Professional development (PD) of teachers is part of the Department of Basic Education‘s (DBE) initiative to encourage school communities to use of information and communication technology (ICT) to improve the quality of Mathematics teaching and learning. The South African Council of Educators stipulates that PD programmes should align with system-wide needs, strengthen learning area content and outcomes, and promote system transformation. Imbedded in this system-wide criterion is The White Paper on e-Education to employ a fully ICT integrated system at all levels of education: management, teaching and learning, and administration by 2013. Mathematics teachers require PD that develops their technological pedagogical and content knowledge (TPACK) and their social professional identity (SPI). The PD of Mathematics teachers for ICT integration can assist the DBE to achieve the aims of The White Paper on e-Education and bridge the technology gap between South Africa and international education systems. Open distance learning (ODL) could be a viable method to deliver PD to Mathematics teachers to address their zone of proximal development, develop their TPACK, and establish and maintain their SPI. This study made use of a fully mixed sequential equal status multi-mode research design and methodologies to develop guidelines for the PD of Mathematics teachers in the pedagogical use of ICT in ODL. The qualitative phase (Phase I) was rooted in the interpretivist paradigm. Through an adjustable exploration of a systematic literature review, the researcher identified 23 core documents, analysed them with Atlas.ti™, and conceptualised four themes according to Engeström‘s third generation activity theory (AT). Phase II (radical exploration phase) of the research design was rooted in the radical structuralist paradigm. In the context of transformation, it developed, validated, and standardised a research instrument for the measurement of Mathematics teachers‘ PD requirements. The instrument was distributed to 300 senior phase (grades 7-9) Mathematics teachers in eight education management district centres of the WCED. The analyses of the quantitative data conceptualised a fifth activity system. The five activity systems from the adjustable and radical exploration phases were symbiotic, and co-dependent. Expansive learning was used for boundary crossing and network building during six phases of this study. The findings from the six phases of the expansive learning cycle indicated that PD of Mathematics teachers in ODL for Phase III implementation of the e-Education policy should be a joint initiative. Fundamentally ICT integration and implementation should start with Department of Basic Education (DBE) initiatives. The DBE and Provincial Departments of Education (PDEs) should conduct a needs analysis of ICT implementation, evaluate previous ICT PD programmes, plan ICT PD strategies aligned with the ICT development plan, as well as with the requirements of the Mathematics teachers. The DBE and PDE should invest in the provision of ICT equipment, afford human capital, reinstate the laptop initiative for teachers, and supply schools with networked-computer facilities to explore online platforms for PD. Mathematics teachers should assess their professional knowledge to construct new philosophies, create a subject network group, and interact as participants and members within their social environments. The standardised instrument could be used to determine and compare the PD of Mathematics teachers in other provinces and contexts. / PhD (Training and development), North-West University, Potchefstroom Campus, 2014

Metacognition is commonly understood in the context of the learners and not their teachers. Extant literature focusing on how Mathematics teachers apply their metacognitive skills in the classroom, clearly distinguishes between teaching with metacognition (TwM) referring to teachers thinking about their own thinking and teaching for metacognition (TfM) which refers to teachers creating opportunities for learners to reflect on their thinking. However, in both of these cases, thinking requires a language, in particular appropriate mathematical language to communicate the thinking by both teacher and learners in the Mathematics classroom. In this qualitative study, which forms part of a bigger project within SANPAD (South Africa Netherlands Research Programme on Alternatives in Development), the metacognitive skills and mathematical language used by Mathematics teachers who teach at two township schools were interrogated using the design-based research approach with lesson study. Data collection instruments included individual interviews and a trigonometric assessment task. Lessons were also observed and video-taped to be viewed and discussed during focus group discussions in which the teachers, together with five Mathematics lecturers, participated. The merging of the design-based research approach with lesson study brought about teacher-lecturer collaboration, referred to in this study as the Mathematics Educators’ Reflective Inquiry (ME’RI) group, and enabled the design of a hypothetical teaching and learning trajectory (HTLT) for the teaching of trigonometric functions. A metacognitive performance profile for the two grade 10 teachers was also developed. The Framework for Analysing Mathematics Teaching for the Advancement of Metacognition (FAMTAM) from Ader (2013) and the Teacher Metacognitive Framework (TMF) from Artzt and Armour-Thomas (2002) were adjusted and merged to develop a new framework, the Metacognitive Teaching for Metacognition Framework (MTMF) to analyse the metacognitive skills used by mathematics teachers TwM as well as TfM. Without oversimplifying the magnitude of these concepts, the findings suggest a simple mathematical equation: metacognitive skills + enhanced mathematical language = conceptualization skills. The findings also suggest that both TwM and TfM are required for effective mathematics instruction. Lastly the findings suggest that the ME’RI group holds promise to enhance the use of the metacognitive skills and mathematical language of Mathematics teachers in Mathematics classrooms. / PhD (Mathematics Education), North-West University, Potchefstroom Campus, 2014

The ongoing debate about the capacity of distance learning (DL) to assist in the development of teaching skills and to improve teaching practice is the focus of many inquiries in the field of teacher education. The practice-based nature of Foundation Phase teaching poses unique challenges for professional development of teachers through DL programmes. In order to address inadequacies identified in the literature and previous research, a practical component was designed and included in the revised version of the Advanced Certificate: Education - Foundation Phase, as part of a bursary project. In 2011 the Northern Cape Department of Education (NCDoE) enrolled 50 practising Foundation Phase teachers for this distance learning programme as the first of three cohorts in the bursary project. A learning portfolio and audio-visual resources, designed according to principles derived from previous research and related literature, formed part of this practical component. The aim was to support teacher applied competence through developing pedagogical content knowledge, self-directedness, and a professional attitude, and through guiding the application of new knowledge and skills in practice. The completed portfolios further served as an instrument for the assessment of teacher performance with regard to applied competence. The purpose of this study was to evaluate the value of the practical component of the revised Foundation Phase ACE programme delivered by the NWU via distance learning with specific focus on the way this component facilitates the development of applied competence and the way the portfolio provides for the assessment of professional classroom