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)

Summaries in English and Afrikaans / In die tesis word die modernistiese en laat/postmodernistiese reduksionistiese benaderings in die Adventiste wêreld nie bloot afgewys nie, nie net omdat dit deel van ons ervaring is nie maar ook omdat die reduksies wat in die moderne en laat/postmoderne tyd ontstaan het in ʼn gemodifieërde sin die boustene is van ʼn hermeneutiese benadering wat poog om holisties en in multiverse sin oorvleuelend te werk met die antieke, moderne en laat/post moderne benaderinge. In ʼn hermeneutiek wat holisties oorvleuelend en multivers integrerend aan die gang is, vorm die vierledige opset van die handelinge en beweginge van God, die menslike bewustelike self, medemens(e) as die ander mens en die natuurlike kosmiese wêreld ʼn misterie van vierledig aktiewe teenwoordighede wat nie-vermengd saambestaan maar tog ontsettend naby aan mekaar is as die voortgaande ervaringskaart van elke konteks en situasie. Juis die uitmekaar ruk van die vierledige aktiewe teenwoordighede inonservaringswêrelde vorm die agtergrond vir moderne teologisme met God alleen speler van die spel, psigologisme met die bewustelike menslike self as die kaptein van sy siel en die meester van sy lot, humanisme waarin die mensheid as kollektiewe menswees die enigste roerder van die menslike brousel in die geskiedenis is en naturalisme waarin die natuurlik kosmiese omgewing die naturaliserende ordeningsagent van die kosmiese chaos is. Wat radikaal deur ʼn holisties oorvleuelende en multiverse integrerende aanpak sny, is dat die vierledige teenwoordighede gedra word asook ingebou is in wat in die Bybels-historiese tydslyn vorendag kom as die vier prominente dade van God se voortgaande skepping, versoening in Jesus Christus, alomvattende vernuwing deur die Gees en voleindende volmaking tot in die aanbreek van die nuwe hemel en die nuwe aarde. Binne die omraming van ʼn hermeneutiek wat holisties oorvleuelend en multiversintegrerend werk, word algemene moderne en postmoderne benaderinge oor tekse, teorieë, menslike handelinge en die natuurlike kosmiese gebeurtenisse beskryf. Terwyl die moderniteit – en ook die postmoderniteit – uitgaan van die hoofsaaklik opponerende verskille tussen sinmakende beskouinge word hier gepoog om eers die oorvleuelingsareas refleksief te betrek en daarna aandag gee aan die verskille. Die drie breë benaderinge wat hoofsaaklik beskryf word is die van fundamentalistiese spieëling, liberale interpretasie en die konsinlike onderhandeling van tekse, teorieë, menslike handelinge en natuurlik kosmiese gebeure.Juis teen hierdie agtergrond word diverse SDA omgangspatrone met die Bybel, ervaringe in die kerklike arena en alledaagse ervaringe in ʼn draaikolk van multivers oorvleuelende en differensiërende refleksiwiteit beskryf. / In the thesis Adventist approaches making use of modernist and late/postmodernistic reductionist philosophies are not rejected out of hand. Not only are the reductions which emerged in the modern and late/modern era part of our experience but they are in a modified sense the building blocks of a hermeneutical approach in which an attempt is made to work in an overlapping holistic and multiverse way with approaches of the ancient world, modernity and late/post modernity. In a hermeneutics that operate holistically with overlaps and in a multiverse integrative sense, the quadruple setting of actions and movements of God, the conscious human self, neighbour(s) as the other human and the natural cosmic world forms a mystery of foursome active presences that do not exist together in a mixed sense but are very close to each other as the continuous experiential map of every context and situation. The dislocation of the foursome active presences in our experiential worlds forms the backdrop of modern theologism in which God is the sole player in the game, psychologism with the conscious human self as the captain of his or her soul, humanism in which humanity as the collectiveness of being human is the only stirrer of the human concoction in history and naturalism in which the natural cosmic environment is the only naturalistic agency that arranges the cosmic chaos. Cutting radically through the holistic overlapping and multiverse integrative approach is that the foursome presences are carried and built into what come to the fore in the biblical historical timeline as the four grand acts of God of continuous creation, reconciliation in Jesus Christ, all embracing renewal through the Holy Spirit and fulfilling fulfilment as in the dawn of the new heaven and the new earth. Within the embrace of a hermeneutics which works with overlaps in a holistically and integrating in a multiverse sense general modernist and late/post modern approaches regarding texts, theories, human doings and natural cosmic events are described. While modernity – and late/post modernity - depart from mainly opposing differences between sense making views the attempt is made here firstly to engage oneself in a reflexive sense with the areas of overlapping and only then to pay attention the differences. The three broad approaches mainly described are that of fundamentalist mirroring, liberal interpretation and consensual negotiation of texts, theories, human doings and natural cosmic events. It is against this background that diverse SDA engagement patterns with the Bible, experiences in the arena of the church and everyday experiences is described in a vortex of holistic overlapping and multiverse integrative reflexivity. / Philosophy, Practical and Systematic Theology / D. Th. (Systematic Theology)

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)