This investigative study was undertaken against the background of the recent calls for back to basics by the Schooling 2025 initiative, as well as to address the 2000 and 2009 Review Committees’ reports on the training and development of teachers and on the variable quality of learning support materials. The act of systemic transformation has led to two curriculum revisions taking place within the South African education sector and has inevitably culminated in the identification of shortcomings in teacher development and learning materials. This study has positioned itself to address these shortcomings at pre-service level through the preparation of Mathematics student teachers as prospective Mathematics teachers. In addressing the issue of inadequate training, the focus of the study was not only on cognition, but also on how affect could influence the learning of Mathematics so as to ensure a more encompassing approach in understanding how student teachers learn and do Mathematics. Integrated research on affect and cognition could lead to optimal performance in the teaching and learning of Mathematics and researchers in mathematics education need to acknowledge the role and impact of the affective domain and integrate it into studies of cognition. If learners are going to become competent learners of Mathematics, their affective responses to Mathematics are going to be much more intense than if they are merely expected to achieve satisfactory levels of performance in low-order mathematical skills. In the studies on mathematics cognition, the focus of mathematical competencies is on abilities and capabilities while, in the affective domain, competencies in mathematics are more than the abilities to perform observable tasks. Rather, the focus of the affective competencies lies in the direction, the degree and the levels of intensities of affect constructs (or their variables) that will define mathematical competencies within the affective domain. Evidentiary (qualitative) data from this study supported the contention that affect does influence the learning of mathematics since there were distinct patterns in the overall expressions of participants towards this aspect of the research. The acknowledgment of the concerns of student teachers during field practicum could possibly help in ameliorating these concerns through the identification of what student teachers were mostly concerned about when teaching Mathematics and how, by addressing these concerns, could help improve their teaching skills and abilities. Based on the quantitative evidence, the three subscales of self, task and impact used in the Student Concerns Questionnaire (SCQ) were modified on the basis of factor analysis to a two-factor model (concerns about self-benefit and concerns about learner-benefit). Some of the statistical results were integrated with the narrative data to provide substantive support for the expressions of student teachers. No classical trends, as noted in the concerns theory, could be detected in this study. It was statistically inferred that a majority of Mathematics student teachers who participated in this study were moderately concerned about most of the concerns statements noted in each of the items on the SCQ. In addressing the variable quality of the learning material the study focused on the development and the use of social context learning packages. The utilisation of these learning packages (in an intervention strategy) was aimed at strengthening social context knowledge and education, and explored its role in the translation (if any) of student teacher concerns within a hierarchical spectrum. The evidence on how student teachers perceived the use of these learning packages was recorded during the interviews. Analyses of the verbal data revealed that the participating student teachers agreed with the use of social context learning packages as part of their Mathematics lessons. In sum, the need to prepare effective Mathematics teachers and raise the academic calibre of prospective Mathematics teachers was fundamental to the overall design of this study. It is trusted that curriculum planners and designers will consider the recommendations of this study to address the so-called inadequacies within the education system of South Africa. / Thesis (PhD (Mathematics Education))--North-West University, Potchefstroom Campus, 2013

