Electronic Theses and Dissertations (Masters)

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Browsing Electronic Theses and Dissertations (Masters) by Author "Ekol, George"

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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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    The Effects of Mathematical Modelling and its Application in Algebraic Functions on Grade 11 Learners’ Performance
    (University of the Witwatersrand, Johannesburg, 2023-07) Ngubane, Sibongiseni; Ekol, George
    To explore the effects of mathematical modelling on Grade 11 learners’ academic performance in algebraic functions, teachers’ self-efficacy and their overall perceptions, is the purpose of this research study. For the achievement of this goal, the research study followed a mixed method for both collecting and analyzing data. However, a pre-test and a post-test, interviews, and a questionnaire were used to collect data. The study content was limited to mathematical modelling in algebraic functions, learners doing pure mathematics in Grade 11, and mathematics teachers in the FET phase only. Eighty-seven (87) Grade 11 learners doing mathematics from one (1) selected school under the ILembe district in KwaZulu Natal participated in the research study, where 44 (51%) formed an experimental group and the other 43 (49%) learners formed a control group. Findings revealed that the experimental group taught through modelling with a guided discovery approach outperformed the control group that was taught through a direct instruction approach to learning. Hence, the difference between the modelling and direct instruction teaching approaches is statistically significant. Six (6) learners from the experimental group were purposively sampled to participate in the semi-structured interviews for the researcher's purposes of exploring learners’ perceptions about mathematical modelling. Learners reported that modelling could improve their level of cognition. Thirty-three (33) mathematics teachers in the FET phase from fourteen (14) high schools in KwaZulu Natal participated in the study by completing a questionnaire about modelling. Findings revealed that teachers have positive attitudes, beliefs, and perceptions about modelling in mathematics education even though there are no teachers’ professional development workshops provided to encourage them based on modelling. This study recommended that the department of education put more efforts into supporting and motivating teachers to implement modelling in mathematics classrooms, provide teachers with professional development workshops based on modelling, design and distribute teaching and learning support documents to all schools providing mathematics, and do follow-up to check the progress in teachers’ developments.