competencies of practising Foundation Phase teachers. The study further aimed to put forward a model for the development of applied practice based on the findings of the study. In order to attain the aims of the study, the literature was explored to firstly determine the elements which contribute to applied competence in effective teacher professional development programmes. The literature was further explored to determine what the body of scholarship indicates with respect to programme design features that support applied competence in DL programmes for teacher professional development. An implementation evaluation study was then conducted on the programme by collecting data from 50 Foundation Phase teachers as the first of three cohorts enrolled for the bursary project. Data were primarily collected through multiple qualitative methods including a focus-group interview, individual interviews, written expectations as well as open ended questions of questionnaires. Descriptive data were also collected through semi-structured questionnaires. Qualitative data were analysed through content analysis to determine the theoretical and conceptual implications of the profile and teaching context of the Northern Cape Foundation Phase teacher enrolled for the DL Foundation Phase ACE programme, the expectations of these teachers regarding the way the practical component would support their applied competence in their contexts, and the teachers’ experiences of the way the programme component supported the development of their applied competence. The study further determined the extent to which the learning portfolios interrogate the elements of applied competence. Quantitative data collected through semi-structured questionnaires were statistically analysed and served to support the interpretation of qualitative data. The investigation was approached from a constructivist paradigm; an approach that falls under an interpretivist philosophical orientation. Although quantitative methods were used to gather descriptive statistical data in support of the qualitative data, the study is grounded in qualitative research methodology where the concern is with the formative evaluation of the DL programme component The findings strongly confirm the value of such a practical component as part of a DL programme to support the elements of applied competence. However, the way the programme accommodates teacher profiles and teaching contexts will greatly influence the sustainability of the programme outcomes in practice. The findings further show that the portfolio as instrument for the assessment of applied competence requires careful planning and should provide strong guidance in the reflective process to support sustained outcomes of the programme in practice. A suggested model for a DL programme for the professional development of Foundation Phase teachers is based on the findings of the study. / PhD (Curriculum Development Innovation and Evaluation), North-West University, Potchefstroom Campus, 2015

Professional development (PD) of teachers is part of the Department of Basic Education‘s (DBE) initiative to encourage school communities to use of information and communication technology (ICT) to improve the quality of Mathematics teaching and learning. The South African Council of Educators stipulates that PD programmes should align with system-wide needs, strengthen learning area content and outcomes, and promote system transformation. Imbedded in this system-wide criterion is The White Paper on e-Education to employ a fully ICT integrated system at all levels of education: management, teaching and learning, and administration by 2013. Mathematics teachers require PD that develops their technological pedagogical and content knowledge (TPACK) and their social professional identity (SPI). The PD of Mathematics teachers for ICT integration can assist the DBE to achieve the aims of The White Paper on e-Education and bridge the technology gap between South Africa and international education systems. Open distance learning (ODL) could be a viable method to deliver PD to Mathematics teachers to address their zone of proximal development, develop their TPACK, and establish and maintain their SPI. This study made use of a fully mixed sequential equal status multi-mode research design and methodologies to develop guidelines for the PD of Mathematics teachers in the pedagogical use of ICT in ODL. The qualitative phase (Phase I) was rooted in the interpretivist paradigm. Through an adjustable exploration of a systematic literature review, the researcher identified 23 core documents, analysed them with Atlas.ti™, and conceptualised four themes according to Engeström‘s third generation activity theory (AT). Phase II (radical exploration phase) of the research design was rooted in the radical structuralist paradigm. In the context of transformation, it developed, validated, and standardised a research instrument for the measurement of Mathematics teachers‘ PD requirements. The instrument was distributed to 300 senior phase (grades 7-9) Mathematics teachers in eight education management district centres of the WCED. The analyses of the quantitative data conceptualised a fifth activity system. The five activity systems from the adjustable and radical exploration phases were symbiotic, and co-dependent. Expansive learning was used for boundary crossing and network building during six phases of this study. The findings from the six phases of the expansive learning cycle indicated that PD of Mathematics teachers in ODL for Phase III implementation of the e-Education policy should be a joint initiative. Fundamentally ICT integration and implementation should start with Department of Basic Education (DBE) initiatives. The DBE and Provincial Departments of Education (PDEs) should conduct a needs analysis of ICT implementation, evaluate previous ICT PD programmes, plan ICT PD strategies aligned with the ICT development plan, as well as with the requirements of the Mathematics teachers. The DBE and PDE should invest in the provision of ICT equipment, afford human capital, reinstate the laptop initiative for teachers, and supply schools with networked-computer facilities to explore online platforms for PD. Mathematics teachers should assess their professional knowledge to construct new philosophies, create a subject network group, and interact as participants and members within their social environments. The standardised instrument could be used to determine and compare the PD of Mathematics teachers in other provinces and contexts. / PhD (Training and development), North-West University, Potchefstroom Campus, 2014

South Africa’s current performance on national and international studies is an indication that all is not well with our literacy teaching. In spite of the implementation of the National Curriculum Statement Grade R-9, illiteracy is currently a serious problem in South Africa. Current international and national documents call for direct, explicit, systematic teaching of reading and language concepts to beginning readers. The five principal components of reading instruction, namely phoneme awareness; phonics; word study and spelling; reading fluency; and text comprehension encompass language instruction at the phoneme, grapheme, syllable, word, sentence, and discourse levels. Teachers need specific and explicit linguistic knowledge to recognise and address the needs of all learners on the continuum of reading and language proficiency. Phonological awareness skills are considered as the most important indicators of early reading skills. Literature suggests a strong positive correlation between phonological awareness skills and reading skills development. Longitudinal studies show that children who don’t have phonological awareness skills have difficulties in reading. Experimental studies on phonological awareness suggest that the implementation of phonological