The development of a mathematics proficiency test for English-, Afrikaans- and Sesotho-speaking learners
| dc.contributor.advisor | Grobler, A. A. | |
| dc.contributor.advisor | Esterhuyse, K. G. F. | |
| dc.contributor.author | Vassiliou, Colleen Patricia | |
| dc.date.accessioned | 2018-01-15T10:20:29Z | |
| dc.date.available | 2018-01-15T10:20:29Z | |
| dc.date.issued | 2003-11 | |
| dc.description.abstract | English: Mathematical Literacy, Mathematics and Mathematical Sciences is a learning area in the intermediate phase, which forms part of the General Education and Training band. This learning band is level one of the National Qualifications Framework and is overseen by the South African Qualifications Authority. The curriculum of this learning area consists of various learning strands, namely numbers and operations, fractions, patterns, shapes and space, measurement, and data. When learners fail to meet the expectations of the curriculum, mathematics becomes a major assessment concern. If this problem is not identified it could hinder the acquisition of more advanced mathematical skills. The first task in helping a learner who is struggling with mathematics is to identify the problem. For learners to succeed at mathematics they need to go through various developmental phases. Various cognitive processes form part of these phases. Often in a young child’s functioning, cognitive problems arise such as the inability to perform various mathematical tasks. For this reason a cognitive model for mathematics was used to reflect upon six key concepts that influence learning and teaching in the Mathematical Literacy, Mathematics and Mathematical Sciences learning area. These concepts include the categories of representing experience; motivation; individual differences; cognitive categories and cognitive processes; instructional procedures; and conceptual learning. Learners need to make sense out of what is going on during a mathematics lesson. To help learners develop meaning, a teacher provides experiences that foster mental manipulations. Psychologists refer to these mental manipulations as cognitive processes. When a learner is unable to carry out the cognitive processes necessary for task completion, mathematics becomes a major assessment concern. If a learner fails to meet the expectations of the curriculum or fails to carry out the cognitive processes necessary for successful task completion, then, in accordance with the aim of this study, the Intermediate Phase Mathematics Proficiency Test can be used to identify and address this problem. During the construction of this test, care was taken to ensure that the test was cross-culturally adapted. Differential Item Functioning was used to limit the possibility of cultural bias. The Item Response Theory and the Classical Test Theory were also used for item analysis and selection. The test was standardised for English-, Afrikaans- and Sesotho-speaking grade four, five and six learners. During standardisation, separate norms for each term were calculated. These norms are available in both stanines and percentile ranks. The test can also be used qualitatively to determine not only the learning strand in which the learner may be experiencing problems, but also the specific cognitive process, such as receiving, interpreting, organising, applying, remembering and problem solving, which might be preventing the learner from reaching his or her full mathematical potential. The Intermediate Phase Mathematics Proficiency Test is also a reliable and valid measuring instrument since the bias of the assessment measure has been decreased. This was done by eliminating any item that was biased towards a specific cultural group. The test can therefore be used in practice with confidence. In a multicultural society like South Africa, the adaptation of assessment measures and the elimination of bias from psychometric tools forms a vital part of the transformation process. The Intermediate Phase Mathematics Proficiency Test is a multicultural test with South African norms. | en_ZA |
| dc.description.abstract | Afrikaans: Wiskundige Geletterdheid, Wiskunde en Wiskundige Wetenskappe is ’n leerarea in die intermediêre fase, wat deel vorm van die afdeling Algemene Onderwys en Opleiding. Hierdie leerafdeling is vlak een van die Nasionale Kwalifikasiesraamwerk en toesig word gehou deur die Suid-Afrikaanse Kwalifikasiesoutoriteit. Die kurrikulum van hierdie leerarea bestaan uit verskeie leerafdelings, naamlik getalle en bewerkings, breuke, patrone, vorms en ruimte, meting en data. Wanneer leerders nie daarin slaag om aan die verwagtinge van die kurrikulum te voldoen nie, word wiskunde ’n groot assesseringsvraagstuk. Indien hierdie probleem nie geïdentifiseer word nie, kan dit die aanleer van meer gevorderde wiskundige