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

In this investigation an attempt was made to determine the misconceptions that engineering students have of the idea of a limit. A comprehensive literature study showed that there are a number of common misconceptions that students normally form. The empirical investigation was done in two phases. A questionnaire on the idea of a limit was given to the students during the first phase. During the second phase six interviews were conducted. The findings were grouped according to the nature of a limit and students' views on the relationship between the continuity of a function at a point and the limit at that point. An analysis of these findings led to the identification of the misconceptions that these students have of the idea of a limit. / In hierdie ondersoek is gepoog om die wanbegrippe wat ingenieursstudente van die limietbegrip vorm, bloot te stel. 'n Omvattende literatuurstudie het 'n aantal algemene wanbegrippe aan die lig gebring. Die empiriese ondersoek het in twee fases plaasgevind. Tydens die eerste fase is 'n vraelys aan die studente gegee in 'n poging om meer te wete te kom van hulle begrip van 'n limiet. Die vraelys is opgevolg deur ses onderhoude. Die responsies is gegroepeer in terme van die aard van 'n limiet en studente se sienings van die kontinuiteit van 'n funksie by 'n punt en die limiet by daardie punt. Die analisering van hierdie responsies het die identifisering van 'n aantal wanbegrippe by hierdie groep studente moontlik gemaak. / Educational Studies / M.Ed. (with specialisation in Mathematics Education)

Please read the abstract in the section, 07resume of this document / Thesis (PhD)--University of Pretoria, 2008. / Orthopaedic Surgery / unrestricted

Low achievement in Mathematics is a problem that faces schools, colleges and universities, not only in South Africa, but worldwide. Many efforts have been made to explore different ways in which teaching and learning can be more effective. ICT provides endless possibili–ties to enhance the teaching and learning of Mathematics. The purpose of this study is to determine teacher–students’ attitude towards ICTs in order to plan for effective, efficient and appropriate methods of Mathematics education. It further aims to determine to what extent these students will be willing to use ICTs in their own studies as well as in the teaching pro–cess in their classrooms, and aims to compare the students’ attitudes across three countries i.e. South Africa, Tanzania and Finland. The population consisted of Mathematics education teacher–students enrolled at the following institutions: School for Continuing Teacher Educa–tion (SCTE) at the North–West University in South Africa (317 students), the Iringa University College, University of Tumaini in Tanzania (111 students), and the University of Joensuu in Finland (56 students). This study followed a quantitative cross–sectional survey design com–prising a single mode research questionnaire to three groups of students in three countries. The instrument that was used was based on the Loyd and Gressard Computer Attitude Sur–vey (1984) (CAS), with a few additional questions to add to the relevance of this study. Questionnaires were completed by each group of students. The questionnaires were posted to each Mathematics teacher–student at the SCTE with a return envelope included. The re–searcher visited Tanzania and administered the questionnaire to the students at their univer–sity and some students in Finland completed the survey online while others completed a pa–per–based copy, which was returned to the researcher. Descriptive statistical techniques, reliability and validity of the instrument scale, inferential statistics (ANOVA), and cross–tabulations were used, and where appropriate, effect sizes were calculated. Findings indi–cated that the teacher–students have a positive attitude to computers and that they are willing to use ICTs in their own studies and in their teaching at school. The comparison of their atti–tudes revealed that the South African and Tanzanian teacher–students have a more positive attitude towards ICTs than the Finnish students. The teacher–students in the two African countries were also more willing to use ICTs than the students in Finland, despite their in–creased exposure and access to technology. To create an environment of effective Mathe–matics education, a number of factors play an important role. Mathematics education sup–ported by good pedagogical content knowledge can be transformed into effective Mathemat–ics education with the aid of a positive computer attitude and willingness to use technology. Together these aspects are supported by the technological pedagogical content knowledge (TPCK) framework. / Thesis (M.Ed.)--North-West University, Potchefstroom Campus, 2011.

