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Teacher Education Quarterly, Winter 2008

The Impact of Professional Development in Mathematics

on Teachers’ Individualand Collective Efficacy:

The Stigma of Underperforming

By Ron Zambo & Debby Zambo

Professionaldevelopmentisanongoingneedforteachersespeciallyintheareaofmathematics,adomainthatisthefocusofstatetestingprograms.Professionaldevelopmentforteachersofmathematicshasbeenshowntohavepotentialpositiveeffectsforbothchangingteachers’beliefsaboutmathematicsinstructionandtheinstructiontheyprovide(Harwell,D’Amico,Stein,&Gatti,2000;Loucks-Horsly&Matsumoto,1999;Nelson,1998;Vacc,Bright,&Bowman,1998).Inparticular,professionaldevelopmenthasthepotentialtochangeteachers’beliefsabouttheirindividualandcollectiveefficacy.Bothtypesofefficacyareimportanttoteachers’persistence,drive,andsuccess(Zimmerman,1995).

Ron Zambo and Debby Zambo are professors in the College of Teacher Education and Leadership at Arizona State University, Phoenix, Arizona.

Individualefficacyishighlyassociatedwithteachermotivation,whichinturnaffectsstudentachievement(Bandura,1993,1997).Teacherswithastrongsenseofindividualefficacytendtospendmoretimeplanning,designing, andorganizingwhat they teach.Theyareopen to new ideas, willing to try new strategies, sethighgoals,andpersistthroughsetbacksandtimesofchange(Goddard,Hoy&WoolfolkHoy,2000).Inotherwords,teacherswithastrongsenseofindividualefficacy

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believetheycananddomakeadifferenceinthelivesoftheirstudentsandthattheirstudentscanandwillachieve.Researchintoindividualefficacyshowsthatitisacomplexconstructcomposedoftwodistinguishablecomponents:personal competenceandpersonal level of influence(Hoy&Woolfolk,1993). Personalcompetenceisa teacher’sperceptionofhisorherabilitytooper-ateatahighlevelofproficiencyinaspecificdomain.ResearcherslikeHoyandWoolfolk(1993)foundthatthepersonalcompetenceofprospectiveteacherstendstogetstrongeraftertheycompletetheirfinalinternship,especiallyifitcontainedmasteryexperiences.Weextendthisideatoinserviceteachersandtheprofessionaldevelopment theyreceive. If teachersattendworkshops thatprovide themwithmasteryexperiencesordirectexperiencesthatleadthemtobelievetheycanmasteradomain,theirpersonalcompetencelevelwillrise(Bandura,1997;Pintrich&Schunk,2002).Thesecondcomponentofindividualefficacyispersonallevelofinfluence,orateacher’sbeliefsregardingthelevelofinfluenceofhisorheractionsonstudentlearning.Teacherswithahighpersonallevelofinfluencebelievethattheireffortscanandwillaffectlearningintheirstudentsinapositiveway. Duetothefactthatteachersworkinacomplexsetting,theyalsohaveanothertypeofefficacycalledcollectiveefficacy.Likeindividualefficacy,collectiveefficacyaffectsachievementbutinabroadersense.Collectiveefficacy,orateacher’sbeliefabouthisorhercolleagues’effectiveness,goesbeyondtheindividualteachertofocusonthefacultyasawhole(Bandura,1993,1997).Justasindividualefficacyhastwocomponents,sodoescollectiveefficacy.Thefirstisgroup competence,whichisateacher’sbeliefthathisorhercolleaguescanoperateatahighlevelofcompetenceandachievegoals.Theothercomponentiscontextual influence orateacher’sperceptionofthedifficultyofteachingathisorherparticularschool,takingintoaccountthenatureofthestudents,availabilityofsupplies,andsoforth(Goddard,Hoy&WoolfolkHoy,2000).BothindividualandcollectiveefficacyandtheirtwocomponentsaresummarizedinFigure1.

