This research investigates the education of entrepreneurship to learners with learning difficulties. It is important to keep in mind the rights and possibilities of a learner with learning difficulties. Two entrepreneurship programmes were presented to two different groups of learners at Oom Paul School. Learners with learning disabilities can be categorised as poor performers, learners with behavioural and emotional problems, development problems (for example a language deficit), as well as learners with permanent disabilities- physically, intellectual and sensorial. An important part of this research will focus on the discussion on the causes of learning difficulties and problems of learners. One of the most important aims in education, especially in teaching learners with learning difficulties, is to guide learners to become a part of adulthood and the business world as a responsible and active member of society. Unfortunately, there are many learners who- after a successful school career seems to get "lost" along the way, because of society's discrimination. Several entrepreneurial programmes have been developed and have been implemented with great success at various schools, with reference in particular to the programmes "Business Ventures" and "Entrepreneurskap: jou eie besigheid". Above mentioned programmes are developed for main stream education and are not necessarily suitable for learners with learning difficulties. According to literary studies on education on entrepreneurship, this study field is relatively new in RSA and that no research regarding entrepreneurship education for learners with learning difficulties has been done. This research has pointed out that the teaching and education of entrepreneurship to learners with learning difficulties can be successful with a few adjustments. The new outcomes-based curriculum for general education and training for further education is Curriculum 2005. This curriculum is learner centred and is beneficiary for the learner with disabilities and difficulties. The principles of outcomes-based curriculum (Curriculum 2005) contribute to the accommodation of all learners in their diversity and needs. The society is looking forward to the implementation of this new curriculum, due to the fact that discrimination against learners with learning disabilities/difficulties will no longer be part of our education. Awareness of entrepreneurship and teaching of entrepreneurship is part of the eight learning areas and also one of the critical outcomes of Curriculum 2005. Entrepreneurial awareness can offer a meaningful contribution to solve an essential problem in the RSA. / Thesis (M.Ed.)--Potchefstroom University for Christian Higher Education, 2000

We consider the broad framework of supervised learning, where one gets examples of objects together with some labels (such as tissue samples labeled as cancerous or non-cancerous, or images of handwritten digits labeled with the correct digit in 0-9), and the goal is to learn a prediction model which given a new object, makes an accurate prediction. The notion of accuracy depends on the learning problem under study and is measured by a performance measure of interest. A supervised learning algorithm is said to be 'statistically consistent' if it returns an `optimal' prediction model with respect to the desired performance measure in the limit of infinite data. Statistical consistency is a fundamental notion in supervised machine learning, and therefore the design of consistent algorithms for various learning problems is an important question. While this has been well studied for simple binary classification problems and some other specific learning problems, the question of consistent algorithms for general multiclass learning problems remains open. We investigate several aspects of this question as detailed below. First, we develop an understanding of consistency for multiclass performance measures defined by a general loss matrix, for which convex surrogate risk minimization algorithms are widely used. Consistency of such algorithms hinges on the notion of 'calibration' of the surrogate loss with respect to target loss matrix; we start by developing a general understanding of this notion, and give both necessary conditions and sufficient conditions for a surrogate loss to be calibrated with respect to a target loss matrix. We then define a fundamental quantity associated with any loss matrix, which we term the `convex calibration dimension' of the loss matrix; this gives one measure of the intrinsic difficulty of designing convex calibrated surrogates for a given loss matrix. We derive lower bounds on the convex calibration dimension which leads to several new results on non-existence of convex calibrated surrogates for various losses. For example, our results improve on recent results on the non-existence of low dimensional convex calibrated surrogates for various subset ranking losses like the pairwise disagreement (PD) and mean average precision (MAP) losses. We also upper bound the convex calibration dimension of a loss matrix by its rank, by constructing an explicit, generic, least squares type convex calibrated surrogate, such that the dimension of the surrogate is at most the (linear algebraic) rank of the loss matrix. This yields low-dimensional convex calibrated surrogates - and therefore consistent learning algorithms - for a variety of structured prediction problems for which the associated loss is of low rank, including for example the precision @ k and expected rank utility (ERU) losses used in subset ranking problems. For settings where achieving exact consistency is computationally difficult, as is the case with the PD and MAP losses in subset ranking, we also show how to extend these surrogates to give algorithms satisfying weaker notions of consistency, including both consistency over restricted sets of probability distributions, and an approximate form of consistency over the full probability space. Second, we consider the practically important problem of hierarchical classification, where the labels to be predicted are organized in a tree hierarchy. We design a new family of convex calibrated surrogate losses for the associated tree-distance loss; these surrogates are better than the generic least squares surrogate in terms of easier optimization and representation of the solution, and some surrogates in the family also operate on a significantly lower dimensional space than the rank of the tree-distance loss matrix. These surrogates, which we term the `cascade' family of surrogates, rely crucially on a new understanding we develop for the problem of multiclass classification with an abstain option, for which we construct new convex calibrated surrogates that are of independent interest by themselves. The resulting hierarchical classification algorithms outperform the current state-of-the-art in terms of both accuracy and running time. Finally, we go beyond loss-based multiclass performance measures, and consider multiclass learning problems with more complex performance measures that are nonlinear functions of the confusion matrix and that cannot be expressed using loss matrices; these include for example the multiclass G-mean measure used in class imbalance settings and the micro F1 measure used often in information retrieval applications. We take an optimization viewpoint for such settings, and give a Frank-Wolfe type algorithm that is provably consistent for any complex performance measure that is a convex function of the entries of the confusion matrix (this includes the G-mean, but not the micro F1). The resulting algorithms outperform the state-of-the-art SVMPerf algorithm in terms of both accuracy and running time. In conclusion, in this thesis, we have developed a deep understanding and fundamental results in the theory of supervised multiclass learning. These insights have allowed us to develop computationally efficient and statistically consistent algorithms for a variety of multiclass learning problems of practical interest, in many cases significantly outperforming the state-of-the-art algorithms for these problems.

