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Research Publications (Applied Sciences)

Permanent URI for this collectionhttp://ir-dev.dut.ac.za/handle/10321/213

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    Designing an APOS Theory : technoscience framework to understand mathematical thinking
    (2021) Mukavhi, Leckson; Brijlall, Deonarain; Abraham, Jose
    The understanding of mathematical thinking is fundamental cognitive and neuroscience phenomenon in mathematics education that can enhance both instructional and pedagogical practice for improved learning outcomes in mathematics. Several studies for the past decades have been thriving to bring out both operational and structural nature of mathematical thinking. This paper presents the novel theoretical framework as a build on to the APOS theory. The APOS theory has managed to successfully explain the mathematics thinking processes involved in the construction of a mathematics concept based on the premises of limited technology integration into mathematics education. Technology and science artefacts are now ubiquitous and constantly advancing and affecting our philosophical assumptions in mathematics education. We carried out a quasi-experiment in a mathematics laboratory involving two groups of 80 students apiece per study year taking Calculus course with differentiated teaching and learning at the University of Zimbabwe. This novel framework, APOS Theory-Technoscience, factored in technological and scientific oriented actions and processes led us to suggest an APOS-T framework as a didactic model for teaching Mathematics in Higher Education. The model could be an emerging digital pedagogy for face to face and remote mathematics instruction.
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    An exploration of the common content knowledge of high school mathematics teachers
    (University of the Free State, 2014) Bansilal, Sarah; Brijlall, Deonarain; Mkhwanazi, Thokozani
    Many studies point to the problem of poor mathematics content knowledge of mathematics teachers in South Africa. The purpose of this study was to investigate teachers’ knowledge of the mathematics they are themselves teaching. Data was generated from the teachers (n = 253) written responses to test that was a shortened form of a previous Grade 12 Mathematics Paper One examination. The sample of teachers were studying towards an Advanced Certificate in Education (an upgrading high school mathematics qualification) at the University of KwaZulu-Natal in South Africa. The findings revealed that the teachers in this sample obtained an average of 57% in the test. Using an APOS theory analysis it was found that many teachers who were working at an action level of a concept would require help and scaffolding to move to process or object levels of understanding of that concept. Furthermore it was found that on average teachers obtained 29% on questions which were at the problem solving level, raising concerns about how these teachers would mediate tasks that are set at high cognitive levels, with their Grade 12 learners.