Some learners in South Africa perform poorly in school, especially in Mathematics. In 2010 the Department of Basic Education announced their concern regarding the pass rate. The National Education Department circulated a report in 2008 on some Grade 3 and Grade 6 learners who took part in a research project and only achieved level one and two in literacy (vocabulary), as well as numeracy (Mathematics). Several factors contribute to this shocking situation, such as the absence of the use of meta-cognitive strategies, number strategies, as well as language strategies. The prime goal of this study was to investigate the use of meta-cognitive strategies and Mathematical vocabulary during problem solving by Grade 7 learners. Three primary schools were invited to participate in the qualitative investigation. From these schools three top achievers (one per school) and three under-achievers (one per school) were invited to participate in the quantitative investigation. The study includes the results of the quantitative aspects of the investigation. Learners had to answer questions about predictions, achievements, control, as well as evaluation during the quantitative investigation. During this process, most of the learners predicted that they would do well and evaluated that they did well, but their marks for the questions about their achievements and control were in fact different. It is important to inform Mathematics teachers and learners about meta-cognitive strategies and Mathematical vocabulary, and the influence it can have on the learners’ achievements, as well as the positive effect during the learning of Mathematics. / MEd (Mathematics Education), North-West University, Potchefstroom Campus, 2014

Some learners in South Africa perform poorly in school, especially in Mathematics. In 2010 the Department of Basic Education announced their concern regarding the pass rate. The National Education Department circulated a report in 2008 on some Grade 3 and Grade 6 learners who took part in a research project and only achieved level one and two in literacy (vocabulary), as well as numeracy (Mathematics). Several factors contribute to this shocking situation, such as the absence of the use of meta-cognitive strategies, number strategies, as well as language strategies. The prime goal of this study was to investigate the use of meta-cognitive strategies and Mathematical vocabulary during problem solving by Grade 7 learners. Three primary schools were invited to participate in the qualitative investigation. From these schools three top achievers (one per school) and three under-achievers (one per school) were invited to participate in the quantitative investigation. The study includes the results of the quantitative aspects of the investigation. Learners had to answer questions about predictions, achievements, control, as well as evaluation during the quantitative investigation. During this process, most of the learners predicted that they would do well and evaluated that they did well, but their marks for the questions about their achievements and control were in fact different. It is important to inform Mathematics teachers and learners about meta-cognitive strategies and Mathematical vocabulary, and the influence it can have on the learners’ achievements, as well as the positive effect during the learning of Mathematics. / MEd (Mathematics Education), North-West University, Potchefstroom Campus, 2014

Hierdie studie handel oor die invloed van twee onderrigbenaderings naamlik tradisioneel en sosiaal-konstruktivisties, op Graad 6-leerders se studieoriëntasie in Wiskunde. Om die omvang hiervan beter in perspektief te plaas is daar gekyk na wat die moontlike verskille is tussen die tradisionele sowel as die sosiaal-konstruktivistiese onderrigbenaderings ten opsigte van Graad 6-leerders se studieoriëntasie in Wiskundeprestasie. Literatuur dui aan dat leerders swak presteer en noem faktore wat moontlik bydra. Verder dui die literatuur aan dat daar nie genoeg navorsing is ten opsigte van ontoereikende wiskundeprestasie nie. Dit is kommerwekkend dat daar tot dusver redelik min navorsing gedoen is wat Graad 6-leerders se ontoereikende prestasie in Wiskunde aanbetref (Rademeyer, 2009) aangesien dit so ’n belangrike rol speel tot die beroepswêreld (Salman et al, 2010). Maree, Pretorius en Eiselen (2003) meen dat verbetering in Wiskundeprestasie moontlik gefasiliteer kan word deur op die leerders se ontoereikende studieoriëntasie te fokus en dít dan so te probeer verbeter. Die konseptuele raamwerk van hierdie studie rus op Vygotsky se sone van proksimale ontwikkeling (Maimane, 2006) sowel as Bronfenbrenner se ekologiese teorie en die konseptuele raamwerk (Santrock, 2001; Bronfenbrenner,2012) Die navorsingsvrae lui dan as volg: Primêre navorsingsvraag: Wat is die verskil tussen die tradisionele sowel as die sosiaal-konstruktivistiese onderrigbenadering ten opsigte van Graad 6-leerders se studieoriëntasie in Wiskundeprestasie? Eerste sekondêre vraag: Hoe verskil die tradisionele onderrigbenadering ten opsigte van die sosiaal-konstruktivistiese onderrigbenadering? Tweede