According to the Sectional Titles Act 95 of 1986, levies are assigned according to the size of a unit, in other words a unit’s participation quota. These levies are used to finance a complex’s insurance, common property electricity and water, lift maintenance, audit fees, management agent fees, salaries and wages, security, swimming pool expenses and general building maintenance. According to the Traditional Costing System, indirect costs are allocated based on a single cost actual expenses over a year are dissected. A regression and correlation analysis was done on the relationship between costs, participation quota and levies. The contribution of the study is that it empirically determines the behaviour of cost items in order to allocate indirect costs more accurately. Consequently, this will result in improved reasonability and will eliminate the cross-subsidisation of units. The objectives were reached as follows: The first objective was reached when it was proved through empirical studies that the Sectional Title is not fair when it states that the allocation of levies must be according to floor space. The second objective was reached when both participation quota and units per complex were identified as cost drivers for each cost item. The third objective was reached by allocating the levy on a 50 percent base according to units and a 50 percent base according to the total area. This could be refined by each complex according to the unique need of the complex. driver. However, various indirect costs are not necessarily subject to this single cost driver. In practice, it has been proven that high volume products are proportionally taxed with indirect costs when compared to low volume products. In many complexes, owners with larger units are of the opinion that their larger units are subsidising those owners with smaller units. In contrast to the traditional costing system, activity-based costing recognises that indirect costs can also be assigned by use of multiple cost drivers. Since these multiple cost drivers – which affect the way costs are assigned – can be identified, indirect costs are assigned more accurately. This study investigates the current method of cost allocation, whereby costs are assigned via participation quota, and makes suggestions on how these costs can be assigned on a more accurate and fair basis in practice. The goal of this study is to challenge the reasonability of the Sectional Titles Act. The objectives of the dissertation are firstly, to determine the cost behaviour of various cost items and whether the participation quota is a fair cost driver for determining the levies that are to be paid; secondly, it investigates alternative cost drivers that will be more applicable to certain cost items; thirdly, to suggest a cost formula to replace the current cost method, that being the allocation of indirect costs via participation quota. Empirical methods have been used in the research. The empirical research was performed using data obtained from ANGOR Property Specialists (Pty) Ltd’s database. A sample of 113 complexes was extracted from the database of which the / Thesis (M.Com. (Management Accountancy))--North-West University, Potchefstroom Campus, 2011

According to the Sectional Titles Act 95 of 1986, levies are assigned according to the size of a unit, in other words a unit’s participation quota. These levies are used to finance a complex’s insurance, common property electricity and water, lift maintenance, audit fees, management agent fees, salaries and wages, security, swimming pool expenses and general building maintenance. According to the Traditional Costing System, indirect costs are allocated based on a single cost actual expenses over a year are dissected. A regression and correlation analysis was done on the relationship between costs, participation quota and levies. The contribution of the study is that it empirically determines the behaviour of cost items in order to allocate indirect costs more accurately. Consequently, this will result in improved reasonability and will eliminate the cross-subsidisation of units. The objectives were reached as follows: The first objective was reached when it was proved through empirical studies that the Sectional Title is not fair when it states that the allocation of levies must be according to floor space. The second objective was reached when both participation quota and units per complex were identified as cost drivers for each cost item. The third objective was reached by allocating the levy on a 50 percent base according to units and a 50 percent base according to