Rationale for the Study TheNo Child Left Behindlegislationrequiresstatestoclassifyschoolsbasedon students meeting the state’s academic standards.A combination of factors,includingscoresonstatespecifictestsandnationallynormedtests,canresultinaschoolbeingawardedalowclassificationorahighclassification.Inourstate,schoolsinthelowclassificationarelabeledunderperforming,andschoolsthatarepersistentlyclassifiedasunderperformingcaneventuallybetakenoverbythestate.AlthoughNo Child Left Behindwasonlyrecentlypassed,manystateshavebeenusingbothstate-specificandnationallystandardizedtestsforyears.Teachershavebeenawareoftheirstudents’achievementlevelsbasedonthosescores,butnowthataccesstoinformationisquickandpublicviatheInternetandothermedia,thatinformationisrapidlyandwidelydisseminated.However,theimplicationsof

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thispublicandopendisplayofstudentachievementonteacherefficacyhavenotbeeninvestigated.Thepurposeofthisstudywastoinvestigatethecomponentsofindividualandcollectiveefficacywithinandbetweentwogroupsofteachersat-tendingasummerworkshopwhocamefromtwodifferenttypesofschooldistricts.Onegroup,whichwecalllow,camefromadistrictwheremanyoftheschoolshadbeenlabeledasunderperformingandtheothergroup,whichwecallhigh,camefromadistrictwithfewunderperformingschools. Giventhepublicnatureofschoolclassification,thethreatofbeingtakenover by the state, and the potential impact of professional development onteacherefficacy,wesetouttoinvestigatetheindividualandcollectiveefficacyof teachersworking in these twodifferentsettings.Ourhypotheseswere: (1)Forbothgroups,scoresforpersonalcompetenceandpersonallevelofinfluencewouldincreasefrompre-toposttest,whereas,scoresforgroupcompetenceandcontextualinfluencewouldnot.Wereasonedthattheworkshopswoulddirectlyinfluenceteachers’skillsandknowledgerelatedtomathematicsteaching,whichwouldchangetheirperceptionsofboththeireffectivenessandtheirinfluenceonstudents.Conversely,wethoughtthattheprofessionaldevelopmentwould

Figure 1. The Two Forms of Efficacy Teachers Have and Components of Each.

Individual efficacy—belief that one is capoable of executing certain behaviors or reaching certain goals in a particular domain, like teaching.

Has two components:

1. Personal competence or perception 2. Personal level of influence orthat one has the ability to operate one’s beliefs regarding the level ofat a high level of competence in a influence of his or her actionsspecific domain. on student learning.

Collective efficacy—one’s belief about the effectiveness of one’s colleagues.

Has two components:

1. Group competence or one’s belief 2. Contextual influence or one’sthat one’s colleagues can operate perception of the difficulty ofat a high level of competence and teaching at one’s particularachieve goals. school.

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havenodirectinfluenceonteachers’viewsoftheircolleaguesorthedifficultyofteachingattheirschool.(2)Teachersinbothgroupswouldscorehigheronpersonalcompetencethanongroupcompetence.Wereasonedthatteacherswhohadtheinitiativetoparticipateintheworkshopsrelatedtomathematicsinstruc-tionwouldalreadyhaveanaffinitytowardsmathematics.Wespeculatedthatthisaffinitywouldinfluencetheirperceptionsofthemselvesasbeingmoreeffectiveinteachingmathematicswhencomparedtotheircolleagues.(3)Teachersinthehighgroupwouldhavehigherscoresforgroupcompetencethanteachersinthelowgroup.We suggest this hypothesis because teachers in bothgroupswereawareofthelabelsputonschoolsintheirdistrictsand,becauseofthis,webelievethatteachersinthehighgroupwouldfeelmorepositiveabouttheircolleagues’effectivenessthanteachersinthelowgroup.Ourrationaleforthishypothesiswasthatteachersinthelowgroupwouldfeellesspositivebecausetheywereinfluencednegativelybythestigmaofhavingschoolsintheirdistrictlabeledasunderperforming.

Methodology

Participants Theparticipantswere634ththrough10thgradeteacherswhovoluntarilypartici-patedintwo-week,summerprofessionaldevelopmentworkshopsonmathematicsproblemsolving.Theworkshopsfocusedonhelpingteachersincreasetheirownproblemsolvingabilityaswellasimprovetheirclassroomproblem-solvinginstruc-tion.Thirty-twooftheteacherswerefromaschooldistrictwithalowincidence(5.3percent)ofschoolslabeledunderperforming.Theother31participantscamefromadistrictwithahighincidence(37.5percent)ofschoolslabeledunderperforming.

