Thesis (MEd)--University of Stellenbosch, 2005. / ENGLISH ABSTRACT: Research shows that misconceptions about calculations develop in many classrooms without being noticed and these are not corrected by repeated routine exercises. The misconceptions formed are at times the result of inappropriate models used to solve problems. An even bigger concern is that these particular models sometimes provide the correct answers by accident. This may result in the learner's belief in the models being reinforced, as described by Swan (n.d.). The aim of this study is to identify the misconceptions related to the use of decimal fractions by Grade 8 and 9 learners and then, through the use of an intervention program, to address the learners' misconceptions and attempt to correct them. Two schools were involved in this study. The group of learners from school A served as a control group to determine the success of the intervention in learners from school B. The results of school A, the frequency and nature of errors were compared with the test results of school B as well as described by interviews with learners from school B. After the diagnostic tests and interview, the learners' answers were compared with those already described in literature. The learners from school B participated voluntarily in the intervention program. Learners from both schools wrote a post-test and the results were compared with those of a pre-test. The conclusion of this study is that there are misconceptions concerning calculations with decimal fractions at Grade 8 and 9 level. These misconceptions are formed during the intermediate phase and are not suitably corrected. The intervention program, for various reasons, had limited success. These reasons are discussed and recommendations are made for future intervention programs. / AFRIKAANSE OPSOMMING: Navorsing toon dat wanbegrippe ten opsigte van berekeninge in baie klaskamers onopgemerk verbygaan en dat dit nie reggestel word deur herhaalde roetine oefeninge nie. Wanbegrippe wat kinders vorm is onder andere die gevolg van onvanpaste modelle wat gebruik word vir die oplos van probleme. 'n Groter gevaar is dat hierdie onvanpaste modelle toevallig die regte antwoord lewer. Dit kan dan veroorsaak dat die leerder se vertroue op die modelle net versterk word, soos Swan (s.j.) dit beskryf. Die doel van hierdie studie is om wanbegrippe ten opsigte van bewerkings met desimale breuke by Graad 8 en 9 leerders te identifiseer en dan deur middel van 'n intervensieprogram die leerders se wanbegrippe aan te spreek en te probeer regstel. Twee skole is by hierdie studie betrek. Die groep leerders van skool A sou dien as 'n kontrolegroep om die intervensie-sukses van die leerders van skool B te bepaal. Die skool A resultate en frekwensie van foute asook die aard daarvan is vergelyk met die toetse van skool B en beskryf op grond van onderhoude met die leerders van skool B. Ná die diagnostiese toets en onderhoud is die leerders se antwoorde vergelyk met dié wat reeds in die literatuur beskryf is. Die leerders van skool B is op vrywillige basis by 'n intervensieprogram betrek. Beide skole se leerders het daarna 'n natoets geskryf en die resultate is vergelyk met dié van die voortoets. Die gevolgtrekking wat uit hierdie studie gemaak word, is dat daar wanbegrippe ten opsigte van bewerkings met desimale breuke op graad 8 en 9 vlak aanwesig is. Hierdie wanbegrippe is in die intermediêre fase gevorm en nie reggestel nie. Die intervensieprogram het om verskeie redes slegs beperkte sukses gehad. Hierdie redes word bespreek en aanbevelings word gemaak vir toekomstige intervensieprogramme.