sekondêre vraag en hipotese: Wat is die verskil in Wiskundeprestasie voor en na die intervensie ten opsigte van die twee onderrigbenaderings? Derde sekondêre vraag en hipotese: Wat is die verskil in studieoriëntasie voor en na die intervensie ten opsigte van die twee onderrigbenaderings? Hierdie studie word beskou deur pragmatisme as ’n wêreldbeskouing en filosofiese fondasie aangesien pragmatisme die heel beste pas by die gemengde navorsingsmetode. Die konvergente navorsingsontwerp is die ideale navorsings-ontwerp vir hierdie studie aangesien dit die bekendste benadering tot die gemengde navorsingsmetode is. Vir die kwalitatiewe data-insameling is ek gebruik gemaak van fokusgroeponderhoude wat drie maal gehou is met beide die groepe, altesaam ses sessies. Daar was sewe leerders wat elk van die groepe verteenwoordig het, veertien leerders altesaam. Daar is gebruik gemaak van ’n individuele onderhoud met die Wiskundeonderwyseres aan die einde van die intervensie tydperk. Die data was geanaliseer deur inhoudsanalise. Die kwantitatiewe data is ingesamel deur die Studieoriëntasievraelys in Wiskunde (Primêr) (SOW(P)) en ook ’n formele wiskunde toets aan die begin en aan die einde van die intervensie tydperk. Daar was twintig leerders wat deelgeneem het aan die tradisionele groep en twintig leerders wat deelgeneem het aan die sosiaal-konstruktivistiese groep. Daar was altesaam veertig leerders betrokke by die studie. Die kwalitatiewe data-analise het uitgedraai op vier verskillende temas: faktore wat Wiskunde makliker maak vir leerders, faktore van Wiskunde wat vir leerders onaangenaam is, faktore van introspeksie en ook ander interessante faktore. Ek het ook observasies en addisionele data vanaf die Wiskundeonderwyseres verkry deur die individuele onderhoud. Vir die doeleindes van die kwantitatiewe data is gebruik gemaak van beskrywende sowel as inferensiële statistieke om die data te analiseer. Daar is gebruik gemaak van die paar-steekproef studente t-toets. Alles is dan na aanleiding van die data-analise bespreek en na aanleiding van my bevindinge en resultate is daar gevind dat daar wel ’n verskil is tussen die tradisionele onderrigmetode en die sosiaal-konstruktivistiese onderrigbenadering. Dit was ook duidelik dat daar ’n waarskynlike verskil tussen die voor-toets en die na-toets van die tradisionele sowel as die sosiaal-konstruktivistiese groep se Wiskundeprestasie is en dus is beide as statisties beduidend aanvaar. Wat die studieoriëntasie aanbetref het die uitkoms getoon dat daar geen verskil was tussen die voor-toets en die na-toets van die tradisionele groep nie, dus toon dit om nie statisties beduidend te wees nie . Daar was wel ’n waarskynlike verandering tussen die voor-toets en die na-toets van die sosiaal-konstruktivistiese groep se studie-oriëntasie en aanvaar ek dit dus as statisties beduidend. / Dissertation (MEd)--University of Pretoria, 2013. / gm2014 / Educational Psychology / unrestricted

Assessment, as an integral part of teaching and learning, gained unprecedented prominence in the curriculum in South Africa post 1994. When the new curriculum was introduced, it was assumed that teachers would effortlessly adapt their teaching and assessment practices, and swiftly implement the curriculum. Fourteen years after the inception of the new curriculum, majority of teachers are still grappling with issues of assessment. Previously, there was an exclusive bias towards summative assessment, which is mainly learning product–orientated and less or no focus on the other assessment typologies such as diagnostic and formative assessment, which are learning process–orientated. Of these typologies, diagnostic assessment is not being used maximally to enhance mathematics learning and inform the nature of the interventions to attend to learners’ needs. The study focused on diagnostic assessment by investigating the impact of a particular model, GIST model, on the learning barriers and learner achievement in mathematics among the grade 9 learners. The investigation of the impact of the GIST model was done through the experimental design in four schools with class sizes of d > 40. Data were collected quantitatively through Study Orientation Questionnaire (SOM) and Mathematics Achievement Test (MAT) as well as qualitatively through interviews, observations and document analysis. The t–test and the analysis of covariance (ANCOVA) revealed that the GIST model improved the learner achievement practically significantly (d = 0.79). However, the GIST model could not mitigate the learning barriers and improve correlations between SOM and MAT. The study, however, does find grounds to conclude that the latter findings can be attributed to teachers’ lacking understanding and implementation of diagnostic assessment, in particular the GIST components. Hence, certain recommendations are posed with regard to the applicable training of teachers in order to empower them to effectively utilize diagnostic assessment and to guide learners in overcoming learning barriers in mathematics. / Thesis (Ph.D. (Mathematics Education))--North-West University, Potchefstroom Campus, 2011.