the total area. This could be refined by each complex according to the unique need of the complex. driver. However, various indirect costs are not necessarily subject to this single cost driver. In practice, it has been proven that high volume products are proportionally taxed with indirect costs when compared to low volume products. In many complexes, owners with larger units are of the opinion that their larger units are subsidising those owners with smaller units. In contrast to the traditional costing system, activity-based costing recognises that indirect costs can also be assigned by use of multiple cost drivers. Since these multiple cost drivers – which affect the way costs are assigned – can be identified, indirect costs are assigned more accurately. This study investigates the current method of cost allocation, whereby costs are assigned via participation quota, and makes suggestions on how these costs can be assigned on a more accurate and fair basis in practice. The goal of this study is to challenge the reasonability of the Sectional Titles Act. The objectives of the dissertation are firstly, to determine the cost behaviour of various cost items and whether the participation quota is a fair cost driver for determining the levies that are to be paid; secondly, it investigates alternative cost drivers that will be more applicable to certain cost items; thirdly, to suggest a cost formula to replace the current cost method, that being the allocation of indirect costs via participation quota. Empirical methods have been used in the research. The empirical research was performed using data obtained from ANGOR Property Specialists (Pty) Ltd’s database. A sample of 113 complexes was extracted from the database of which the / Thesis (M.Com. (Management Accountancy))--North-West University, Potchefstroom Campus, 2011

In the context of broadband wireless communications using code division multiple access (CDMA), the main multiple access (MA) options include single-carrier direct sequence CDMA (SC-DS-CDMA) using time-domain direct sequence spreading [1, p. 728], multicarrier CDMA (MC-CDMA) using frequency-domain spreading [2, 3] and multicarrier DS-CDMA (MC-DS-CDMA) using time-domain direct sequence spreading of the individual sub-carrier signals [4, 5]. It was shown in [6] that MC-DS-CDMA has the highest degrees of freedom in the family of CDMA schemes that can be beneficially exploited during the system design and reconfiguration procedures. An amalgam of MC-CDMA and MC-DS-CDMA known as time and frequency domain spreading (TF-domain spreading) MC-DS-CDMA was proposed in [6]. TF-domain spreading MC-DS-CDMA has several benefits over conventional MC-DS-CDMA with regard to both capacity and performance [7]. However, in contrast to conventional MC-DS-CDMA, TF-domain spreading MC-DS-CDMA introduces MUI, which necessitates the use of joint detection at the receiver. Recently, multiple input multiple output (MIMO) or multi-antenna TF-domain spreading MC-DS-CDMA schemes have been proposed in the literature that e ciently exploit both the spatial and frequency diversity available in MIMO frequency-selective channels [8, 9]. Although an extensive amount of research has been done on single and multi-antenna TF-domain spreading MC-DS-CDMA schemes that achieve both spatial and frequency diversity in frequency-selective slow fading channels [6–9], very little research considers the time-selectivity of the wireless channels encountered. Thus, the above-mentioned schemes may not be su ciently e cient, when communicating over wireless channels exhibiting both frequency-selective and time-selective fading. There are very few MC-DS-CDMA schemes in the literature that consider the time-selectivity of the wireless channels encountered. This study considers the design of single and multi-antenna TF-domain spreading MC-DS-CDMA, for frequency-selective block-fading channels, which are capable of exploiting the full diversity available in the channel (i.e. spatial, frequency and temporal diversity), using various methods of joint detection at the receiver. It has been shown that the diversity gain in block-fading channels can be improved by coding across multiple fading blocks [10–12]. Single-antenna TF-domain spreading MC-DS-CDMA is considered for the quasi-synchronous uplink channel, and multi-antenna TF-domain spreading MC-DS-CDMA is considered for the synchronous downlink channel. Numerous simulated bit error rate (BER) performance curves, obtained using a triply selective MIMO channel platform, are presented in this study using optimal and sub-optimal joint detection