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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 Subject "APOS theory."

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    Exploring learners’ understanding of mathematical concepts necessary in the learning of grade 11 algebraic functions: the case of three schools in uMgungundlovu District.
    (2019) Ndlovu, Nkosinathi Emmanuel.; Goba, Barbara Busisiwe.
    The purpose of this study was to explore learners’ understanding of mathematical concepts in the learning of grade 11 algebraic functions in uMgungundlovu district, KwaZulu-Natal. In order to gain insights into learners’ understanding of mathematical concepts in learning grade 11 algebraic functions, APOS theory was used as a theoretical lens to explore learners’ level of understanding of functions. This study describes the mathematical concepts that are important in the learning of grade 11 algebraic functions. The CAPS document was used to analyse the mathematical concepts for functions to be learnt in grade 11. The data was gathered through written tasks and interviews of grade 11 learners in three schools in one district in KwaZulu-Natal. The research approach used for this study was the mixed method. Sixty grade 11 learners (twenty in each school) were purposively selected; however, this sample selection was conveniently done since learners were able to participate in the study after school. This study employed the interpretive paradigm and nine learners (three from each school) were interviewed during data collection. Multiple methods were employed for data collection in this study. Qualitative data was organised using interview transcripts and quantitative data was organised using the APOS analytical framework. The findings of this study confirm that learners’ level of understanding of algebraic functions at an object level is extremely poor.
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    Exploring the use of GeoGebra to enhance Grade 12 learners’ knowledge construction of trigonometric 2D and 3D concepts in one school in King Cetshwayo District.
    (2023) Mbatha, Philisiwe Promise.; Ngcobo, Annatoria Zanele.
    It is evident in the literature that mathematics is the school subject that learners struggle with the most, especially the concepts of trigonometry. This study explored the effectiveness of GeoGebra as a pedagogical tool to enhance Grade 12 learners’ conceptual understanding of 2D and 3D trigonometry. The study was located within the interpretive paradigm and a qualitative case study methodology was employed. Thirty Grade 12 learners were purposively selected from a high school in the King Cetshwayo District Municipality of the province of KwaZulu-Natal in South Africa. Data was collected using activity worksheets administered as a pre-test and a post-test, with lessons conducted using GeoGebra. Data was also collected using semistructured interviews, focus group interviews and observations. The study was underpinned by APOS (Action, Process, Object and Schema) theory, which was used to analyse the mental constructions displayed by participants. To understand and explain the extent to which participants had been able to make mental constructions, a genetic decomposition model was used. The genetic decomposition model developed by Arnon et al., (2014) was used to understand and describe the extent to which participants were able to make the mental structures necessary to master a particular mathematical concept. The study found that learners’ conceptual understanding of 2D and 3D trigonometry improved from the pre-test, administered before they had engaged with concepts using GeoGebra, to the post-test, which was administered after learners had integrated GeoGebra into their conceptual development. This indicates that GeoGebra may have facilitated improved knowledge construction for these learners. These findings have implications for mathematics educators, curriculum developers and further researchers, as they offer insights into the potential benefits of incorporating dynamic software tools like GeoGebra to enhance the teaching and learning of trigonometry in the high school context. Ultimately, this study contributes to the on-going discourse on effective technology integration in mathematics education and offers practical recommendations for educators seeking innovative approaches to engage and empower their students through trigonometric learning experiences.