Instruments and Analysis Groupcompetenceandcontextualinfluence,subscalesofcollectiveteacherefficacy,weremeasuredbeforeandaftertheworkshopsusingthe21-itemLikertscaleCollec-tive Efficacy Questionnaire designedbyGoddard,Hoy,andWoolfolk-Hoy(2000).Thequestionnairewasadaptedformathematicsbyaddingtheword“mathematics”whereappropriate.Forexample,oneoriginalitemrelatedtogroupcompetencewas,“Teachersinthisschoolhavewhatittakestogetchildrentolearn.’Theitemwasmodifiedto,“Teachersinthisschoolhavewhatittakestogetchildrentolearnmathematics.”Anitemrelatedtocontextualinfluencewasmodifiedto,“Teachersinthisschoolreallybelievethateverychildcanlearnmathematics.”Thisquestionnaireuseda6-pointscale,wherea6indicatedthehighestefficacyanda1thelowest. Personalcompetenceandpersonallevelofinfluence,subscalesofindividualefficacy,weremeasuredwiththe25-item,LikertscaleEnoch & Riggs Elementary Science Efficacy Questionnaire (1990).Thequestionnairewasadaptedformath-ematicsinstructionbyreplacingtheword“science”withtheword“mathematics.”

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Amodifieditemrelatedtopersonalcompetencewas,“Iunderstandmathematicsconceptswellenoughtobeeffectiveinteachingmathematics.”Amodifieditemrelatedtopersonallevelofinfluencewas,“Increasedeffortinmathematicsteachingproduceslittlechangeinsomestudents’mathematicsachievement.”Anadditionalmodificationtothisquestionnairewasthattheoriginal5-pointscalewaschangedtoa6-pointscale,wherea6indicatedthehighestefficacy.Thischangewasmadeinordertofacilitatebetterthedirectcomparisonsofscoresbetweencollectiveandindividualefficacy.AnalysisofthequestionnaireswascompletedusingSPSS. Inadditiontohavingtheteacherscompletethequestionnaires,weinterviewedthemusingthefollowingfivequestions:

What is the incentive thatmotivatesyou toparticipate inprofessionaldevelopment?

Whatmakesaninserviceprogramgoodforyou?

Whatmakesaninserviceprogrambadforyou?

Whydon’totherteachersyouknowattendasmanyprofessionaldevelop-mentactivitiesasyoudo?

Comments to thesequestionswere recordedonaudiotapeand transcribed.We,thetworesearchers,readthroughtheinterviewtranscriptstolocatepatternsinwords,phrases,andevents.Weformedinitialcategoriesandwentontoformulatethemes.Asresearchers,weconstantlysharedourinterpretationsanddiscussedanydifferencesuntilagreementwasreached.Wemetbimonthlyascriticalfriendstoconfirmanddisconfirmourfindings.

Results

Within Groups Comparisons Inregardtothefirsthypothesis,paired-samplettestsindicatedthattheteach-ersinthelowgroupshowedasignificantincreasefrompre-toposttestonpersonalcompetence, with means and standard deviations of 4.96 (.66) and 5.40 (.51)respectively(t (30)=4.88,p <.01).Teachersinthehighgroupalsohadsignificantgainsforpersonalcompetencefrompre-toposttestwithmeansandstandardde-viationsof5.18(.62)and5.50(.37)respectively(t (31)=3.24, p <.01).However,only teachers in the lowgrouphad significant gainspre-toposttest ongroupcompetence,withmeansandstandarddeviationsof3.91 (.80)and4.23(.70)respectively(t (30)=2.76,p <.01).Therewerenosignificantpre-toposttestdif-ferencesbygroupsforanyothervariables.(Meansandstandarddeviationsofallfourvariablesbygrouppre-andposttestareshowninTable1.) Inregardtothesecondhypothesis:teachersinthelowgroupscoredsignificantlyhigheronpersonalcompetencethanongroupcompetenceonbothpretest[4.96(.66)

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comparedto3.91(.80): t(30)=6.32,p <.01]andposttest[5.40(.51)comparedto4.23(.70):t (30)=8.03,p <.01].Teachersinthehighgroupalsoscoredsignificantlyhigheronpersonalcompetencethanongroupcompetenceonbothpretest[5.18(.62)comparedto4.56(.60):t(31)=4.71,p <.01]andposttest[5.50(.37)comparedto4.68(.60):t(31)=8.6.47,p <.01].