algorithms at the receiver. In addition, this study investigates the impact of spatial correlation on the BER performance of the MC-DS-CDMA schemes considered. From these simulated results, one is able to conclude that TF-domain spreading MC-DS-CDMA designed for frequency-selective block-fading channels performs better than previously proposed schemes designed for frequency-selective slow fading channels, owing to the additional temporal diversity exploited under the block-fading assumption. AFRIKAANS : In die konteks van bre¨eband- draadlose kommunikasie deur die gebruik van kodeverdelingveelvuldige toegang (KVVT) behels die belangrikste veelvuldigetoegang- (VT) opsies enkel-draer direkte-sekwensie KVVT (ED-DS-KVVT), deur die gebruik van tyd-domein direkte sekwensie-verspreiding [1, p. 728], veelvuldigedraer-KVVT (VD-KVVT) deur die gebruik van frekwensiedomein-verspreiding [2, 3] en VD-DS- KVVT deur die gebruik van tyd-domein direkte sekwensie-verspreiding van die individuele sub-draerseine [4, 5]. Daar is in [6] aangetoon dat VD-DS-KVVT die hoogste vlakke van vryheid in die familie KVVT-skemas het wat voordelig benut kan word gedurende sisteemontwerp en rekonfigurasieprosedures. ’n Amalgaam van VD-KVVT en VD-DS-KVVT bekend as tyd-en-frekwensiedomeinverspreiding (TF-domeinverspreiding) VD-DS-KVVT is voorgestel in [6]. TF-domeinverspreiding VD-DS-KVVT het verskeie voordele bo konvensionele VD-DS-KVVT wat sowel kapasiteit as werkverrigting betref [7]. In teenstelling met konvensionele VD-DS-KVVT benut TF-domeinverspreiding VD-DS-KVVT multi-gebruiker-interferensie, wat die gebruik van gesamentlike opsporing by die ontvanger noodsaak. In die onlangse verlede is in die literatuur veelvuldige-inset-veelvuldige-uitset- (VIVU) of veelvuldige-antenna TF-omeinverspreiding VD-DS-KVVT-skemas voorgestel wat sowel die ruimtelike as frekwensiediversiteit wat in VIVU frekwensie-selektiewe kanale beskikbaar is, e ektief gebruik [8, 9]. Hoewel uitgebreide navorsing onderneem is oor enkel- en multi-antenna TF-domeinverspreiding VD-DS-KVVT-skemas wat sowel ruimtelike as frekwensie diversiteit in frekwensie-selektiewe stadig deinende kanale bereik [6–9], oorweeg baie min navorsing die tyd-selektiwiteit van die draadlose kanale wat betrokke is. Bogenoemde skemas mag dus nie e ektief genoeg wees nie wanneer kommunikasie plaasvind oor draadlose kanale wat sowel frekwensie-selektiewe as tyd-selektiewe wegsterwing toon. Baie min VD-DS-KVVT-skemas in die literatuur skenk aandag aan die tyd-selektiwiteit van die betrokke draadlose kanale. Die studie ondersoek die ontwerp van enkel- en multi-antenna TF-domeinverspreiding VD-DS-KVVT vir frekwensie-selektiewe blokwegsterwingkanale, wat in staat is om die volle diversiteit wat in die kanaal beskikbaar is, te benut (i.e. ruimtelike, frekwensie- en tyddiversiteit), deur die gebruik van verskeie metodes van gesamentlike opsporing by die ontvanger. Daar is aangetoon dat die diversiteitwins in blokwegsterwingkanale verbeter kan word deur kodering oor veelvuldige deinende blokke [10–12]. Enkel-antenna TF-domeinverspreiding VD-DS-KVVT word oorweeg vir die kwasi-sinchroniese opverbinding-kanaal, en multi-antenna TF-domeinverspreiding VD-DS-KVVT vir die sinchroniese afverbinding-kanaal. Talryke gesimuleerde bisfouttempo (BFT) werkverrigtingkurwes wat verkry is deur die gebruik van ’n drie-voudige selektiewe VIVU-kanaalplatform, word in hierdie studie aangebied, deur die gebruik van optimale en sub-optimale gesamentlike opsporingsalgoritmes by die ontvanger. Daarbenewens ondersoek hierdie studie die impak van ruimtelike korrelasie op die BFT-werkverrigring van die VD-DS-KVVT-skemas wat oorweeg word. Uit hierdie gesimuleerde resultate is dit moontlik om tot die gevolgtrekking te kom dat TF-domeinverspreiding VD-DS-KVVT wat ontwerp is vir frekwensie-selektiese blokwegsterwingkanale beter werkverrigting toon as vroe¨er voorgestelde skemas wat ontwerp is vir frekwensie-selektiewe stadig deinende kanale, te danke aan die ekstra tyddiversiteit wat deur die blokwegsterwing-aanname benut word. Copyright / Dissertation (MEng)--University of Pretoria, 2010. / Electrical, Electronic and Computer Engineering / unrestricted

