UPPER-SECONDARY TEACHERS’ PERCEPTIONS OF THE MATURA …

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PreliminarycommunicationUDC37.091.27:51(045)

UPPER-SECONDARY TEACHERS’ PERCEPTIONS OF THE MATURA EXAM IN MATHEMATICS

AmandaGlavaš1,LjerkaJukićMatić2,SaraPrša3

1FacultyofHumanitiesandSocialSciences,JosipJurajStrossmayerUniversityofOsijek,Croatia2DepartmentofMathematics,JosipJurajStrossmayerUniversityofOsijek,Croatia3 Strojarskaitehničkaškola,Osijek,[email protected];[email protected];[email protected]

Received:4February2021

This� paper� reports� a� study� on�mathematics� teachers’� perceptions� of�the�Matura�mathematics� exam� in�Croatia.� The� study� focuses� on� the�suitability�of�mathematics�school� textbooks� for�students’�preparation�for� the�exams,� the�complexity�of� the� tasks� in� the�exams,� the�grading�and� scoring� of� the� exams,� and� teachers’� level� of� satisfaction� with�student�achievement.�The�study�used�a�convenience�sampling�method.�It�was�conducted�through�a�questionnaire�administered�to�308�upper�secondary�mathematics� teachers.�The�findings� showed� that� teachers�do�not�perceive�school�textbooks�as�suitable�resources�to�prepare�for�the�higher�level�exam.�Furthermore,�the�teachers�believe�that�the�test�length�is�not�appropriate�i.e.,�the�time�given�to�students�for�the�higher�level� exam� is� insufficient.� On� average� they� are� satisfied� with� their�students’�results,�but�are�undecided�about�the�criteria�and�scoring�of�the�Matura.�Vocational� school� teachers�showed�more�dissatisfaction�with�the�requirements�and�outcomes�of�the�Matura�exam�compared�to�grammar�school�teachers.�The�results�of� this�empirical�study�can�be�taken�as�a�good�starting�point�for�re-assessing�the�requirements�of�the�Matura�exam�in�mathematics.

Keywords:��Matura� exam,� mathematics� teacher,� teacher� attitudes,�textbooks,�school-leaving�examination�in�mathematics

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METODIČKI OGLEDI, 28 (2021) 1, 217–242A. Glavaš et al., Upper-secondary...

1. Introduction

Anationalsecondaryschool-leavingexamination,calledtheMa-tura,wasintroducedintheCroatianeducationalsystemin2010(NN,1/2013).Itisaformofgraduationofupper-secondaryschool,function-ingasanexit examfrom the secondaryeducationsystem(Holmeet�al.,2010).School-leavingexamsarealsoknownasexitexams,stategraduateexamsorcertificateexams.TheMaturaisanexternalexamconductedby theNationalCentre forExternalEvaluationofEduca-tion(NCVVO,2020).Inexternalexams,externalactorshavecontroloverthetestingprocessliketestdesign,assessment/scoring,useoftheresults/outcome,andtheindividualteachercannotobjecttohowtheseprocessesareimplemented(JonssonandLeden,2019).TheMaturaisalsoahigh-stakesexambecauseithasimportantconsequencesforstu-dentsonthebasisoftheirperformance,namelyithasanentrancefunc-tion to thedesiredhigher education institution.Lastly, theMatura isconductedinastandardisedmanner(Primoracet�al.,2009).Thismeansthatalltesttakershavetositforthesametestandunderthesamecon-ditions,sometimesalsoat thesametime(Jonsson andLeden,2019).Standardisationsecurescomparabilityamongthetesttakers.

MathematicsisoneofthecompulsorysubjectsintheMatura.Con-sideringthattheMaturawasimplementedmorethantenyearsagoandgiventhemultiplerolesithas,wearguethatitisimportanttoexaminehowmathematicsteachersviewtheexam.Therefore,weconductedastudy to investigatemathematics teachers’perceptionsof theMaturaexaminmathematicsintermsof:generalrequirements;themathemat-icstextbookused;studentachievementintheexam;andthecompat-ibilityofstudents’finalschoolgradesinmathematicswiththegradesachievedintheMaturamathematicsexam.

2. Matura in Croatia

2.1. General outline of the Matura exam in mathematics

TheMaturaissetofexamswhicharecompulsoryforstudentsfin-ishingfouryearsofgrammarschool (NN,1/2013).Upper-secondaryschoolsinCroatiaincludegrammarschools(generalorspecialisinginnaturalsciences,mathematics,foreignlanguages,orclassicallanguag-

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es),vocationalschools,andart schools.Vocationalschools last fromone tofiveyearsdependingon the typeofeducationprogrammere-quiredforaparticularprofession,i.e.thevocationalcurriculumforob-tainingaqualification.TheMaturaexamisnotmandatoryforstudentsinvocationalschools,butcanbe takenby thosestudentswhoattendfour-andfive-yearvocationalschools,whowanttocontinuetohighereducation.Studentswhocomplete four-year art schoolsmayalso sitfortheMaturaexams.TheMaturaisorganisedandconductedbytheNationalCentre forExternal Evaluation ofEducation,which is alsoresponsible formarking the exams and awarding grades.Grades areawardedaccordingtotheaverageofthepopulation’sresults,andtherearenopre-setcriteriaforpassingtheexam(NCVVO,2018).