Between Groups Comparisons Inregardtothethirdhypothesis:analysisofvariancewasusedtodeterminetheeffectofgroup(loworhigh)onthefourvariables.Therewasasignificantef-fectforgroupongroupcompetencebothpretestandposttest.Meansandstandarddeviationspreworkshopforthelowandhighgrouprespectivelywere:3.91(.80)and4.56(.60);F(1,61)=3.32,p <.01.Scorespostworkshopwere4.23(.70)and4.68(.60);(F(1,61)=7.466,p <.01.Therewasnosignificanteffectforgrouponanyoftheotherthreevariables.

Responses to the Interview Questions Whilesurveyscansupplymuch insight into teachers’perceptions,surveysarealsosubject tobiasanddistortion.Therefore, toenhancethereliabilityandcredibilityofthisstudy,interviewquestionswerealsoasked.Duetospacelimita-tionsnotallinterviewquestionswillbediscussed.However,theanswerstotwoquestions;Whatistheincentivethatmotivatesyoutoparticipateinprofessionaldevelopment?andWhydon’totherteachersyouknowattendasmanyprofessionaldevelopmentactivitiesasyoudo?wereofparticularinterest.Theresultsoftheanalysisofthosequestionsfollow. Teachers ingeneralstated that theyattendedprofessionaldevelopmentop-

Table 1. Within Group Means and Standard Deviations of all Componentsfor Individual and Collective Efficacy, Pre and Post.

Pre Post

Individual Efficacy PersonalCompetence low 4.96(.66) 5.40(.51)*­ high 5.18(.62) 5.50(.37)*­PersonalLevelofInfluence low 4.26(.47) 4.46(.53) high 4.31(.48) 4.33(.58)

Collective Efficacy GroupCompetence low 3.91(.80) 4.23(.70)*­ high 4.56(.60) 4.68(.60)ContextualInfluence low 3.55(.99) 3.70(.90) high 4.04(.96) 3.91(1.06)

*­Significantatthe.01level.

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portunitiessothattheycouldbebetterteachersand,asaresult,thatstudentscouldlearnmore.Forexample,one6th-gradeteachersaid,

Itakethese[workshops]formybenefitsoIcanlearnmoreinformationtoimproveteaching.ItisimportanttoimprovemyteachingbecauseI’mnotsomeonewhocoulddothesamethingayearafteryear....Itrytomakeitbetterforthem[students]tolearntheconcept...weareworkingonornewideas.

Similarly,a2nd-gradeteachersaid,“Iliketobealittleaheadoftheballgameinmybuilding,andifItaketheseclassesIwilllearnmoreandI’mgoingtolearnthingsthatIcanusewithmystudentstoimprovetheirachievement.”A7th-gradeteachersaid,“IwanttogivethekidsthebesteducationIcan!” Whereasa1st-gradeteachersaid,

EverythingIdoandeveryclassItake,Igetonenewideathatkindofgetsmeenthused again about something that I’ve taught over and over. It gives me achancetoseeotherapproachesthathopefullyIcanusetocatchsomekidsthataren’tgettingit.

Teachers in thisgroupalsogenerallybelievedthat theircolleagueswerenotinvolvedinprofessionaldevelopmentbecauseofotherobligations.Alongthesesamelines,theybelievedthatthattheircolleaguesprobablyfeltthattheyalreadydidagoodenoughjobteachingmathematicsandsoattendingtheworkshopswouldbeaninefficientuseoftheirfreetime.Forexampleone4th-gradeteachersaid,“Maybethey[teachersnotattending]havedifferentcommitments,morefamilycommitments.”A3rd-gradeteachernoted,“It’sbecauseoffamilyobligationandtimealsoothercom-mitmentsbecausesometeachershavetoworkinthesummerandtheyjustcan’tdoit.”Likewise,a4th-gradeteachersaid,“Foralotofpeopleitisprobablytime,kidsorasecondjob.SomepeoplefeeltheyaredoinganOKjob[teachingmathematics]sotheydon’tcaretocommitthemselvestomoredevelopment.”

