/rise

• Contact–CherylOrdorica,CaliforniaStateUniversity–Chico,[email protected]

References

Ranta,J.(2015).Secondarymathematicsteacherrecruitmentcampaignimplementationguide.Washington,DC.AssociationofPublicLandGrantUniversities.Retrievedfrombit.ly/MATHImplGuide.


161

ComparingNoyceScholars’DecisionstoTeachandPerspectiveson

Teachingtonon-NoyceScholars

JenniferWhitfieldTexasA&[email protected]

Scholarshipsthataredesignedtocombattheteachershortageproblemandincreasethenumberofteachersinhigh-needfieldsgenerallyincludesomefinancialincentive.Theextenttohowthefinancialincentiveeffectsthescholar’sdecisiontobecomeateacher,orteachinlow-incomeschools,isdifficulttomeasure,butsomeworkhasbeendonetorevealcontributingfactors.Onefactorthatwasfoundtoimpactscholars’decisionstoacceptthefundingwastheamountawarded.Scholars’wereinfluencedmorewhenthefinancialincentivecoveredahigherproportionoftheirtuition(Darling-Hammond,2007;Henry,Bastian,&Smith,2012;Liou&Lawrenz,2011).

FortheNoyceTeachingScholarshipspecifically,researchhasfoundthatmanyoftheNoyceScholarswouldhaveenteredtheteachingprofessionregardlessofthefinancialincentive(Bull,Marks,&Salyer,1994;Liou,Desjardins,&Lawrenz,2010).However,forthoseNoyceScholarswhomightnothaveotherwiseconsideredacareerinteaching,thefinancialincentivehadalargerimpactontheirdecisiontoentertheteachingprofession(Liou&Lawrenz,2011).

Competitivescholarshipsappeartoattractindividualswithsignificantlyhigheracademiccredentialsandhigherlevelsofhumancapitalintoteaching,butunlessthescholarshipprogramsrequirerecipientstoworkinhigh-needschools,theytendtoteachinschoolsandclassroomswithmorehigh-achievingandlow-povertystudents(Henryetal.,2012).ThefinancialincentiveofferedbytheNoyceScholarshiphadthemostinfluenceonrecruitingteacherstohigh-needschoolsandtowardcompletingtheircertificationprogram,butlessofaninfluenceonstayinginahigh-needsschoolforlongperiodsoftime(Liouetal.,2010;Liou,Kirchhoff,&Lawrenz,2010;Liou&Lawrenz,2011).Usingscholarshipsasamechanismtorecruitteachersintotheeducationprofessionandintoteachinginhighneedfieldshasitsownsetofchallenges.Thus,itisnecessarytocontinuetostudythesechallengesandmodifythemtomeettheneedsoftheforecastedteachermarket.

ThoughtheaforementionedresearchprovidessomeinsightonfactorsthatinfluenceNoyceScholars’decisiontoentertheteachingprofessionandhowthefinancialincentiveofthe


162

scholarshipimpactedtheirdecisiontoteach,littleresearchhasbeenconductedoncharacteristicsuniquetoNoyceScholars.ComparingtheperceptionsoftheNoyceScholarsonvariousaspectsofteachingandtheteachingprofessionwithasimilargroupofteachersthatdidnotreceivetheNoycescholarshipmayshedsomelightondifferencesbetweenNoyceScholarsandnon-NoyceScholars.Theresearchquestionsthatguidedthisstudywere:

1. HowdotheNoyceScholars’perceptionsofteachingandoftheteachingprofessiondifferfromtheperceptionsofagroupofnon-NoyceScholarswhowerecertifiedfromthesameteacherpreparationprogram?

2. HowdoNoyceScholars’decisionsaboutteachingandoftheteachingprofessiondifferfromtheperceptionsofagroupofnon-NoyceScholarswhowerecertifiedfromthesameteacherpreparationprogram?

TheworkoftheMathematicsTeacherEducationPartnership(MTE-P)addressesthesignificantnationalshortageofwell-preparedsecondarymathematicsteachers.Onefocusistherecruitmentofstudentsintotheteachingprofession.DatafromthisstudymayinformtheMarketingforAttractingTeacherHopefuls(MATH)researchactionclusterintheirworktorecruitstudentsintotheprofession.Identifyinghowandwhengroupsofstudentsmakedecisionstobecometeacherscanhelpwhenmarketingvariousteacherpreparationprograms.

MethodsandInstrumentation

Forthisquasi-experimentalstudy,weappliedstratifiedmatchedsamplingtocomparethedecisionsandperceptionsofparticipantswhoreceivedaNoycescholarshiptothoseparticipantswhodidnotreceiveaNoycescholarship.TargetedparticipantswerestudentswhoreceivedtheirsecondarymathematicsorscienceteachingcertificationfromauniversityinthesouthwesternregionoftheUnitedStatessometimefrom2002to2014.Additionally,alltargetedparticipantswerepreparedbythesameundergraduateteacherpreparationprogram.Thedataforthisstudywasgeneratedfromonesurvey,administeredelectronically,tothe61participants(29NoyceScholarsand32non-NoyceScholars)inthesummerof2015.

