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An Investigation into the challenges of translating mathematical terminologies into Xitsonga

- Sambo, Tintswalo Teressa

Authors: Sambo, Tintswalo Teressa
Date: 2024-04
Subjects: Mathematical linguistics , Mathematics , Translating and interpreting
Language: English
Type: Master's theses , text
Identifier: http://hdl.handle.net/10948/63495 , vital:73382
Description: Mathematics in South Africa is one of the subjects that is considered ‘difficult’ by many learners. The proof of this statement is reflected by the low mathematical pass rate in many South African schools. One of the challenges that has been highlighted by learners and teachers is that the language of mathematics is challenging. This implies that learners find it difficult to understand some of the mathematical terminologies and content that is being taught. The main reason for the challenge of grasping mathematical terminologies that has been cited by learners and educators is the language of learning and teaching (LOLT). Mathematics is taught in English in most South African schools even though many learners speak one of the indigenous South African official languages (if one excludes English and Afrikaans) at home and get to use and be exposed to English as the medium of learning and teaching only at school. While mathematics remains a challenge in South Africa, research shows that when home languages are used in a mathematics classroom, it enhances the learners understanding. However, it is not always simple to transfer mathematics from English to an African language. There are complexities associated with translation that include the lack of vocabulary in the target language which in this case is Xitsonga. The lack of terminologies in Xitsonga is one of the challenges that occur during the process of translation. This purpose of this research is to examine the challenges of translating mathematical terminologies from English into Xitsonga and to find the strategies that can be used to assist learners to improve their understanding of mathematics. As such, a qualitative research method will be used to select the mathematical terminologies extracted froma mathematics bilingual dictionary with the aim of examining the quality of the translation and identifying the challenges that have been experience by translators. , Thesis (MA) -- Faculty of Humanities, School of Language, Media and Communication, 2024
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Date Issued: 2024-04

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Mathematical modelling of the tumour treatment with chemotherapy

- Nyaweni, Fundile Sindy

Authors: Nyaweni, Fundile Sindy
Date: 2024-04
Subjects: Mathematical models , Mathematics , Chemotherapy
Language: English
Type: Master's theses , text
Identifier: http://hdl.handle.net/10948/64289 , vital:73672
Description: In this study, a cancer disease model incorporating predator-prey dynamics between immune cells and tumor cells, as well as competition between tumor cells and normal cells, is formulated in an attempt to understand the interaction dynamics that govern the complex interplay within the tumor microenvironment. Mathematical analysis is employed to derive conditions for the boundedness of solutions and to discuss disease thresholds such as the basic reproduction number, R0. Equilibrium points are identified, and stability conditions for the system are derived. Sensitivity analysis is used to assess uncertainties in the parameters of the model, specifically their impact on R0. Numerical simulations are conducted, utilizing the Runge-Kutta scheme to solve the model. Furthermore, optimal control (OC) techniques are applied to examine the role of chemotherapy in enhancing tumor cell elimination and minimizing adverse effects on immune cells and normal cells. The improved model, incorporating normal cells, anticancer drugs, and immune cells, allows for a more comprehensive analysis of the dynamic interactions within the biological system. The optimal control is determined using the forward-backward sweep numerical method. The numerical simulation is carried out in MATLAB to validate and complement the analytical findings. The results indicate that a low concentration of the drug leads to a prolonged period for tumor clearance. Conversely, a higher drug concentration results in quicker tumor clearance, albeit with adverse effects on normal and effector cells. The OC identifies when to stop the treatment once the tumor clears. Furthermore, OC facilitates the regeneration of normal and immune cells beyond treatment, in contrast to a control scenario without optimization. The findings highlight the importance of early detection and careful chemotherapy dosage selection for effective and personalized cancer treatment strategies. , Thesis (MSc) -- Faculty of Science, School Computer Science, Mathematics, Physics and Statistics, 2024
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Date Issued: 2024-04

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The development of South African secondary school teachers to adopt a STEAM approach: A mixed method study