Discussion Astrongsenseofefficacyinfluencesteachers’expectations,attributions,andgoals.Itmakesadifferenceinteachermotivation,whichinturnaffectshowwelltheir students achieve (Bandura, 1997;Goddard, Hoy&WoolfolkHoy, 2000).Thisstudywasconductedwithteachersattendingtwo-weeksummerprofessionaldevelopmentworkshopsonmathematics.Additionalcomparativeresearchusinglargersamplessizes,differentgroups,varioussettings,andalongitudinalapproachisneededtodefinitivelyanswertheinitialhypothesisposed.However,withthesecautions inmind,weoffer somegeneral insights thatmaybehelpful toothersinterestedinteacherefficacy. Regardingourfirsthypothesis,pretestscoreswererelativelyhighonpersonalcompetenceforboththelowandhighgroupandtheyimprovedsignificantlyforeachofthegroups.SimilartoHoyandWoolfolk(1993)wefoundthattheper-

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sonalcompetenceofteacherstendstogetstrongerastheygainexperienceandlearnmoreaboutadomain.Interviewdatasubstantiatethattheintentofteachersinparticipatingintheworkshopswastolearnmoreaboutmathematicsteaching.Teacherswhoattendedtheseworkshopshadamasteryorientation.Theywantedtoimprovetheirmathematicsteachingforthebenefitoftheirstudentsandbelievedthattheycould.Theyperceivedthemselvesascapableteachersofmathematicsandwereinterestedinlearningnewideas,skills,andstrategies.Severalofthequotesintheresponsetointerviewquestionsaddressthisissuealongwiththisonefroma5th-gradeteacher:

I’maprettygoodmathteacher,butI’malwayslookingfornewwaysofteach-ing andways toget thingsacrossbetter.Therearealwayschildrenyoucan’treach,butthemoreIlearn,themoreideasIhave,andthemoreopportunitiesorwaysIhavetohelpchildren.

Anotherinterestingfindingregardinggroupcompetencewasthattherewasasig-nificantdifferencepre-toposttestbutonlyforteachersinthelowgroup.Thelowgroup’ssignificantincreasemaybeduetothefactthattheseteachershadtheopportunitytoworkwiththeircolleaguesandthatthissharedtimeincreasedtheirperceptionofeachother’scompetence.Thestigmaofworkingatanunderperformingschoolseemedtobetemporarilyovercomewhenteachersworkedwithcolleaguescollectively. Therewerenosignificantincreasesforpersonallevelofinfluenceorcontextualinfluence.Thisindicatesthatteacherstendedtobelievethateventhoughtheyhadbecomebetterteachersthroughparticipationinprofessionaldevelopment,therewerestillstudentswhotheywouldnotbeabletoaffect.Theworkshopsincreasedteachers’beliefsregardingtheiractionsonstudentlearningbutnotsignificantly.Perhapsteachersattheadequatelyperformingschoolfelttheirinfluenceorsomeotherfactorwasalreadyaffectingtheirstudents,whereasteachersinthelowgroupfeltthattheirpersonalinfluencewouldhavelittleaffectonstudents’learning.Thisfindingleadstoinsightintoteacherexpectations.Theworkshopshelpedteacherslearnnewstrategiesandgainpersonalefficacy,buttheydidlittletoraiseteach-ers’beliefsthattheirstudentswouldachieve.Futureprofessionaldevelopmentinmathematicsshouldnotonlyofferstrategiestoimproveteachingbutitshouldraiseteacherexpectationsaswell. Regardingcontextualinfluenceorone’sperceptionofthedifficultyofteachingataparticularschool,therewasnosignificantdifference,andsurprisinglyscoresfellslightlyforthehighgroup.Itisreasonablethatattendanceataworkshopwouldnotaffectteachers’perceptionsrelatedtoenvironmentfactorsrelatedtotheschoolandcommunityinwhichtheyteach. Regardingoursecondhypothesis,teachersinbothgroupsindicatedhigherlevelsofpersonalcompetencecomparedtocollectivecompetence.Commentsduringinter-viewssupporttheviewthathighlevelsofparticipationinprofessionaldevelopmentprogramsincreasedtheirPersonalCompetenceforteachingmathematics.However,