Thissurveywasadaptedfromtwoothersurveys;theSchoolsandStaffingSurvey(SASS)createdbytheNationalCenterforEducationalStatistics(NCES,2012)andtheNoyceScholarSurveydevelopedattheUniversityofMinnesotafortheNoyceEvaluationReport(UniversityofMinnesota,2012).Theresultingsurveycontained70questionsthatwereclassifiedintoninesections:PersonalInformation(PI),EmploymentInformation(EI),DecisionsonBecomingaSTEMTeacher(DBST),MentoringandInductionExperiences(MIE),ImpressionsofTeachingandCurrentJob(ITCJ),PlansforGraduateEducation(PGE),TeacherPreparation(TP),SchoolClimateandTeacherAttitudes(SCTA),andtheNoyceScholarship(NS).

Thequestionsonthesurveyhadavarietyofanswertypes.Somequestionsusedcategoricalscales,somewereordinalscales,andotherswereopen-ended.Mostoftheordinal


163

scalequestionshadmulti-partstatementswhereparticipantsrankedthestatementsonfour-orfive-pointLikertscales.Thefullsetofquestionsusedforthesurveycanbefoundataggieteach.tamu.edu/noyce-monitoring-and-evaluation-project.

Results

Responsesfromthesurveywereanalyzedtodetermineanystatisticallysignificantdifferencesbetweentwoindependentgroupsofparticipants,NoyceScholarsandnon-NoyceScholars,acrossfourcategoriesofthesurvey.Thefourcategoriesare:DecisionsonBecomingaSTEMTeacher(DBST),PlansforGraduateEducation(PGE),TeacherPreparation(TP),andSchoolClimateandTeacherAttitudes(SCTA).Somequestionswithincategorieswereanalyzedonastatement-by-statementbasisandforotherslatentvariableswerecreatedviaanExploratoryFactorAnalysis.Forthelatentvariables,correspondingfactorscoreswerecalculatedandMann-WhitneyUtestswereusedtodetermineanysignificantdifferencesbetweenthegroupsonboththelatentvariablesandthestatement-by-statementanalysis.ThetwocategoriesthatproducedstatisticallysignificantdifferencesbetweengroupswereDBSTandPGE.NostatisticallysignificantdifferencesbetweenNoyceScholarsandnon-NoyceScholarswerefoundfortheTPandSCTAcategories.

DecisionsonbecomingaSTEMteacher.TheDBSTcategorycontainedtwonominalscalequestions.Thefirstquestionwas“DidanyofthefollowinghelpyoudecidetobecomeaSTEMteacher?”Alistofninestatementsfollowedthisquestionandparticipantsrespondedtoeachstatementwith“yes”or“no.”Responsestotwoofthesestatementswerestatisticallysignificant.Thefirstofthesetwowas,“Iliketheflexibilityand/orautonomyofSTEMteaching.”ResultsoftheMann-WhitneyUtest(p=0.011)indicatedthatnon-Noyceparticipantswereinfluencedmorebytheflexibilityand/orautonomyofSTEMteachingthantheNoyceparticipants.Glass’effectsizevalue(∆=0.863)suggestedahighpracticalsignificance.

Thesecondstatementthatproducedastatisticallysignificantdifferencewas“Ifeelthatateachingcareeris/willbeconducivetomyfamilylife.”.ResultsoftheMann-WhitneyUtest(p=0.005)indicatedthatnon-Noyceparticipantswereinfluencedmorebyateachingcareerbeingconducivetofamilylife(M=0.88,SD=0.336)thanNoyceparticipants(M=0.55,SD=0.506).Glass’effectsizevalue(∆=0.982)suggestedahighpracticalsignificance.

ThesecondquestionintheDBSTcategorythatproducedastatisticallysignificantdifference(p=0.033)betweennon-Noyce(M=1.69,SD=0.471)andNoyceparticipants(M=1.41,SD=0.501)was“AtwhatpointinyourlifedidyoudecidetobecomeaSTEMteacher?”ThefrequencycountsindicatethatsignificantlymoreNoyceparticipantsdecidedtobecomeaSTEMteacherbeforetheageof18(n=17)thannon-Noyce(n=12).Additionally,significantlymorenon-NoyceparticipantsdecidedtobecomeaSTEMteacherbetweentheagesof19and


164

22(n=22)thanNoyce(n=10).Glass’effectsizevalue(∆=0.594)suggestsamoderatepracticalsignificance.

Plansforgraduateeducation(PGE).ThePGEcategorycontainedtwonominalscalequestions.Thefirstquestionwas“Sincegraduatingfromtheuniversityhaveyoutakenanygraduatelevelclasses?”Participantsrespondedwith“yes”or“no.”TheMann-WhitneyUtestproducedstatisticallysignificantdifference(p=0.042)betweenthetwogroups.TheseresultsindicatethatNoyceparticipantshadtakensignificantlymoregraduatelevelclassessincegraduatingfromtheuniversitythannon-Noyceparticipants.Glass’effectsizevalue(∆=0.564)suggestsamoderatepracticalsignificance.

Thesecondquestionregardingplansforpost-baccalaureateeducationwas“Sincegraduatingfromtheuniversityhaveyoureceivedanyadvanceddegrees?”andparticipantsresponded“yes”or“no.”AMann-WhitneyUtestindicatedthattherewasastatisticallysignificantdifference(p=0.036)betweenthetwogroups.TheseresultsindicatethatsignificantlymoreNoyceparticipantshadobtainedamaster’sdegreethannon-Noyceparticipants.Glass’effectsizevalue(∆=0.647)suggestsamoderatepracticalsignificance.

