Thesis (PhD)--Stellenbosch Universityh, 1995. / ENGLISH ABSTRACT: This study investigates the influence of readability of mathematics examination questions on achievement. The aim of any mathematics examination is to assess whether the aims of a specific mathematics programme have been realized. Readability factors that unnecessarily prevent a clear understanding of questions could jeopardize this aim. The important issue is, therefore, whether there are indeed readability factors in mathematics examination questions that cause comprehension problems for students and, if there are, do they hav~ any effect on test scores? The issue of readability is of even greater importance for second language readers. In the South Mrican context, the reading problems of second language readers are of particular importance as most students at school are second language learners. An important question would therefore be: What readability factors cause comprehension difficulties for second language students, especially those whose mother tongue is not kindred to English? Furthermore, what is the influence of cultural factors on readability? This study provides answers to these and other related questions for mathematics text at senior secondary school level. Protocol analysis was used to ascertain what readability problems are experienced by students when reading examination questions in mathematics. Three different language groups, comprising 17 -18-year-old students, were used in the study: English First Language students and two groups who had English as a second language. One second language group had Mrikaans as first language while the other group comprised Mrican students whose mother tongue is unrelated to English. A framework was developed to analyse the protocols and it comprised five categories: unfamiliar vocabulary structural problems obscure information visualization difficulties non-verbal factors Mter the protocol study, students were asked to adapt the examination questions to a more comprehensible form. Students' adaptations addressed lexical, syntactical, discourse and non-verbal factors. Most of the readability problems identified in the literature study were verified in the empirical study. However, the empirical study generated additional readability problems that are mainly restricted to mathematics text and relate to nonverbal factors like mathematical expressions. During the last phase of the empirical study a composite test was used to test the hypothesis that improved readability of the common language used in mathematics examination questions' will improve achievement. Nine socalled "word problems" from previous examination papers were set in three different versions: original, adapted and non-verbal. The hypothesis was confirmed in a number of important cases. A significant finding of the study was, therefore, that readability factors not only influence the comprehension of mathematics examination questions, but also have a marked influence on students' achievement levels. The results of the empirical study are reported quantitatively as well as qualitatively. Other results include the following: Not only second language students, but also first language students experienced a variety of readability problems. All three language groups demonstrated the same level of competency on the non-verbal versions. When comparing test scores of the verbal versions, differences in achievement levels between the different language groups were often caused by linguistic and cultural factors. Cultural thought patterns, typical of a mother tongue but absent in a second language, were often a source of comprehension difficulties for second language readers. This study has led to certain conclusions for teaching and examination practice. For example, factors influencing the readability of ordinary English should be considered with other factors when writing mathematics examination questions. Furthermore, the distinctly different reading needs of second language students suggest that examination papers be set, so that the language needs of second language learners are accommodated. Guidelines for writing more readable examination questions were developed and are presented as a readability checklist. Suggestions for further research include the investigation of the influence of readability on achievement in authentic examination conditions. / AFRIKAANSE OPSOMMING: Hierdie studie ondersoek die invloed van leesbaarheid van wiskunde eksamenvrae op prestasie. Die doel van enige wiskunde eksamen is om vas te stel of die doelwitte van 'n spesifieke wiskunde program bereik is. Leesbaarheidsfaktore wat die volledige begryp van vraestelle onnodig belemmer, kan die bereiking van hierdie doel verhinder. Dit is dus belangrik om