Electronic Theses and Dissertations (PhDs)

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

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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.