Educators strive to improve student learning outcomes and there are numerous theories suggesting how this is best achieved. However, application of these theories to the coal face of a classroom is often fraught with obstacles resulting in poor outcomes. Constraints imposed by educational policy, school systems, structures and the individual students themselves, realistically require adaptation of theoretical techniques if genuine learning is to be imparted to students. This paper discusses some of the issues surrounding the practical implementation of new methodologies into the classroom and identifies important factors that affect teenagers in their learning of mathematics. Working within the constraints, constantly confronted with obstacles, can be frustrating and demoralising. This paper reflects on twenty years of classroom teaching of mathematics to students with relatively poor socio-economic backgrounds and the lessons learnt from them that may assist teachers to remain enthusiastic and creative with the energy to truly improve mathematics education. Key issues explored in the paper include: ‘Realities of a teacher’s working day’, ‘The learning of mathematics within a government secondary system’, and ‘What can be done to ensure mathematical learning takes place?’

Text in English, with abstracts and keywords in English, Afrikaans and isiZulu / South Africa has been known to have the highest rate of gender-based violence globally. This qualitative study locates gender-based violence using the interpretive phenomenological paradigm and multicultural feminism as both allowed participants’ to be given a voice. This study thus enabled women who have been abused to discuss their perception of their own experiences. The primary aim of the study is orientated towards an increased understanding of the possible barriers that prevent women from leaving their abusers. The main findings point out how victim manipulation, financial abuse, isolation and responses by social and legal services serve as barriers to the women leaving their abusive partners. The secondary aim contributes to an understanding of the risk factors influencing gender-based violence. Furthermore, the study explores the impact of prolonged abuse on the participants. The criteria used for the selection were women with diverse backgrounds from the Inanda district, who have lived in abusive relationships for two years or longer. Eight participants completed the research process and were selected using the purposive sampling method. Significantly, this study provides an insight into the reality of how women process and give meanings to their experiences of abuse. Hence, the research sought to inform the literature and the greater community on the lived experiences of women in abusive relationships. / Suid-Afrika het wêreldwyd die hoogste persentasie van geslagsgebaseerde geweld. Hierdie kwalitatiewe studie plaas geslagsgebaseerde geweld met behulp van die interpretatiewe fenomenologiese paradigma en multikulturele feminisme, aangesien albei die deelnemers 'n stem laat kry. Hierdie studie het dus vroue wat mishandel is, in staat gestel om hul persepsie van hul eie ervarings te bespreek. Die primêre doel van die studie is gerig op 'n groter begrip van die moontlike hindernisse wat vroue verhoed om hul misbruik te verlaat. Die belangrikste bevindings wys daarop hoe manipulasie van slagoffer, finansiële mishandeling, isolasie en reaksies deur maatskaplike en regsdienste dien as hindernisse vir die verlaat van hul vrouens met hul maat. Die sekondêre doel dra by tot die begrip van die risikofaktore wat geslagsgebaseerde geweld beïnvloed. Verder ondersoek die studie die impak van langdurige mishandeling op die deelnemers. Die kriteria wat gebruik is vir die keuring was vroue met verskillende agtergronde uit die distrik Inanda, wat al twee jaar of langer in beledigende verhoudings leef. Agt deelnemers het die navorsingsproses voltooi en is met behulp van die doelgerigte steekproefmetode gekies. Hierdie studie bied 'n insig in die werklikheid van hoe vroue hul ervarings van mishandeling verwerk en betekenisse gee. Daarom het die navorsing probeer om die literatuur en die groter gemeenskap in te lig oor die ervarings van vroue in beledigende verhoudings. / Iningizimu Afrika yaziwa ukuthi inesilinganiso esiphakeme kunazo zonke sodlame olususelwa ebulilini emhlabeni jikelele. Lolu cwaningo lwekhwalithi lubheka udlame olususelwa ebulilini kusetshenziswa ukuhumusha okuyi-phenographical paradigm kanye nobungqingili bezamasiko njengoba bobabili abahlanganyeli bavunyelwe ukuba banikezwe izwi. Lolu cwaningo lwenze ukuthi abesifazane abahlukunyeziwe bakhulume ngokubona kwabo ngokwenzeka kwabo. Inhloso yokuqala yocwaningo isekelwe ekuqondeni okwandayo kwemigoqo