vas te stel of daar wel leesbaarheidsfaktore in wiskunde eksamenvrae bestaan wat vir leerlinge begripsprobleme veroorsaak en, indien wel, of hulle enige effek op toetspunte het. Vir tweedetaallesers is die kwessie van leesbaarheid van nog groter belang. In die SuidAfrikaanse opset is die leesprobleme van tweedetaal lesers 'n uiters aktuele saak aangesien die meeste skoolleerlinge tweedetaal leerders is. Belangrike vrae is dus: Watter faktore veroorsaak leesbaarheidsprobleme vir tweedetaalleerlinge, veral diegene met 'n nie-verwante moedertaal en, watter invloed het kultuur op leesbaarheid? Hierdie ondersoek bied antwoorde op hierdie en ander verwante vrae ten opsigte van wiskunde eksamenvrae op senior sekondere vlak. Protokol analise is gebruik om vas te stel watter leesbaarheidsprobleme ondervind word wanneer leerlinge wiskunde eksamenvrae lees. Drie verskillende taalgroepe, bestaande uit 17 -18-jarige leerlinge, het aan die ondersoek deelgeneem: Engels Eerstetaalleerlinge en twee groepe wat Engels as tweede taal gehad het. Een van die tweedetaal groepe het Afrikaans as eerste taal gehad terwyl die ander groep bestaan het uit Afrikane wie se moedertaal nie aan Engels verwant is nie. 'n Raamwerk is ontwikkel om die protokolle te analiseer en het uit die volgende vyf kategoriee bestaan: onbekende woordeskat strukturele probleme onduidelike inligting visualiseringsprobleme nie-verbale probleme Gedurende die tweede fase van die ondersoek is leerlinge gevra om die vrae tot 'n meer verstaanbare vorm aan te pas. Leerlinge se aanpassings het leksikale, sintaktiese, diskoers en nie-verbale faktore aangespreek. Sommige leesbaarheidsprobleme wat in die literatuurstudie gei'dentifiseer is, is in die empiriese ondersoek geverifieer. Die empiriese ondersoek het egter addisionele leesbaarheidsprobleme uitgelig wat meerendeels wiskundig van aard is en verband hou met nie-verbale faktore soos wiskunde uitdrukkings. Gedurende die laaste deel van die empiriese ondersoek is 'n samegestelde toets gebruik om die volgende hipotese te toets: Verbeterde leesbaarheid van die gewone taal wat in wiskunde eksamenvrae gebruik word, sal die prestasie van leerlinge verb et er. N ege sogenaamde woordsomme is op verskillende maniere gestel: oorspronklik, aangepas en nie-verbaal. Die hipotese is in 'n hele aantal belangrike gevalle bevestig. Een van die bevindinge van die ondersoek was dus dat leesbaarheidsfaktore nie slegs be grip ten opsigte van wiskunde eksamenvrae bei:nvloed nie, maar ook 'n beduidende invloed op prestasie het. Die resultate van die empiriese ondersoek word kwalitatief sowel as kwantitatief weergegee. Ander resultate sluit die volgende in: Nie slegs tweedetaal leerlinge nie, maar ook eerstetaal leerlinge het 'n verskeidenhied van leesbaarheidsprobleme ondervind Al drie taalgroepe het op die nie-verbale weergawe dieselfde bekwaamheidsvlak getoon. Verskille in die prestasievlakke tussen die verskillende taalgroepe op die verbale weergawes is baiekeer deur taalkundige en kulturele faktore veroorsaak Kulturele denkpatrone wat tipies is van 'n leerling se moedertaal, maar nie in die tweedetaal voorkom nie, het dikwels tot begripsprobleme by tweedetaal lesers gelei. Hierdie ondersoek het sekere gevolgtrekkings v1r o~derrig- en eksamenpraktyk. Byvoorbeeld, faktore wat die leesbaarheid van gewone Engels bei:nvloed, behoort saam met ander faktore in ag geneem te word wanneer wiskunde eksamenvraestelle opgestel word. Verder is daar duidelike aanduidings dat aparte vraestelle vir eerste- en tweedetaal leerlinge opgestel moet word sodat die taalbehoeftes van tweedetaal leerlinge in ag geneem kan word. Riglyne vir die skryf van meer leesbare eksamenvrae is saamgestel en as 'n oorsiglys aangebied. Voorstelle vir verdere navorsing sluit in die ondersoek na die invloed van leesbaarheid op prestasie in ware eksamen omstandighede.

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 (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.

published_or_final_version / Education / 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 Education

published_or_final_version / Education / Master / Master of Education

published_or_final_version / abstract / Education / Master / Master of Education

published_or_final_version / abstract / Education / Master / Master of Education

The Outreach Project of the University of the Western Cape has since 1982 through various computer supported services been assisting grade 12 mathematics learners and educators at previously disadvantaged Western Cape high schools. This thesis described and appraised the MICSES2000 program of the Outreach Program, the latest innovative computer enhancing service to schools, with respect to its implementation, perceived and achieved programs by participating educators.