Poor mathematics performance in South African schools is a major concern (Reddy et al., 2014) and learners’ opportunity to learn is one of the concepts that needs to be explored in schools (Dowd, Friedlander & Guajardo, 2014). Several authors (Gür, 2009; Ebert, 2017; Rohimah & Prabawanto, 2019) state that learners believe that trigonometry is difficult and abstract compared with the other topics of mathematics. Opportunity to learn (OTL) is defined as the degree to which learners during instruction get exposed to the content of the mathematics intended curriculum (Reeves & Muller, 2005). The term “mathematical tasks” refers to classwork problems, homework problems, projects, investigations and assignments. These tasks play a vital role in effective teaching and learning. Learners’ OTL was explored according to the types and nature of tasks selected by the teacher, and the pedagogical approach and strategies used by teachers and the influence of these two aspects on the time spent on tasks and learner engagement. This study therefore aimed to answer the research question about the extent to which mathematics tasks provided Grade 10 learners an opportunity to learn trigonometry. A two-part conceptual framework was used: the first part focused on the task selection in terms of its nature and cognitive demand and the second part focused on the teacher-specific factors such as teachers’ approaches and strategies. The influence of these two parts on the implementation of the tasks by the learners in terms of time-on-task and learner engagement was then described. A qualitative approach was followed, and a descriptive case study was conducted with two Grade 10 mathematics teachers from two formerly disadvantaged public schools in Gauteng Province. A qualitative research approach was used in which document analysis and classroom observations served as data collection techniques. A deductive analysis approach was implemented. The study revealed that teachers mainly gave learners recall-type and routine procedure questions involving pure mathematics, which according to CAPS’ cognitive demands, are classified as lower order thinking tasks. There was a lack of higher order mathematics tasks that could have provided the learners with and OTL trigonometry effectively. The study further revealed that both teachers’ approaches were dominated by a teacher-centred approach where the focus was on the teachers and where teachers mainly used direct teaching as teaching strategy where learners were directed to learn through memorisation and recitation techniques. Although, due to the small sample, the study’s results cannot be generalised, I believe that the findings will contribute to pre- and in-service teacher training, where teachers come to realise the importance of appropriate mathematics tasks to contribute to learners’ OTL. Moreover, the study’s findings highlight the need to engage the four cognitive levels, namely knowledge (20%), routine procedures (35%), complex procedures (30%), and problem solving (15%) in the types of tasks. The value of teachers’ choices regarding the teaching approaches and strategies used should never be under-estimated. Future research could possibly build on this study by examining the implementation of tasks to enhance learners’ in-depth understanding of trigonometry. / Dissertation (MEd)--University of Pretoria, 2021. / Science, Mathematics and Technology Education / MEd / Unrestricted

The thesis processes data from the research of the company H-edu, which developed a course to help students understand the issue of fractions in the difficult times of Covid-19. Using a large number of materials, an interactive environment, videos and professional guidance, the company helped those interested in understanding the basic principles for perceiving and counting fractions. The thesis compares the results before entering the course and after its completion, which presents the details associated with the course and allows for an evaluation of the course design. The data also helps to identify where students make the most mistakes. Furthermore the thesis contains information on how to identify more demanding tasks or why students might need more time during calculations. At the same time, it explains the importance of gradation of tasks associated with higher success of respondents. The thesis also deals with the structure of questions that affect the representation of incorrect answers. For the most frequently recorded incorrect answers the thesis explains its cause and the procedure by which the respondents came to the wrong result. Recurring errors highlight the need for thorough explanation and practice of the substance. Moreover, the thesis contains a detailed analysis of the...

The development of multiple theoretical models and measures of impulsivity has led to inconsistent use of this term and disagreement regarding the most salient predictors of alcohol-related outcomes. The present study examined whether self-report and behavioral measures of impulsivity measure the same construct and how eight conceptually distinct facets of impulsivity relate to alcohol-related outcomes. Participants completed measures and tasks to assess alcohol use, alcohol problems, trait impulsivity, and behavioral impulsivity. The UPPS-P and behavioral measures of impulsivity were largely uncorrelated with each other. Negative urgency and alcohol use emerged as direct predictors of alcohol-related problems. Lack of premeditation demonstrated an indirect effect on alcohol-related problems. Results support previous research suggesting behavioral and self-report measures of impulsivity do not assess the same construct. Further, results suggest that negative urgency may be the most predictive of alcohol-related problems when accounting for self-report and behavioral components of impulsivity.

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This thesis investigates the analysis and optimization of safety and performance-critical computational tasks for autonomous robots, operating in unknown and unstructured environments with complex objectives under strict computational and power constraints. Our primary contribution is a novel safety-performance (SP) metric that emphasizes on safety while rewarding enhanced performance of real-time computational tasks, expanding the notion of nominal safety in the autonomous vehicle domain. We adopt the Stochastic Heterogeneous Parallel Directed Acyclic Graph (SHP-DAG) model to capture the uncertain nature of robotic applications and their required computations, modeling execution times using probability distributions instead of deterministic worst-case execution time (WCET). We argue that computational tasks enabling robotic autonomy, such as localization and mapping, path planning, task allocation, depth estimation, and optical flow, must be scheduled and optimized to guarantee timely and correct behavior while allowing for runtime reconfiguration of scheduling parameters. To attain computational awareness in autonomous robots, we conduct a data-driven study of these computational tasks from the resource management perspective, profiling and analyzing their timing, power, and memory performance across three embedded computing platforms. Our SP metric allows us to apply the schedulers First-In-First-Out (FIFO) and Completely Fair Scheduler (CFS) of the Linux kernel on complex robotic computational tasks and compare the SP metric with baseline metrics, such as average and worst-case makespan. Extensive experimental results on NVIDIA Jetson AGX Xavier hardware demonstrate the effectiveness of the proposed SP metric in managing computational tasks while balancing safety and performance in robotic systems. Our findings reveal a correlation between task performance and a robot's operational environment, which justifies the concept of computation-aware robots and highlights the importance of our work as a crucial step towards this goal. Finally, we also integrate a custom scheduler with the FIFO priorities with our SHP-DAG and show the efficacy of our framework in comparison to default fair scheduler. / Doctor of Philosophy / This paper explores how to improve the safety and performance of autonomous robots operating in unpredictable and complex environments. These robots need to carry out various tasks such as mapping, path planning, and depth estimation, while managing limited computing power and energy resources. To achieve this, we introduce a new safety-performance (SP) metric that prioritizes safety while rewarding better task performance. We use a cutting-edge model that captures the uncertainty of robotic tasks and their required computing resources. By doing so, we can better schedule and optimize these tasks to ensure timely and correct behavior while allowing for adjustments to scheduling parameters during operation. Our study investigates the performance of key computing tasks on various embedded computing platforms. By comparing our SP metric with traditional measures, we can demonstrate the effectiveness of our approach in managing these tasks while balancing safety and performance in robotic systems. We also do system integration of a real-time scheduler with robotic tasks, which shows the efficacy of our framework. Our findings show a connection between a robot's environment and its computing performance, highlighting the importance of our work as a critical step towards creating smarter and safer autonomous robots that can better adapt to their surroundings.