WhatwasLearnedfromthisWork

TheNoyceScholars,ingeneral,madedecisionsabouttheirfutureplansatyoungeragesandfordifferentreasonsthanthenon-NoyceScholars.SignificantlymoreNoyceScholarsdecidedtobecometeachersbeforetheageof18thannon-NoyceScholars.Furthermore,externalfactorslikeflexibilityorautonomyofSTEMteachingandconducivenesstofamilylifeseemedtobelessofaninfluenceonNoyceScholars’decisionstoteach.ThismaysuggestthatNoyceScholarsweremoreactivelythinkingabouttheirfuturecareerswhilestillinhighschool.Additionally,NoyceScholarsmaydecidetobecometeachersforreasonsotherthan“flexibilityorautonomyofSTEMteaching”and“conducivenesstofamilylife”fordecidingtobeateacher.NoyceScholarsappeartobelessinfluencedduringtheircollege-agedyearsonmakingacareerchoicesincemanyofthemmadethedecisionbefore18.Non-NoyceScholars,ontheotherhand,seemtobeentercollegelessdecidedonacareerchoiceandmaybemoreinfluencedbyexternalfactorswhenchoosingacareer.Thus,whenrecruitingteachersintotheprofessionduringthecollegeyears,externalfactorslike“flexibilityorautonomyofSTEMteaching”and“conducivenesstofamilylife”maybegoodaspectsoftheteachingprofessiontohighlighttorecruitcollegeagedstudentsintotheteachingprofessionoratleasttogetthemthinkingaboutselectingteachingasacareer.

ResultsinthePGEcategoryalsoindicatethatNoyceScholarsdecidetoinvestintheirgraduateeducationatahigherratethantheirnon-Noycecounterparts.Thiscouldbedue,inpart,tothehighacademicachievementthatNoyceScholarshadtodemonstrateasanundergraduatetoreceivetheNoycefunding.Noycescholarsmayvalueeducation,ingeneral,


165

morethanthenon-Noycestudents.Additionally,receivingthescholarshipfundsasanundergraduatecouldhaveputtheNoyceScholarsinapositionwheretheyhadlessstudentloandebtandthus,morewillingnesstoinvestmoneyingraduatestudies.Thisnotioncannotbefullysupportedbytheresultsofthisstudy,butitissomethingthatcouldbeexploredinfuturestudies.

Conclusion

OneofthereasonsMTE-Pwasformedwasto“addressthesignificantnationalshortageofwell-preparedsecondarymathematicsteacherswhocansupporttheirstudentsinachievingtheCommonCoreStateStandardsforMathematics”(AssociationofPublicandLand-GrantUniversities,ND).TheNoyceScholarsareagroupofwell-preparedsecondarymathematicsteachers.DiscoveringanyuniquecharacteristicsabouttheNoyceScholarsmaygivesomeinsighttohowbetterrecruithigh-achievingstudentsintotheteachingprofession.Thisstudyprovidessomeexamplesofsuchinsight.

ForMoreInformation

• CorrespondenceconcerningthisarticleshouldbeaddressedtoJenniferG.Whitfield,DepartmentofMathematicsMailStop3257,TexasA&MUniversity,CollegeStation,TX77843.

• Contact:[email protected]

• TheNationalScienceFoundationDivisionofUndergraduateEducationAward1439907supportedthisresearch.

References

AssociationofPublicandLandGrantUniversities.(ND).MathematicsTeacherEducationPartnership,Retrievedfromwww.aplu.org/projects-and-initiatives/stem-education/mathematics-teacher-education-partnership/index.html

Bull,K.S.,Marks,S.,&Salyer,B.K.(1994).Futureteacherscholarshipprogramsforscienceeducation:Rationaleforteachinginperceivedhigh-needareas.JournalofScienceEducationandTechnology,3(1),71-76.

Darling-Hammond,L.(2007).Weneedtoinvestinmathandscienceteachers.ChronicleofHigherEducation,54(17),B20.Retrievedfromchronicle.com/article/We-Need-to-Invest-in-Math-and/14523

Henry,G.T.,Bastian,K.C.,&Smith,A.A.(2012).Scholarshipstorecruitthe“bestandbrightest”intoteaching:Whoisrecruited,wheredotheyteach,howeffectivearethey,andhowlongdotheystay?EducationalResearcher,41(3),83-92.

Liou,P.Y.,Desjardins,C.D.,&Lawrenz,F.(2010).InfluenceofscholarshipsonSTEMteachers:Clusteranalysisandcharacteristics.SchoolScienceandMathematics,110(3),128-143.


166

Liou,P.Y.,Kirchhoff,A.,&Lawrenz,F.(2010).PerceivedeffectsofscholarshipsonSTEMmajors’commitmenttoteachinginhigh-needschools.JournalofScienceTeacherEducation,21(4),451-470.