Summaries in English, Afrikaans and Zulu / Orientation: Security personnel work in a high risk and consequently high stress environment. This may negatively affect their wellbeing. Owing to the high crime rate in South Africa, one of the continuous stressors security personnel experience might be fearing for their lives. If security personnel fail to use effective coping strategies they will remain stressed, and this may have a negative impact on them, and their organisation or community. Challenges such as work stress in the South African security industry have not been comprehensively researched or documented (Sibanyoni, 2014). Consequently, no South African questionnaire measuring coping with stress or a stress management model for dealing with stress in a security environment, could be found. Research purpose: The general aim of the research was to develop a valid and reliable coping questionnaire and stress management model for high stress security occupations. Research methodology: A questionnaire development process, as suggested by scientific literature, was followed. The process entailed (1) determining coping strategies by means of a literature review, (2) developing the coping questionnaire, (3) administering the questionnaire to the target population, and (4) statistical analysis. The stress management model was developed by combining the results of the confirmatory factor analysis (CFA) and canonical correlation analysis (CCA). The development of the questionnaire was based on a sample of 381 active duty security personnel working in a high stress security environment in South Africa. Main findings: The study resulted in the development of a psychometrically sound 39-item questionnaire. The following 12 empirically validated healthy and unhealthy coping strategies were identified: (1) social support, (2) group cohesion, (3) physical exercise, (4) relaxation, (5) social media addiction, (6) healthy sleeping habits, (7) healthy diet, (8) training, (9) humour, (10) religion, (11) avoidance, and (12) denial. CFA confirmed both the construct and content validity, and composite reliability. The questionnaire was found to be invariant, and could thus be applied to different groups in high stress security occupations. A stress management model indicating the interrelationship between personality and coping was also developed. Contribution/value-add: The main contribution of this study was the development of a valid coping questionnaire and stress management model. By identifying the specific coping strategies, targeted stress management interventions could be developed. This could contribute to the overall wellness of security personnel working in high stress occupations, resulting in a healthy organisation and sound relationships with the community. Security organisations could also use the model during assessments to identify candidates with personality traits that would lead to healthier coping strategies, thereby selecting personnel that could better adapt to a security environment. / Oriëntasie: Sekuriteitspersoneel werk in ’n hoë risiko en gevolglik ’n stresvolle omgewing. Dit kan hulle welstand negatief beïnvloed. As gevolg van die hoë misdaadsyfer in Suid-Afrika kan een van die deurlopende stressors wat sekuriteitspersoneel ervaar ’n vrees vir hulle lewens wees. Indien sekuriteitspersoneel nie effektiewe streshantering strategieë gebruik nie, kan hulle voortdurend stres ervaar en dit kan ’n negatiewe impak op hulleself, hulle organisasie of gemeenskap hê. Uitdagings soos beroepstres in die Suid-Afrikaanse sekuriteitsindustrie is nog nie deeglik nagevors of gedokumenteer nie (Sibanyoni, 2014). Gevolglik kon daar vir die sekuriteitsomgewing geen Suid-Afrikaanse vraelys wat streshantering meet of ’n stresbestuursmodel gevind word nie. Doel van die navorsing: Die algemene doel van die navorsing was om vir stresvolle sekuriteitsberoepe ’n geldige en betroubare streshanteringsvraelys en stresbestuursmodel te ontwikkel. Navorsingsmetodologie: ’n Vraelys ontwikkelingsproses, soos deur wetenskaplike literatuur voorgestel, is gevolg. Die proses het die volgende behels: (1) die vasstel van die streshantering strategieë deur middel van ’n literatuuroorsig, (2) die ontwikkeling van die streshanteringsvraelys, (3) administrasie van die vraelys aan die teiken populasie en (4) statistiese analise. Die stresbestuursmodel is ontwikkel deur die resultate van die bevestigende faktoranalise (BFA) en die kanoniese korrelasie analise te kombineer. Die ontwikkeling van die vraelys is gebaseer op ’n steekproef van 381 aktiewe diens sekuriteitspersoneel wat in Suid-Afrika in ’n stresvolle sekuriteitsomgewing werk. Hoofbevindinge: Die studie het tot ’n psigometries betroubare 39-item vraelys gelei. Twaalf empiries gestaafde gesonde en ongesonde streshantering strategieë is geïdentifiseer naamlik: (1) sosiale ondersteuning, (2) groep kohesie, (3) fisiese oefening, (4) ontspanning, (5) sosiale media verslawing, (6) gesonde slaapgewoontes, (7) gesonde dieet, (8) opleiding, (9) humor, (10) godsdiens, (11) vermyding