Low achievement in Mathematics is a problem that faces schools, colleges and universities, not only in South Africa, but worldwide. Many efforts have been made to explore different ways in which teaching and learning can be more effective. ICT provides endless possibili–ties to enhance the teaching and learning of Mathematics. The purpose of this study is to determine teacher–students’ attitude towards ICTs in order to plan for effective, efficient and appropriate methods of Mathematics education. It further aims to determine to what extent these students will be willing to use ICTs in their own studies as well as in the teaching pro–cess in their classrooms, and aims to compare the students’ attitudes across three countries i.e. South Africa, Tanzania and Finland. The population consisted of Mathematics education teacher–students enrolled at the following institutions: School for Continuing Teacher Educa–tion (SCTE) at the North–West University in South Africa (317 students), the Iringa University College, University of Tumaini in Tanzania (111 students), and the University of Joensuu in Finland (56 students). This study followed a quantitative cross–sectional survey design com–prising a single mode research questionnaire to three groups of students in three countries. The instrument that was used was based on the Loyd and Gressard Computer Attitude Sur–vey (1984) (CAS), with a few additional questions to add to the relevance of this study. Questionnaires were completed by each group of students. The questionnaires were posted to each Mathematics teacher–student at the SCTE with a return envelope included. The re–searcher visited Tanzania and administered the questionnaire to the students at their univer–sity and some students in Finland completed the survey online while others completed a pa–per–based copy, which was returned to the researcher. Descriptive statistical techniques, reliability and validity of the instrument scale, inferential statistics (ANOVA), and cross–tabulations were used, and where appropriate, effect sizes were calculated. Findings indi–cated that the teacher–students have a positive attitude to computers and that they are willing to use ICTs in their own studies and in their teaching at school. The comparison of their atti–tudes revealed that the South African and Tanzanian teacher–students have a more positive attitude towards ICTs than the Finnish students. The teacher–students in the two African countries were also more willing to use ICTs than the students in Finland, despite their in–creased exposure and access to technology. To create an environment of effective Mathe–matics education, a number of factors play an important role. Mathematics education sup–ported by good pedagogical content knowledge can be transformed into effective Mathemat–ics education with the aid of a positive computer attitude and willingness to use technology. Together these aspects are supported by the technological pedagogical content knowledge (TPCK) framework. / Thesis (M.Ed.)--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

This study investigated misconceptions in Algebra of students enrolled for a N2 Engineering certificate at a Further Education and Training College. The study aimed to investigate these students’ misconceptions relating to Algebra which prohibited them to successfully complete their artisanship. The purpose of the research was to determine (i) the nature of these misconceptions, and (ii) the value of screencasts as a technology-enhanced learning (TEL) tool to improve instruction. The research gap that the researcher addressed related to the Mathematics misconceptions that the N2 students had, and whether these misconceptions could be adequately addressed by screencasts. The study method used was a case study design and methodology while simultaneously collecting quantitative and qualitative data. The findings encompassed the determining of main Mathematics misconceptions, producing screencasts, and assessing the screencasts with the intended target group. The study followed a four-phase strategy of testing, interviewing and analysing, and reflection based on qualitative and quantitative research strategies. During the quantitative research the research participants completed a biographical questionnaire, as well as a customised diagnostic Algebra test. The study sample comprised two groups from different trimesters at a rural FET college in the Northern Cape in Kathu, South Africa. The total population of full-time N2 Engineering students related to 113 participants. The diagnostic test comprised twelve questions from the three main Algebra concepts relating to: (i) exponents, (ii) equations, and (iii) factorisation. The same customised diagnostic test confirmed the misconceptions within the same group. Six questions from the customised diagnostic test identified the central misconceptions. The researcher consequently designed, developed, implemented and evaluated screencasts with the intended student population according to the design principles identified during the study. The six questions formed the basis of a second diagnostic test, which was used in phase three with interviews of ten research participants as part of phase 4 of the evaluation of the screencasts. At the end of the second trimester students were ask to complete a questionnaire regarding their use and perceptions of the screencasts—23 participants completed this voluntary questionnaire. At the end of the trimester ten participants were asked to explain their method of calculations during a walk-through evaluation while answering Algebra problems. The results indicated a number of misconception categories: (i) The main reason for misconceptions relating to equations was the participants’ inadequate understandings of the basic concepts of multiply methods used in equations; (ii) Index laws seemed to be the biggest misconception where participants demonstrated insufficient understanding of the laws; and (iii) The participants did not comprehend the basic concepts of factorisation—they could not identify which method to use while factorising. The qualitative findings indicate that the participants found the screencasts valuable when they prepared for tests and examinations, as well as when they did not understanding a basic Mathematics concept. Access to technology in rural areas remains an obstacle to integrate technology learning tools on a large scale at the FET College. / MEd (Curriculum Development), North-West University, Potchefstroom Campus, 2015