MathematicsisoneofthecompulsoryexamsintheMatura.Itcanbetakenattwolevels:thehigherlevel(A)andthebasiclevel(B)(NCV-VO,2020).Studentsselectwhichleveloftheexamtotakebasedontherequirements of the higher education institution theywish to attend.Thehigherlevel(A)oftheMaturaexaminmathematicsalsoaffordsaccess to those institutions that require the basic level (B). Studentswhotakethebasiclevel(B)ofthemathematicsexamarenoteligibletoapplyforinstitutionswhichrequirethehigherlevel.Thehigherlevelexaminmathematicscorrespondstothemathscurriculumofgrammarschools (NCVVO, 2020).However, the number of hours taught dif-feraccordingtotheeducationprogrammeoftheschool.Forinstance,grammarschoolswithafocusonforeignlanguageshavemathematicsthreehoursperweekforallfouryears.Grammarschoolsspecializedinmathematicshaveatleastfourhoursofmathematicsperweekforallfouryears.However, thehigher levelexaminmathematicsalsocor-respondstomostfour-yearvocationalschoolprogrammeswheremath-ematicsis taughtat least threehoursperweek(NCVVO,2020).Thebasic level exam inmathematics corresponds to the cross-section ofotherfour-yearuppersecondaryprogrammeswheremathematicshastheminimalnumberofhoursperweek.Forcomparison, some four-yearvocationalschoolshavemathematicstwohoursperweekforallfour yearswhich places vocational students in a difficult position intermsofaccesstothehigherlevelMaturaexaminmathematics.

Thehigherlevelexaminmathematicslastsupto180minutes,andthebasiclevelexamlastsupto150minutes(NCVVO,2020).Thebasic

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levelexamhas28tasksintotal–16multiplechoiceand12shortan-swersandparticipantscanachieveamaximumof40points.Thehigherlevel examhas30 tasks in threecategories–15multiplechoice,13shortanswersand2longanswersandparticipantscanachieveamaxi-mumof60points.

2.2. Studies related to the Matura in Croatia

Evenbefore theMaturawas introducedinto theCroatianeduca-tionalsystem,Bezinović(2009)pointedoutthatitpromotesinequal-itybecausestudentsfromgrammarandvocationalschoolsareexposedtocompletelydifferentcurriculaduringtheirsecondaryeducationbuthaveto/will takethesameexam.Namely,theuppersecondaryvoca-tionalschoolcurriculainCroatiapromotediversity,whilsttheMaturaconcentratesononesetoflearningoutcomes.Recently,Baketaet�al.(2020)conductedastudyrelatedtotheperceptionofequalityandfair-nessoftheMaturafromthepointofviewofupper-secondaryschoolprincipals.Theopinionsoftheprincipalsofgrammar,vocationalandmixedsecondaryschoolsdifferintermsoffairnessofaccesstohighereducation.TheprincipalsofvocationalandmixedschoolsbelievethattheMaturaismoretailoredtogrammarschoolstudents.Moreover,theybelievethatthisinequityisreflectedintheenrolmentrequirementsofhighereducationinstitutionswhichcallforthehigherlevelMaturaex-ams.Consequently,vocationalstudentsare less likely tobeacceptedinto thehighereducation institutionof theirchoice.Evidenceof thiswasalsoshowninthestudyofŽauharet�al.(2016)whoanalysedthestructureofstudentsenrolledattheFacultyofMedicineandtheFacultyofHealthStudiesattheUniversityofRijeka,beforeandaftertheintro-ductionoftheMatura.Theirstudyshowedthattheproportionofstu-dentswhohadattendedgrammarschoolsincreasedsignificantlyaftertheintroductionoftheMaturacomparedtotheproportionofstudentswhohadattendedvocationalschools.

2.3. Research foci

Ourliteraturesearchshowsthat thenumberofstudiesrelatedtoMaturaexams is small.Studies that examine themathematics teach-

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ers’role,beliefsorpractices in thecontextof theMatura,arepracti-callynon-existent.MathematicsteachersworkwithstudentsteachingthemandpreparingthemfortheMaturaexamthroughupper-secondaryschool,butalsohavetheopportunitytoparticipateinthedevelopmentoftasksfortheMaturaexams,toreviewexammaterialsandmarktheexampapers(thetasksthatrequireshortandlonganswers)everyyear.Accordingly,wedesignedastudythataimedtocoverteachers’opin-ionsandattitudesaboutseveralaspectsoftheMaturaexaminmath-ematics.Theresearchfociofthisstudyareonteachers’opinionsandattitudesconcerning:

–thesuitabilityofschooltextbooksforpreparingstudentsfortheMaturaexam

–thedesignofMaturamathematicsexamsovertheyears–scoringintheMaturaexaminmathematics–satisfactionwiththeresultsobtainedbytheirstudents.Moreover,weare interested in lookingat teachers’opinionsand

attitudesinrelationtothetypeofschoolatwhichtheyteach.

3. Studies related to the research themes

Inthissectionweproviderelevantresultsandstudiestosupportourresearchthemes.

3.1. Mathematics textbooks

Thefirstresearchthemeinourstudyisrelatedtomathematicstext-books.Mathematicstextbooksgreatlyinfluencemathematicsteachingpractice,maybemorethaninotherschoolsubjects(Fanet�al.,2013).Becauseofthis,thetextbookusedbythestudentsaffectstheopportuni-tiestolearnthattheyareprovidedwith.Studiesinvestigatingstudentachievement insomeformofexternalevaluation, likeTIMSSorna-tionalexams,showedthatthereisacorrelationbetweenbetterstudentachievementandmathematicstextbooksthathavehighercognitivelev-eltasks(Hadar,2017;Törnroos,2005).TextbookanalysishasshownthatCroatianlowerandupper-secondarymathematicstextbooksmost-ly contain taskswith a lowcognitive level, namelyprocedural tasks

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dominateoverconceptualones(GlasnovićGracin,2018;Glavašet�al., 2019).

3.2. Design of exam tasks in mathematics

Oursecondresearchthemeisconcernedwithteachers’perceptionsoftheMaturaexaminmathematicsovertheyears.Thisthemeisap-proached from the perspective of task design inmathematics educa-tionanditscomplexity.Theterm‘complexity’refers to theextent towhichthetaskdiffersfromperformingasimplecalculationtoacom-plexsynthesisintegratingproblemsolving,communicating,reasoning,andmakingconnections(Suurtammet�al.,2016). Mathematicsteach-ersshouldbeawareofMaturaexamtaskfeatures,nottoteach�to�the�test,buttoenhancetheirteachingpracticeifnecessaryandtopreparestudents for theMaturaexamadequately.Moreover, acomponentofteachingmathematicsisrelatedtotheselection,modification,design,utilizationandevaluationoftasks(Dietekeret�al.,2018)andsuchworkisachievedusingthetextbooksorothercurriculummaterials,suchaspastpapersoftheexam.

