Towhomitmayconcern,
IwouldliketoraiseseveralissuesraisedregardingtheassessmentoftheMCAT(Achievement
Standard91027)forboth2015and2016.TheMCATexaminationsfor2015and2016weremuch
harderthaninpreviousyears,especiallythe2016papers.Thiswasduetoanimbalanceinthe
numberofproblemssetinapurelymathematicalcontext(6outof17)versusareal-lifecontext(11
outof17)in2015.Typicallystudentsfind"mathematicalcontext"questionsmorestraightforward
than"real-lifecontext"questions.Thebalancewassomewhatcorrectedinthe2016examinations
papers,althoughnotcompletely.TheAchievementStandard91027statesthat:
"Problemsaresituationsthatprovideopportunitiestoapplyknowledgeorunderstandingof
mathematicalconceptsandproceduresandmethods.Thesituationwillbesetinareal-lifeor
mathematicalcontext."
Tomycolleaguesandme,thisimpliesabalancebetweenthesetwostylesofquestion,notaheavy
favouringofoneovertheother.Thiswascompoundedbyhaving3outof17questionsinthe2015
papersinvolvingsimultaneousequations.Inthe2016paperstherewere10outof19questionsthat
involvedtheuseofquadraticequationsandexpressions.Moststudentsfindsuchquestions
particularlydifficult.TheAchievementStandard91027Specificationstatesthat:
Studentsneedtobefamiliarwithproceduresrelatedto:
• factorising
• expanding
5
• simplifyingalgebraicexpressionsinvolvingexponents,suchas (2x 4 ) 3or 12a 8a 7
• substitutingvaluesintoformulae
3x x + 2
3x 2 -12
• manipulatingandsimplifyingexpressionssuchas
or
4
3
x -2
1 2
1 1 1
• rearrangingformulaesuchas E = mv or + = 2
u v f
• solvinglinearequationsorinequationssuchas5x+12=3-2xor3(x-2)<7
• solvingquadraticequationssuchas(8x+3)(x-6)=0,x2+5x–6=0,3x2=10x-8
(completingthesquareandthequadraticformulaarenotrequired)
x
• solvingsimpleequationsinvolvingexponentssuchasx3=8,5 =125
• solvingpairsofsimultaneouslinearequationswithtwounknowns.
Therewasfartoomuchweightingtowardsharderconceptslikesimultaneousequations,quadratics,
andforminggeneralsolutions.Someofthemorestraight-forwardconceptswerenotcoveredatall.
Also,therewereseveralquestionsrelatingtoalgebraicgraphsinboththe2015and2016papers,
despitetherebeingabsolutelynomentionofgraphingintheAchievementStandardSpecification.
Thetypesofquestiondetailedinbulletpoints3,5,6,7,8werefareasier,comparedtothe2015and
2016papers.Someexamplesofthesequestionsare:
Solve𝒙𝟑 = 𝟖intheAchievementStandardSpecificationversesSolve𝟑𝟐𝟎 = 𝟓𝒓𝟑 inthe2015(A)
MCATpaper,orforwhatvaluesofpis𝟏𝟎×𝟐𝒑-𝟏 < 𝟏𝟔𝟓inthe2016(B)paper.
Solve𝒙𝟐 + 𝟓𝒙– 𝟔 = 𝟎intheAchievementStandardSpecificationversesFactorise𝟑𝒙𝟐 − 𝟏𝟏 + 𝟔
inthe2015MCAT(A)paper.
𝟏
𝑳
𝟐
𝟗.𝟖
Rearrange𝑬 = 𝒎𝒗𝟐 intheAchievementStandardSpecificationverses𝑻 = 𝟐𝝅
inthe
2016(A)MCATpaper.
Furthermore,somequestionsinboththe2015and2016MCATpaperswereessentiallythesameas
theLevel290284paper.BoththeMCATandLevel290284papergradedthesequestionsatthe
samelevelofAchieved.Ihaveprovidedanexampleofthisbelow.
Factorise𝟐𝒙𝟐 − 𝟏𝟓𝒙 + 𝟏𝟖fromthe2015(B)MCATpaper.
Factorise6𝒙𝟐 − 𝟏𝟏𝒙 − 𝟏𝟎fromtheLevel290824paper.