Liou,P.Y.,&Lawrenz,F.(2009).UniversityofMinnesotaevaluationoftheRobertNoyceTeacherScholarshipProgram,finalreportsectiontwo:Factoranalysisoftheevaluationquestionnaire.Retreivedfromwww.cehd.umn.edu/EdPsych/NOYCE/Reports/default.html

Liou,P.Y.,&Lawrenz,F.(2011).Optimizingteacherpreparationloanforgivenessprograms:Variablesrelatedtoperceivedinfluence.ScienceEducation,95(1),121-144.

NationalCenterforEducationalStatistics.(2012),Teacherquestionnaireschoolsandstaffingsurvey2011-2012schoolyear.Retrievedfromnces.ed.gov/surveys/sass/pdf/1112/SASS4A.pdf

UniversityofMinnesota.(2012),Instruments,Retrievedfromwww.cehd.umn.edu/EdPsych/NOYCE/Instruments.html

167

CLOSINGREMARKS


168

FromImprovementtoTransformation


[email protected]

[email protected]

[email protected]

TheeventoftheFifthAnnualMathematicsTeacherEducationPartnership(MTE-P)conferenceisareasonabletimetoreflectuponMTE-PeffortstotransformsecondarymathematicsteacherpreparationprogramsintheUnitedStates,assesscurrentinitiatives,anddeterminepotentialactionsthatcanandshouldbeattemptedinthenearfuture.MTE-Phassteadilymovedfromformingactionplansandpartnerships,totestinginterventions,toimplementingtransformationaleffortsinvolvingmultipleinstitutionsinmultiplestates.Thisyear’sconferencefocusedonlearninghowtomakeMTE-PworktransformativebyusingtheinnovationsdevelopedbymultipleRACsatmultiplesitestoleveragemeaningfulchangeinbothlocalpartnershipprograms,andinthelargersystemofsecondarymathematicsteacherpreparation.

GuidingPrinciples

OneofMTE-P’sinitialeffortswastocreateasetGuidingPrinciples(revised:MTE-P,2014)thatdescribedandestablishedasharedvisionforsecondarymathematicsteacherpreparation,avisionnecessaryfortheoverallcontinuityanddirectionofourlocalandnetworkedefforts.Moreover,thisvisionwasexpectedtobealivingdocument,tobeexploredandrefinedbyMTE-Pmembersaswellasothersinvolvedinpreparingsecondarymathematicsteachersby:

1. buildinganationalconsensusonwhateffectivesecondarymathematicsteacherpreparationprogramsneedtodoinordertodevelopteachercandidateswhopromotemathematicalexcellenceintheirfuturestudents;

2. enhancingcommunicationamongthepartnersinvolvedinasecondarymathematicsteacherpreparationprograminordertoclarifyprogramgoals,toassesstheeffectivenessoftheprogram,andtoguideprogramdevelopmentandrevision;

3. servingastheframeworkforanemergingnationalresearchanddevelopmentagendarelatedtosecondaryteachermathematicspreparation;and

1



169

4. helpingtoorganizetheidentification,development,anddisseminationofresourcessupportingeffectivesecondarymathematicsteacherpreparationprograms.

Atpresent,MTE-PhastenGuidingPrinciplesthatmustbeconsideredintheefforttoaddresstheidentifiedproblem,thereformofsecondarymathematicsteacherpreparationprograms.TheGuidingPrinciplesareorganizedintothreesections:Partnerships;TeacherCandidateKnowledge,Skills,andDispositions;andProgramStructures.Eachoftheseareasarecriticalinfluencesonprograms;however,theirinteractionsmaybeevenmoreimportant.ThemannerinwhichtheseGuidingPrinciplesinteractisevidencedinMTE-P’sprimarydriverdiagram,arepresentationoftheworkingtheoryofpracticeimprovement.Thisdriverdiagram,Figure1,servestocreateacommonlanguageamongthecommunityanddirectstheeffortstosolvethissharedproblem.

Figure1.ThedriverdiagramoftheMTE-Partnership.

Vision

Theseprinciplesledtothedevelopmentoftwoaims:(1)Createa“goldstandard”inwhichprogramsdocumentthattheirgraduatesarecapableofprovidingtheambitiousinstructionanddeeplearningcompelledbyCommonCoreStateStandardsforMathematicsandothercollegeandcareer-readystandards,basedonbenchmarkstobedevelopedbyMTE-

Creating a “gold standard” Programs document that their graduates are capable of providing the ambitious instruction and deep learning compelled by CCSSM, based on benchmarks to be developed by the MTE-Partnership

More and better new teachers To prepare <target number> of graduating secondary mathematics teachers with an emphasis on increasing diversity.

Creating a VisionCreating a common vision of and commitment to SMTP

among stakeholders

Content KnowledgeDeveloping candidates'

knowledge of mathematics needed to support student

learning of content and practices

Clinical Preparation Developing and supporting mentor teachers who can

provide field experiences that support candidates'

development of instructional practices.

Recruitment and RetentionAttract and maintain an adequate supply of candidates

Primary Drivers

Active Learning in Mathe-matics. Use of active learning strategies in introductory university mathematics courses.

Aim Research Action Clusters (RACs)

MODULE(S)2 (Mathematics of Doing, Understanding, Learning and Educating for Secondary Schools). Developing modules to build particular mathematical knowledge needed to teach.

Clinical Experiences. Innovative models supporting candidates' development of effective mathematical teaching practices.