The aim of this study was to investigate the experiences of mothers of primary school learners diagnosed with attention deficit hyperactivity disorder (ADHD). The main determinant of parenting stress was contained in the primary symptoms of ADHD, namely, attention deficit, hyperactivity and impulsive behaviour, as well as in the disruptive effects on others in the immediate environment. The three primary symptoms of ADHD as listed above, often result in such secondary problems as learning deficiencies, poor self-image and inadequate social relations. Seven mothers of learners with ADHD were selected to participate in the empirical investigation. A qualitative research model was employed with specific use of a list of questions, participatory perception and unstructured interviews. Results obtained from the empirical research indicated that the symptoms of ADHD as manifested by the learners, as well as the accompanying secondary problems, impacted negatively on the mothers of these learners. / Educational Studies / M. Ed. (Skoolvoorligting)

Reading is one of the most important skills (although a complex cognitive activity) a learner has to master during the early years of schooling. The reading process involves elements of a learner’s psychological, physical, linguistic, cognitive, emotional and social worlds. Despite the fact that all learners have to be able to read, there is an increasing awareness among professionals of the developmental and educational implications of reading difficulties with school-going learners world wide. Reading is a critical tool for the mastery of all other subjects a learner will meet and one of the best predictors of long-term learning achievement. Therefore, the need for support must be considered a priority area. After a thorough investigation and literary study, it is evident that the effective identification of learning difficulties needs a thorough understanding. Educators must realise that a given learner, who responds favourably to one instructional system, may respond very unfavourably to another, because learners are all unique individuals. To be able to combine speech sounds in a way that recipients can understand the message, learners have to be ready to develop an understanding of phonology, morphology and syntax, therefore maturation must always precede learning and, in the context of this study, emergent literacy must precede reading. Maturation is characterised by a fixed order of progression wherein the pace may vary, but not the sequence. The creative use of language is entirely dependent on the ability to assemble simple building blocks of sound into the complex structure we call sentences.It is widely accepted that music may be used to promote language development and the most crucial aspect in both music and language development is the perception of sound and the core in music and language are the ability to listen. The aim of this study was to investigate the use of music and related activities as part of an intervention strategy to improve reading skills, such as phonics, of learners who have reading difficulties. The researcher proved that a wellplanned intervention method and learning strategy through music activities may be used to develop the reading skills in learners who have reading difficulties. / Educational Studies / D. Ed. (Inclusive Education)

This study was prompted by serious problems regarding specific teaching and learning problems in calculus at the technikon. The general aims were to identify and analyze particular teaching and learning problems relating to 2nd level engineering courses in calculus and to recommend improvements which could increase student performance in engineering calculus courses. An extensive study revealed world wide concern in calculus reform. The empirical research instruments consisted of structured questionnaires given to staff and students from nine technikons plus interviews. Five serious problem areas were identified: student ability in mathematics, content difficulty, background difficulties, timetable pressures and lecturer's presentation. The impact of training technology on calculus was investigated. Recommendations were that routine exercises can be done on computer with extra tutorial time for computer laboratory projects. Background recommendations suggested that schools give more time to trigonometry and coordinate geometry and that bridging courses at technikons for weaker students be developed. / Curriculum and Instructional Studies / M. Ed. (Didactics)