awareness training has positive effects on the development of reading and spelling abilities. Phonological awareness is a key component in the prevention of reading failure. The information collected through the assessment of phonological awareness, enables teachers to make informed decisions about modifications of the literacy learning programme and implement reading interventions to prevent failure of reading acquisition. This early, preventative intervention reduces the possibility that learners fall behind in reading. The teaching of phonological awareness is par excellence for emergent literacy in the grade R class. Phonological awareness can be improved through the systematic, explicit instruction thereof. Therefore, teachers need to be able to implement a variety of phonological awareness activities in their classroom instruction. Teachers need content knowledge about phonological awareness, and how to implement it successfully. The purpose of this study was to determine: What a SWOT analysis reveals about grade R-teachers’: * Current in-depth knowledge of phonological awareness. * Preparedness to teach phonological awareness. * Implementation of instructional practices relevant to phonological awareness. * Perceptions of the support received from DoBE, in terms of relevant documentation, teaching and learning support material and professional development. The limitations, if any, in the teacher support documents of the DoBE, regarding the teaching of phonological awareness in grade R and to make suggestion with regard to the improvement thereof. What the perceptions of grade R teachers are about their in-depth knowledge, instructional practices and preparedness, concerning phonological awareness, after the implementation of a teacher training programme, focussing specifically on phonological awareness. The study was conducted utilizing a case study with thirteen grade R teachers from Lichtenburg, and the surrounding towns, Koster, Coligny and Itsoseng in the North West Province, Department of Basic Education, in South Africa. Data was collected in three phases, using questionnaires, interviews, observations and document analyses. In the first phase, the researcher gathered information on the knowledge and implementation of phonological awareness before the intervention (i.e., a teacher training programme). In the second phase, the teachers received training about the concept of phonological awareness and its relevance in reading acquisition. The training programme included relevant teaching activities as well as learning and teaching support material. In the third phase, the researcher trained the participants in the implementation of phonological awareness and gathered data about the implementation process. The results indicated that if teachers received explicit training about phonological awareness and are provided with relevant learning and teaching support material, they are able to implement phonological awareness activities in grade R classrooms. The results of this study have implications for teacher training. The concept of phonological awareness, its relevance in reading acquisition as well as relevant teaching activities need to be included in the training of grade R teachers. / Thesis (Ph.D. (Learning and Teaching))--North-West University, Potchefstroom Campus, 2011.

South Africa’s current performance on national and international studies is an indication that all is not well with our literacy teaching. In spite of the implementation of the National Curriculum Statement Grade R-9, illiteracy is currently a serious problem in South Africa. Current international and national documents call for direct, explicit, systematic teaching of reading and language concepts to beginning readers. The five principal components of reading instruction, namely phoneme awareness; phonics; word study and spelling; reading fluency; and text comprehension encompass language instruction at the phoneme, grapheme, syllable, word, sentence, and discourse levels. Teachers need specific and explicit linguistic knowledge to recognise and address the needs of all learners on the continuum of reading and language proficiency. Phonological awareness skills are considered as the most important indicators of early reading skills. Literature suggests a strong positive correlation between phonological awareness skills and reading skills development. Longitudinal studies show that children who don’t have phonological awareness skills have difficulties in reading. Experimental studies on phonological awareness suggest that the implementation of phonological awareness training has positive effects on the development of reading and spelling abilities. Phonological awareness is a key component in the prevention of reading failure. The information collected through the assessment of phonological awareness, enables teachers to make informed decisions about modifications of the literacy learning programme and implement reading interventions to prevent failure of reading acquisition. This early, preventative intervention reduces the possibility that learners fall behind in reading. The teaching of phonological awareness is par excellence for emergent literacy in the grade R class. Phonological awareness can be improved through the systematic, explicit instruction thereof. Therefore, teachers need to be able to implement a variety of phonological awareness activities in their classroom instruction. Teachers need content knowledge about phonological awareness, and how to implement it successfully. The purpose of this study was to determine: What a SWOT analysis reveals about grade R-teachers’: * Current in-depth knowledge of phonological awareness. * Preparedness to teach phonological awareness. * Implementation of instructional practices relevant to phonological awareness. * Perceptions of the support received from DoBE, in terms of relevant documentation, teaching and learning support material and professional development. The limitations, if any, in the teacher support documents of the DoBE, regarding the teaching of phonological awareness in grade R and to make suggestion with regard to the improvement thereof. What the perceptions of grade R teachers are about their in-depth knowledge, instructional practices and preparedness, concerning phonological awareness, after the implementation of a teacher training programme, focussing specifically on phonological awareness. The study was conducted utilizing a case study with thirteen grade R teachers from Lichtenburg, and the surrounding towns, Koster, Coligny and Itsoseng in the North West Province, Department of Basic Education, in South Africa. Data was collected in three phases, using questionnaires, interviews, observations and document analyses. In the first phase, the researcher gathered information on the knowledge and implementation of phonological awareness before the intervention (i.e., a teacher training programme). In the second phase, the teachers received training about the concept of phonological awareness and its relevance in reading acquisition. The training programme included relevant teaching activities as well as learning and teaching support material. In the third phase, the researcher trained the participants in the implementation of phonological awareness and gathered data about the implementation process. The results indicated that if teachers received explicit training about phonological awareness and are provided with relevant learning and teaching support material, they are able to implement phonological awareness activities in grade R classrooms. The results of this study have implications for teacher training. The concept of phonological awareness, its relevance in reading acquisition as well as relevant teaching activities need to be included in the training of grade R teachers. / Thesis (Ph.D. (Learning and Teaching))--North-West University, Potchefstroom Campus, 2011.