MATH (Marketing to Attract Teacher Hopefuls). Models for developing and launching market-ing campaigns that rebrand teaching to appeal to more students.

STRIDES (Secondary Teacher Retention & Induction in Diverse Educational Settings). To improve teacher retention rates in early career secondary math teachers.


170

P;and(2)producemoreandbetterteachers,specificallyincreasingthequantityofwell-preparedcandidatesby40%bytheyear2020.Toachievethoseaims,fourprimarydriverswereidentified:creatingavision,clinicalpreparation,contentknowledge,andrecruitmentandretention.ResearchActionClusters(RACs)formedtobegintostudytheissuesraisedintheGuidingPrinciples,withtheaimsinmindforthework.

Fromtweakingtotransformation

ThathistoryofworkintheMTE-Partnershiphascreatedaferventoftinkering,studying,revising,andre-implementingasmembersoftheRACscarryoutPlan-Do-Study-Act(PDSA)cycles.WhichbringsustothepresentopportunitytorefocusonthechargeoftheMTE-Partnership,totransformsecondarymathematicsteacherpreparationprogramsintheUnitedStates.Thisconferencelaunchestheprojectintoafifthyearofworkonthistransformation.Thegatheringservedasanopportunitytostepbackandshareoutwhatthecommunityislearningasittinkers,tweaks,andstudiesitsefforts.Butalsothecommunitywasredirectedtoconsiderthetheoryunderlyingandmeasuresthatindicatesuccesswiththetransformationofsecondarymathematicsteacherpreparation(considerFigure2).Havinglookedback,wehopetoexaminetheactivityofthisfifthconferenceandconsiderwhatmaybenextstepsfortheMTE-Partnership.

Figure2.Amodeltosupportconsistent,continuousclassroomchange.

TheMTE-Partnershiptoday

OnestrengthoftheMTE-Partnershipisthenumberoflocalteamsthatformtheoverallpartnership;itisanetworkedimprovementcommunity(NIC).Thisnetworkpermitseffortsinmultipleareastobesharedandreplicatedinacollaborative,controlled,cyclicprocessthatoffersbothbreadthanddepth—afoundationalelementofimprovementscience(Bryketal.,2015).

NetworkedImprovementCommunitiesandImprovementScience

TheMTE-Partnershipfollowstheprinciplesofimprovementsciencetoacceleratehowthefieldofmathematicseducationlearnstoimprove.Thecoreprinciplesofimprovementscienceare:maketheworkproblem-specificanduser-centered;variationinperformanceisthe


171

coreproblemtoaddress;seethesystemthatproducesthecurrentoutcomes;wecannotimproveatscalewhatwecannotmeasure;anchorpracticeimprovementindisciplinedinquiry;andaccelerateimprovementsthroughnetworkedcommunities.

MTE-Pisorganizedasnetworkedimprovementcommunityinalignmentwithimprovementscience,andisakeyconstructforinvolvingpractitionersinboththeimplementationandtheresearchoftheinnovationtargetedbythevisionandactionplans.NICsofferchannelsofcommunicationthatprovidebuilt-inopportunitiestoleveragelocalrepeatedstudiesofdisciplinedinquiry(e.g.,Plan-Do-Study-ActCycles)intostate-wideornation-wideimpact.Scalinguptheinnovationisthenextautomaticstepasadditionalpartnershipsdecidetotesttheinnovationforthemselvesandsharetheresults.

Partnerships

TheMTE-Partnershipprojectisarelationship-focusedenterprise,inwhichseveraltypesarepartnershipsareprevalent.Theformationoflocalteams,consistingofatleastoneuniversitywithasecondarymathematicsteacherpreparationprogram,oneschooldistrict,andoneadditionalmember(openeducationalcategory).MTE-Pbenefitsintwowaysfromthisstructure:(1)partnershipsbetweenuniversityprogramsandK-12schoolscontainsthemostimportantstakeholdersintheprocessofsecondarymathematicsteacherpreparation,and(2)havinganopencategoryforlocalpartnersresultedinawiderangeofstakeholdersintheoverallMTE-Pmembership.Thesetwobenefitsarebothwell-alignedtothefirstNICprinciple,makingtheworkproblem-specificanduser-centered.

AsecondtypeofpartnershipiscarriedoutamongindividualswhoparticipateinResearchActionClusters(RACs).FiveactiveRACsareworkingtoaddressvariouscomponentsoftheGuidingPrinciples.Collectivelytheseeffortshavethepotentialtoformaclearandcompellingsetofpathwaysforteachingandteacherpreparationthatwillbesharedbymanyinstitutionsandstates.

Forexample,twelvepartnerinstitutionsareinvolvedintheActiveLearningMathematics(ALM)RAC,bringingdifferentlocalcontextstotheeffort.ALMaimstoimprovestudentsuccessinundergraduatemathematicscourses,especiallyPre-calculusthroughCalculus2,bychangingthewayundergraduatemathematicsistaught,shiftingfromapassivetoanactiveroleforthelearner.Thissetofpartnerinstitutionsshareacommonvisionoftransformingundergraduatemathematicsteachingandlearningthroughtheuseofactivelearning,althougheachlocalteammayapproachtheproblemdifferently.Commonmeasures,usedtodocumenteachprogram’sprogress,offermeaningfulcomparisonsofeffortsamongthedifferentprogramsandallowtheMTE-Partnershiptojudgecollectiveimpact.