The catalogue of the Matura exam in mathematics (NCVVO,2020)prescribeswhichmathematicaldomainsandassociatedlearningoutcomesmayappear,butnotwhatmustappearintheexam.Thisalsocontributestotaskdesignanditscomplexity.

3.3. Grades awarded by teachers and external evaluation

The third research theme in our study is concerned with scor-ing in theMaturaexams inmathematicsand, consequently,with thegradesstudentsobtainintheexamandthoseawardedbytheteacher.Thereliabilityofateacher’sgradeisimportantforschools,teachers,families, and students. Some studies have examined the relationshipbetween thegradesgivenby the teachersandsomeformofexternalexamination. Inoneway, the teachers’gradesaremore reliable thanoutsidemeasurebecauseof theirholisticnature, i.e. the teacherscanmakereliablejudgementsaboutstudentachievementbecauseoftheirinteractionswithstudentsovertime(Marlowet�al.,2014).Incontrast,formalassessmentcanbeconsideredmoreaccurateandobjectivethan

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theteacher’sassessment(Blacket�al.,2011).Areviewofstudieswhichexamined theaccuracyof teacher judgementcomparedwithexternalexamsdescribedmixedresults–somestudiesreportedstrongaccuracyandsomestudiesreportedweakaccuracy(Brookhart,2013).

3.4. The impact of students’ Matura exam results on teachers

Ourfourthresearch themeisconcernedwith teachersatisfactionwithstudents’resultsattheMaturaexaminmathematics.Theresultsofsuchahigh-stakesexamcanhavevariousconsequencesforteachers.Somecountries implementedpolicies to evaluate teachers’ effective-nessbasedontheirstudents’examresults.Thismeansthatteachersarebeingheldaccountableforstudentsuccess.Suchpoliciescontributetoanincreaseinjob-relatedstressexperiencedbyteachers(e.g.Ryanet�al.,2017)andhaveanegativeeffectonteacherself-efficacy(Abramset�al.,2003).Moreover, teachersoften feeluncomfortableorhumili-atedwhen their students’passing ratesarepresentedat schoolmeet-ings(Booher-Jennings,2005).Sometimeslowpassingscoresresultinpenaltiesforteachers(vonderEmbseet�al.,2016).Ontheotherhand,teachers’dissatisfactionwithstudents’resultscanleadtothenarrow-ingofthecurriculumandteachingonlytothetest(e.g.Abramset�al.,2003).InCroatia,teachersarenotpenalisedforstudents’lowscoresintheMatura,butitispossiblethattheresultsimpacttheirself-efficacyandteachingpractice.

4. Methodology

4. 1. Participants and data collection

Thestudypresentedinthispaperwasconductedin2019,usingaconveniencesamplingmethod(Cohen�et�al.,2018).The teachers forthestudywererecruitedthrougharesearchparticipationpoolatalo-caluniversitywheremanyteachersparticipatedinmathematicsprofes-sionaldevelopmentworkshopsorconferences.Wesentanemailtotheparticipantswith a link to the digital formof the questionnaire.Theparticipants’responseswerecollectedanonymously,meaningthatwedidnotcollectanyinformationthatcouldrevealtheteacher’sidentity

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suchasname, email address,ornameof the school.Data collectionbeganattheendofJuly2019andlastedforamonth.Completionofthequestionnairetookabout15minutes.

We took care that the sample of teachers for the study to someextentagreeswith theofficialdataonstudentswho took theMaturaexam inmathematics in2018.Thereforeparticipantswereasked so-cio-demographicquestionsthatprovidedinformationontheirgender,yearsofservice,careeradvancement,typeofschooltheyworkat,andwhethertheycorrectedMaturaexams(Table1).Among392uppersec-ondary school programmes inCroatiawhose students took the stategraduationexamin2019,189(48%)aregrammarschools,and203(52%)arevocational schools (MZO,2018).Thesampleof teacherswhoparticipatedinthisstudyagreeswiththistosomeextent:51%oftheteachersworkinvocationalschools,andtherestworkingrammarschools.Morethan40%oftheteachersparticipatedinmarkingMaturaexamsinmathematics.Giventheinformationwehaveabouttheteach-erswhoparticipatedinthestudy,webelievetheirattitudesandopinionsareagoodrepresentationofupper-secondarymathematicsteachersinCroatia.

Table 1.Informationabouttheparticipants

Participant information N (%)

Gender

Female 268(87%)

Male 40(13%)

Typeofschool

Grammar(non-mathematics) 112(36%)

Grammar(mathematics) 38(12%)

Vocational 158(51%)

Teachingexperience

<5years 37(12%)

6-15years 95(30%)

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16-25 84(27%)

26-34 71(23%)

35+ 21(7%)

Teacherpromotion

Nopromotion 168(54.4%)

Teachermentor 90(29.2%)

Teacheradviser 50(16.2%)

ExperienceinmarkingMaturaexams

Participant 130(42%)

Non-participant 178(58%)

4.2. Instrument

Wedesignedaquestionnairethatsoughttocaptureallrelevantas-pectsof the research themes.Thequestionnaire (Appendix,Table2)contained32itemstodeterminetheopinionsandattitudesofmathe-maticsteacherson:thesuitabilityofschooltextbooksforstudentprepa-rationfortheexam;thedesignandcomplexityoftasksintheMaturaexamovertime;thequalityofpassingcriteriaandscoringmethodsfortheMaturaexaminmathematics;andteachersatisfaction.Eachitemwastobeevaluatedonafive-pointLikert-typescalewhere1=stronglydisagreeand5=stronglyagree.Theresult isexpressedas themeanvalueoftheresponse.