Text in Afrikaans / Due to the radical reform in mathematics education worldwide, the mathematics curriculum underwent dramatic changes in order to meet the new objectives in mathematics. This has placed a huge responsibility on curriculum compilers and the authors of mathematics textbooks and mathematics teachers to enhance the cognitive development of learners. This study takes the view that: What happens in the class is what you get. Based on the above statement, the foundation of mathematics teaching, namely the mathematics curriculum, the mathematics textbook and the teacher’s instruction in the teaching venue were scrutinised. During a diagnostic examination of teachers’ interpretation, knowledge and application of the mathematics curriculum and the content of mathematics textbooks on the East Rand, the following problems regarding mathematics teaching emerged: The most important finding of TIMMS is that the differences in performance in mathematics between different countries can be linked to the way teachers interpret and present the content of mathematics. Research has revealed that the interaction of teachers with curriculum content follow a dynamic and constructive application instead of direct application based on the mathematics curriculum. Teachers often change the prescriptions and order of content in the mathematics curriculum to suit their teaching style, knowledge and previous experience. Consequently, align application of mathematical concepts and skills does not take place and this creates a gap in learners’ cognitive development. It also leaves a gap in the application of the Type 5 cognitive development tasks in mathematics which enable a verifying deductive application of concepts. The action research created a structure which could meet this need. Authors of mathematics textbooks present their own vision, interpretation and style in mathematics textbooks, which influences the order of mathematics content and concepts. The result is that mathematics content and concepts are at times not aligned with representations in the mathematics curriculum and objectives are therefore not reached. The different interpretations of mathematics textbooks by teachers differ greatly and these differences place great pressure on teachers to decide how the mathematics textbook will be used in the teaching venue. In this study a mathematics textbook profile and a task analysis were formulated in the cause of action research which will enable teachers to make a professional analysis which they can use. Because a variety of mathematics textbooks are selected for use in schools, teachers assume that these approved mathematics textbooks focus on the curriculum. They therefore slavishly follow the mathematics textbooks without consulting the mathematics curriculum. Shortcomings in mathematics textbooks and teachers’ own interpretation of mathematics content leave a big gap in their own alignment of mathematics teaching. To satisfy this need, an assessment profile and an methodology for alignment are provided to enable teachers to monitor the curriculum alignment presentation of concepts and skills. / As gevolg van die radikale hervorming in wiskunde-onderrig wêreldwyd het die wiskundekurrikulum dramatiese veranderings ondergaan ten einde die nuwe doelstellings in wiskunde te bereik. Dit het enorme verantwoordelikheid geplaas op kurrikulumsamestellers en outeurs van wiskundehandboeke en wiskunde-onderwysers om die kognitiewe ontwikkeling van leerders te bevorder. In hierdie studie is van die volgende standpunt uitgegaan: What happens in the class is what you get. Derhalwe is die fondasie van wiskunde-onderrig, naamlik die wiskundekurrikulum, wiskundehandboek en die onderwyser se instruksies in die klaskamer ondersoek. In `n diagnostiese ontleding van onderwysers se interpretasie, kennis en toepassing van die wiskundekurrikulum en die wiskundehandboekinhoude aan die Oos-Rand het die volgende probleme in verband met wiskunde-onderrig na vore gekom: Die belangrikste bevinding van TIMMS is dat die verskille in wiskundeprestasie tussen lande verband hou met die wyse waarop onderwysers die wiskudekurrikuluminhoude interpreteer en aanbied. Navorsing toon dat die interaksie van onderwysers met kurrikulummateriaal op ʼn dinamiese en konstruktiewe toepassing geskied in plaas van direkte toepassing vanuit die wiskundekurrikulum. Onderwysers verander dikwels die wiskundekurrikulum se voorskrifte en volgorde van inhoude om by hulle onderrigstyl, kennis en vorige ervarings te pas. Die gevolg is dat geen inlyntoepassing van wiskundebegrippe en vaardighede plaasvind nie en dit laat ʼn leemte in leerders se kognitiewe ontwikkeling. Verder laat dit ʼn leemte in die toepassing van die 5-tipe kognitiewe ontwikkelingstake in wiskunde wat ʼn verifiërend deduktiewe toepassing van begrippe bewerkstellig. In die aksienavorsing is ʼn struktuur geskep wat in hierdie behoefte voorsien. Outeurs van wiskundehandboeke het ʼn eie visie, interpretasie en styl wat hulle in wiskundehandboeke aanbied. Dit het ʼn invloed op die volgorde van wiskunde-inhoude en begrippe en gevolglik is wiskunde-inhoude en -begrippe soms nie inlyn geplaas met voorstellings van die wiskundekurrikulum nie, en word doelstellings nie bereik nie. Onderwysers se verskillende interpretasies van wiskundehandboekinhoude verskil radikaal van mekaar en plaas gevolglik groot druk op onderwysers om ʼn keuse te maak wat betref die gebruik van ʼn wiskundehandboek vir gebruik in die klaskamer. In die studie is ʼn wiskundehandboekprofiel en ʼn taakontleding tydens aksienavorsing geformuleer wat onderwysers in staat sal stel om ʼn professionele ontleding te maak vir gebruik. As gevolg van die verskeidenheid wiskundehandboeke wat gekeur word vir gebruik in skole neem onderwysers aan dat hierdie gekeurde wiskundehandboeke op die kurrikulum gerig is. Gevolglik word wiskundehandboeke slaafs nagevolg sonder om die wiskundekurrikulum te raadpleeg. Tekortkominge in wiskundehandboeke en die eie interpretasie van wiskundeinhoude deur onderwysers laat ʼn groot leemte in hul eie inlynwiskunde-onderrig. Om te voorsien in hierdie behoefte is ʼn assesseringsprofiel en ʼn inlynmetodiek saamgestel om onderwysers in staat te stel om die inlynaanbieding van begrippe en vaardighede te monitor. / Curriculum and Instructional Studies / D. Ed. (Didaktiek)