TheMarketingtoAttractTeacherHopefuls(MATH)RAChasalsorespondedtotheGuidingPrinciples,andspecificallytherecruitmentchallengeintheprimarydrivers.MATH


172

developedaSecondaryMathematicsTeacherRecruitmentCampaignGuidewww.surveymonkey.com/r/MATHImplGuide,whichisnowbeingimplementedandevaluatedby14differentlocalteams.TheresultsandproductsofPDSAcyclesconductedoverthepasttwoyearsbyteamswithinthisRACaredocumentedatpadlet.com/ed_dickey/vhle4gisbq82.

EachofthethreeotherRACS,ClinicalExperiences,MODULE(S)^2,andSTRIDESareexaminingotherelementsoftheprogrammaticefforttoprepareandretainmoresecondarymathematicsteachers.TheRACstructureisthedrivingforcefortheMTE-Partnership,eachformedbyandrepresentingmultiplepartnerships.Thisstructurecreatesworkingteamssmallenoughtobeefficientinplanningandimplementinginnovationsbutwithbuilt-inconnectionstomakescaling-upthoseinitiativesseamlessandinformative.EachRACisaNICinandofthemselvesandcollectivelytheyformalargernation-wideNIC.

Stateofaffairs

Improvementscienceisauser-andproblem-centeredapproachedtoimprovingeducation,explicitlydesignedtoacceleratelearning-by-doing.Atpresent,muchproductiveworkhasbeenaccomplishedinthe“learning-by-doing”spiritamidthevastMTE-Partnership.Ithasproventobeanorganizationcapableoflearningandimproving,embracingchangeandvaluingthepreviouslyinvisibleproblemsastheyemerge.

Lookingforward

Theeditorsoftheconferenceproceedingshadtheopportunitytocloselyreviewthenumerousactivitiesreportedoutattheconference,bechallengedbythepresentationsoftheplenarysessions,andexaminethenewideasgeneratedbytheRACswhiletherewishtoclosewiththoughtsaboutandchallengesregardingthefuturedirectionoftheMTE-Partnership.

GuidingPrinciples

InrevisitingtheGuidingPrinciples,driverdiagram,andworkoftheRACs,wewereintriguedtonoticetheMTE-PartnershipcurrentlyhasRACsthatrespondstronglyto61%(20of33) oftheIndicatorsofthetenGuidingPrinciples.Werecognizethislimitedfocuswasnecessaryandintentionalfromthebeginningoftheprojectasparticipantsrecognizedthecomplexityofthetaskandrealizednoteverythingcouldbedoneatonce.Workinggroupssetprioritiesfortheirareasbasedonwhattheythoughtcouldbeaddressedhadthemostpotentialtoleveragechange.RACswereformedfromthesediscussionswhichhelpedfocustheworkandachievecompletedproductsoverthefirstfewyears.

ThereareseveralIndicatorsoftheGuidingPrinciplesthathavenotbeenstronglyorexplicitlyaddressedbythecurrentRACS,listedinTable1.Forexample,thenotionofsharedengagementandresponsibility(1C)canbefoundinfoundinelementsoftheworkofsomeRACs.TheClinicalExperiencesRACreliesonstrongpartnershipsbetweenschoolsandcolleges


173

ofeducation,collectivelydesigningandsharingresponsibilityforsuccess.However,notallconstituentsareactivelyengagedtothedegreefoundinGuidingPrinciples.Todate,thislevelofcommitmentofthesite-levelpartnersacrossallRACsremainsachallenge.ThischallengeiscloselytiedtoGuidingPrinciple2anditsIndicators.

Table1.SpecificIndicatorsoftheMTE-PGuidingPrinciplesnotcurrentlyaddressedbyRACs.

# GuidingPrincipleandIndicators1. PartnershipsastheFoundation 1.C.SharedEngagementandResponsibility2. CommitmentsbyInstitutionsofHigherEducation 2.A.InstitutionalFocus 2.D.InstitutionalSupportforFaculty4. Candidates’KnowledgeandUseofMathematics 4.D.NatureofMathematics5. Candidates’KnowledgeandUseofEducationalPractices 5.A.DesignofInstruction 5.B.InstructionalMethods 5.C.AssessmentandReflection 5.D.UseofInstructionalTechnology 5.E.AttentiontoDiversity6. Professionalism,Advocacy,andLeadership 6.A.Integrity 6.B.IntellectualSpirit 6.C.SenseofJustice 6.D.StewardshipandLeadership

GuidingPrinciples4and5alludetocontentandpedagogicalcontentknowledge.TheActiveLearningMathematicsandMODULE(S2)RACsareintentionalaboutcreatingamorerobustunderstandingofthecontentofthediscipline,mathematicalhabitsofmind,andthespecializedknowledgeofMathematicsnecessaryforteaching.However,thereisnospecificefforttoensure“teachercandidatesunderstand,andareabletoconveytotheirstudentsthatmathematicsisalivingandevolvinghumanendeavorthatreliesonlogicandcreativity,anditisvaluableforcitizenship,fortheworkplace,aswellasforitsintrinsicinterest”(MTE-P,2014,p.4).Thefocusonstudent’slearningeducationalpractices,especiallythosespecifictosecondarymathematicsinstructionisnotyetaddressedbytheMTE-Partnership.WedorecognizeafundamentalelementoftheClinicalPracticesRACistoprovidepreserviceteachersopportunitiestopracticeandreceivefeedbackoneducationalpractices,whichgreatlycontributestolearning.Ontheotherhand,theClinicalPracticesRACaddressesasmall,butessential,partofmathematicsteachereducationprograms.