The questionnairewas designed exclusively for the purposes ofthisstudy,thusitwasnecessarytoperformanexploratoryfactoranaly-sis(EFA)usingtheprincipalaxisfactoring(PAF)methodbeforepro-cessing the data. Initially, all itemswere examined and this resultedin recoding items 11 and 22.TheKaiser-Meyer-Olkin andBartlett’stest(0.876,p=0.000)wereusedtoexaminetheadequacyofthedata.Weretainedfivefactorswhosecharacteristicrootsexceed1.Thefac-torsobtainedbytheanalysisofthemaincomponentsexplainatotalof63.21%ofthevarianceofthemanifestvariables.

Thefirstfactorreferstotheteacher’sopiniononthesuitabilityofthetextbooksusedtopreparestudentsforthebasicleveloftheMatura

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exam(items1–4).Thesecondfactorrelatestoteachers’opinionsonthesuitabilityofthetextbooksusedtopreparestudentsforthehigherlevelMaturaexam(items5–8).Thethirdfactor,whichreferstothedesignoftheMaturaexamovertime,consistsof4items(recoded11,15,18,19).Thefourthfactorconsistsoffiveitems(23,25,26,27,29),andreferstotheteachers’opinionaboutthescoringoftheMaturaexam.Thefifthfactor, referring to the criteria of theMatura exam, consists of threeitems(20,21,24).TherotatedfactormatrixcanbeseeninTable3.

Table 3.Rotatedfactormatrix

Factors

1 2 3 4 5

Item6 .853 .283 -.057 .084 .096Item5 .815 .181 -.034 .135 .144Item7 .784 .288 -.073 .170 .071Item8 .771 .346 -.137 .034 .117Item2 .328 .815 -.120 .219 .122Item4 .343 .712 -.165 .215 .169Item1 .363 .695 -.108 .215 .156Item3 .411 .672 -.053 .300 .111Item29 -.009 -.086 .771 -.027 -.022Item26 -.159 -.060 .716 -.154 -.166Item23 .045 -.067 .643 -.033 .022Item27 -.034 -.041 .633 -.089 -.253Item25 -.169 -.065 .609 -.089 -.217Item15 .170 .193 -.005 .808 .148Item18 .116 .177 -.104 .784 .124Item11 -.043 .121 -.255 .646 -.065Item19 .211 .165 -.020 .502 .259Item20 .065 .081 -.113 .096 .810Item21 .108 .107 -.143 .108 .729Item24 .155 .164 -.261 .106 .547

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However,thefactoranalysisexcludedalargenumberofitems(9,10,12,13,14,16,17,22,28,30,31,32),whichwefindrelevant toour study, thereforewe included them in the results section aswell.Dataanalysisincludeddescriptiveanalysis,ANOVAvarianceanalysis,Games-HowellandBonferroniposthocpairedcomparisons,t-testandcorrelations.TheanalysiswasperformedintheSPSS.

5. Results and discussion

Inthispart,wepresenttheresultsonmathematicsteachers’opin-ionsandattitudesconcerningfouraspectsoftheMaturaexaminmath-ematics:thesuitabilityofcurrentlyvalidtextbooks(variablesTextbookA&TextbookB);thedesignoftheexamovertime(variableDesign,Items9,10,12,13,16&17);scoringandcriteriaforpassing(variableScoring,variableCriteria,Items22,28,30);andtheteachers’satisfac-tionwith the students’ results (Items31&32).Descriptive statisticsfornewvariablesandotheritemscanbeseeninTable4.ProportionalresponsedistributionsfortheItems9,10,12,13,16,17,22,28,30,31&32arepresentedinFigure2.Inthefollowingsubsectionswepresentresultsinmoredetail.

Table 4.Descriptivestatisticsforthequestionnaireitemsandcreatedvariables

α N M SD

TextbookA 0.92 308 3.11 1.10

TextbookB 0.92 308 3.76 1.08

Design 0.81 308 3.24 .97

Criteria 0.78 308 3.34 .92

Scoring 0.82 308 2.69 .86

Item9(AppropriatenessAlevel) 308 4.06 1.07

Item10AppropriatenessBlevel) 308 2.37 1.17

Item12(DemandingAlevel) 308 2.30 1.20

Item13(DemandingBlevel) 308 1.72 .99

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Item16(TimelengthAlevel) 308 3.28 1.39

Item17(TimelengthBlevel) 308 4.39 .95

Item22(Scoringcorrect-incorrect) 308 2.94 1.21

Item28(Lowpassingscore) 308 3.35 1.31

Item30(Scoringcomplications) 308 3.86 1.14

Item31(Satisfaction) 308 3.44 1.04

Item32(Grade) 308 3.35 .99

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Item9Item10Item12Item13Item16Item17Item22Item28Item30Item31Item32

1 2 3 4 5

Figure 1. Proportionalresponsedistributionfortheselecteditems

5.1. The suitability of currently valid textbooks

In this section,we describe results for the variablesTextbook�A (Cronbach’sα=0.918)andTextbook�B�(α=0.921)onteachers’opin-ionsonthesuitabilityofschool textbooksforpreparingstudents(in-dependentlyandwith the teacher’shelp) for thehigher levelMaturaexam (A) and for the basic level (B), respectively.Teacher’ opinionisexaminedconcerningthetype,numberandappropriatenessoftext-booktasks.VariableTextbook�Awascreatedfromitems1–4,andText-book�B�fromitems5–8.Onaverage,teachersbelievethattextbooksare

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moresuitableforpreparingstudentsforthebasiclevel(M=3.76,SD=1.08)thanforthehigherlevel(M=3.11,SD=1.10).Theanalysisalsoshowedastatisticallysignificantdifferenceinopiniononthesuitabilityof textbooks for taking thehigherandbasic levelof theMatura (t=-12.731,df=307,p<0.001).

Also, there are statistically significant differences between theteachers from vocational and non-mathematics specialized grammarschoolswhenitcomestothesuitabilityoftextbooksforthebasiclevel(Table5).TheteachersfromvocationalschoolsassessedthesuitabilityoftextbooksforpreparationfortheMaturawithalowerscore(Table6, p=0.008).Therewerenostatisticallysignificantdifferenceswithregardtothetypeofschooltheyworkatandthesuitabilityoftextbooksforthepreparationforthehigherlevel(Table5).

