Electronic Theses and Dissertations (Masters)

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Browsing Electronic Theses and Dissertations (Masters) by Department "Department of Mathematics education"

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    Investigating In-service Teachers’ Beliefs and Self-efficacy about Mathematical Modelling Using a Structural Model of Professional Competence for Teaching Mathematical Modelling
    (University of the Witwatersrand, Johannesburg, 2023-07) Khoza, Siyabonga Jabulane; Ekol, George
    In this study, I investigate in-service teachers’ beliefs and self-efficacy about teaching mathematical modelling. I further understood teachers’ perceptions about teaching modelling in the Grades 10 - 12 CAPS mathematics curriculum. The purpose of the study was to reveal teachers’ beliefs and SEF to support the development of teachers' modelling competency. The study was underpinned by a structural model of professional competence for teaching mathematical modelling among in-service teachers. A structured questionnaire with a 5 Likert scale was used to collect data on the ISTs' beliefs, SEF, and prior knowledge about teaching modelling in the Grade 10 – 12 CAPS curriculum. Further semi-structured interview sessions were secured with three participants to further confirm quantitative data. Thus, a ‘Sequential explanatory research design from a mixed method research design’ was used to report the collected data. From the questionnaire obtained results, three major themes were formulated from the research questions and used to analyse, present, and discuss the data, which were ISTs’ beliefs about mathematical modelling, ISTs’ self-efficacy about mathematical modelling, and ISTs’ prior knowledge about modelling. From the qualitative data, four themes stood out from the data during the transcription process, namely, teachers are more product-driven than process, learners should take the lead during mathematical modelling, the curriculum timeframe limits learners from exploring modelling, and the limitation of mathematics content in the curriculum. What was revealed from the data is that teachers do believe in the existence of modelling in the mathematics curriculum. Teachers showed being constructivists in the classroom when teaching mathematics in general, including modelling. Their prior experiences with teaching modelling showed that it has contributed to their belief in teaching and learning modelling. Though teachers' beliefs and prior knowledge in this study showed to be developed and acquired respectively, to sufficiently show competencies of teaching modelling in the classroom. However, their SEF to diagnose learners' abilities during their modelling processes showed to be limited. Meaning, teachers did not show confidence in their abilities to diagnose learners' abilities when modelling, and it was not confirmed if they can identify learners' abilities when solving mathematical tasks in general. I believe in South African modelling can be taught and learnt in the classroom if it is sufficiently catered for in the curriculum and if teachers get the necessary support in teaching modelling. The value of the study is an important contribution to teachers' mathematical modelling competency.
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    Variation in Teachers’ Choice and Use of Examples within a Mathematics Department: Affordances in The Introduction of Functions
    (University of the Witwatersrand, Johannesburg, 2023-10) McLachlan, Kathryn Anne; Essien, Anthony A.
    In mathematics classrooms, the examples that teachers choose and use impact the affordances for learning that are offered to their students. This study investigates to what extent such affordances for learning might differ within different teachers’ classes within one mathematics department at a school in Johannesburg. In the department that was analysed, teachers have the agency to choose their own examples and to structure the teaching of mathematical topics themselves. In a case study design, three teachers from this department were observed teaching their two introductory lessons on Grade 10 functions. All of the examples used in their lessons were extracted and analysed using variation theory. The examples were first analysed in and of themselves, and then with the teachers’ mediation. The teachers were also interviewed to provide insight into their intended object of learning for the lessons. Of interest in the analysis was how the multiple representations of functions were integrated in the lessons. The analysis indicates that the affordances for learning across the three classes differed substantially, both regarding the sequencing of objects of learning within the topic of functions, and in the aspects and features that were opened up for discernment. These findings raise questions regarding how much agency teachers within one department should have in structuring the teaching of objects of learning and in selecting examples to use in their lessons.