174

Anattentiontothedevelopmentofasenseofsocialjustice,includingequitablepedagogyandattentiontodiversity,hasnotyetreceivedthedirectandconcentratedattentionthesechallengescallfor—thisisevidencedbythestronginterestandrequeststhatemergedfromthediversityandequitysessionoftheconference.Morebroadly,thepartnershipdoesnotyethavearesearchclusterthatattendstothedevelopmentofprofessionalism,advocacy,andleadership.AsSTRIDESbeginstomature,wesuspecttheyarelikelytotakeupsomeoftheissuesidentifiedintheIndicators.

TakingstockofwhereMTE-Pissuccessfulandwherethereremainsgoalsyettobeaddressedshouldhelpdefinenextprioritiesofthepartnership.DoesMTE-Phaveanexplicit,commonlyunderstoodplanofwhenandhowandwhenMTE-PwilladdressadditionalindicatorsoftheGuidingPrinciples?AresomeoftheseindicatorscriticalforRACsand/orlocalteameffectiveness?Whatsupportsdolocalteamsneedtoaddressthissetofindicators?HowcantheMTE-PartnershipanswerthesequestionsandmonitoritsprogressonaddressingtheGuidingPrinciples?

Asevidencedbytheconferencegoals,severalindicatorsthathaveyettoreceiveexplicit,focusedattentionpointtowardissuesofequity,socialjustice,andadvocacyaswellasthechallengesofinstitutionalchange,anunderlyingelementofprogramreform.Thesearelong-termtargetsforchange.WearehopefultheworkoftheMTE-PRACsassharedinthissetofproceedingsmaysetthestagesoeffortscanbelaunchedtosuccessfullyaddressthosetargetsinthenearfuture.

Equity,SocialJustice,andAdvocacy

MTE-PartnershipmembersrecognizedthatalthoughanumberoftheRACsincludedissuesofequityandsocialjusticeintheirplanning,theresultantactivitiesandstrategiesthatmightimpactthisconstructhavebeenlessthanclear.Assuch,onegoalfortheFifthAnnualMTE-PartnershipConferencewasto,“makeequityandsocialjusticemoreexplicitasanessentialcomponentofthepartnershipaim.”Partofthetimesetasideforworkatthisconferencewasdedicatedtoaddressingequityandsocialjusticeandtheadvocacyforit.AtthebeginningoftheconferenceaworksessiononEquityandSocialJusticewasheldandopentoallparticipants;theresultsofthisworksessioncanbefoundintheseproceedings.Additionally,theRACswereaskedtoexplicitlyaddressequityandsocialjusticeintheirindividualworkingsessions.AttheendoftheconferenceeachRACincludedintheirreportstheresultsoftheirfocusedconversationsandconnectionstoEquityandSocialJustice.IftheGuidingPrinciplesaretocontinuetodirectthework,itseemsthechallengesandquestionsthatemergedinboththeworksessionandRACmeetingsmustbefollowedupon.


175

Transformation

ReviewoftheGuidingPrinciplesmadeevidentthatnumerouselementsoftheMTE-Partnershipchargepointdirectlytothecomplexityofprogramtransformation.Severalelementsoftransformationareflourishingatpresent.RACsareengagedineffortstoexpandtheirworktoadditionalpartnershipsthroughPlan-Do-Study-Actcycles,testingandevaluatingtheproductsandmaterialsthathavebeendeveloped.Astheycontinuetorefinetheirinnovationsandscale-uptheirinfluencethelargerMTE-PartnershipNetworkImprovementCommunityispoisedtosupportandconnecttheirwork.Forexample,theMTE-PHubhelpstoshowcasetheworkoftheRACs,providesfundingtohelpwithface-to-faceRACmeetings,servesasarepositoryforRACmaterials,andhostsandsupportseventssuchasthisconference.

YetsustainabilityoftheRACsmustcontinuetoreceivepriority;pursuitoffundinginsupportoftheworkisoneelementofthechallenge.MuchoftheeffortsofRACmembersarevolunteerandcancausestressandunduepressureovertime.Manyhavesubmittedgrantproposalsandsomehavereceivedfunding.ButthequestionstillloomsastohowtheRACscanbetransformedintomoresustainablenetworks?HowcantheMTE-Partnershiphelpuniversities,especiallytheadministratorsunderwhichtheMTE-Pfacultyserve,understandtheimpactimprovementsciencehasmadeontheircampuses?