Table 5.OnewayANOVA

SS df MS F p

TextbookABetweenGroups 6.120 2 3.060 2.535 .081WithinGroups 368.147 305 1.207Total 374.267 307

TetxbookBBetweenGroups 10.148 2 5.074 4.437 .013*

WithinGroups 348.773 305 1.144Total 358.921 307

DesignBetweenGroups .392 2 .196 .206 .814WithinGroups 291.181 305 .955 Total 291.573 307

ScoringBetweenGroups .679 2 .340 .448 .639WithinGroups 231.102 305 .758Total 231.781 307

CriteriaBetweenGroups 1.168 2 .584 .694 .500WithinGroups 256.490 305 .841Total 257.658 307

Appropriateness Alevel(Item9)

BetweenGroups 1.616 2 .808 .658 .519WithinGroups 374.446 305 1.228Total 376.062 307

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Appropriateness Blevel(Item10)

BetweenGroups 4.529 2 2.264 1.654 .193WithinGroups 417.533 305 1.369Total 422.062 307

LengthlevelA(Item16)

BetweenGroups 26.953 2 13.477 7.204 .001*


Demanding Alevel(Item12)

BetweenGroups .031 2 .015 .011 .989WithinGroups 444.083 305 1.456Total 444.114 307

Demanding Blevel(Item13)

BetweenGroups 6.497 2 3.248 3.381 .035*

WithinGroups 293.045 305 .961Total 299.542 307

Satisfaction(Item31)

BetweenGroups 10.334 2 5.167 4.904 .008*


Teacher’sgrade(Item32)

BetweenGroups 8.347 2 4.173 4.339 .014*

WithinGroups 293.328 305 .962Total 301.675 307

Note.*p<0.05

TeacheropinionisconsistentwithresearchontheanalysisofthecontentofmathematicstextbooksinCroatia(GlasnovićGracin,2018;Glavašet�al.,2019),whereitwasfoundthatproceduraltasksdominateinCroatianmathematicstextbooksandtasksthatdemandhighercogni-tivelevelsarevastlyunderrepresented.ThebasicleveloftheMaturaexaminmathematicsisinaccordancewithlessdemandinguppersec-ondaryschoolprogrammes;thus,thisresultisnotunexpected.More-over,theteachersfromvocationalschoolsweretheleastsatisfiedwiththetextbooktheyuse.SchooltextbooksinCroatiamustbeapprovedbytheMinistryofScienceandEducationinCroatiaandteacherscanindependentlyselectatextbookfromamongthem(NN,116/2018).Fu-tureresearchcouldexaminewhichtextbookmathematicsteachersfromvocationalschoolsuseastheirprimarycurriculummaterial.

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Table 6.Posthocpairedcomparisons,withGames-Howell/Bonferroniadjustmentdependingonthehomogeneityofvariances

School type M (SD)Post hoc paired comparisons

with Games-Howell /Bonferroni adjustment, Md (p)

Variablesanditems VS MGS GS VS&

MGS VS&GS GS&MGS

TextbookB 3.6(1.13)

3.75(0.99)

3.99(0.99)

-.154a (.686)

-.392a (.008*)

.239a (.416)

Item13 1.85(1.02)

1.76(1.09)

1.54(0.86)

.092(1.0)

-.313(.030*)

-.221(.706)

Item16 3.35(1.30)

3.92(1.32)

2.96(1.46)

-.573a (.053)

.382a (.072)

-.955

a(.001*)

Item31 3.33(1.07)

3.92(1.09)

3.42(.94)

-.586(.006*)

-.086(1.00)

0.499(.032*)

Item32 3.18(.99)

3.54(.96)

3.52(.98)

-.362a (.127)

.337

a(.016*)-.025a (.989)

Note.*p<0.05,a=Games-Howellposthoctest,otherwiseBonfferoni,VC=vocationalschool,MGS=mathematicsspecializinggrammarschool,GS=non-mathematicsspecializinggrammarschool,Md=meandifference

5.2. Design of the Matura exam in mathematics over time

InthissectionwerefertothedesignoftheMaturaexaminmath-ematicsoverthelast10yearswithregardtothecomplexityofthetasks,thelengthofexamsandschoolprogrammes.Forthedescriptivestatis-tics,wereferthereadertoTable4.

Fromitems11(recoded),15,18and19,wecreatedanewvariablecalledDesign(α=0.81),whichexaminestheopinionofparticipantsonthedesigncomplexityoftheMaturatasksovertheyears.Onaverage,teachersareundecided(M=3.24,SD=0.97)andthereisnostatisti-callysignificantdifferencewithregardtothetypeofschoolinwhichtheteacherswork(Table5).

Teachersgenerallydisagreethatthebasiclevelexamismoreap-propriateforgrammarschoolsthanvocationalschools(Item10,M=2.37,SD=1.17).Moreover,wedidnotdetectastatisticallysignificant

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differenceintheteachers’responsesdependingonthetypeofschoolatwhichtheyteach(Table5).Forthislevelexam,teachersbelievethatthetimelengthissufficient(Item17,M=4.39,SD=0.95),anddonotconsiderthattasksaretoodemanding(Item13,M=1.72,SD=0.99).However, the teachers’ responses to this question differ significantlydependingonthetypeofschoolatwhichtheywork(Table5).Thereisstatistically significantdifferencebetween teachersofvocationalandnon-mathematicsgrammarschools (Table6,p=0.030);namelyteach-ersfromthevocationalschoolsdisagreewiththestatementtoalesserextent,meaning that thebasic level is challenging for their students.This is also supported, for instance, bypsychometric analysis of theMaturaexamfor2018(Bugarin,et�al.,2020)whichshowedthat thebasiclevelwasquitedifficultforexamcandidates.Vocationalschoolstudentsconstitutedaround70%ofthosecandidates.

