3. Electronic Theses and Dissertations (ETDs) - All submissions
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Item Teachers' use of examples to promote mathematical proficiency in statistics(2019) Zulu, SibongileExamples are a prevalent and a powerful tool used in the teaching and learning of Mathematics. In statistics, where data sets used are normally extracted from real life situations, the use of examples is indispensable. This study examines what examples are used and how teachers use them to promote (or fail to) mathematical proficiency in statistics as the outcome of the learning process. Variation theory is employed through the patterns of variation to assess whether the use of examples leads to learning. To ascertain that the use of examples results in the attainment of mathematical proficiency, the strands of mathematical proficiency by Kilpatrick, Swafford and Findell, (2001), are incorporated in the theoretical framework. This study involves observing lessons interactions between Grade 10 teachers and learners, and interviewing teachers after observing the lessons at a school in Johannesburg. An analytical framework derived from variation theory and strands of mathematical proficiency is then used as an assessment tool. Findings show that in and of themselves examples do not necessarily help to achieve the intended object of learning nor mathematical proficiency. More poignant, whatever the teacher’s intention to convey the object of learning through the use of examples, and no matter how the teacher enacts it, learners could still fail to grasp the lived object of learning and attain mathematical proficiency.Item Metacognitive skills of second year extended and main stream University mathematics students: a case study(2017) Moolman, RuanMany universities have introduced so called extended degrees where students’ first year workload is spread over two years to prevent the decline of graduates in mathematics and science. It has been put forward that extended degree courses should include the explicit training of mathematics students in the use of metacognitive skills. This is based on research that shows that successful students in mathematics are able to apply such metacognitive skills and that these skills play an important role in mathematical problem solving. Such skills are concerned with the actual regulation, coordination and control of one’s own learning activities and cognitive processes. Given that extended degree students generally perform weakly in mathematics in comparison to main stream students (non-extended degree students) this research study sets out to consider the differences in the use of metacognitive skills of these two student groupings. A qualitative case study was used to investigate collaborative solving of mathematical problems of one student pair. Students were trained in the use of metacognitive skills by using the metacognitive intervention method called IMPROVE. The student pair was video-recorded during talk-aloud protocols twice before explicit training in the IMPROVE method, and after instruction in order to evaluate students’ development in the use of metacognitive skills. Video recordings were transcribed noting students’ verbal and non-verbal actions and the coding of transcriptions in conjunction with content analysis was used in determining differences in students’ metacognitive skills. Since students worked collaboratively, instances where students acted as so-called social triggers of each other’s metacognitive skills, were also investigated. With student-researcher interaction during observations, the researcher was also regarded as a social trigger of students’ metacognitive behaviour. Apart from these social triggers, environmental triggers of students’ metacognitive skills were also scrutinised. Environmental triggers included the effect of task difficulty and the intervention of the IMPROVE method on students’ metacognitive skills. This study on the social and environmental triggers of individual’s metacognitive skills contributes to the relatively young field in viewing metacognition as cognitive activity that operates on multiple levels during collaborative problem solving, and that metacognition cannot solely be explained in terms of individualistic conceptions but also by social and environmental triggers. Results from the study show that, in general, the main stream student exhibited a greater number of metacognitive skills compared to the extended degree student. Furthermore, it seems that the IMPROVE method as an environmental trigger, had an effect on the development of both students’ metacognitive behaviour. Research findings of the study also reveal that the researcher’s intervention mainly resulted in the students acting as social triggers for each other’s metacognitive behaviour. Furthermore, it was found that there were a greater number of occurrences in which the main stream student acted as social trigger for the extended degree student’ metacognitive behaviour. The level of task difficulty also seems to have acted as environmental trigger for students’ metacognitive behaviour. As an exploratory study, the findings of this study are not generalizable.Item Assessing the algebraic attainment of South African grade 9 learners: designing a test using Rasch analysis(2017) Ehrlich, Samantha AnneSouth African learners perform poorly in national and international mathematics assessments (Howie, 2004). A contributing factor to this poor performance is low mathematics knowledge of mathematics teachers in South Africa (Howie, 2003). One means of addressing this is professional development programs. The Wits Maths Connect Secondary Project runs such a program. A test is required by the project in order to assess whether learners are making learning gains after being taught by teachers who participated in this program. The focus of this study is the design of a test used to assess learners’ algebraic attainment. The aim is to design an informative and fair test using Rasch analysis. A sample of 235 learners’ responses to 47 questions was analysed using the Rasch model. In this study, the mean person measure was 2,87 (SD=1,38) logits, while the mean item measure was 0,41 (SD=2,25) logits, suggesting that overall, the test was too difficult. For the learners who wrote this test the person separation index is 1,78 and the person reliability 0,76. This implies that the test may not be not sensitive enough to distinguish between learners of high attainment from learners with low attainment. Various ways of improving the test are discussed.Item Connecting metacognition and mathematical proficiency: a case study of South African matriculants(2016) Price, Charmaine SmithThis dissertation investigated the possible connection between the two constructs of metacognition and the strands of mathematical proficiency. Using a small convenience sample of Grade 12 learners at a public all-girls high school in Johannesburg, South Africa, the teacher/researcher examined if training in metacognitive knowledge influenced the learners’ conceptual understanding, procedural fluency, strategic competence and heuristic strategy use. Two instruments (pre-test and post-test) developed by the researcher and completed by the students were on-line assessments of metacognition utilising written self-reports of strategy use that occurred simultaneously with mathematical problem solving. Qualitative analyses were applied to the data and learners demonstrated declarative, procedural and conditional metacognitive knowledge in their explicit heuristic and content-specific strategies. The learners also demonstrated strategies which could be inferred from their working. The study showed evidence of mixed transferability of metacognitive training to mathematical proficiency. Questions for further research are provided.