Text in Afrikaans, abstract in Afrikaans and English / Die gebruik van simbole maak wiskunde eenvoudiger en kragtiger, maar ook moeiliker verstaanbaar. Laasgenoemde kan voorkom word as slegs eenvoudige en noodsaaklike simbole gebruik word, met die verduidelikings en motiverings in woorde. Die krag van simbole le veral in die feit dat simbole as substitute vir konsepte kan dien. Omdat die krag van simbole hierin le, skuil daar 'n groot gevaar in die gebruik van simbole. Wanneer simbole los is van sinvolle verstandsvoorstellings, is daar geen krag in simbole nie. Dit is die geval met die huidige benadering in skoolalgebra. Voordat voldoende verstandsvoorstellings opgebou is, word daar op die manipulasie van simbole gekonsentreer. Die algebraiese historiese-kenteoretiese perspektief maak algebra meer betekenisvol vir leerders. Hiervolgens moet die leerlinge die geleentheid gegun word om oplossings in prosavorm te skryf en self hul eie wiskundige simbole vir idees spontaan in te voer. Hulle moet self die voordeel van algebraiese simbole beleef. / The use of symbols in algebra both simplifies and strengthens the subject, but it also increases its level of complexity.This problem can be prevented if only simple and essential symbols are used and if the explanations are fully verbalised. The power of symbols stems from their potential to be used as substitutes for concepts. As this constitutes the crux of mathematical symbolic representation, it also presents a danger in that the symbols may not be comprehended. If symbols are not related to mental representations, the symbols are meaningless. This is the case in the present approach to algebra. Before sufficient mental representations are built, there is a concentration on the manipulation of symbols. The algebraic historical epistemological perspective makes algebra more meaningful for learners. Learners should be granted the opportunities to write their solutions in prose and to develop their own symbols for concepts. / Mathematics Education / M. Sc. (Wiskunde-Onderwys)

Thesis (PhD) -- University of Stellenbosch, 2005. / ENGLISH ABSTRACT: The researcher encountered the following problems while teaching braille IWSic notation to blind learners at the Pioneer School in Worcester: • Young learners learning to read braille IWSic notation with the piano as mediwn appeared to struggle technically. For example, blind children experienced difficulty finding the correct keys over seven octaves; they had generally weak posture; they had to learn to play one part with one hand while the other hand would read; they had to memorise the music for each clef individually and then combine them cognitively; they had to memorise the soprano, alto, tenor and bass parts of a piece; they often experienced discouragement because of the very slow progress they made compared with their sighted peers. • Although learners seemed to find the recorder technically more manageable, currently available braille recorder tutors proved to be inadequate. This inadequacy was a result of the tutors having been designed for the sighted child. The researcher thus set out to design a more appropriate approach than is currently available for teaching braille music notation to the blind, with the recorder as medium. The research method was qualitative and included a literature survey which covered the following unique needs of the blind learner: • psychological • emotional and social • concept development • motor skills (orientation, laterality, posture, coordination) • tactile perception • creativity and self expression The qualitative research also included video observation of a series ofiodividual and group lessons. The lesson material emerged from a programme designed by the researcher and was based on the literatme study. An observation panel. together with the researcher, evaluated the lessons on predetenDned coded assessment criteria 'The lessons and progrannne were adapted according to feedback from the lessons. The qualitative research includes interviews with five blind learners and six teachers of braille music notation. The interviews were designed to gather information on how blind learners can more appropriately be taught the braille music code. The unique needs of blind learners, in particular those concerning orientation and perceptual awareness, are considered in this alternative approach for teaching braille music notation to blind learners. 'The alternative programme is skills based and can be used convElliently in conlunetion with the Outcomes- Based Education (OBE) modeL / AFRIKAANSE OPSOMMING: Die navorser het die volgende probleme ondervind tydens baar onderrig van braille musieknotasie aan blinde leerders by Pionierskool in Worcester: • Dit wil voorkom asofjong leerders wat braille musieknotasie moet aanleer met die klavier as medium, tegniese probleme ondervind. Blinde kinders het dit byvoorbeeld moeilik gevind om die korrekte toetse oor sewe oktawe te vind; oor die algemeen was hulle houding swak; hulle moes leer om een stemparty met een hand te lees terwyl die ander hand gespeel het; hulle moes die musiek vir elke sleutelteken apart memoriseer en die stemme kognitiefbymekaar sit; hulle moes die sopraan, alt. tenoor en bas stempartye van 'n stuk memoriseer, hulle is baie keer moedeloos, weens hulle stadige vordering, in vergelyking met hulle siende portuurgroep. • A1hoewel dit gelyk het asof leerders die bioldIuit tegnies meer hanteerbaar gevind het, blyk huidige beskikbare braille bloldluit handleidings nie geskik te wees nie. Hierdie ontoereikendheid is as gevolg van die feit dat die handleidings vir die siende kind ontwerp IS. Derhalwe het die navorser gepoog om 'n meer toeganklike benadering te ontwikkel as wat tans beskikbaar is vir die onderrig van braille misieknotasie aan die blinde, met die bioldIuit as medium. Die ondersoekmetode was kwalitatief van aard en het onder andere 'n literatuuroorsig ingesluit wat die volgende unieke behoeftes van die blinde leerder ingesluit het: • siellnmdig • emosioneel en sosiaal • konsep ontwikkeling • motoriese vaardighede (oriëntasie, lateraliteit, houding, koOrdinasie) • gevoelswaarneming

