learner errors and misconceptions in elementary analysis a…

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1、Volume3,Number3,2010LEARNERERRORSANDMISCONCEPTIONSINELEMENTARYANALYSIS:ACASESTUDYOFAGRADE12CLASSINSOUTHAFRICAKakomaLuneta,PaulJ.Makonye1Abstract:Thepaperfocusesonanalysinggrade12learnererrorsandthemisconceptionsincalculusatasecondaryschoolinLimpopoProvince,SouthAfrica.Aspartoftheanalysist

2、hepaperoutlinesthenatureofmathematicserrorsandmisconceptions.Codingoflearners’errorswasdonethroughthelensofatypologicalframework.Theanalysisshowedthatmostoftheerrorsandmisconceptionswereduetoknowledgegapsinbasicalgebra.Alsonotedwasthaterrorsandmisconceptionsincalculuswererelatedtolearners

3、’over-dependenceonproceduralknowledgewhichhadnoconceptualbasis.Ontheotherhand,learnerssometimeshadsoundconceptualknowledgeforwhichtheyhadnotacquiredalliedproceduralknowledgeneededtoperforminparticularquestions.Implicationsofthestudytothewidermathematicseducationcommunityarehighlighted.Key

4、words:Errors,misconceptions,differentialcalculusIntroductionCurriculumreformperspectivesinmathematicseducationarticulatedinmanyresearchpapersandpolicydocumentsaimatdeepeningandincreasingeachlearner’smathematicallearningandachievement(NationalCurriculumStatement(NCS),1998;NationalMathemati

5、csAdvisoryPanel(NMAP),2008).Theperspectivessuggestshiftsfromteacher-centredtolearner-centredapproaches.Thelearner-centredapproachesimplythatteachingmustalsobedirectlyresponsivetothedifficultiesexperiencedbylearnersonthelearningplatform,suchasthemathematicalerrorsandmisconceptionstheyexper

6、ience.InaworkshoporganisedformathematicsteachersbytheSouthAfricanDepartmentofEducation,teacherswererequiredtooutlinethetopicsthattheyfoundproblematictoteach.Theteachersrevealedthatamongotherscalculuswasoneofthem.Onewonderswhytoalargeextenttheteachingandlearningofmathematicsissodifficultan

7、dineffective.Tothisquest,wesuspectedthatpoorperformanceinmathematicsiscorrelatedtolearnererrorsandmisconceptions.TheanatomyoflearnererrorsandmisconceptionsAlthougherrorsandmisconceptionsarerelated,theyaredifferent.Anerrorisamistake,slip,blunderorinaccuracyandadeviat