Thesis (MEd)--Stellenbosch University, 2001. / ENGLISH ABSTRACT: The study of three-dimensional boxes is widely regarded as a suitable topic for entry-level geometry. In order to inform teaching and curriculum design this study takes children's intuitive knowledge of boxes as point of departure to research the following aspects: • the meaning children assign to boxes • children's ability to create and manipulate mental images • children's strategies to solve a three dimensional construction problem • possible age and gender differences • the role of measurement • possible links with Van Hiele's thought levels Revised clinical interviews were conducted with groups of six to ten children. Each child could select an object from a set provided by the researcher and had to build a box from cardboard into which the object could fit. The problem-solving processes were captured on video. The children's boxes, verbal utterences and overt manipulation of the materials as well as the empirical referent objects were analised. The researcher made use of grounded theory procedure to analise and categorise the data. The research indicates that young children are not necessarily aware of the shape and structural properties of three-dimensional boxes. It is also evident that children's ability to represent properties of shape of boxes through language, drawing and hand movements does not necessarily indicate adequate understanding of the structural properties of boxes to enable them to build a box from two-dimensional materials. The research further indicates that aspects of representation that are judged to be based on lack of knowledge of conventions in a medium such as drawing, may have deeper intuitive and conceptual roots. An alternative view of childrens spatial/geometric thought on VanHiele level 0 is described based on their assignment of meaning to geometric tasks. / AFRIKAANSE OPSOMMING: Drie-dimensionele houers word allerweë as geskikte konteks vir aanvangsmeetkunde-onderrig beskou. In hierdie studie word kinders se intuïtiewe begrip van alledaagse houers of bokse as vertrekpunt gebruik om die volgende aspekte te ondersoek met die oog daarop om inligting te bekom vir kurrikulering: • die betekenis wat kinders aan bokse (as meetkundige objekte) toeken • kinders se vermoë om 'n denkbeeld te skep en te manipuleer • kinders se strategieë om 'n drie-dimensionele konstruksieprobleem op te los • moontlike ouderdoms- en geslagsverskille • die rol wat meting speel wanneer 'n drie-dimensionele konstruksieprobleem opgelos word • moontlike ooreenkomste met Van Hiele-denkvlakke 'n Taakgerigte ondersoek (revised clinical interview) is met groepies van ses tot tien kinders op 'n slag gedoen. Elke kind kon 'n voorwerp kies uit 'n versameling en moes 'n houer of boks uit karton bou waarin die voorwerp kon pas. Die probleemoplossingsproses is met 'n videokamera afgeneem. Die kinders se voltooide houers, taaluitinge en overte hantering van die empiriese verwysingsvoorwerpe en die materiaal waarmee hulle gewerk het, is as data ontleed. Die navorser het gebruik gemaak van die analitiese prosesse wat beskryf word as begronde teorie-ontwikkeling om die data te ontleed en te kategoriseer. Die navorsmg hat aangetoon dat jong kinders nie noodwending bewus is van die vorm- en strukturele eienskappe van drie-dimensionele houers nie. Verder is dit duidelik dat kinders se voorstellings van veral vormeienskappe van houers deur middel van taal, handbewegings en tekeninge, nie impliseer dat hulle die nodige begrip van die struktuur het om so 'n houer uit tweedimensionele materiaal te kan vervaardig nie. Die navorsing het verder aan die lig gebring dat aspekte van kinders se ruimtelike kennis wat voorheen as aanduiding van gebrekkige kennis van konvensies beskou is, moontlik dieper konseptuele wortels het. 'n Alternatiewe beskouing van kinders se ruimtelik-meetkundige denke op Van Hiele Vlak 0 word ook voorgestel.

Thesis (MEd (Curriculum Studies))--University of Stellenbosch, 2010. / ENGLISH ABSTRACT: Mathematical modelling is becoming a popular teaching and learning approach in mathematics education. There is however a need within the modelling domain to identify exactly what modelling competencies are and how these competencies develop. This study examines how mathematical modelling competencies develop in Grade 7 students working in groups. Modelling is placed in the field of mathematics teaching and learning as a significant means of learning mathematics. Modelling competencies are identified and characterised from existing literature and explored through empirical generation and collection of data. The study is qualitative in nature and uses a mixed approach of design research and some aspects of grounded theory. Students’ progress through a modelling program is documented while the modelling competencies of students stereotyped as weak and strong are also investigated. The findings firmly support earlier research that competencies do develop in students who are exposed to modelling. A comprehensive picture of the modelling situation is presented since this study merges competencies from other studies into a detailed analysis of the modelling situation - it presents an authentic modelling situation of students working in groups and furthers the discussion on modelling competencies. The analysis of the data suggests that the development of modelling competencies is complex and interrelated but that competencies do develop progressively in groups involved in modelling tasks. Recommendations for additional studies include studies of a longer duration and a full investigation into the link between modelling and language ability. / AFRIKAANSE OPSOMMING: Wiskundige modellering is besig om ‘n populêre onderrig- en studiebenadering in wiskundeonderwys te word. Daar is egter ‘n behoefte om die modelleringsbevoegdhede te identifiseer in hierdie veld en om te weet hoe hierdie bevoegdhede ontwikkel. Hierdie studie ondersoek watter bevoegdhede in wiskundige modellering by Gr.7 studente wat in groepe saamwerk ontwikkel. Modellering is in die studieveld van wiskundeonderrig en -leer geplaas as 'n betekenisvolle leerwyse in wiskunde. Modelleringsbevoegdhede word vanuit bestaande literatuur en navorsing geïdentifiseer en beskryf deur empiriese generering en versameling van data. Die studie is kwalitatief van aard en gebruik ‘n gemengde benadering van ontwikkelingsondersoek en sekere aspekte van begronde teorie. Studente se vordering in die modelleringsprogram is gedokumenteer terwyl die modelleringsbevoegdhede van gestereotipeerde swak en sterk studente ook ondersoek is. Die resultate bevestig vroeëre navorsing dat bevoegdhede ontwikkel word deur studente wat blootgestel is aan modellering. ‘n Omvattende beeld van die modelleringsituasie is in hierdie studie aangebied waardeur modelleringsbevoegdhede, soos geïdentifiseer in ander studies, tot ‘n gedetailleerde analise van die modelleringsituasie saamgevoeg word. Dit verteenwoordig dus ‘n outentieke modelleringsituasie van studente wat in groepe saamwerk en bevorder so die gesprek oor modelleringsbevoegdhede. Die analise van die data suggereer dat die ontwikkeling van modelleringsbevoegdhede kompleks en geïntegreerd is, en dat bevoegdhede progressief ontwikkel in groepe wat betrokke is by modelleringstake. Aanbevelings vir addissionele studies sluit langer ondersoektydperke in en 'n dieper ondersoek na die verband tussen modellering en taalvaardigheid.