engahle ivimbele abesifazane ukuba bashiye abahlukumezi babo. Okutholakele okukhulu kuveza ukuthi ukuxhaphaza izisulu, ukuhlukunyezwa ngokwezimali, ukwahlukaniswa nezimpendulo ngezinsizakalo zezenhlalo nezomthetho kusebenza njengezithiyo kwabesifazane beshiya abalingani babo abahlukumezayo. Inhloso yesibili inomthelela ekuqondeni kwezimpawu zobungozi ezinomthelela udlame olususelwa ebulilini. Ngaphezu kwalokho, lolu cwaningo lubheka umthelela wokuhlukunyezwa isikhathi eside kwabahlanganyeli. Abangu-8 ababambe iqhaza baphothula inqubo yokucwaninga futhi bakhethwa besebenzisa indlela enamasampula enenjongo. Okusemqoka ukuthi lolu cwaningo luhlinzeka ngokuqonda kweqiniso lokuthi abesifazane basebenza kanjani futhi banikeze izincazelo kulokho kwabo okuhlukumezeka. Ngakho-ke, lolu cwaningo lufune ukwazisa izincwadi kanye nomphakathi omkhulu ngokuhlangenwe nakho kokuphila kwabesifazane ebudlelwaneni bokuhlukumeza. / Psychology / M.A. (Psychology)

Die Stixel-Welt ist eine neuartige und vielseitig einsetzbare Zwischenrepräsentation zur effizienten Beschreibung dreidimensionaler Szenen. Heutige stereobasierte Sehsysteme ermöglichen die Bestimmung einer Tiefenmessung für nahezu jeden Bildpunkt in Echtzeit. Das erlaubt zum einen die Anwendung neuer leistungsfähiger Algorithmen, doch gleichzeitig steigt die zu verarbeitende Datenmenge und der dadurch notwendig werdende Aufwand massiv an. Gerade im Hinblick auf die limitierte Rechenleistung jener Systeme, wie sie in der videobasierten Fahrerassistenz zum Einsatz kommen, ist dies eine große Herausforderung. Um dieses Problem zu lösen, bietet die Stixel-Welt eine generische Abstraktion der Rohdaten des Sensors. Jeder Stixel repräsentiert individuell einen Teil eines Objektes im Raum und segmentiert so die Umgebung in Freiraum und Objekte. Die Arbeit stellt die notwendigen Verfahren vor, um die Stixel-Welt mittels dynamischer Programmierung in einem einzigen globalen Optimierungsschritt in Echtzeit zu extrahieren. Dieser Prozess wird durch eine Vielzahl unterschiedlicher Annahmen über unsere von Menschenhand geschaffene Umgebung gestützt. Darauf aufbauend wird ein Kalmanfilter-basiertes Verfahren zur präzisen Bewegungsschätzung anderer Objekte vorgestellt. Die Arbeit stellt umfangreiche Bewertungen der zu erwartenden Leistungsfähigkeit aller vorgestellten Verfahren an. Dafür kommen sowohl vergleichende Ansätze als auch diverse Referenzsensoren, wie beispielsweise LIDAR, RADAR oder hochpräzise Inertialmesssysteme, zur Anwendung. Die Stixel-Welt ist eine extrem kompakte Abstraktion der dreidimensionalen Umgebung und bietet gleichzeitig einfachsten Zugriff auf alle essentiellen Informationen der Szene. Infolge dieser Arbeit war es möglich, die Effizienz vieler auf der Stixel-Welt aufbauender Algorithmen deutlich zu verbessern. / The Stixel World is a novel and versatile medium-level representation to efficiently bridge the gap between pixel-based processing and high-level vision. Modern stereo matching schemes allow to obtain a depth measurement for almost every pixel of an image in real-time, thus allowing the application of new and powerful algorithms. However, it also results in a large amount of measurement data that has to be processed and evaluated. With respect to vision-based driver assistance, these algorithms are executed on highly integrated low-power processing units that leave no room for algorithms with an intense calculation effort. At the same time, the growing number of independently executed vision tasks asks for new concepts to manage the resulting system complexity. These challenges are tackled by introducing a pre-processing step to extract all required information in advance. Each Stixel approximates a part of an object along with its distance and height. The Stixel World is computed in a single unified optimization scheme. Strong use is made of physically motivated a priori knowledge about our man-made three-dimensional environment. Relying on dynamic programming guarantees to extract the globally optimal segmentation for the entire scenario. Kalman filtering techniques are used to precisely estimate the motion state of all tracked objects. Particular emphasis is put on a thorough performance evaluation. Different comparative strategies are followed which include LIDAR, RADAR, and IMU reference sensors, manually created ground truth data, and real-world tests. Altogether, the Stixel World is ideally suited to serve as the basic building block for today''s increasingly complex vision systems. It is an extremely compact abstraction of the actual world giving access to the most essential information about the current scenario. Thanks to this thesis, the efficiency of subsequently executed vision algorithms and applications has improved significantly.