Teachers believe that the higher level exam ismore appropriateforgrammar schools thanvocational schools (Item9,M=4.06,SD=1.07).Onaverage,theyareundecidedaboutthelengthoftheexam(Item16,M=3.28,SD=1.39),but thereexists statistically signifi-cantdifferencebetweentheteachersfromnon-mathematicsgrammarschoolsandmathematicsgrammarschools(Table6,p=0.001);name-ly, teacherswhowork in non-mathematics grammar schools believethatnotenoughtimeisgivenforthehigherlevelexam.Itseemsthatteacherswouldproposeanincreaseinthedurationofthehigherlevelexam.But an increase in the amount of time allocated for the exammayaffectstudents’performance.Somestudiesexaminedhowextend-edconditionsaffectstudents.Laitusiset�al.(2007)foundthatstudentstakingahigh-stakesexamunderextended-timeconditions(i.e.,moretime-on-task,butnotmore items)experiencednodifference inexamperformance.Thiswouldappeartoconfirmtheteachers’viewthatstu-dents’performancewouldimproveiftheyhadmoretimetocompletetheexam.ButAckermanandKanfer(2009)cautionthatthereismuchtolearnabouthowstudentsregulatetheirefforttoachievehigherscoresdespitelongertestsessions.

Teachersdonotconsiderthatthehigherleveltasksaretoodemand-ing(Item12,M=2.30,SD=1.20).Thereisnostatisticallysignificantdifferencedependingonthetypeofschooltheyworkat(Table5).Ad-ditionally,thecorrelationcoefficientshowedthatteacherswhoconsider

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thetasksatthehigherleveltobetoodemanding,alsoconsiderthatthedurationoftheexamisinsufficient(Spearmanr =-0.344,p<0.001).ThiscorrespondstothepsychometricanalysisofdifficultyofMaturaexamsconductedbyNationalCentre(Kapovićet�al.,2019;Bugarin,et�al.,2020),whichshowedthatthehigherlevelexamsaremostlyofaveragedifficultywith an average task index at both levels between0.4and0.5.Thehigherlevelexaminmathematicsisthethresholdforstudentswhoenrolintechnicalandnaturalsciencestudyprogrammes.Thusthetasksshouldmoredemandingthantasksinthebasiclevel.Thequestionistowhatextent,ifteachersbelievethatthetextbookstheyusearenotsuitableforpreparingstudentsadequatelyfortheexam?

5.3. Scoring and the criteria for passing the Matura exams

InthissectionwedescriberesultsforthevariableScoring,variableCriteria,Items22,28,and30.Forthedescriptivestatistics,wereferthereadertoTable4.

ThevariableCriteria (α=0.78)examinestheteachers’opinionsontheexistingcriteriaforscoringtheMaturaexams,namelywhetherthecurrentscoringprovidesarealpictureofstudents’knowledgeandwhetheritcorrelateswiththeirgradingcriteria.Thevariablewascre-atedfromitems20,21,24.Itseemsthatteachersareundecidedwhethertheexistingscoringcriteriaareappropriate(M=3.34,SD=0.92).Giv-enthatitisdifficulttostudycriteriawithouttakingthescoringmethodintoaccount,wecreatedthevariableScoring(α=0.82).Thisvariablewas created from Items23, 25, 26, 27, 29.Herewe also found thatteachersareundecidedaboutscoringmethods(M=2.69,SD=0.86).Statisticallysignificantdifferencebetween the teachersdependingontheschoolwheretheyworkwasnotdetectedineithervariable(Table5).Onaverage,teachersareundecidedaboutwhethertasksshouldbescoredaseithercorrectorincorrect(Item22,M=2.94,SD=1.21)butbelievethatscoringtheentiresolutionprocedurewouldmakemarkingcomplicated(Item30,M=3.86,SD=1.14).

ThescoringoftheMaturaexamsisprescribedbytheexaminationcatalogue(NCVVO,2020).Atthebasicleveltherearemultiplechoicetasksandshortanswertasks,whereacorrectanswerreceivesonepoint.Atthehigherlevel,inadditiontothesetwotypesoftasks,therearealso

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longanswertaskswherethesolutionprocedureisalsoscored,notjustthesolution.MostteacherswereundecidedabouttheappropriatenessofthescoringoftheMaturaexams,butbelievethatscoringthesolutionprocedurewouldmakemarkingtheexamsmoredifficult.Incontrast,various researchershavepointedout that scoring the solutionproce-dure is beneficial from a psychometric perspective because a higherdistributionofpointspertaskincreasestestreliability(e.g.Ebel,1979).Withinmathematicseducation,someresearchers(SwanandBurkhardt,2012;Suurtammet�al.,2016)arguethattheexamitemsshouldprovidestudents an opportunity to demonstrate theirway of thinking i.e., toexplainandargumenttheirsolutions,eveniftheendresultisincorrect.Moreover,theyarguethatincreasingthenumberofpointsinthetasksallowsdifferentlevelsofachievementwhichwouldbeveryusefulinaccomplishingtheexitfunctionoftheMatura.Thefactthattheteach-ersareundecidedastowhethercurrentscoringgivesarealpictureofstudentknowledgeandabouttheappropriatenessofthescoring,showstheneedforrevisingthecurrentscoringmethodsintheMaturaexaminmathematics.

Further,teachersareundecidedwhetherthelowcriteriaforpass-ingtheexamhasaneffectonstudentmotivationinpreparingfortheexam(Item28,M=3.35,SD=1.31).Thepassinggradeovertheyearshasvariedbetween24–25%correctanswersfor thebasic level,and25–28%forthehigherlevel.Perhapsahigherpassingthresholdwouldmotivatestudentstobetterprepareforgraduationbecausesomestudiesshowthathigh-stakestestscanmotivatestudentstoputmoreeffortintolearning,especiallyinthecaseofmathematics(e.g.,Ryanet�al.,2007;Simzaret�al.,2015).

5.4. Satisfaction with the students’ results on the Matura exam

Inthissection,wedescribetheresultsforItems31and32whichare related to teacher satisfactionwith theMaturaexam.For thede-scriptivestatistics,wereferthereadertoTable4.