ENGLISH ABSTRACT: This thesis sets out to examine Moodle use to assist Deaf and Hard of Hearing Grade 9 learners with understanding mathematics problem-solving. The methodology used in this research project is that of formative evaluation. In this qualitative data analysis I worked as a participant-observer with three Deaf and H/H Grade 9 learners from a local school for the Deaf and H/H. These learners engaged in a course constructed in Moodle based on ratio and rate. The course was designed along the lines of a constructivist pedagogical model, different levels of learning as well as including multi representational features. Through the qualitative analysis of the interviews conducted with learners who participated in the research project and observation done by the teacher researcher, three categories emerged i.e. Weaknesses, Potential strengths and Learner suggestions. Although the findings indicate that different factors negatively impact Deaf and H/H learners’ ability to solve mathematics problems, it also highlights the representational features of mathematics content via Moodle, and how it can assist Deaf and H/H learners with the struggle with mathematics problem-solving. / AFRIKAANSE OPSOMMING: Die doel van hierdie navorsingsprojek is om te evaluereer of Moodle gebruik deur Dowe en Hardhorende graad 9 leerders hulle kan help met moeilikhede wat hulle ondervind met wiskunde probleem oplossing. Die navorsing is ‘n formatiewe evaluering. Binne hierdie kwalitatiewe data ontleding werk ek as ‘n deelnemer-navorser met 3 Dowe en Hardhorende graad 9 leerders by ‘n plaaslike skool vir Doof en Hardhorende leerders. Hierdie leerders het deelgeneem in leeraktiwiteite wat ontwerp is in Moodle en wat gebasseer is op verhouding en koers. Die leeraktiwiteite is ontwerp inlyn met ‘n konstruktivistiese pedagogiese model, verskillende vlakke van leer en multi voorstellings formate. Drie kategorieë o.a Tekortkominge, Moontlike Sterkpunte en Leerder voorstelle, het onstaan tydens die kwalitatiewe data ontleding waar onderhoude met die deelnemers gevoer asook observasie wat gedoen is deur die deelnemer-navorser. Alhoewel die bevindinge daarop dui dat verskillende faktore negatief inwerk op Dowe en Hardhorende leerders se vermoë om wiskunde problem op te los, wys dit ook uit die vermoë van Moodle om wiskunde probleme voor te stel en hoe hierdie voorstellings Dowe en Hardhorende leerders kan help met wiskunde probleem oplossing.

published_or_final_version / Education / Doctoral / Doctor of Philosophy

published_or_final_version / Curriculum Studies / Doctoral / Doctor of Philosophy

published_or_final_version / Education / Master / Master of Science in Information Technology in Education

published_or_final_version / Education / Master / Master of Science in Information Technology in Education

published_or_final_version / abstract / Education / Master / Master of Education

published_or_final_version / Education / Master / Master of Education