Background: Business process compliance management has recently attracted a lot of attention in both business and academia as it enables organizations to not only control and monitor their business processes from a legal point of view but also to avoid financial penalties and undesirable consequences to their reputation. Objective: This thesis aims to provide a framework that would enable organizations to: 1- Discover business processes that violate regulations, laws and policies; 2- Discover the importance level of business processes based on the organization’s goals; 3- Determine the impact of compliance-related process modifications on business goals, including conflicting goals between stakeholders, and on policies; and 4- Enable organizations to measure the level of business process compliance for one or multiple policies. Methodology: A systematic literature review in the area of goal-oriented business process compliance management and measurement has been conducted, which showed that balancing legal compliance obligations with business objectives remains a difficult challenge. A new Indicator-based Policy Compliance Framework (IPCF), which combines policy and rule models together with models capturing business goals (with their relative importance to the organization) and business processes, has been proposed. This framework builds on the User Requirements Notation (URN), which is the first international standard to combine goal modeling with scenario modeling. The intents and objectives of policies have been modeled, as well as the goals and business processes of organizations, and indicators are used to measure the compliance level of policies. This enables the detection of non-compliant business processes and the evaluation of the impact of compliance-related process modifications on business goals. Human resource policies and business processes are used as an example to illustrate the method. Aerodrome security regulations and business processes are then used to validate the method in a real-life environment. Comparisons to related work, evaluation against different sets of criteria, and tool support complement the framework validation. Results: The Indicator-based Policy Compliance Framework enables organizations to discover business processes that violate policies as well as other types of rules, regulations, and laws. Guidelines for modeling legal text with URN’s Goal-oriented Requirement Language (GRL) are proposed. Furthermore, IPCF helps determine the impact of compliance-related process modifications on business goals, including conflicting goals between stakeholders, and on policies. In addition, as policies sometimes apply differently to different types of organizations, a new profile for GRL, with suitable stereotypes, well-formedness constraints, and a modified analysis algorithm defined for GRL model families is used to evaluate the satisfaction level of individual goal models that are members of a larger family model. Finally, the proposed IPCF enables organizations to measure the level of business process compliance for one or multiple policies, and such measures can be visualized directly in URN models but also through interactive Business Intelligence portals, for a wider diffusion.