Mostteachersaresatisfiedwiththeirstudents’resultsontheMaturaexaminmathematics(Figure1,Item31).Theteachers’attitudesdifferdependingonthetypeofschoolatwhichtheywork(Table5).AscanbeseeninTable6,thereisastatisticallysignificantdifferencebetween

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theteachersfrommathematicsgrammarschoolsandnon-mathematicsgrammar schools (p = 0.006) and between teachers frommathemat-icsgrammarschoolsandvocationalschools(p=0.032).Furthermore,thereisastatisticallysignificantcorrelationbetweenteachers’opinionsregardingthesuitabilityoftextbooksforthehigherlevelandsatisfac-tionwith their students’ results (Spearman r = 0.238p < .001), andregardingthesuitabilityoftextbooksforthebasiclevelandsatisfactionwiththeirstudents’results(Spearmanr =0.244,p<0.001).

MostteachersbelievethatthegradeachievedattheMaturaexamcorrespondstotheirfinalgrades(Figure1,Item32).However,teacheropiniondifferssignificantlydependingonthetypeofschoolatwhichtheywork(Table5),namelybetweenthosefromvocationalschoolsandnon-mathematicsgrammarschools(p=0.016),withthelatterbelievingthattheirfinalgradesareclosertothegradesachievedattheMatura(Table6).ThereportontheMaturainCroatiain2018and2019showsmoderatecorrelationbetweenschoolgradesandthegradesobtainedintheMaturaexaminmathematics,whichmeansthatstudentswhohavehigherschoolgradesmostlyhavehighergradesontheMaturaexaminmathematics(Kapovićet�al.,2019;Bugarinet�al.,2020).However,thereportalsoshowsthat thegradesachievedontheMaturaexamwereslightlylowerthanthegradesachievedatschool.Forinstance,inthe2018examthebasiclevelMaturagradeswerelowerthantheschoolgradeswhilethehigherlevelMaturagradeswereclosertothegradesgivenbytheteachers.

ThefindingsofthestudypointtotheunfairnessandinequalityofMaturaexams.Theteachersfromvocationalschoolsaretheleastsat-isfiedwithstudentachievementontheMaturaexam(Table6).Somevocationalschoolstudentsonlyhavemathematicsasasubjectfortwoyearsintheirupper-secondaryeducation,whilesomehaveitforfouryearsbutperhapsonlyonehourperweek.Ifvocationalschoolstudents,whohavebeentaughtalessdemandingmathscurriculum,choosetositforthehigherlevelexam,theyhavetofillanygapsintheirknowledgeontheirown.Itispossiblethattheydonothaveadequatecurricularre-sourcestoconverttheireducationalexperiencetothevaluesmeasuredon theMatura tests (Ćosić,2017).On theotherhand, somestudentshavemathscurriculasimilartogrammarschools.Theseandtheabove-mentionedconsiderationsledustotheconclusionthatmanyvocational

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schoolstudentsareatadisadvantage,i.e.accesstohighereducationisnotavailabletothemtothesameextentasitistogrammarschoolstu-dents.Therefore,thelowlevelofteachersatisfactionwithvocationalstudents’resultsisagoodindicatoroftheinequalitytheirstudentsex-perience.

Moreover,vocationalschoolmathematicsteachers’opinionsofthetextbooks, thehigherandbasic levelexam,andstudentachievementcouldalsobeindicativeofstress-relatedissues.EventhoughtheMatu-raiselectiveinvocationalschool,thoseteachersfeelpressuretoensurethe successof their students.The studybyĆosić (2017) showed theMatura expanded subject teachers’ classroompractices in vocationalschools.Teachersfeltthatvocationalcurricula,whichhasfewerhoursandalightersubjectload,disadvantagedtheirstudentsindemonstrat-ing thekindofknowledgeandskill requiredat theMaturaexamina-tions.Additionally,theyfeltresponsibleforconvertingtheirstudents’learningintogoodMaturaresults.

Although the Matura is designed as a school-leaving exam forgrammarschoolstudents,whodonothaveanyvocationalqualificationonfinishingschoolandareexpectedtocontinuetheireducation,math-ematicsgrammarschoolstudentsmaychoosetotakethebasiclevelofthe exam.This shows thediscrepancybetween thedesign intentionsof theMaturaand theCroatianeducationalsystem.ManyvocationalschoolstudentstaketheMaturaeveryyear(Kapovićet�al.,2019;Buga-rinet�al., 2020),but somestudiesalready show that theirnumber isdecreasingincertainhighereducationinstitutions(Baketaet.�al,2020;Žauharet�al.,2016).

6. Conclusion

Thestudyreported in thispaperrepresents teachers’voicesonahigh-stakestestinCroatia.Teachersareasignificantfactorintheedu-cationsystemandtheiropinionsandattitudesabouthigh-stakestestsarereflectedintheirteachingpractice:inthestrategiestheyusetoworkwithstudentsintheclassroomorinthechoiceofcurriculummaterials(e.g.Au,2011;Leightonet�al.,2010).Therefore,itisimportanttoheartheirvoicesontheproblemstheyencountersuchasthesuitabilityofmathematics textbooks for students’exampreparation, students’ lack

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ofmotivationconnectedwiththe(low)passingcriteria,andtheirbe-liefsonthemismatchedscoringofcomplextasksinMaturaexamsinmathematics.Thelatterstemsnotonlyfromtheperspectiveofteach-ers,butalsofromtheperspectiveofexammarkers(Table1).Thus,theresultsofthisempiricalstudycanbetakenasagoodstartingpointforre-assessingtherequirementsoftheMaturaexaminmathematicsmorethantenyearsafteritsintroduction.

6.1. Limitations

Onelimitationofourstudyisconnectedwiththemethodologicalaspectofthestudy.Wedidnotdifferentiatebetweenvocationalschoolprogrammesandtheirmathscurricula,soourresultscanbeconceivedasoverlysimplistic.Futureresearchshouldaddressthisissue.More-over,therewerenoartschoolteachersincludedinthestudy;itwouldbefruitfultoengagewiththoseteachersandincludetheirvoices.

