# Masters Degrees (Mathematics and Computer Science Education)

Permanent URI for this collectionhttps://hdl.handle.net/10413/7141

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# Browsing Masters Degrees (Mathematics and Computer Science Education) by Author "Brijlall, Deonarain."

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Item The application of artifacts in the teaching and learning of grade 9 geometry.(2005) Jojo, Zingiswa Mybert Monica.; Brijlall, Deonarain.; Maharaj, A.The main focus of the study was to explore how the experiences that the learners went through in the Technology class during the construction and design of artifacts, could be used to inform the teaching of Geometry in the mainstream Mathematics classes. It was important to find out how the teaching of Geometry would allow the learners to both reflect and utilize the Geometry they know, as a starting point or springboard for further study of Geometry. Data was collected through observations, structured and semi-structured interviews of a sample of twenty grade 9 learners of Mashesha Junior Secondary School of Margate in KwaZulu Natal. It was collected through observation of drawings and completely constructed double-storey artifacts at different intervals of designing. Observations and notes on every activity done by the learners for example, measurements, comparisons, estimations, scaling, drawings use of symmetry and perspective drawing were kept and analyzed. Data for the interviews was collected in the form of drawings, photographs, transcriptions of video and audiotapes. The observations in particular were looking for the Geometry in finished artifacts. Interviews with the learners were directed at how each learner started drawing a house to the finish. When and how scale drawing, projections, angles made and length preservation were used by the learner, was of utmost importance. It is believed that grade 9 learners of Mashesha have Geometric experiences which can be used to inform the teaching of Geometry in mainstream mathematics. It was found that this experience brought by the learners from the Technology construction of artifacts could cause the learners to find mainstream mathematics interesting and challenging. It is also believed that the use of projective Geometry already employed by the learners can be incorporated in mainstream mathematics so as to improve how learners understand Euclidean Geometry. In this way, it is believed, that the teaching of Geometry will allow the learners to utilize and reflect the Geometry already known to them. This Geometry would therefore be used as a starting point for further study of Geometry. Suggestions for further research and recommendations for the improvement of Geometry teaching and learning have also been made.Item Closure operators on complete lattices with application to compactness.(1995) Brijlall, Deonarain.; Sturm, Teo.; Jordens, Olav.No abstract available.Item The design and implementation of a classroom-based support programme in trignometry for use by underqualified educators.(2005) Mkhize, Sabelo Andrias.; Brijlall, Deonarain.; Maharaj, A.The main purpose of the study was to show the necessity of a classroom-based educator in-service support programme. Educators have unique problems being derived from the uniqueness of their school situations. Thus, the feeling that this kind of support could improve the quality of mathematics teaching and learning.Item Exploring pre-service teachers' mental constructions of matrix algebra concepts : a South African case study.Ndlovu, Zanele Annatoria.; Brijlall, Deonarain.At the university where the study was conducted matrix algebra is one of the first advanced mathematics courses that pre-service teachers encounter. The transfer of knowledge from a primarily procedural or algorithmic school approach to formal presentation of concepts is a priority for conceptualisation of matrix algebra concepts. However, it seems to be creating many difficulties for many pre-service teachers. This is due to the fact that many of them are barely coping with procedural aspects of mathematical concepts. The aim of conducting the study was to explore the pre-service teachers’ mental constructions when learning matrix algebra. The study was guided by the belief that understanding the mental constructions the pre-service teachers made when learning mathematical concepts leads to improved instructional methods. The study is underpinned by APOS theory (Action, Process, Object and Schema) and uses APOS theory to describe the nature of mental constructions displayed by pre-service teachers when learning matrix algebra concepts. To understand and explain the mental constructions made or not made, the preliminary genetic decompositions for matrix algebra concepts was used to analyse the nature of mental constructions made by these pre-service teachers together with triad mechanism which originates from Piaget’s work of reflective abstraction. APOS theory is an extension of reflective abstractions so using these two tools to analyse pre-service teachers’ mental constructions strengthen the trustworthiness of this study. As part of this research project several case studies were conducted where groups of first and second year students were exposed to teaching and learning of some of matrix algebra concepts. These concepts explored are the ones that these students learn under matrix algebra at this university. These concepts were first taught to students and students were expected to express their thinking through solving matrix algebra related problems during tutorials and taking part in the interviews. Analysis of written work and interviews from ten pre-service teachers provided insight into their mental constructions, revealing ways in which they understood the concepts. In explaining and synthesising the results major themes emerged from which conclusions were drawn about the mental constructions that were or not made in the learning of matrix concepts. Several themes emerged which were categorised in certain headings in order to identify patterns that emerged from all tasks. What mostly transpired across all tasks was that background knowledge and understanding of notation are important aspects for students to understand in order to conceptualise the concepts in matrix algebra. It was noted that those students who had a weak schema of basic algebra were not able to make the necessary mental constructions or vice versa. Also, it was noted that students often made nonstandard notation and linguistic distinctions. For example, students use A11 when referring to entries of a matrix or use |𝐴| while determining the determinant of matrix C. Moreover, evidence from their responses revealed that many pre- service teachers had limited knowledge constructed of the taught concepts. This was observed as they struggle to represent the solutions of a system geometrically, recognise concepts in different registers and unable to link major concepts. Findings from this study revealed that the mental constructions made by pre-service teachers in most cases concur with the preliminary genetic decompositions. In terms of APOS theory students responses revealed that many were mainly operating at an action and process stages, with few pre-service teachers operating at an object stage. Since difficulties with the learning of linear algebra by average students are universally acknowledged, this study provided a modified itemised genetic decomposition which is anticipated to help in the teaching and learning of matrix algebra concepts. The aim of providing the modified genetic decomposition is to contribute in the teaching and learning of advanced mathematics as lectures could use the modified genetic decomposition to analyse the mental constructions of their students when learning matrix algebra concepts. Besides making a contribution to the teaching and learning of some mathematical concepts, the modified genetic decomposition is a contribution to APOS theory as it is shown it can be used in other mathematical concepts in different context.Item Learners' conceptual understanding of congruent triangles in transformation geometry(2011) Mbili, Lungelo Aaron.; Brijlall, Deonarain.No abstract.Item Using artefacts to support an embodied approach to learning trigonometry : a case study of grade 10 learners.(2013) Niranjan, Caresse.; Brijlall, Deonarain.The purpose of this study was to explore the role of artefacts (manipulatives) in the teaching and learning of trigonometric ratios in grade 10. The study focused on how the use of manipulatives aided learners’ mathematical proficiency in the use of trigonometric ratios. The foundation of this research was a case study contained in the interpretative paradigm involving five grade 10 mathematics learners at a secondary school in South Africa. The data collected included a range of methods such as: Activity sheet containing written responses of learners. Observations. Semi-structured interviews. The results in this research was analysed qualitatively. The research findings in this case study indicated that the learners were interested and motivated and that the use of manipulatives assisted learners in understanding the concept of trigonometric ratios. In addition the results showed that the use of manipulatives in teaching and learning mathematics played a positive role in leaners understanding of trigonometric ratios at grade 10 level. The findings of my case study were similar to other research studies regarding the significance of using artefacts (manipulatives) in classrooms in teaching and learning of mathematics. The findings support other research findings that confirm that manipulatives were important mediating tools in the development of conceptual and procedural understanding of mathematical concepts.