Wits School of Education (ETDs)

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Browsing Wits School of Education (ETDs) 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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    Secondary school mathematics teachers' identity and mathematical discourse in instruction
    (University of the Witwatersrand, Johannesburg, 2023-08) Masondo, Wanda; Carrim, Nazir; Pournara, Craig
    More often than not, a disjuncture tends to exist between teaching practices that are encouraged during professional development (PD) interventions and what in-service teachers actually do when teaching mathematics. The study reported in this thesis uses the notion of teacher identity to examine in-service teachers’ experiences of learning and their new ways of teaching mathematics after they had participated in a PD intervention called the Transition Maths 1 (TM1) course. The theoretical framework for the study draws on Wenger’s (1998) social theory of learning as a foundational framework, and on Sfard and Prusak’s (2005) narrative identity and Darragh’s (2016) performative identity frameworks to analyse teachers’ mathematics teaching identity. The integration of Wenger’s (1998) social theory of learning, Darragh’s (2016) performative identity and Sfard and Prusak’s (2005) narrative identity frameworks is a key contribution of this study to research teacher identity in the field of mathematics education. The inclusion of Darragh’s (2016) performative identity framework harnessed Wenger’s (1998) social theory of learning and Sfard and Prusak’s (2005) narrative identity frameworks. Drawing on Wenger’s (1998) to analyse teachers’ identities in relation to what they actually do when teaching mathematics in the classroom was going to be limited for the study. Thus, the study has emphasised the learning and teaching of linear equations (a specific domain of mathematics), whilst researchers in mathematics education who draw from social theories and identity often render mathematics invisible. The findings of the study revealed that the teachers shared a positive sense of identity towards learning and teaching mathematics. The teachers’ positive sense of identity emerged from being conscious of achieving lesson goals through exemplification and explanatory communication. However, the teachers were not paying much attention to how they invite learners to participate in their lessons. The characterisation of the teachers in how they achieve lesson goals from their mathematical discourse in instruction became their actual teaching identity. The teachers’ designated teaching identity highlighted aspects where there was a “mismatch” between their mathematical discourse in instruction and what was promoted in the TM1 course. Nonetheless, the gap between the teachers’ actual and designated teaching identities remained relatively narrow when considering that there were fewer aspects where teachers were not competent in their mathematical discourse in instruction. The study employs an explanatory mixed methods research design. The use of the explanatory mixed methods research design and its elaboration in this study is another key contribution to researching teacher identity. In the quantitative processes, 45 teachers who participated in the TM1 course completed a closed-ended questionnaire. The questionnaire was analysed using Exploratory Factor Analysis to explore teachers’ shared experiences of participating in the TM1 course, which demonstrated that the inclusion of the quantitative processes can be valuable to research teacher identity. In the qualitative processes, four teachers were selected for observations when teaching learners mathematics and for individual interviews to talk about their learning and teaching of the subject. The observations were analysed using Mathematics Discourse in Instruction framework to understand the teachers’ teaching practices. The interviews were analysed using narrative analysis to confirm and expand on the teachers’ experiences of learning and teaching mathematics.
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    The Impact of Learning Mathematical Vocabulary of Functions using the Frayer Model on Conceptual Understanding and Mathematical Performance of Grade 11 Learners
    (University of the Witwatersrand, Johannesburg, 2023-09) Madzore, Edwin; Mofolo-Mbokane, Batseba
    This study investigated the impact of integrating the learning of mathematical vocabulary and the learning of mathematical content by Grade 11 learners in secondary schools in Gauteng province, South Africa. The main research question of the study is: what affordances does the integration of focused vocabulary and mathematical content learning provide for conceptual understanding and performance in mathematics? A cohort of Grade 11 learners (n=157) took part in this quasi-experimental study with control (n=83) and experimental (n=74). The experimental group was exposed to explicit learning of mathematical vocabulary using the Frayer model, while the control group used any other method preferred by their teachers. During the posttest, learners from the experimental group outperformed their counterparts in associating mathematical vocabulary with a mathematical graph. The study showed that the Frayer model is an effective strategy for learning mathematical vocabulary. When learners learnt mathematical vocabulary using the Frayer model, they mastered more vocabulary than their peers in the control group and this translated into improved conceptual understanding and performance in mathematics. There is a positive moderate correlation (r = 0.61) between the quantity of correct mathematical vocabulary that learners know and the marks those learners obtain in a mathematics test. The study further showed that it is possible to adopt Content and Language Integrated Learning (CLIL) in South African Schools.
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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.