The influx of Black pupils seeking admission to Indian schools began in 1990 after the Democratic Movement's "all schools for all people" campaign was announced. The medium of instruction in Indian schools is English which is also the mother tongue. Therefore Black pupils who come on transfer from schools in the KwaZulu township are immediately faced with a language problem as they are taught in the mother tongue untii standard three, when they switch to English. This research project arose as a result of the researcher's experience with Black pupils, whom he - felt were severely linguistically underprepared for academic study in the senior primary phase. Furthermore, most present day teachers were trained for monocultural schools and have little or no experience of multicultural education. The main problem that this research focuses on includes the learning problems encountered by Black pupils in Indian primary schools and the concomitant teaching problems their teachers experience. / Educational Studies / M. Ed. (Didactics)

The problem of feature selection is critical in several areas of machine learning and data analysis such as, for example, cancer classification using gene expression data, text categorization, etc. In this work, we consider feature selection for supervised learning problems, where one wishes to select a small set of features that facilitate learning a good prediction model in the reduced feature space. Our interest is primarily in filter methods that select features independently of the learning algorithm to be used and are generally faster to implement compared to other types of feature selection algorithms. Many common filter methods for feature selection make use of information-theoretic criteria such as those based on mutual information to guide their search process. However, even in simple binary classification problems, mutual information based methods do not always select the best set of features in terms of the Bayes error. In this thesis, we develop a general approach for selecting a set of features that directly aims to minimize the Bayes error in the reduced feature space with respect to the loss or performance measure of interest. We show that the mutual information based criterion is a special case of our setting when the loss function of interest is the logarithmic loss for class probability estimation. We give a greedy forward algorithm for approximately optimizing this criterion and demonstrate its application to several supervised learning problems including binary classification (with 0-1 error, cost-sensitive error, and F-measure), binary class probability estimation (with logarithmic loss), bipartite ranking (with pairwise disagreement loss), and multiclass classification (with multiclass 0-1 error). Our experiments suggest that the proposed approach is competitive with several state-of-the art methods.