Assessment, as an integral part of teaching and learning, gained unprecedented prominence in the curriculum in South Africa post 1994. When the new curriculum was introduced, it was assumed that teachers would effortlessly adapt their teaching and assessment practices, and swiftly implement the curriculum. Fourteen years after the inception of the new curriculum, majority of teachers are still grappling with issues of assessment. Previously, there was an exclusive bias towards summative assessment, which is mainly learning product–orientated and less or no focus on the other assessment typologies such as diagnostic and formative assessment, which are learning process–orientated. Of these typologies, diagnostic assessment is not being used maximally to enhance mathematics learning and inform the nature of the interventions to attend to learners’ needs. The study focused on diagnostic assessment by investigating the impact of a particular model, GIST model, on the learning barriers and learner achievement in mathematics among the grade 9 learners. The investigation of the impact of the GIST model was done through the experimental design in four schools with class sizes of d > 40. Data were collected quantitatively through Study Orientation Questionnaire (SOM) and Mathematics Achievement Test (MAT) as well as qualitatively through interviews, observations and document analysis. The t–test and the analysis of covariance (ANCOVA) revealed that the GIST model improved the learner achievement practically significantly (d = 0.79). However, the GIST model could not mitigate the learning barriers and improve correlations between SOM and MAT. The study, however, does find grounds to conclude that the latter findings can be attributed to teachers’ lacking understanding and implementation of diagnostic assessment, in particular the GIST components. Hence, certain recommendations are posed with regard to the applicable training of teachers in order to empower them to effectively utilize diagnostic assessment and to guide learners in overcoming learning barriers in mathematics. / Thesis (Ph.D. (Mathematics Education))--North-West University, Potchefstroom Campus, 2011.

lnternasionaal, sowel as nasionaal bestaan daar besorgdheid oor leerders se ontoereikende prestasie in wiskunde. In postapartheid Suid-Afrika is ontoereikende prestasie in wiskunde 'n wesenlike probleem. Talle studies is reeds onderneem om hierdie verskynsel te verklaar omdat wiskundeprestasie van kardinale belang is vir enige ontwikkelende land. Navorsing het onder meer aangetoon dat wiskundeprestasie op skoal een van die beste voorspellers van sukses op tersiere vlak is en dat daar 'n statistiese betekenisvolle verband bestaan tussen wiskundeprestasie en aspekte van studie-orientasie in wiskunde (insluitende studiegewoontes, wiskunde-angs, houding jeens wiskunde, effektiewe tydsbestuur, ouerverwagting, asook leerders se sosiale en ervaringswereld in wiskunde). Verskeie ander faktore beïnvloed ook wiskundeprestasie, met inbegrip van bekwaamheid, belangstelling, leerders se agtergrond en die gehalte van onderrig. Oor die afgelope 20 jaar fokus navorsers op onder meer die invloed van sosiale, kognitiewe en metakognitiewe, konatiewe en affektiewe fasette van prestasie in wiskunde. Die doel van hierdie studie was om ondersoek in te stel na die fasette van emosionele intelligensie en die dimensies van studie-orientasie in wiskunde wat moontlik 'n rol kan speel in die middel-adolessent se wiskundeprestasie. Die studie het veral gefokus op die aard van emosionele intelligensie en studie-orientasie in wiskunde, die aard en betekenis van wiskundeprestasie, die mate waartoe ('n kombinasie van fasette van) emosionele intelligensie en studie-orientasie middeladolessente se wiskundeprestasie voorspel en hoe verskillende taal-, geslag- en graadgroepe (in hierdie studie verteenwoordig) se prestasie in hierdie opsig vergelyk. Die studie het plaasgevind vanuit 'n sosio-konstruktivistiese paradigma wat uit die interpretivistiese paradigma ontwikkel het. Seide kwantitatiewe en kwalitatiewe datainsamelingstegnieke (KWAN-kwal) is in hierdie studie ge"implementeer ten einde die moontlike verband tussen emosionele intelligensie, studie-orientasie in wiskunde en die middel-adolessent se wiskundeprestasie te ondersoek en te beskryf. Altesaam 435 leerlinge in graad 9 en 11 aan die drie Engelsmedium-hoerskole in die Mafikeng area het aan die studie deelgeneem. Die kwantitatiewe komponent van die studie het bestaan uit die implementering van twee gestandaardiseerde vraelyste. Leerders is gevra om 'n El-vraelys, naamlik die Bar-On EQ-i: YV™ en die Studieorientasievraelys in Wiskunde (SOW) te voltooi. Kwalitatiewe tegnieke wat in hierdie studie