The purpose of this study was to increase the student's understanding of the measures of area and perimeter of polygons. The goal of the project was to create a supplemental geometry unit to develop the concept of the area and perimeter of a polygon without the use of formulas and numbers and to measure the effectiveness of this unit on student understanding. Two high school geometry classes with under 28 students each participated in this study.

The purpose of this study is to investigate the role of physical manipulatives in the teaching and learning of measurement in Grade 8. The study focuses on how the use of physical manipulatives promotes learners' mathematical proficiency in relation to the five strands of Kilpatrick, Swafford and Findell (2001). The basis of the research is a case study in the interpretive paradigm involving 18 out of a cohort of 270 Grade 8 learners in the school where I teach. The data was collected using a range of methods including: (i) baseline assessment tasks, first piloted using 7 Grade 8 learners and then given to the target group; (ii) an intervention programme with intervention tasks; (iii) a post-intervention task; (iv) observations during the intervention; and (v) individual interviews. The results of the baseline assessment and the post-intervention tasks were analysed both quantitatively and qualitatively. My research findings indicate an overall improvement of the performance after learners engaged in using physical manipulatives. The average mark of the learners in the baseline assessment task was 23% and after the intervention programme the average mark was 31 %. The responses from the learners interviewed showed that they were motivated and that the use of physical manipulatives assisted them in understanding the concepts of measurement, in particular surface area and volume. The results of my study thus reveal that the use of physical manipulatives in teaching and learning mathematics has a positive role to play in learners' understanding of surface area and volume at the Grade 8 level. The fmdings of this case study support other research regarding the importance of using physical manipulatives in teaching and learning mathematics. They align with other findings that assert that manipulatives are essential mediating tools in the development of the conceptual and procedural understanding of mathematical concepts, clarifying and helping learners to visualize abstract mathematical concepts.

As the need to remain connected increases, more and more people are turning to wireless mesh networks because they reduce the need for network infrastructure. Unfortunately, TCP does not perform well in such networks. HxH, an alternate protocol, has shown great promise in simulations, but since it relies on exploiting passive feedback, real measurements are needed to determine how effective the protocol really is. This thesis uses a measurement study on a wireless mesh network to characterize the performance of the HxH protocol in real-world networks. Several aspects of the HxH protocol do in fact perform well on real networks, but the high rate of packet loss renders other aspects of the protocol ineffective.

Graphs are used to model a wide range of systems from different disciplines including social network analysis, biology, and big data processing. When analyzing these constantly changing dynamic graphs at a high frequency, performance is the main concern. Depending on the graph size and structure, update frequency, and read accesses of the analysis, the use of different data structures can yield great performance variations. Even for expert programmers, it is not always obvious, which data structure is the best choice for a given scenario. In previous work, we presented an approach for handling the selection of the most efficient data structures automatically using a compile-time approach well-suited for constant workloads. We extend this work with a measurement study of seven data structures and use the results to fit actual cost estimation functions. In addition, we evaluate our approach for the computations of seven different graph metrics. In analyses of real-world dynamic graphs with a constant workload, our approach achieves a speedup of up to 5.4× compared to basic data structure configurations. Such a compile-time based approach cannot yield optimal results when the behavior of the system changes later and the workload becomes non-constant. To close this gap we present a run-time approach which provides live profiling and facilitates automatic exchanges of data structures during execution. We analyze the performance of this approach using an artificial, non-constant workload where our approach achieves speedups of up to 7.3× compared to basic configurations.

Graphs are used to model a wide range of systems from different disciplines including social network analysis, biology, and big data processing. When analyzing these constantly changing dynamic graphs at a high frequency, performance is the main concern. Depending on the graph size and structure, update frequency, and read accesses of the analysis, the use of different data structures can yield great performance variations. Even for expert programmers, it is not always obvious, which data structure is the best choice for a given scenario. In previous work, we presented an approach for handling the selection of the most efficient data structures automatically using a compile-time approach well-suited for constant workloads. We extend this work with a measurement study of seven data structures and use the results to fit actual cost estimation functions. In addition, we evaluate our approach for the computations of seven different graph metrics. In analyses of real-world dynamic graphs with a constant workload, our approach achieves a speedup of up to 5.4× compared to basic data structure configurations. Such a compile-time based approach cannot yield optimal results when the behavior of the system changes later and the workload becomes non-constant. To close this gap we present a run-time approach which provides live profiling and facilitates automatic exchanges of data structures during execution. We analyze the performance of this approach using an artificial, non-constant workload where our approach achieves speedups of up to 7.3× compared to basic configurations.