Abstract in English, Afrikaans and Xhosa / Critical thinking competencies are not only seen as crucial for success in higher education, but also for future personal and workplace success. These competencies are commonly cited as a graduate attribute or goal of higher education, and resulting research has tended to focus on exploring and measuring the development of critical thinking competencies in students within higher education. However, few researchers have explored the curriculum and practice of academic staff within higher education in relation to their influence on developing critical thinking competencies in students, or how they theorise about the development of these competencies as part of their professional practice. Within the South African context, there is a perception of a decline in the development of critical thinking competencies within the secondary school system. This has informed policy imperatives to improve access and success in South African higher education through additional support for students, as well as through research into the first-year experience. Within a constructivist paradigm, and adopting a qualitative approach, this study takes the first year of higher education as its context in order to explore the curriculum, assessment, pedagogical and andragogical practices of academic staff designed to develop critical thinking competencies in first-year students. The aim is to explore how academic staff construct their theory and practice in order to contribute to the Scholarship of Teaching and Learning in South African Higher Education. Phenomenological case study research methods, which draw on data collection through semi-structured interviews and document analysis, enabled a better understanding of the lived experience of academic staff within private higher education. Academic staff, as research participants, were able to describe deliberate actions taken in their teaching practices to facilitate the development and assessment of critical thinking competencies. The findings revealed that academic staff – while having no coherent, well-articulated construction of critical thinking competencies – feel that such competencies are essential for academic and future life success. This not only affirmed previous research reviewed, but aligned to the inclusion of explicit and implicit references to critical thinking competencies found in the curriculum and assessment documents. Recommendations for professional development responded specifically to these findings. / Kritiese denkvaardighede word nie net as wesentlik vir sukses in hoër onderwys beskou nie, maar ook vir toekomstige sukses, op persoonlike vlak en in die werkplek. Hierdie bevoegdhede word algemeen aanvaar as dié van ‘n gegradueerde of as oogmerk in hoër onderwys. Gevolglik was ondersoeke geneig om te fokus op die verkenning en meting van die ontwikkeling van kritiekedenkbevoegdhede by studente binne die hoër onderwys. Min navorsers het egter die kurrikulum en praktyk van akademiese personeel binne die hoër onderwys met betrekking tot hul invloed op die ontwikkeling van kritiekedenkbevoegdhede in studente verken nie, of hoe hulle teoretiseer oor die ontwikkeling van hierdie bevoegdhede as deel van hul professionele praktyk. Binne die Suid-Afrikaanse konteks is die persepsie dat die ontwikkeling van kritiekedenkbevoegdhede binne die sekondêreskoolstelsel afneem. Dit het bygedra tot beleidsimperatiewe om toegang en sukses in die Suid-Afrikaanse hoër onderwys te verbeter deur bykomende ondersteuning aan studente te gee, asook deur die eerstejaarervaring te ondersoek. Binne ‘n konstruktivistiese paradigma, en deur gebruik te maak van ‘n kwalitatiewe benadering, neem hierdie studie die eerste jaar van hoër onderwys as konteks ten einde die kurrikulum, assessering, pedagogiese en andragogiese praktyke van akademiese personeel wat ontwerp is om kritiekedenkbevoegdhede by eerstejaarstudente te verken. Die doel is om na te volg hoe akademiese personeel hul teorie en praktyk saamstel ten einde by te dra tot die Kundigheid in Onderrig en Leer in Suid-Afrika se Hoër Onderwys. Fenomenologiese gevallestudienavorsingsmetodes wat steun op die inwin van data deur middel van semigestruktureerde onderhoude en dokumentontleding, het gelei tot beter begrip van die geleefde ervaring van akademiese personeel binne privaat hoër onderwys. Akademiese personeel, as navorsingsgenote, kon optrede beskryf wat doelbewus in hul onderrigpraktyke geneem word om die ontwikkeling en assessering van kritiekedenkbevoegdhede te fasiliteer. Die bevindinge het getoon dat akademiese personeel – sonder koherente, goed geartikuleerde konstruksie van kritiekedenkbevoegdhede – voel dat sulke vaardighede wesentlik is vir akademiese en toekomstige sukses in die lewe. Dit het nie net vorige navorsing bevestig nie, maar gestrook met die insluiting van eksplisiete en implisiete verwysings na kritiekedenkbevoegdhede binne die kurrikulum- en assesseringsdokumente. Aanbevelings vir professionele ontwikkeling het spesifiek op hierdie bevindinge reageer. / Ubuchule bokucinga nzulu abubonwa kuphela njengecebo elibalulekileyo lokuphumelela kwimfundo ephakamileyo, bukwabonwa njengecebo lokuphumelela komntu kwizinto zakhe nakwindawo axelenga kuyo. Obu buchule bukholisa ukuchazwa njengenjongo yemfundo ephakamileyo, kwaye uphando lweziphumo luthande ukugxininisa ekuqwalaseleni