In hierdie studie word die etiologiese verband tussen verstadigde neurologiese integrasie en latere leerproblematiek by kinders met klinies betekenisvolle neonatale bilirubienmetings ondersoek. Resente navorsing dui aan dat kinders met klinies betekenisvolle bilirubienmetings tydens die neonatale fase ‘n groter risiko loop om later verstadigde neurologiese integrasie te vertoon, veral weens die kwesbaarheid van die neonatale brein vir toksiene. Hierdie navorsingsresultate suggereer ‘n verband tussen klinies betekenisvolle neonatale bilirubienmetings en latere leerproblematiek, aangesien spesifieke breinareas wat deur neonatale bilirubien aangetas word ook vaardighede medieer wat belangrik is vir prestasie in sekere leerareas, te wete lees, skryf en reken. Neonatale fisiologiese geelsug is nie altyd met die blote oog sigbaar nie, en derhalwe word simptome soos oormatige slaperigheid en ingekorte behoefte aan voeding dikwels deur onervare moeders geïgnoreer, omdat die baba nie opmerklik “geel” is nie. Verder word neonatale fisiologiese geelsug nie altyd as sodanig gediagnoseer nie, weens verskeie faktore soos ontoereikende primêre gesondheidsorgdienste op die afgeleë platteland, tuisgeboortes en vroeë ontslag van moeders en babas uit klinieke en hospitale, veral gesien in die lig daarvan dat neonatale geelsug piekvlak tussen dag drie en dag sewe bereik. Bilirubienmeting is nie standaard prosedure by afgeleë klinieke nie, en waar ‘n rowwe skatting deur die klinieksuster op ‘n klinies betekenisvolle bilirubientelling dui, word moeders dan dikwels aangeraai om natuurlike fototerapie (sonlig) toe te pas. Verdermeer vind opvolgkonsultasies by ‘n klinieksuster dikwels eers plaas nadat die baba ongeveer een maand oud is, en voorligting aan die moeder rakende moontlike kwesbaarhede wat verband hou met klinies betekenisvolle neonatale bilirubienmetings is gebrekkig. Sodanige ouers kan dus heeltemal onbewus wees van die potensiële skade wat aangerig kan word aan die ontwikkelende brein, en intervensie vind gevolglik nie tydig plaas nie. Betekenisvolle duidinge wat uit hierdie navorsingsprojek mag voortvloei, kan derhalwe benut word ten einde spesifieke kwesbaarhede in kinders met klinies betekenisvolle neonatale bilirubienmetings tydig te kan identifiseer; en hoë-risiko leerders se moontlike latere leerproblematiek deur tydige intervensie tydens die voorskoolse jare te ondervang, voordat pobleme in die grondslagfase manifesteer. ‘n Empiriese ondersoek is uitgevoer waarby 37 deelnemers betrek is. Gebaseer op die resultate van die data-analise en interpretasie van die resultate word die hipotese aanvaar. Relevante aanbevelings met betrekking to praktykverbetering en verdere navorsing word gemaak. ENGLISH: With this study the etiological link between delayed neurological integration, high neonatal bilirubin measures and learning difficulties were investigated. Recent research findings suggest that children with high neonatal bilirubin measures are at a greater risk for delayed neurological integration later on, especially because of the susceptibility of the neonatal brain for toxins. The results of this research project suggest an etiological link between neonatal hyperbilirubinemia and learning difficulties at a later stage, since specific brain-areas which are affected by the bilirubin do mediate skills important for performance in certain learning areas, e.g. reading, writing and arithmetic. It is not always possible to notice neonatal physiological jaundice; hence, inexperienced mothers tend to ignore symptoms like sleepiness and lack of appetite, merely because their babies do not appear “yellowish”. Neonatal physiological jaundice is often misdiagnosed due to various factors like inadequate primary health care services in rural areas, home births and early discharge from hospitals - particularly in light of the fact that jaundice peaks between day three and day seven after birth. Measurement of neonatal bilirubin levels is not a standard procedure at rural clinics, and mothers are often advised to make use of natural phototherapy (sunlight) when the baby appears “yellowish”. Follow-up consultation often occurs when the baby is already one month old; hence mothers often receive inadequate information concerning neonatal hyperbilirubinemia. Parents might therefore be totally unaware of the potential vulnerability and harm to the developing brain, and intervention often does not take place. Significant indicators of this research project can be used to identify well in advance specific vulnerabilities in learners with neonatal hyperbilirubinemia, as well as potentially high-risk learners during the pre-school years, before such vulnerabilities escalate during the foundation phase. An empirical study with 37 participants was conducted. Based on the data analyses and interpretation of the results, the hypothesis was accepted. Relevant recommendations concerning best practice and further research were done. / Thesis (PhD)--University of Pretoria, 2008. / Educational Psychology / unrestricted

There are numerous problems associated with the teaching of Euclidean geometry at secondary schools today. Students do not see the necessity of proving results which have been obtained intuitively. They do not comprehend that the validity of a deduction is independent of the 'truth' of the initial assumptions. They do not realise that they cannot reason from diagrams, because these may be misleading or inaccurate. Most importantly, they do not understand that Euclidean geometry is a particular interpretation of physical space and that there are alternative, equally valid interpretations. A possible means of addressing the above problems is tbe introduction of nonEuclidean geometry at school level. It is imperative to identify those students who have the pre-requisite knowledge and skills. A number of interesting teaching strategies, such as debates, discussions, investigations, and oral and written presentations, can be used to introduce and develop the content matter. / Mathematics Education / M. Sc. (Mathematics)