Underachievement in Mathematics hangs over South African Mathematics learners like a dark cloud. TIMSS studies over the past decade have confirmed that South African learners‟ results (Grades 8 and 9 in 2011) remained at a low ebb, denying them the opportunity to compete and excel globally in the field of Mathematics. It is against this backdrop that the researcher investigated the meaningful understanding of the important yet challenging algebraic concept of Proportion. The theoretical as well as the empirical underpinnings of the fundamental idea of Proportion are highlighted. The meaningful learning of Algebra was explored and physical, effective and cognitive factors affecting meaningful learning of Algebra, views on Mathematics and learning theories were examined. The research narrowed down to the meaningful understanding of Proportion, misconceptions, and facilitation in developing Proportional reasoning. This study was embedded in an interpretive paradigm and the research design was qualitative in nature. The qualitative data was collected via task sheets and interviews. The sample informing the central phenomenon in the study consisted of a heterogeneous group of learners and comprised a kaleidoscope of nationalities, both genders, a variety of home languages, differing socio-economic statuses and varying cognitive abilities. The findings cannot be generalised. Triangulation of the literature review, the analysis of task sheets and interviews revealed that overall the participants have a meaningful understanding of the Proportion concept. However, a variety of misconceptions were observed in certain cases. Finally, recommendations are made to address the meaningful learning of Proportion and its associated misconceptions. It is hoped that teachers read and act on the recommendations as it is the powerful mind and purposeful teaching of the teacher that can make a difference in uplifting the standard of Mathematics in South African classrooms! / MEd (Mathematics Education), North-West University, Potchefstroom Campus, 2014

This study investigated misconceptions in Algebra of students enrolled for a N2 Engineering certificate at a Further Education and Training College. The study aimed to investigate these students’ misconceptions relating to Algebra which prohibited them to successfully complete their artisanship. The purpose of the research was to determine (i) the nature of these misconceptions, and (ii) the value of screencasts as a technology-enhanced learning (TEL) tool to improve instruction. The research gap that the researcher addressed related to the Mathematics misconceptions that the N2 students had, and whether these misconceptions could be adequately addressed by screencasts. The study method used was a case study design and methodology while simultaneously collecting quantitative and qualitative data. The findings encompassed the determining of main Mathematics misconceptions, producing screencasts, and assessing the screencasts with the intended target group. The study followed a four-phase strategy of testing, interviewing and analysing, and reflection based on qualitative and quantitative research strategies. During the quantitative research the research participants completed a biographical questionnaire, as well as a customised diagnostic Algebra test. The study sample comprised two groups from different trimesters at a rural FET college in the Northern Cape in Kathu, South Africa. The total population of full-time N2 Engineering students related to 113 participants. The diagnostic test comprised twelve questions from the three main Algebra concepts relating to: (i) exponents, (ii) equations, and (iii) factorisation. The same customised diagnostic test confirmed the misconceptions within the same group. Six questions from the customised diagnostic test identified the central misconceptions. The researcher consequently designed, developed, implemented and evaluated screencasts with the intended student population according to the design principles identified during the study. The six questions formed the basis of a second diagnostic test, which was used in phase three with interviews of ten research participants as part of phase 4 of the evaluation of the screencasts. At the end of the second trimester students were ask to complete a questionnaire regarding their use and perceptions of the screencasts—23 participants completed this voluntary questionnaire. At the end of the trimester ten participants were asked to explain their method of calculations during a walk-through evaluation while answering Algebra problems. The results indicated a number of misconception categories: (i) The main reason for misconceptions relating to equations was the participants’ inadequate understandings of the basic concepts of multiply methods used in equations; (ii) Index laws seemed to be the biggest misconception where participants demonstrated insufficient understanding of the laws; and (iii) The participants did not comprehend the basic concepts of factorisation—they could not identify which method to use while factorising. The qualitative findings indicate that the participants found the screencasts valuable when they prepared for tests and examinations, as well as when they did not understanding a basic Mathematics concept. Access to technology in rural areas remains an obstacle to integrate technology learning tools on a large scale at the FET College. / MEd (Curriculum Development), North-West University, Potchefstroom Campus, 2015