nasekulinganiseleni ukuphuhliseka kwezakhono zokucinga nzulu kubafundi bemfundo ephakamileyo. Noxa kunjalo, bambalwa abaphandi bolwazi abakhe baqwalasela ukusetyenziswa kwekharityhulam ngabahlohli bemfundo ephakamileyo malunga nefuthe ekuphuhliseni izakhono zokucinga nzulu kubafundi, okanye iingcingane zophuhliso lokuphuhliseka kwezi zakhono njengenxalenye yomsebenzi wabo. Kwimeko yoMzantsi Afrika kukho imbono yokuba ziyaphelelwa izakhono zokucinga nzulu kwinkqubo yemfundo yezikolo zeesekondari. Oku kukhokelele ekusekeni iinkqubo zempumelelo kwimfundo ephakamileyo ngokunika inkxaso eyongezelelekileyo kubafundi, nangokuphanda ngamava abafundi abakunyaka wokuqala. Ngokujonga kwinkalo ethi imfundo yinkqubo yokusebenza, nangokusebenzisa indlela yophando lomgangatho, esi sifundo sithatha unyaka wokuqala wemfundo ephakamileyo njengemeko nendawo yokuqwalasela ukusetyenziswa kwekharityhulam, uhlolo, ukufundiswa kolutsha nasebekhulile ngabahlohli ekuphuhliseni izakhono zokucinga nzulu kubafundi bonyaka wokuqala. Injongo kukuqwalasela ukuba abahlohli bayiqulunqa njani ingcingane nokusebenza ukuze kuncediswe kubungcali bokufundisa nokufunda kwimfundo ephakamileyo yoMzantsi Afrika. Iindlela zophando zeemeko ezithile, ezifumana iinkcukacha zolwazi ngokuqhuba udliwano ndlebe oluphantse lwangqongqo, nangokuphengulula imibhalo, kwanceda ukuba kuqondakale ngcono amava abahlohli bemfundo ephakamileyo yabucala. Abahlohli abangabathathi nxaxheba kuphando baye bakwazi ukuchaza izenzo ezingqalileyo ezenzelwe ukuphuhlisa nokuhlola izakhono zokucinga nzulu. Okufunyanisiweyo kwadulisa ukuba abahlohli – lo gama bengenasakhelo sibambekayo nesinokuchazwa gca sezakhono zokucinga nzulu – bayaqonda ukuba ezi zakhono zingundoqo kwimpumelelo kwezemfundo nakubomi obuzayo. Oku akwanelanga nje ukungqina okuvezwe luphando lwangaphambili, koko kongeze kosele kuthethwa ngqo okanye mayana, kwimibhalo yekharityhulam nohlolo, malunga nezakhono zokucinga nzulu. Iingcebiso zophuhliso zisabele ngqo koko kufunyanisiweyo. / Curriculum and Instructional Studies / D. Phil.(Education in the subject Curriculum Studies)

Text in Afrikaans, abstract in English and Afrikaans / Due to the radical reform in mathematics education worldwide, the mathematics curriculum underwent dramatic changes in order to meet the new objectives in mathematics. This has placed a huge responsibility on curriculum compilers and the authors of mathematics textbooks and mathematics teachers to enhance the cognitive development of learners. This study takes the view that: What happens in the class is what you get. Based on the above statement, the foundation of mathematics teaching, namely the mathematics curriculum, the mathematics textbook and the teacher’s instruction in the teaching venue were scrutinised. During a diagnostic examination of teachers’ interpretation, knowledge and application of the mathematics curriculum and the content of mathematics textbooks on the East Rand, the following problems regarding mathematics teaching emerged: The most important finding of TIMMS is that the differences in performance in mathematics between different countries can be linked to the way teachers interpret and present the content of mathematics. Research has revealed that the interaction of teachers with curriculum content follow a dynamic and constructive application instead of direct application based on the mathematics curriculum. Teachers often change the prescriptions and order of content in the mathematics curriculum to suit their teaching style, knowledge and previous experience. Consequently, align application of mathematical concepts and skills does not take place and this creates a gap in learners’ cognitive development. It also leaves a gap in the application of the Type 5 cognitive development tasks in mathematics which enable a verifying deductive application of concepts. The action research created a structure which could meet this need. Authors of mathematics textbooks present their own vision, interpretation and style in mathematics textbooks, which influences the order of mathematics content and concepts. The result is that mathematics content and concepts are at times not aligned with representations in the mathematics curriculum and objectives are therefore not reached. The different interpretations of mathematics textbooks by teachers differ greatly and these differences place great pressure on teachers to decide how the mathematics textbook will be used in the teaching venue. In this study a mathematics textbook profile and a task analysis were formulated in the cause of action research which will enable teachers to make a professional analysis which they can use. Because a variety of mathematics textbooks are selected for use in schools, teachers assume that these approved mathematics textbooks focus on the curriculum. They therefore slavishly follow the mathematics textbooks without consulting the mathematics curriculum. Shortcomings in mathematics textbooks and teachers’ own interpretation of mathematics content leave a big gap in their own alignment of mathematics teaching. To satisfy this need, an assessment profile and an methodology for alignment are provided to enable teachers to monitor the curriculum alignment presentation of concepts and skills. / As gevolg van die radikale hervorming in wiskunde-onderrig wêreldwyd het die wiskundekurrikulum dramatiese veranderings ondergaan ten einde die nuwe doelstellings in wiskunde te bereik. Dit het enorme verantwoordelikheid geplaas op kurrikulumsamestellers en outeurs van wiskundehandboeke en wiskunde-onderwysers om die kognitiewe ontwikkeling van leerders te bevorder. In hierdie studie is van die volgende standpunt uitgegaan: What happens in the class is what you get. Derhalwe is die fondasie van wiskunde-onderrig, naamlik die wiskundekurrikulum, wiskundehandboek en die onderwyser