Priorthe2015,theMCATpapersgavesimplerquadraticstofactoriseorsolve.Onceagain,Ihave
providedsomeexamplesbelow.
Factorise𝒙𝟐 − 𝟑𝒙 − 𝟒𝟎fromthe2014(A)MCATpaper.
Solve𝒙𝟐 + 𝟒𝒙 − 𝟏𝟐 = 𝟎fromthe2013(A)MCATpaper.
Factorise𝒙𝟐 − 𝟑𝒙 − 𝟐𝟖fromthe2012(A)MCATpaper.
Asaresultofthepointsraisedabove,thesufficiencytogainanAchievedgradewasreducedtoonly
3correctanswersoutof17intotalinthe2015paper.Inthe2016papersitwas3outof19correct
answersforanAchievedgrade.Itwas6correctanswersinthe2013and2014papers.Noperson
wouldthinkthat3outof19wouldbeapassinggrade.Thebarhadtobesetsolowduetothe
difficultyofthe2015and2016papers;otherwisetoomanystudentswouldhavefailed.Irecallthere
wasalargeteacherbacklashoverthe2015paperbeingsodifficult,yetthiswasonlyexacerbatedin
the2016paperdespitereassurancesbyNZQAthattheissuesraisedwouldnothappenagain.This
showsacompletelackofunderstandingoftheAchievementStandardSpeciationforAchievement
Standard91027byNZQA.Thiscallsintoquestionwhetherornotthe2015and2016paperswere
moderatedbyarangeofcurrentmathematicsteachers,andthatmoderationwastakenonboardby
theNZQA.Ihaveeverheardofsecondyearcalculusstudentsanduniversitylecturersstrugglingwith
questionsinthe2016papers.
Iknowthattherehasbeenmuchconcernfrommathematicsteachers,principals,students,parents,
andmathematicsassociationsacrossNewZealand.TheresponsefromanNZQArepresentativewas:
"Thepartsofthepaperwe'vebeentoldsomestudentsfoundmorechallengingthantheyexpected
relatetoapplyingknowledgetousemathsconceptsandmethodstosolvealgebraicproblems,rather
thanansweringstraightforwardskillsquestions(forexample,beingaskedanopenendedquestion
andformulatingamathematicresponsewhichpresentsfindings),Answeringquestionsinthiswayis
inlinewiththeNCEAstandardthatthepaperrelatestoandMCATpapershaveincreasinglybeen
includingquestionsofthisnatureoverthelastfewyears."
ThestatementaboverelatestotheExcellencesectionoftheAchievementStandardSpecification
only,yetnowheredoesitmentionthelevelofabstractionneededtoanswertheharderquestionsin
the2016MCATpapers.TheAchievementsectionoftheAchievementStandardSpecificationsimply
statesthatstudentsneedto“Applyalgebraicproceduresinsolvingproblems.”TheNZQAseemto
haveaveryuniqueviewofwhatan“algebraproblem”is.TheNZQAtakesthisdefinitionas“an
overlycomplexandoftenambiguouswordproblemwithnoscaffolding”.Theinternationally
accepteddefinitionofan“algebraproblem”couldbeanyoneoftheexampleslistedinthebullet
pointsoftheAchievementStandardSpecification.EveniftheNZQA’sinterpretationofan“algebra
problem”isacceptable,questionsshouldbemorelikethefollowingexample.
Anumberismultipliedbyitselfthreetimes.Theresultiseight.Whatisthisnumber?
SuchaquestionisinlinewiththeninthbulletpointintheAchievementStandardSpecification.
Instead,theNZQAcameupwiththefollowingquestionfromthe2016(A)paper.
Forwhatvaluesofnis𝟔×𝟐𝒏=𝟏 > 𝟏𝟐𝟑
ForthesakeofthestudentsacrossNewZealand,cantheNZQApubliclyacknowledgetheobvious
errorsmadeintheMCAToverthepasttwoyears,andensurethattheseerrorswillnothappenin
future?Ilookforwardtohearingyoureply.
PeterWebb,
Principal’sNomineeandConcernedMathematicsTeacher,
SaintPatrick’sCollege,
Wellington.