en (12) ontkenning. BFA het die konstruk- en inhoudsgeldigheid so wel as die saamgestelde betroubaarheid bevestig. Die vraelys is invariant en kan dus op verskillende groepe in hoë stres sekuriteitsberoepe toegepas word. ’n Stresbestuursmodel wat die verwantskap tussen persoonlikheid en streshantering aandui is ook ontwikkel. Bydrae/waardetoevoeging: Die belangrikste bydrae van hierdie studie was die ontwikkeling van ’n geldige streshanteringsvraelys en stresbestuursmodel. Deur die spesifieke streshantering strategieë te identifiseer kan gefokusde streshantering intervensies ontwikkel word. Dit kan tot die algehele welstand van sekuriteitspersoneel wat in stresvolle beroepe werk bydra en derhalwe ’n gesonde organisasie en goeie verhoudings met die gemeenskap. Sekuriteitsorganisasies kan ook tydens keurings die model gebruik om kandidate met persoonlikheidstrekke, wat tot gesonder streshantering strategieë sal lei, te identifiseer en dus personeel kies wat beter by ’n sekuriteitsomgewing sal aanpas. / Isimo somqondo: Abasebenzi bezokuphepha basebenza ezindaweni ezinobungozi obuphakeme nengcindezi ephakeme. Lokhu kungaba nomthelela omubi esimeni sabo sempilo. Ngenxa yezinga lobugebengu eliphezulu eNingizimu Afrika, okukodwa okudala ingcindezi ngokuqhubekayo kubasebenzi bezokuphepha ukwesabela izimpilo zabo. Uma abasebenzi bezokuphepha bengasebenzisi amasu aphumelelayo okubhekana nalezi zimo, bazohlala benengcindezi futhi lokhu kungaba nomphumela omubi kubona, enhlanganweni yabo noma emphakathini wabo. Ucwaningo ngezinselelo ezinjengokucindezeleka emsebenzini ezimbonini zokuphepha lapha eNingizimu Afrika alwenziwanga futhi akubhaliwe kabanzi ngakho (Sibanyoni, 2014). Kanjalo, alutholakalanga uhlu lwemibuzo lwaseNingizimu Afrika olungalinganisa ukuthi abasebenzi bezokuphepha babhekana kanjani nengcindezi kanye nomlinganiso olawula ingcindezi ukubhekana nengcindezi ezindaweni zezokuphepha. Inhloso yocwaningo: Inhloso enkulu yocwaningo kwakuwukuqamba uhlu lwemibuzo oluqinisekile noluthembekile ukubhekana nengcindezi nomlinganiso wokulawula ingcindezi emisebenzini yezokuphepha enengcindezi ephakeme. Indlela yokwenza ucwaningo: Isenzo sokuqamba uhlu lwemibuzo njengoba kuhlongozwa yimibhalo yezesayensi silandelwe kulolu cwaningo. Lesi senzo sibe (1) nokuthola amasu okubhekana nengcindezi ngokubhekisa emibhalweni ehloliwe, (2) nokuqamba uhlu lwemibuzo ephathelene nokubhekana nengcindezi, (3) nokunikeza uhlu lwemibuzo kubantu abathintekayo, kanye (4) nokwenza uhlaziyo lwezibalo. Umlinganiso wokulawula ingcindezi wenziwe ngokuhlanganisa imiphumela yeConfirmatory Factor Analysis (CFA) neyeCanonical Correlation Analysis (CCA). Ukuqanjwa kohlu lwemibuzo kweyeme esampuleni labasebenzi bezokuphepha abangama-381 abamatasa emsebenzini abasebenza ezindaweni ezinengcindezi ephakeme eNingizimu Afrika. Okukhulu okutholakele ocwaningweni: Ucwaningo lube nomphumela ekuqanjweni kohlu lwemibuzo oluqinisekile ngokwesayikhomethri olunemibuzo angama-39. Kukhonjwe amasu okubhekana nengcindezi ayishumi nambili aqinisekiswe ngokubukisiswa asesimeni esiphilile nesingaphilile sempilo, okubalwa kuwo, (1) uxhaso lomphakathi, (2) ukuba ndawonye kweqembu, (3) ukuzivocavoca umzimba, (4) ukuziphumuza, (5) ukuba yisigqili semithombo yomphakathi, (6) imikhuba emihle yokulala, (7) uqeqesho, (8) amahlaya, (10) inkolo, (11) ukuxwaya, kanye (12) nokwala. ICFA iqinisekise ukuba neqiniso kombono nokuqukethwe, kanye nokwethembeka okuxubile. Kutholakele ukuthi uhlu lwemibuzo aluguquki futhi lungasetshenziswa emaqenjini ehlukene emisebenzini yezokuphepha anengcindezi ephakeme. Kuthuthukiswe nomlinganiso olawula ingcindezi okhombisa ubudlelwano phakathi komuntu isibili nokubhekana nengcindezi. Umnikelo: Umnikelo omkhulu walolu cwaningo kube ukuqamba uhlu lwemibuzo oluqinisekile ukubhekana nengcindezi kanye nomlinganiso wokulawula ingcindezi. Ngokukhomba amasu aqondene nokubhekana nengcindezi, kungathuthukiswa izindlela ezihlosiwe zokulawula ingcindezi. Lokhu kunganikela esimeni esihle sempilo yabasebenzi bezokuphepha abasebenza imisebenzi enengcindezi ephakeme, okuzoholela enhlanganweni esesimeni esihle nasebudlelwaneni obuhle nomphakathi. Izinhlangano zezokuphepha nazo zingawusebenzisa lomlinganiso ngesikhathi sokuhlola ukubona abafundi abanezici ezinomthelela omuhle, kumasu abhekana nengcindezi asesimeni esihle, ezizobenza bakhethe abasebenzi abazongena kahle ezindaweni zokuphepha. / Industrial and Organisational Psychology / D. Phil. (Industrial and Organisational Psychology)

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)

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)