vaardighede belemmer. Die eerste taak tydens hulpverlening aan die leerder wat sukkel met wiskunde, is om die probleem te identifiseer. Vir leerders om sukses te behaal in wiskunde, moet hulle deur verskillende ontwikkelingsfases beweeg. Verskeie kognitiewe prosesse vorm deel van hierdie fases. Dit gebeur dikwels dat daar in die jong kind se funksionering kognitiewe probleme ontstaan, soos byvoorbeeld die onvermoë om verskeie wiskundige take uit te voer. Om dié rede is ’n kognitiewe model vir wiskunde gebruik om te besin oor die ses sleutelkonsepte wat die leer en onderrig van Wiskundige Geletterdheid, Wiskunde en Wiskundige Wetenskappe beïnvloed. Hierdie konsepte sluit in: die kategorieë van die weergee van ervaring; motivering; individuele verskille; kognitiewe kategorieë en kognitiewe prosesse; onderrigprosedures en konseptuele leer. Leerders moet sin maak uit dit wat aangaan gedurende ’n wiskunde-les. Om leerders te help om betekenis te ontwikkel, verskaf die onderwyser ervaringggeleenthede wat verstandelike bewerkings aanmoedig. Sielkundiges noem hierdie verstandelike bewerkings, kognitiewe prosesse. Wanneer ’n leerder nie in staat is om die nodige kognitiewe prosesse uit te voer wat nodig is vir taakvoltooiing nie, word wiskunde ’n groot assesseringsvraagstuk. Indien ’n leerder nie daarin slaag om aan die verwagtinge van die kurrikulum te voldoen nie of misluk in die uitvoering van kognitiewe prosesse wat nodig is vir suksesvolle taakvoltooiing, kan die Intermediêre Fase Wiskundige Vaardigheidstoets, in ooreenstemming met die doel van hierdie studie, gebruik word om hierdie probleem te identifiseer en aan te spreek. Tydens die opstelling van hierdie toets is sorg geneem om te verseker dat die toets kruis-kultureel aangepas is. Differensiële Itemfunksionering is gebruik om die moontlikheid van kulturele vooroordeel te beperk. Die Itemresponsteorie en die Klassieke Toetsteorie is ook gebruik vir itemanalise en -seleksie. Die toets is gestandaardiseer vir Engels-, Afrikaans- en Suid-Sotho-sprekende leerders van graad vier, vyf en ses. Gedurende standaardisasie is aparte norms vir elke term bereken. Hierdie norms is beskikbaar in beide staneges en persentielrange. Die toets kan ook kwalitatief gebruik word om nie net die leeraspek waarmee die leerder probleme ondervind te bepaal nie, maar die spesifieke kognitiewe proses, soos byvoorbeeld ontvangs, interpretering, organisering, toepassing, onthou en probleemoplossing, wat die leerder daarvan kan weerhou om sy of haar volle wiskundige potensiaal te bereik. Die Intermediêre Fase Wiskundige Vaardigheidstoets is ook ’n betroubare en geldige meetinstrument omdat die vooroordeel van die assesseringsmeting verminder is. Dit is gedoen deur enige item wat bevooroordeeld teenoor ’n spesifieke kulturele groep is, uit te skakel. Om die rede kan die toets met vertroue in die praktyk gebruik word. In ’n multikulturele samelewing soos Suid-Afrika, vorm die aanpassing van assesseringsmaatstawwe en die uitskakeling van vooroordeel in psigometriese toetse, ’n baie belangrike deel van die transformasieproses. Die Intermediêre Fase Wiskundige Vaardigheidstoets is ’n multilkulturele toets met Suid-Afrikaanse norms. | af |
| dc.identifier.uri | http://hdl.handle.net/11660/7605 | |
| dc.language.iso | en | en_ZA |
| dc.publisher | University of the Free State | en_ZA |
| dc.rights.holder | University of the Free State | en_ZA |
| dc.subject | Current educational system in South Africa | en_ZA |
| dc.subject | Intermediate phase | en_ZA |
| dc.subject | Outcomes Based Education | en_ZA |
| dc.subject | Mathematical Literacy, Mathematics, Mathematical Sciences learning area | en_ZA |
| dc.subject | Learning strands | en_ZA |
| dc.subject | Assessment | en_ZA |
| dc.subject | Learning-teaching process of the cognitive model for mathematics | en_ZA |
| dc.subject | Cognitive theorists | en_ZA |
| dc.subject | Cognitive processes | en_ZA |
| dc.subject | Development of a test | en_ZA |
| dc.subject | Standardisation of a test | en_ZA |
| dc.subject | Item analysis and selection | en_ZA |
| dc.subject | Cross-cultural test adaptation | en_ZA |
| dc.subject | Differential Item Functioning | en_ZA |
| dc.subject | Classical Test Theory | en_ZA |
| dc.subject | Item Response Theory | en_ZA |
| dc.subject | Norm determination | en_ZA |
| dc.subject | Mathematics proficiency test | en_ZA |
| dc.subject | Mathematical ability -- Testing | en_ZA |
| dc.subject | Educational tests and measurements. | en_ZA |
| dc.subject | Competency-based educational tests -- South Africa | en_ZA |
| dc.subject | Thesis (Ph.D. (Counselling Psychology))--University of the Free State, 2003 | en_ZA |
| dc.title | The development of a mathematics proficiency test for English-, Afrikaans- and Sesotho-speaking learners | en_ZA |
| dc.type | Thesis | en_ZA |