Die Mobilität von Personen und Gütern, insbesondere in Städten, ist der Motor einer Volkswirtschaft. Dieser Motor kommt jedoch ins Stottern, wenn Staubildung im Stadtstraßennetzwerk einsetzt. Eine unvermeidbare Ursache von Staubildung stellen Verkehrsstörfälle dar, die schlimmstenfalls zu Gridlocks führen können. In der Folge werden hohe Kosten für Verkehr, Wirtschaft und Umwelt verursacht. Mit welchen Gegenmaßnahmen kann die Staubildung im Netzwerk effektiv bewältigt werden? Wie können entsprechende Gegenmaßnahmen realistisch noch vor einem praktischen Einsatz bewertet werden? Ausgehend von diesen Fragestellungen, widmet sich diese Dissertation der Entwicklung eines ereignisorientierten Routenwahlmodells für den Stadtstraßenverkehr und eines selbstorganisierten Störfallmanagements als Gegenmaßnahme zur Reduzierung negativer Auswirkungen der Staubildung. Zur Modellierung des Routenwahlverhaltens in ereignisreichen Stadtstraßennetzen wird das ereignisorientierte Routenwahlmodell entwickelt. Der Ausgangspunkt des Modells ist die diskrete Wahltheorie. Entscheidungsprozesse einzelner Autofahrer werden vor und während der Fahrt direkt simuliert. Der Entscheidungsprozess ist dabei maßgeblich von Beobachtungen lokaler Verkehrsbedingungen geprägt. Somit wird nachgebildet, dass Autofahrer flexibel auf unvorhergesehene Ereignisse durch Routenwechsel reagieren können. Auf diese Weise ist eine realistische Simulation des Routenwahlverhaltens von Autofahrern in der Stadt möglich. Das ereignisorientierte Routenwahlmodell ist zudem generisch formuliert. Es lässt sich zur Bewertung von Gegenmaßnahmen für störfallbedingte Staubildung einsetzen und bedient darüber hinaus ein breites Anwendungsspektrum. Der zweite Beitrag dieser Dissertation ist ein selbstorganisiertes Konzept für ein Störfallmanagement in Stadtstraßennetzen als Gegenmaßnahme zur Staubildung. Es vereint zwei lokal wirkende Prinzipien, deren Ausgangspunkte die Lichtsignalanlagen im Stadtnetzwerk sind. Mit verlängerten Rotzeiten werden Fahrzeuge an einer Kreuzung an der Einfahrt in einen Straßenabschnitt gehindert, wenn ein vorgesehener Rückstaubereich ausgeschöpft ist, da andernfalls Blockaden auf den Kreuzungen entstehen. Gleichzeitig werden noch freie Richtungen an der Kreuzung durch verlängerte Grünzeiten attraktiver gestaltet, um Autofahrer zum Umfahren der Staubildung zu motivieren. Die Anwendung der lokalen Wirkungsprinzipien stellt sich vollständig selbstorganisiert, d.h. ohne Vorgabe eines Planers, mit dem Ausmaß der Staubildung im Netzwerk ein. Simulationsstudien in zwei unterschiedlich komplexen Netzwerken haben die Machbarkeit des selbstorganisierten Störfallmanagements nachgewiesen. Gegenüber einem gewöhnlichen Netzwerk konnte für alle untersuchten Störfälle die Akkumulation zusätzlicher Fahrzeuge im Netzwerk während des Störfalls signifikant reduziert werden. / The mobility of people and goods, especially in urban areas, is of significant importance for national economies. However, recurrent congestion in urban road networks, caused by increased traffic demand, considerably restrains mobility on a daily basis. Another significant source of congestion are traffic incidents which even might lead to gridlock situations. Congestion raises high costs for traffic, economy and environment. Which countermeasures should be applied for an effective management of urban congestion? How can appropriate countermeasures be realistically evaluated? Based on these questions, this thesis is devoted to the development of an event-oriented route choice model for urban road traffic and a self-organized incident management strategy as an effective countermeasure for urban congestion. The first contribution of this thesis is an event-oriented route choice model for urban road networks. It is based on discrete choice theory and models decision-making processes of individual motorists before and during their journey. A key aspect of the proposed model is the motorist's ability to observe local traffic conditions. These observations are then included in the decision process. In this way, it can be modeled that motorists respond to unforeseen events by route revisions. This allows a realistic simulation of the route choice behavior of motorists in naturally eventful urban road networks. Furthermore, the event-oriented route choice model is flexibly formulated. It can be used for the evaluation of countermeasures for incident-related congestion and, moreover, allows a wide range of applications. The second contribution of this thesis is a self-organized concept of an incident management strategy in urban road networks as a countermeasure for urban congestion. It combines two locally acting principles on the basis of traffic lights in an urban road network. The inflow of vehicles into a road segment is regulated with restricted or skipped green times as soon as an allocated queuing capacity is depleted. Otherwise, blockages would result on the intersection. At the same time, yet free alternative directions are served with regular or even extended green times and, thus, might become more attractive to the driver than the original congested direction. The application of these local principles is realized in a completely self-organized manner, thereby scaling directly with the extent of congestion in the urban road network. Simulation studies in two networks with different complexity have proven the feasibility of the self-organized incident management. Compared to an ordinary network, the extents of additional vehicles due to investigated incidents were significantly reduced.

Engineers frequently use computerized numeric models to calculate and predict water levels and current patterns for rivers, bays, and other bodies of water. This computation often involves an iterative process known as incremental loading that can cause frustration and consume a lot of time. Although the steering module in the Surface-water Modeling System (SMS) automates incremental loading to minimize user interaction, it can still be very time consuming. This thesis examines the steering module and the incremental loading process to improve its efficiency. Specifically, the RMA2 and FESWMS models are utilized. Two methods of improving efficiency are examined. The first includes creating predicted solution files for each step of the incremental loading process. These predictions allow the steering module to take larger steps and decrease the computation time. The second method changes the algorithm used to determine the size of each step. Finally, the interface to the process was examined and simplified to require minimal input and to make the input more intuitive.

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