Le programme -Une école adaptée à tous ses élèves-, qui s'inscrit dans la réforme actuelle de l'éducation au Québec, nous a amenée à nous intéresser aux représentations dans les grandeurs en mesure en mathématiques des élèves en difficulté d'apprentissage. Nous nous sommes proposés de reconduire plusieurs paramètres de la recherche de Brousseau (1987, 1992) auprès de cette clientèle. La théorie des champs conceptuels (TCC) de Vergnaud (1991), appliquée aux structures additives, a été particulièrement utile pour l'analyse et l'interprétation de leurs représentations. Comme méthode de recherche, nous avons utilisé la théorie des situations didactiques en mathématiques (TSDM), réseau de concepts et de méthode de recherche appuyé sur l'ingénierie didactique qui permet une meilleure compréhension de l'articulation des contenus à enseigner. Grâce à la TSDM, nous avons observé les approches didactiques des enseignants avec leurs élèves. Notre recherche est de type exploratoire et qualitatif et les données recueillies auprès de 26 élèves de deux classes spéciales du deuxième cycle du primaire ont été traitées selon une méthode d'analyse de contenu. Deux conduites ont été adoptées par les élèves. La première, de type procédural a été utilisée par presque tous les élèves. Elle consiste à utiliser des systèmes de comptage plus ou moins sophistiqués, de la planification aux suites d'actions. La deuxième consiste à récupérer directement en mémoire à long terme le résultat associé à un couple donné et au contrôle de son exécution. L'observation des conduites révèle que les erreurs sont dues à une rupture du sens. Ainsi, les difficultés d'ordre conceptuel et de symbolisation nous sont apparues plus importantes lorsque l'activité d'échange demandait la compétence "utilisation" et renvoyait à la compréhension de la tâche, soit les tâches dans lesquelles ils doivent eux-mêmes découvrir les rapports entre les variables à travailler et à simuler les actions décrites dans les énoncés. En conséquence, les problèmes d'échanges se sont révélés difficiles à modéliser en actes et significativement plus ardus que les autres. L'étude des interactions enseignants et élèves a démontré que la parole a été presque uniquement le fait des enseignants qui ont utilisé l'approche du contrôle des actes ou du sens ou les deux stratégies pour aider des élèves en difficulté. Selon le type de situation à résoudre dans ces activités de mesurage de longueur et de masse, des mobilisations plurielles ont été mises en oeuvre par les élèves, telles que la manipulation d'un ou des étalon(s) par superposition, par reports successifs, par pliage ou par coupure lorsque l'étalon dépassait; par retrait ou ajout d'un peu de sable afin de stabiliser les plateaux. Nous avons également observé que bien que certains élèves aient utilisé leurs doigts pour se donner une perception globale extériorisée des quantités, plusieurs ont employé des procédures très diverses au cours de ces mêmes séances. Les résultats présentés étayent l'hypothèse selon laquelle les concepts de grandeur et de mesure prennent du sens à travers des situations problèmes liées à des situations vécues par les élèves, comme les comparaisons directes. Eles renforcent et relient les grandeurs, leurs propriétés et les connaissances numériques. / -An education system adjusted to all its pupils-, in line with the present reform of the education system of Québec has led us in this project, to examine how students with learning problems deal with numbers and measurements in mathematics. In the present study, our purpose is to double-check many of the parameters defined in the work of Brousseau (1987, 1992). The theory of the conceptual fields of Vergnaud (1991)applied to the additives structures, was particularly useful in our analysis of the facts and the interpretation of their representations. In this work, the methodology we adopted is the Didactic engineering, wich allow a better understanding in articulating the contents to each. Using Theory of didactic situations in mathematics, we examined the didactic approaches the teachers have in their relationship with their students. The data for our study, which is of the exploratory and qualitative type, was collected with twenty six students of the second cycle of the primary school. That data was analysed in conformity with a medthodology of content analysis. The examination of the student's behavior revealed two attitudes. Almost all the students used the first attitude, which is of the procedural type. It consisted in using counting systems more or less sophisticated from the planning to the folowing actions involved. The second attitude implied memorizing for the long term, the result associated with a specific couple of actions and the control of their execution. The observaton of the student's attitudes reveals that the errors they made are related to a semantic disruption in their interpretation of the varied tips and strategies the teachers tried to help them with to solve the different problems. Thus, it appeared to us that the difficulties at the conceptual and symbolization levels were more important when the exchange activity involved their competence to evaluate and activity related to the understanding to the task to achieve. In other terms, they had more difficulty with the tasks where they had to establish by themselves to link between the variables, and simulate the actions involved by those tasks. Consequently, the tasks involving exchange operations happened to be more difficult to translate into actions, and were clearly more problematic than the other tasks. The study of the interaction between teachers and students revealed that only teachers used words in the process, where they used the approach of the control of the actions, or the approach of control of the meaning or both strategies to help students with problems. Depending on the type of problem encountered during these activities of measurements of length and masses, the students had recourse to numerous experiments such as manipulation of the standard measure(s). They proceeded by superimposing, by successive deferments, by folding, by cutting when the standard was exceeding in size; or by reduction or addition of some amount of sand to bring into balance the scale. We noticed also that despite the fact that certain students used their fingers to have a global idea of the external measures of the quantities, many of those same students had recourse to a diversity of other procedures during the same test. The result presented here support the hypothesis that says that the concepts of size and measurement get more meaning in a specific context, where they relate to real situations lived by the students, as well as by direct comparisons. They reinforce and establish links between the so-called sizes, their properties and the numeric knowledge.