The topic of assessment has attracted wide-spread attention in the discipline of music education in recent decades. However, most research centres on school-based assessment, and then mainly on the assessment of practical music subjects. Current assessment practices in music literacy programmes (such as 'paper-and-pencil' and standardized tests) counteract what is arguably the most important goal of music education, namely the development of musicianship. Therefore, in this study, my aim is to investigate assessment practices in music literacy courses for young adults, and to show how assessment in these courses can contribute to the development of musicianship. In order to reach these aims, the terms 'musicianship' and 'music literacy' are defined. The importance of a guiding philosophy for assessment is highlighted and constructivism is discussed as an example of such a philosophy, since constructivist principles largely correspond with the principles of assessment and adult education. Principles for effective assessment are subsequently established before being applied to the assessment of music literacy outcomes. Finally, the need for further research about various topics that can inform assessment practices in music subjects is pointed out. / Thesis (M.Mus.)--North-West University, Potchefstroom Campus, 2007.

Thèse diffusée initialement dans le cadre d'un projet pilote des Presses de l'Université de Montréal/Centre d'édition numérique UdeM (1997-2008) avec l'autorisation de l'auteur.

Les neumes aquitains dont les formes sont proches de celles des liquescences, bien qu’ils soient utilisés indépendamment des situations phonétiques, sont traditionnellement considérés comme les « graphies particulières » propres aux versaria polyphoniques : Paris, Bibliothèque nationale de France, fonds latin, 3549 et 3719. La présente thèse identifie ces neumes comme l’oriscus spécial, d’une forme rare, employé en plus de l’oriscus aquitain normatif. Dans le versarium 3719 l’usage de l’oriscus spécial est lié aussi aux autres phénomènes notationnels, comme les liaisons entre les éléments neumatiques descendants. La thèse relève l’existence de l’oriscus spécial dans un petit nombre de manuscrits de la notation aquitaine monodique, parmi les 150 manuscrits de la Bibliothèque nationale de France. Quant aux phénomènes notationnels adjacents à l’oriscus de cette forme, ils appartiennent à une évolution graphique du tractulus/punctum aquitain le plus fortement prononcée au Sud-ouest du domaine de la notation aquitaine. Les graphies particulières ne sont donc pas circonscrites strictement au sein des versaria polyphoniques aquitains, comme cela a été supposé jusqu’à présent. L’oriscus spécial remplit des fonctions spécifiques dans les versaria polyphoniques aquitains, principalement, l’ornementation des intervalles en vertical et la coordination de la rencontre des voix. Ainsi, en intégrant cet oriscus dans l’arsenal de sa neumatique, la notation aquitaine de conception monodique s’adapte à la tâche de noter les chants polyphoniques, adéquatement aux besoins de l’écriture musicale du discantus orné. / The neumes which are close in their shape to the Aquitanian liquescence signs, but are used independently of the phonetic circumstances, are usually considered as the “neumatic peculiarities” specific to the Aquitanian versaria: Paris, Bibliothèque nationale de France, lat. 3549 and lat. 3719. The present thesis identifies these neumes as the Aquitanian special oriscus of an uncommon shape, employed in the versaria additionally to the Aquitanian oriscus of the common shape. This oriscus is connected to some other notational phenomena of the versarium 3719, like the ligatures that occur in the down-going neumes.The present thesis reveals the existence of the special oriscus in a small amount of sources, among the 150 manuscripts of the Bibliothèque nationale that carry Aquitanian neumatic notation. As to the other notational phenomena connected to the oriscus, these belong to a graphical development of the Aquitanian tractulus /punctum which shows itself most strongly in the South-west of the Aquitanian notation area. The neumatic peculiarities are therefore not contained exclusively in the corpus of Aquitanian polyphonic versaria, as it was supposed.The special oriscus carries some specific functions in the polyphonic versaria. Basically, these functions are related to the ornamentation of an interval between the voices and the process of the voice alignment. Therefore, we conclude that the Aquitanian notation, by integrating the special oriscus and conferring on it some specific functions, adapts itself adequately to the needs of the polyphonic language which was developed by the florid Aquitanian discantus in the late XIth and the early XIIth centuries.