ge"implementeer is, sluit in fokusgroeponderhoude, observasie, veldnotas en die gebruik van 'n reflektiewe joernaal. Daar is een fokusgroeponderhoud by elk van die drie deelnemende skole gevoer om die leerders wat aan die navorsing deelgeneem het se menings en opinies rakende wiskunde en wiskundeprestasie te peil. Die resultate het aangedui daarop dat 'n kombinasie van die fasette van emosionele intelligensie en die dimensies van studie-orientasie as moontlike voorspellers van die middel-adolessent se wiskundeprestasie beskou kan word. Die volgende Elkomponente het as voorspellers van wiskundeprestasie na vore getree: Algemene gemoedstoestand, Aanpasbaarheid en lntrapersoonlike gedrag. Die volgende SOW dimensies was voorspellers van wiskundeprestasie: Probleemoplossing, Studiegewoontes, lnligtingverwerking en Wiskundeangs. Temas wat uit die kwalitatiewe aspek van my studie na vore getree het as moontlik bydraend tot leerders se ontoereikende wiskundeprestasie, verwys spesifiek na uitdagings op makro-, meso- en mikrovlak binne die Suid-Afrikaanse konteks. ENGLISH : There is both internationally and nationally great concern about the poor achievement of learners in mathematics. Inadequate performance in mathematics is a substantial problem in post-apartheid South Africa. Numerous studies have been undertaken to explain this phenomenon, since mathematics achievement is of cardinal importance to any developing country. Research has shown inter alia that mathematics achievement at school is one of the best predictors of success at tertiary level and that there is a statistically significant correlation between mathematics achievement and aspects of study orientation in mathematics (including study habits, mathematics anxiety, attitude towards mathematics, effective time management, parents' expectations, learners' social world and mathematics experience). Various other factors also affect mathematics achievement, including competence, interest, learners' background and the quality of tuition. Over the past 20 years, researchers have focused on issues such as the impact of social, cognitive and metacognitive, conative and affective facets on achievement in mathematics. The aim of this study was to examine the facets of emotional intelligence and the dimensions of study orientation in mathematics that might play a role in the mathematics achievement of the middle adolescent. The study focused especially on the nature of emotional intelligence and study orientation in mathematics, the nature and meaning of mathematics achievement, the extent to which (a combination of facets of) emotional intelligence and study orientation predict(s) the mathematics achievement of middle-adolescents and also compared the performance of the different language, gender and grade groups (represented in this study). The study was based on a socio-constructivist paradigm, which had developed from the interpretivist paradigm. Both quantitative and qualitative data-gathering techniques (QUAN-qual) were implemented so as to examine and describe the possible relationship between emotional intelligence, study orientation in mathematics and the mathematics achievement of the middle adolescent. Altogether 435 learners in Grades 9 and 11 from the three English medium high schools in the Mafikeng region took part in the study. The quantitative component of the study comprised the implementation of two standardised questionnaires. Learners were asked to complete an El questionnaire, the Bar-On EQ-i: YV™, and the Study Orientation Questionnaire in Mathematics (SOM). Qualitative techniques implemented in the study included focus group interviews, observation, field notes, and the use of a reflective journal. One focus group interview was conducted at each of the three participating schools to gauge the views and opinions of learners participating in the research on mathematics achievement. The results indicated that a combination of the facets of emotional intelligence and the dimensions of study orientation could be considered potential predictors of the middle adolescent's mathematics achievement. The following EI components also emerged from the results as predictors of mathematics achievement: General mood, Adaptability and Intrapersonal behaviour. The following SOM dimensions were predictors of mathematics achievement: Problem-solving behaviour, Study habits, Information processing and Mathematics anxiety. Themes that emerged from the qualitative aspect of my study as potential contributors to learners' inadequate mathematics achievement refer specifically to challenges at the macro, meso and micro level within the South African context. / Thesis (PhD)--University of Pretoria, 2012. / Educational Psychology / unrestricted