se instruksies in die klaskamer ondersoek. In `n diagnostiese ontleding van onderwysers se interpretasie, kennis en toepassing van die wiskundekurrikulum en die wiskundehandboekinhoude aan die Oos-Rand het die volgende probleme in verband met wiskunde-onderrig na vore gekom: Die belangrikste bevinding van TIMMS is dat die verskille in wiskundeprestasie tussen lande verband hou met die wyse waarop onderwysers die wiskudekurrikuluminhoude interpreteer en aanbied. Navorsing toon dat die interaksie van onderwysers met kurrikulummateriaal op ʼn dinamiese en konstruktiewe toepassing geskied in plaas van direkte toepassing vanuit die wiskundekurrikulum. Onderwysers verander dikwels die wiskundekurrikulum se voorskrifte en volgorde van inhoude om by hulle onderrigstyl, kennis en vorige ervarings te pas. Die gevolg is dat geen inlyntoepassing van wiskundebegrippe en vaardighede plaasvind nie en dit laat ʼn leemte in leerders se kognitiewe ontwikkeling. Verder laat dit ʼn leemte in die toepassing van die 5-tipe kognitiewe ontwikkelingstake in wiskunde wat ʼn verifiërend deduktiewe toepassing van begrippe bewerkstellig. In die aksienavorsing is ʼn struktuur geskep wat in hierdie behoefte voorsien. Outeurs van wiskundehandboeke het ʼn eie visie, interpretasie en styl wat hulle in wiskundehandboeke aanbied. Dit het ʼn invloed op die volgorde van wiskunde-inhoude en begrippe en gevolglik is wiskunde-inhoude en -begrippe soms nie inlyn geplaas met voorstellings van die wiskundekurrikulum nie, en word doelstellings nie bereik nie. Onderwysers se verskillende interpretasies van wiskundehandboekinhoude verskil radikaal van mekaar en plaas gevolglik groot druk op onderwysers om ʼn keuse te maak wat betref die gebruik van ʼn wiskundehandboek vir gebruik in die klaskamer. In die studie is ʼn wiskundehandboekprofiel en ʼn taakontleding tydens aksienavorsing geformuleer wat onderwysers in staat sal stel om ʼn professionele ontleding te maak vir gebruik. As gevolg van die verskeidenheid wiskundehandboeke wat gekeur word vir gebruik in skole neem onderwysers aan dat hierdie gekeurde wiskundehandboeke op die kurrikulum gerig is. Gevolglik word wiskundehandboeke slaafs nagevolg sonder om die wiskundekurrikulum te raadpleeg. Tekortkominge in wiskundehandboeke en die eie interpretasie van wiskundeinhoude deur onderwysers laat ʼn groot leemte in hul eie inlynwiskunde-onderrig. Om te voorsien in hierdie behoefte is ʼn assesseringsprofiel en ʼn inlynmetodiek saamgestel om onderwysers in staat te stel om die inlynaanbieding van begrippe en vaardighede te monitor. / Curriculum and Instructional Studies / D. Ed. (Didaktiek)

Abstract is in English, Zulu and Afrikaans / South Africa is facing a challenge regarding the shortage of South African (SA) engineers. The National Certificate (Vocational) (NC(V)) was introduced by Department of Education (DoE) in 2007 to address this challenge. However, there has been a cry and dissatisfaction from the government, industry, community and other stakeholders that NC(V) engineering curriculum is not addressing the shortage of engineers. SA has one engineer per 2 600 people compared to international norms, where one engineer serves 40 people. It has been ten years since the introduction of NC(V) curriculum, SA should not be in this state of importing engineers if the NC(V) engineering is achieving the goals of National Development Plan 2030. Since lecturers are the implementers of the NC(V) engineering curriculum, it was necessary to investigate their experiences in search for improvement of the curriculum and to find out the challenges facing lecturers which are hindering the success of this curriculum. Lecturers, Senior Lecturers and a Head of Department (HoD) as the primary implementers of the engineering curriculum were involved in the study as participants. There were 15 participants for this study who are lecturing in one selected college but at two different campuses which is why the qualitative research approach was employed, making use of a multiple case study. They took part in semi-structured individual interviews and shared their experiences with the researcher. Their experiences revealed that lecturers are experiencing challenges with the implementation of NC(V) engineering curriculum. Their main challenge was the minimum requirement, which is a Grade 9 pass. Their concern was that no matter what they try, a learner who has not mastered Mathematics up to Grade 12 will struggle with engineering subjects. Emanating from this challenge, low attendance rate, low pass rate, low throughput rate and high drop-out rate is experienced by participants every year. One of the aims of the Transformative Learning Theory (used as one of the theories in the theoretical framework) is to allow lecturers to identify challenges and design improvement plans on their own. This study has indicated that Technical Vocational Education and Training (TVET) colleges have challenges that are hindering teaching and learning. It was evident that some lecturers believe that government officials should resolve such challenges. However, on engaging with different lecturers they realised that they have the capacity to address classroom-based challenges. If this can be the case in every college, teaching and learning will improve because that will mean lecturers are focusing on teaching and learning and taking ownership of their subjects and students. The governance challenges, such as reviewing the NC(V) curriculum yearly, provide subject specific training to upskill lecturers and implementing Work Integrated Learning (WIL) in the professional development of lecturers were recommended to be addressed by the Department of Higher Education and Training (DHET). / INingizimu Afrika ibhekene nenselelo mayelana nokusweleka konjiniyela. Uhlelo lwemfundo iNational Certificate (Vocational) (NC(V)) lwethulwa