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STAVOVISREDNJOŠKOLSKIHNASTAVNIKAMATEMATIKEOISPITIMADRŽAVNEMATUREIZMATEMATIKE

AmandaGlavaš,LjerkaJukićMatić,SaraPrša

U�ovom�radu�predstavljena�su�mišljenja� i�stavovi�nastavnika�matematike�o�ispitima�iz�matematike�na�Državnoj�maturi�u�Hrvatskoj.�Cilj�rada�bio�je� ispitati�mišljenja� nastavnika� o� prikladnosti� srednjoškolskih� udžbenika� matematike� za�pripremu�učenika�za�ispite�državne�mature,�općim�zahtjevima�ispita,�ocjenjivanju�i� bodovanju� na� ispitima� te� o� uspjehu� učenika.� Istraživanje� je� provedeno� putem�upitnika� na� prigodnom�uzorku� od� 308� nastavnika�matematike� koji� poučavaju� u�srednjim� školama� u� Hrvatskoj.� Rezultati� pokazuju� da� nastavnici� matematike�školske�udžbenike�ne�smatraju�prikladnima�za�pripremu�učenika�za�ispit�više�razine.�Nastavnici� smatraju� da� je� vrijeme� predviđeno� za� ispit� više� razine� nedovoljno.�

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Većinom�su�zadovoljni�rezultatima�svojih�učenika,�no�neopredijeljeni�su�po�pitanju�kriterija� i� bodovanja� na� maturi.� Nastavnici� strukovnih� škola� u� većoj� su� mjeri�nezadovoljni� zahtjevima� i�postavkama�državne�mature�u�odnosu�na�gimnazijske�nastavnike.�Rezultati�ovog�empirijskog�istraživanja�mogu�poslužiti�kao�polazište�za�ponovno�razmatranje�općih�zahtjeva�državne�mature�iz�matematike�nakon�više�od�deset�godina�nakon�njezina�uvođenja.

Ključne riječi:��Državna�matura,�nastavnici�matematike,�stavovi�nastavnika,�škol-ski�udžbenici,�ispit�iz�matematike

Appendix

Table 2.Questionnaireitems

1.ThetasksinthetextbookaresuitableforpreparingstudentsforthehigherlevelMaturaexam.

2.TheschooltextbookprovidesasufficientnumberoftasksformetopreparemystudentsforthehigherlevelMaturaexam.

3.ThetasksinthehigherlevelMaturaexamareofthesametypeasthetasksintheschooltextbook.

4.Ibelievethatstudentscanpreparequitewellforthehigherlevelexamusingonlythetasksfromthetextbook.

5.ThetasksinthetextbookaresuitableforpreparingstudentsforthebasicMaturaexam.

6.TheschooltextbookprovidesasufficientnumberoftasksformetopreparemystudentsforthebasiclevelMaturaexam.

7.ThetasksinthebasiclevelMaturaexamareofthesametypeasthetasksintheschooltextbook.

8.Ibelievethatstudentscanpreparequitewellforthebasicexamusingonlythetasksinthetextbook.

9.Ibelievethatthetasksinthehigherlevelexamaremoreappropriateforgrammarschoolsthanforvocationalschools.

10.IbelievethatthetasksatthebasiclevelMaturaexamaremoreappropriateforgrammarschoolsthanforvocationalschools.

11.IbelievethatthecomplexityoftheMaturatasksisincreasingfromyeartoyear.

12.IthinkthatthetasksatthehigherlevelMaturaexamaretoodemanding.

13.IthinkthatthetasksatthebasiclevelMaturaexamaretoodemanding.

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14.ThecontentitemsintheMaturadonotdeviatesignificantlyfromeachotherfromyeartoyear.

15.IbelievethatthecomplexityoftheMaturatasksisthesameeveryyear.16.IthinkthatthetimeallowedforcompletingthehigherlevelMatura

examissufficientgiventhecomplexityofthetasks.17.IthinkthatthetimeallowedforcompletingthebasicMaturaexamis

sufficientgiventhecomplexityofthetasks.18.Ibelievethatthereisnodifferenceinthecomplexityofthetasksinthe

firstandcurrentMaturaexams.19.IcanmakeassumptionsonthecontentofthenextMaturaexambased

onthecontentofpreviousexams.20.IbelievethatthecriteriaforscoringthetasksatMaturaareappropriate.21.ThecriteriaforscoringtheMaturatasksalignwithmycriteriafor

exams22.IthinkthatitisappropriatetoscoremosttasksattheMaturaonthe

principleofcorrect-incorrect.23.Ibelievethatthesolutionprocedureshouldbeevaluatedinagreater

numberoftasks.24.Ibelievethattheexistingcriteriaforevaluatingtasksgivearealpicture

ofstudents’knowledge.25.Ibelievethattheexistingcriteriaforscoringtasksreducetheoverall

resultinMaturaexamsinmathematics.26.IbelievethattheoverallresultsoftheMaturawouldbebetterwitha

changeintheexistingscoringcriteria.27.Ibelievethatthescoringoftaskswith2ormorepointsdoesnotmatch

thenumberoftaskoutcomesandthecomplexityofthetask.28.Ibelievethatthelowcriteriaforpassingtheexamaffectsthe

motivationofstudentstopreparefortheexam.29.IbelievethattheresultsoftheMaturaexamwouldbeimprovedifthe

solutionprocedurewerescoredinagreaternumberoftasks.30.Ibelievethatscoringthecompletesolutionprocedureinagreater

numberoftaskswouldmakemarkingtheexammoredifficult.31.Asateacher,Iamsatisfiedwiththeresultsofmystudentsatthe

Matura.32.IbelievethatthegradesattheMaturaagreewithmyschoolgrades.

UPPER-SECONDARY TEACHERS’ PERCEPTIONS OF THE MATURA …

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