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ariseinpersonalcompetencedidlittletoaffecttheirbeliefsoftheircolleague’scom-petencetooperateatahighlevelandachievegoals.Thisself-centeredperceptionisinterestingandmightstemfromthefactthattheyweregivingupprecioussummerfreetime.Thewordsofoneoftheparticipants,an8th-gradeteacher,reinforcethisidea,“Ittakesefforttostretchyourselfandittakessacrifice.It’smucheasiernottobothertoattendsummerworkshopsandcontinuetodothesameoldthings.” Inregardtothethirdhypothesiswefoundthatteachersinthehighgrouphadsignificantly higher ratings for group competence compared to teachers in thelowgroup.Webelievethatthiseffectcouldindeedbyanartifactofthestigmaofunderperforming.Teachersinthelowgroupwerewellawarethatmorethanone-thirdoftheschoolsintheirdistrictshadbeenlabeledunderperforming,andthisknowledgecouldaffecttheirresponsestoitemssuchas,“Teachersinmyschoolhavewhatittakestogetchildrentolearnmathematics.”Thehighgroupwasawarethattheirdistrictwasvirtuallyfreeofunderperformingschools.Forthem,thelogi-calassumptionwasthatteachersaredoingagoodjob. The workshops attended by the teachers in this study increased their per-sonalcompetence,presumablybyincreasingtheirknowledgeofmathematicsandmathematicsinstruction,buttheydidlittletoincreaseteachers’perceptionsthattheycouldaffecttheirstudents’achievement.Datacollectedinthisstudyarenotadequatetoanswerthatquestion. Manyfactorsinfluencetheeffectivenessofschoolsasmeasuredbystudenttestscores,whicharethebasisforclassifyingschoolsfortheNoChildLeftBehindlegislation.Thosefactorsinclude(butarenotlimitedto)thecommunityenviron-ment,SESofstudents,accessibilityofresources,schoollevelanddistrictlevelleadership,andqualityofteaching.Professionaldevelopmentopportunitiescanhelpindividualteacherstoimprovetheirteachingskillsandresultingainsintheirbeliefsofindividualefficacy.However,havingseveralteachersfromthesameschoolparticipateinthesameprofessionaldevelopmentmayresultin“groupthinking”thatcanheightencollectiveefficacyaswell.Thisconclusionisreiteratedina7th-gradeteacher’swords,

It’s important tobewithagroupyoucanlearnwith.It’s important tobewithotherteachersatmyschoolwhocanhelpmelearnsomeoftheharderconcepts.It’sbestwhenweseewhoisstronginwhatarea.Thatgivesusconfidenceeventhoughourschoolwasunderperforming.

Professionaldevelopmentinmathematicshasthepotentialtoaffectteachers’personalcompetencewhethertheyworkataloworhighperformingschool.Italsohasthepotentialtoraisethegroupcompetenceofteachersinunderperformingdis-trictswhentheycometogetherandworkasateam.Raisingteachers’beliefsaboutpersonalcompetenceandgroupcompetencecouldhaveapositiveeffectonstudentperformance.However,theyareonlypartoftheanswerbecausepersonallevelofinfluenceandcontextualinfluencealsoplayanimportantrole.Teachersneedto

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believeintheirstudentsandholdhighexpectationsforeachandeveryone.Addition-ally,unlessthenegativeeffectsofotherrelatedfactors,forexample,thestigmaofunderperforming,resources,leadership,andsofortharealleviated,underperformingschoolswillbehardpressedtoimprovetoacceptablelevels.Professionaldevelopmenthasthepotentialtoaffectteacherefficacyanditdoessoforsomegroupsofteachersmorethanothers.Toraiseteachers’efficacyitisimportanttounderstandthecomplexityofteacherefficacyandkeeptheseideasinmind.

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