- Steyn, Catherina

Authors: Steyn, Catherina
Date: 2023-04
Subjects: Professional Development , Social Cognitive Theory , Mathematics
Language: English
Type: Doctoral's theses , text
Identifier: http://hdl.handle.net/10948/63218 , vital:73234
Description: Creativity is seen as one of the most important skills required for success in the 21st century and therefore teachers should set the example and become creative and innovative when skilfully applying their knowledge to teach. In STEAM, art is included in the STEM (Science, Technology, Engineering and Mathematics) mix as a new innovative educational approach which is believed to increase creativity. The advantages of STEAM are widely accepted for a number of reasons and it has become very popular in countries that are known for their excellent mathematics performance, but it is unknown in most South African schools. Although a few studies have been done on STEAM in South Africa there is a lack of research on the professional development of mathematics teachers and the adoption of the STEAM approach in the mathematics classroom. This mixed methods study aims to determine the diffusion of the STEAM approach, and the influence of professional development on that diffusion and adoption in the South African Mathematics classroom. A convergent triangulation design was used in conjunction with a simultaneous quantitative and qualitative approach involving three different groups of participants. The quantitative approach concentrated on the hypothesis that secondary school mathematics teachers still embrace traditional teaching methods. The qualitative approach was directed towards answering the question on the knowledge and awareness of STEAM and the adoption of the innovation. The combination of two theories, namely Roger’s Diffusion of Innovations and Bandura’s Social Cognitive Theory were found to provide the most suitable framework to describe the process in the findings. The instrument used in the quantitative approach was an online questionnaire and in qualitative approach the data was collected using interviews, assignments and questionnaires. It was found that although Mathematics teachers are open to learning about innovations, they still rely on traditional teaching methods. Teachers recognise the advantages of STEAM and want to use it but feel constrained by the curriculum, the pressure to perform and a lack of resources. Short activities that are curriculum based are welcomed and used by the teachers. However, they struggle to set up their own iii activities and then abandon the idea. In addition, they are not comfortable with projects involving teachers from other disciplines or including art activities in a mathematics lesson. The adoption of STEAM becomes much easier if there is a strong professional learning community and support from school management. The positive reactions of the learners on the STEAM activities motivate the teachers to adopt the approach. The diffusion of STEAM into the mathematics classroom is not instant but takes an average of two to three years. This time factor should be taken into consideration when planning a professional development programme. The programme should include scaffolding to assist teachers to become confident in using STEAM activities but also in using technology which is the key to finding and using new activities. , Thesis (PhD) -- Faculty of Education, 2023
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Date Issued: 2023-04

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An intervention for enhancing the mathematics teaching practices of grade four teachers in the Nelson Mandela Metropolitan area

- Botha, Adele

Authors: Botha, Adele
Date: 2011
Subjects: Mathematics -- Study and teaching , Mathematics , Mathematics -- Handbooks, manuals, etc , Mathematics teachers
Language: English
Type: Thesis , Doctoral , PhD
Identifier: vital:9499 , http://hdl.handle.net/10948/d1008176 , Mathematics -- Study and teaching , Mathematics , Mathematics -- Handbooks, manuals, etc , Mathematics teachers
Description: Mathematics is regarded as a driving force in economies worldwide. The performance of South African learners in mathematics over the past decade has highlighted that problems are being experienced across all grades. This situation needs to be addressed with urgency. The South African Department of Education stated that quality learning must be the objective for all grades. The implementation of good teaching practices plays a crucial role in improving the quality of education and in guiding learners towards quality learning. To achieve quality mathematics teaching and learning it is imperative to determine what good mathematics teaching practices are. The identification of good mathematic teaching practices will provide a yard stick to measure the mathematics teaching competency of teachers. This study identifies a set of good mathematics teaching practice indicators and evidences applicable to teachers in the Intermediate phase as a first contribution. These indicators and evidences frame the second research contribution: an assessment instrument entitled “A Classroom Observation Tool for Observing Mathematics Teaching Practices in Primary Schools”. As a third research contribution a generic profile of a Grade four mathematics teacher has been built. This generic profile has been built through an analysis of data gathered by means of self-assessment questionnaires completed by the research sample, as well as through applying the observation tool. The value of the generic profile lies in the identification of shared strengths and shared improvement opportunities in the mathematics teaching practice of the sample and as such, it forms the basis of a theory on Grade four mathematics teaching practice. The fourth research contribution is the design and application of an intervention that addresses the shared improvement opportunities. The research study concludes by comparing pre-intervention classroom observation data with post-intervention classroom observation data and reporting on the impact of the intervention.
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Date Issued: 2011

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A probability operator

- Sinclair, Allan M

Authors: Sinclair, Allan M
Date: 1965
Subjects: Mathematics , Probabilities
Language: English
Type: Thesis , Masters , MSc
Identifier: vital:5423 , http://hdl.handle.net/10962/d1007702 , Mathematics , Probabilities
Description: From Introduction: In probability theory it is often convenient to represent laws by characteristic functions, these being particularly suited to classical analysis. Trotter has suggest ted that probability laws can also be represented by probability operators. These operators are easily handled since they are continuous, and hence bounded, positive linear operators on a normed linear space. This representation arises because distribution functions and their complete convergence correspond to probability operators and their complete convergence. Hence the relations between distribution functions and probability operators will be discussed before the introduction of probability laws.
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Date Issued: 1965

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