L'évaluation et la notation des élèves font l'objet de débats actuels dans la communauté éducative (Rey & Feyfant, 2014). Les situations d’évaluation à l’école créent une « pression évaluative » et plusieurs ouvrages rapportent la tension et la peur que les élèves subissent. Les recherches sur le stress scolaire montrent que la détresse concernant les situations évaluatives est vue comme la première cause de l’anxiété et du stress à l’école. Outre les multiples problèmes de santé physique et mentale, ce stress peut produire un impact négatif sur les résultats scolaires.La question principale de notre recherche est : Est-ce que l’évaluation et la notation sont une source de stress chez les élèves et, si oui, perturbe-t-elle leur performance lors de la restitution des connaissances ? Nous avons conduit deux études expérimentales avec 126 élèves de collège en situation scolaire réelle, en faisant appel à des méthodes de la psychologie expérimentale et des neurosciences. Les résultats des deux expériences révèlent que lorsque les élèves de cette âge (11-12 ans) sont notés, ils subissent un stress important. Bien que ce stress n’altère pas la performance de façon majeure, il induit de moindres performances pour les objets les plus difficiles à catégoriser. Quand le temps de réponse est limité, les filles sont plus stressées par la notation que les garçons qui sont très stressés par le temps limité de réponse.Ces résultats posent une vraie question sur les finalités d’une évaluation des connaissances des élèves et jettent le doute sur ce qui est vraiment évalué : les connaissances acquises, ou les capacités des élèves à gérer le stress ? / The discussions on evaluation at school have been topical in the educational and academic community (Rey & Feyfant, 2014). Evaluating settings create a « test results pressure » and many studies report a constant fear which student feel in relation to such a pressure. Previous research reveals that assessments situations are the major source of school anxiety and stress in most western countries. Besides the important health and mental problem, ce stress may produce a negative effect on school results. The research question we try to find the answer is: if evaluations and assessments are a source of stress in young scholar students and if yes, in what way do they interfere with cognitive performance in situations of knowledge restitution.We conducted an experimental study in a real school context (n=126 students). We used the methodology and procedures of experimental psychology and neurosciences. The results of both experiments show that assessment situations are very stressful for the students of this age (11-12 y.o.). Even if the general performance was not much altered by the stress, the number of correct answers on very difficult pictures was inferior under stress. The girls were more stressed by the evaluating context, the boys were more affected by response time constraints. These results raise doubts as to whether an assessment context allows young school children to fully access to their personal resources and to show their real performance. One can doubt what is exactly assessed during evaluation: the true level of acquisition of school knowledge by students or, rather, their capacity to cope with stress induced by the evaluative pressure to perform well.

Abstract not available

Dans le cadre de cette thèse nous avons étudie l'implantation des algorithmes de l'arithmétique en ligne. En particulier, la réalisation de deux circuits destines aux applications exigeant une précision infinie est exposée. En effet, dans de nombreux domaines tels que la génération de nombres aléatoires, cryptographie, calcul formel, arithmétique exacte, réduction de fraction en précision infinie, calcul modulaire, traitement d'images..., les opérateurs classiques manquent d'efficacité. Face a ce type de problèmes, un remède peut être apporte par le calcul en ligne selon lequel les calculs sont faits en introduisant les opérandes en série chiffre a chiffre en notation redondante. Nous obtenons ainsi un haut degré de parallélisme et une précision variable linéairement. Le premier circuit présenté implante un algorithme de pgcd nomme Euclide offrant, d'après les simulations, le meilleur compromis cout matériel/performance. Il donne également les coefficients de Bezout. Ce circuit est appelé a résoudre les problèmes lies au temps de calcul du pgcd par les méthodes classiques rencontrées dans beaucoup d'applications. Une deuxième application montre la possibilité de fusionner des opérateurs en ligne afin d'obtenir un opérateur complexe. L'exemple traite dans cette thèse est celui de la distance euclidienne: z=x#2+y#2 utilisée, entre autres, pour la resolution du moindre carre des systèmes linéaires

Thesis (M.Mus.)--North-West University, Potchefstroom Campus, 2007.