wuMnyango wezeMfundo ngonyaka ka 2007 ukuze uxazulule le nkinga. Yize-kunjalo kuye kwaba khona ukungagculiseki ngasohlangothini lukahulumeni, lwezimboni, lomphakathi kanye nakwezinye izinhlaka ezidlala indima yenkinga yokuntuleka konjiniyela. INingizimu Afrika (SA) inonjiniyela oyedwa kubantu abayi 2 600 uma iqhathaniswa nezinga lomhlaba lokuthi unjiniyela oyedwa kufanele ibhekane nabantu abayi 40. Sekudlule iminyaka eyishumi selokhu kwethulwa lezi zinhlelo, ngakho-ke, iSA akufanele izithole isesimeni sokudinga onjiniyela abavela ngaphandle uma ngabe izinhlelo ezikhona ziyanceda ekufinyeleleni izimpokophelo zoHlelo lwezokuThuthukisa iZwe National Development Plan 2030. Njengoba abafundisi bangabaqhubi bezinhlelo zobunjiniyela, phecelezi NC(V), nokho sasikhona isidingo sokuphenya lokho abahlangabezana nakho ukuze kuthuthukiswe izinhlelo futhi kuvunjululwe izinselele ezibhekene nabafundisi, okuyizinselele ezikhinyabeza impumelelo yalezi zinhlelo. Abafundisi, abafundisi abaphezulu kanye neziNhloko zoMnyango Head of Department (HoD) njengabaqhubi bokuqala bezinhlelo bebebambe iqhaza kulolu cwaningo. Abadlalindima abayi 15 bebefundisa kwikholeji ekhethiwe, kodwa emagatsheni amabili ehlukene, lokho okwenza isizathu kusetshenziswe uhlelo locwaningo oluzinze kwizingxoxo, ngokusebenzisa izinhlobonhlobo zocwaningo lotho. Kwenziwe izinhlolovo ezimbaxambili zocwaningo kanti abadlalindima bavezele umcwaningi ulwazi lwabo. Baye baveza ukuthi behlangabezene nezingqinamba uma besebenzisa izinhlelo zobunjiniyela NC(V). Inselele enkulu abahlangabezene nayo kuye kwaba yisidingo sokuphumelela uGreyidi 9. Inkinga enkulu yabo ukuthi bethi bezama ngamandla kulokho abakwenzayo, umfundi owehluleke esifundweni seMethamethiki ukufikela kuGreyidi 12 uzohlangabezana nobunzima ukuze aphumelele ezifundweni zobunjiniyela. Okubhebhethekiswa yile nselele, yizinga eliphansi labafundi abahambela lesi sifundo, izinga eliphansi labafundi abaphumelelayo kanye nezinga eliphezulu labafundi abayeka ukufunda njalo nje ngonyaka. Enye yezinhloso zethiyori yemfundo eguqulayo (used as one of the theories in the theoretical framework) ukuvumela abafundisi ukuba bakwazi ukubona izinselele futhi badizayine izinhlelo zokuzithuthukisa ngokwabo. Lolu cwaningo luye lwaveza ukuthi amakholeji. Phecelezi Vocational Education and Training (TVET) colleges ahlangabezene nezinselele eziphazamisa uhlelo lokufunda nokufundisa. Kuye kwacaca ukuthi abanye abafundisi babekholelwa ekutheni abasebenzi bakahulumeni kufanele baxazulule izinselele ezinjengazo lezi. Yize-kunjalo, ngemuva kokuxoxisana nabafundisi abahlukahlukene, baye bazwisisa ukuthi banamandla okuqeda izinselele ezisemagunjini okufunda. Uma ngabe lokhu kuyenzeka ngempela kuwo wonke amakholeji, ngakho-ke uhlelo lokufunda nokufundisa luzothuthuka ngoba lokho kuzochaza ukuthi abafundisi bagxile ohlelweni lokufunda nokufundisa kanti ngokunjalo baba yibo abalawula izifundo kanye nabafundi babo. Izinselele zokuphatha, ezinjengokubuyekezwa kohlelo lwemfundo, phecelezi NC(V) njalo nje ngonyaka, lunikeza ukuqeqeshwa okuthile okuthuthukisa abafundisi. Ukulandela uhlelo lwemfundo oluhlangene nomsebenzi olumayelana nokuthuthukiswa ngokomsebenzi wabafundisi kuyinto enconywe ukuba ilungiswe uMnyango weMfundo ePhakeme kanye nokuQeqeshwa (Department of Higher Education and Training). / ʼn Tekort aan ambagslui staar Suid-Afrika in die gesig. Om hierdie rede het die Departement van Onderwys in 2007 die Nasionale Sertifikaat (Beroepsgerig) (NS(B)) ingestel. Tot die ontevredenheid van die regering, die bedryf, die gemeenskap en ander belanghebbendes vul hierdie kurrikulum nie die tekort aan nie. In Suid-Afrika is daar een ambagspersoon vir elke 2 600 mense teenoor die internasionale norm van een ambagspersoon per 40 mense. Hierdie kurrikulum is meer as tien jaar gelede ingestel en SA moet tans ambagslui invoer. Die oogmerke van die Nasionale Ontwikkelingsplan 2030 word dus nie verwesenlik nie. Aangesien dosente die NS(B) kurrikulum vir werktuigkundiges implementeer, moes hulle belewenisse ondersoek en hulle probleme bepaal word om die kurrikulum te verbeter. Dosente, senior dosente en departementshoofde, as die implementeerders van hierdie kurrikulum, het aan die studie deelgeneem. Die 15 deelnemers is verbonde aan een kollege wat twee kampusse het. Daarom is ʼn kwalitatiewe navorsingsbenadering gevolg en ʼn veelvuldige gevallestudie gebruik. ʼn Halfgestruktureerde onderhoud is met elke deelnemer gevoer. Uit die onderhoude blyk dat dosente moeite met die implementering van die NS(B) kurrikulum ondervind. Die grootste struikelblok is die minimumvereiste van Graad 9. Al doen hulle ook wat, ʼn leerder wat nie Graad 12-wiskunde geslaag het nie, sal tegniese vakke nie kan bemeester nie. Afgesien hiervan is die bywonings- en slaagsyfer sowel as die omset jaar na jaar laag en die uitsaksyfer hoog. Die transformatiewe leerteorie is deel van die teoretiese raamwerk. Die oogmerk hiervan is dat dosente self probleme aantoon en met verbeteringsplanne kom. In hierdie studie is bevind dat kolleges vir tegniese beroepsgerigte onderwys en opleiding (TBOO) met probleme te kampe het wat onderrig en leer belemmer. Sommige dosente is van mening dat staatsamptenare hierdie probleme moet oplos. Ná gesprekke het talle dosente egter besef dat hulle oor die vermoë beskik om self hulle klaskamerprobleme op te los. As dit van alle kolleges waar is, sal onderrig en leer verbeter omdat dosente hulle op onderrig en leer sal toespits en vir hulle vakke en studente verantwoordelik sal wees. Vakopleiding word gegee om aan bestuursprobleme, soos die jaarlikse hersiening van die NS(B)-leerplan, die hoof te bied. Daar word aanbeveel dat die Departement van Hoër Onderwys en Opleiding toesien dat werkgeïntegreerde leer deel uitmaak van dosente se professionele ontwikkeling. / Curriculum and Instructional Studies / M. Ed. (Curriculum Studies)