HowcanMTE-PartnershipmaketheworkoftheRACsmorevisibleanddesirable?Muchofthishasbeenleftuptotheindividualpartnerships,buttheremaybeakeyrolefortheRACsandtheMTE-PartnershipHub.HowareRACsperceivedatthelocalsites?HowcantheHubhelpwithvisibility,persuasion,inimplementation,andevaluationatthelocallevels?VariousformsofpresentationsdosharePlan-Do-Study-Actcycles,butthedetailshowoftheNetworkedImprovementCommunitiesfoldintotheprocessarescarce.SuzanneWilson’smodeloftweakingourwaytotransformationthroughtheoryandmeaningfulmeasures(Figure2)seemstofittheMTE-Pprocesswell.Butitleavesuswiththechallengetolearnhowprogramtransformationcantakeplace.ThefifthconferenceconcludedwithanemergingworkinggrouponProgramTransformation—clearlyanextneededconsideration.

Improvementsciencecontinuestobeaperfectmatchtothischallenge.ItallowstheMTE-Partnershiptoengageinaniterativeprocessoverconsiderableperiodsoftime.Further,thegoalofprogramtransformationisnotaboutafinalstate,buttowelcomeandengageincontinuousimprovement.Theoverallgoalistodevelopthenecessaryknowledge-baseandactionstepsforthereformofsecondarymathematicsteacherpreparationtospreadeffectivelywithinandbeyondtheMTE-Partnership.

Summary

MTE-Phascomealongwayinfiveyears.Startingwithvaguehazyideasaboutchangingteachereducation,MTE-Phasmanagedtodevelopcommonvisionacrosshundredsof


176

individualsrepresenting30states.WithRACsasadrivingforce,thisprojecthasevolvedfrominspirationtoinnovationtoaction.AlthoughMTE-Pcanpointtomanysignificantandimportantaccomplishmentsoverfiveyears,theworkisjustbeginning.Changingsecondarymathematicsteacherprogramsseemstobeaherculeantaskthathasresistedpasteffortsofsignificantchange.Ontheotherhand,MTE-Pisaspecialgroup,intermsofsize,scope,anddedication,thathasachancetomakeamuch-neededdifference.

Atthispointinitsevolution,MTE-PhasfourmatureRACs(MATH,ALM,CERAC,andMODULE(S2),withSTRIDESinanascentstate),thathavecreatedproductsthatcanbeusedbyanyofthepartnerships.Wilson(2011)identifieda“downwardcycle”inconsideringthechallengestoeffectivemathematicsteacherpreparation(modifiedbyMartin&Strutchens,Figure3).TheRACsoftheMTE-Partnershipmaybebeginningtoreversethisdownwardtrend.AtthisphaseofdevelopmentMTE-PhasevolvedtobegintodeterminewhichcombinationoftheseinnovationsarecapableofhelpinganypartnershipteamcontributetoMTE-P’stwinaims,tocreatea“goldstandard”forsecondarymathematicsteacherpreparation,andtoproducemoreandbetterteachers.PerhapsmaterialsfromalltheRACsmustbeimplementedwithahighdegreeoffidelitytoachieveameasurableeffectonthesetwoaims.Ontheotherhand,therequirementsformakingadifferencecouldbelessstringent.Thecurrentmovefrominnovationtotransformationsetsthestagetoanswerquestionsofthisnature.

Figure3:Reversingthe“downwardcycleinmathematicsteacherpreparation”(Martin&Strutchens,inpress).

TheMTE-PartnershipNetworkedImprovementCommunityprovidesastructureinwhichindividualeffortsoftransforminglocalmathematicsteacherpreparationthrough


177

integratingmultiplesetsofRACmaterialsintotheirprogramscontributetoanationwidestudythathasthepotentialpowertoprovideanswerstoquestionsaboutcomplexissues.Asthecommunitymakesprogresstowarditsaimsthroughrapidtestsofchange,italsolearnsmuchaboutthedetailandcomplexityoftheproblem.Oureffortsforimprovementaregroundedinapurposefulfraternityofexpertise,creating,sharing,andbuildingonthehardworkofoneanother.TheMTE-Partnershiphasplacedusinauniquepositionthatofferstheopportunitytocreateevidencethatjustifiesmeaningfulchange.

References

Bryk,A.S.,LeMahieu,P.G.,Gomez,L.M.,&Grunow,A.(2015).Learningtoimprove:HowAmerica’sschoolscangetbetteratgettingbetter.Boston,MA:HarvardEducationPress.

Martin,W.G.&Strutchens,M.E.(inpress).Transformingsecondarymathematicsteacherpreparationviaanetworkedimprovementcommunity:Focusonclinicalexperiences.ICME-13MonographonSecondaryMathematicsTeacherPreparation.


Wilson,S.M.(2011).EffectiveSTEMteacherpreparation,instruction,andprofessionaldevelopment.PaperpreparedfortheworkshopoftheCommitteeonHighlySuccessfulSchoolsonProgramsforK-12STEMEducation.Washington,DC:NationalResearchCouncil.

MATHEMATICSTEACHEREDUCATIONPARTNERSHIP

aprojectofthe

AssociationofPublicLandGrantInstitutionsScienceandMathematicsTeacherInitiative

www.mte-partnership.org

PROCEEDINGS OF THE FIFTH ANNUAL MATHEMATICS TEACHER EDUCATION PARTNERSHIP CONFERENCE · PROCEEDINGS...

Documents

Transcript of PROCEEDINGS OF THE FIFTH ANNUAL MATHEMATICS TEACHER EDUCATION PARTNERSHIP CONFERENCE · PROCEEDINGS...