Browsing by Author "Willers, Hendrik Stephanus"

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    Investigating the beliefs about problem-solving of mathematics teachers at independent secondary schools in South Africa
    (Stellenbosch : Stellenbosch University, 2019-04) Willers, Hendrik Stephanus; Lampen, C. E.; Stellenbosch University. Faculty of Education. Dept. of Curriculum Studies.
    ENGLISH ABSTRACT : The South African National Curriculum Statement (NCS) for Mathematics calls for teaching that facilitates and promotes problem-solving as a routine activity and which promotes learning and teaching from a constructivist paradigm. This is in line with international curricula. However, teachers have found it difficult to incorporate problem-solving into their teaching and to include problem-solving questions in their school-based assessments, even in privileged school environments. Researchers argue that teachers’ beliefs about the nature of Mathematics and the teaching and learning of Mathematics significantly influence their teaching practices. Teachers who hold a constructivist belief about the teaching and learning of Mathematics have been shown to incorporate problem-solving in their teaching more readily. However, those with traditionalist beliefs find it difficult to include the reformed practices called for by the reformed curricula. This research therefore investigated the beliefs of practising secondary Mathematics teachers about problem-solving, the nature of Mathematics, and the teaching and learning of Mathematics, and how their beliefs related to their implementation of problem-solving activities as required by the NCS. This research is a quantitative case study, augmented by open-ended questions and semistructured interviews. The participants were Mathematics teachers working at predominantly privileged secondary schools in South Africa. As these schools offer a positive teaching and learning environment with qualified and experienced teaching staff, a reasonable expectation would be that the aims and objectives of the reformed curriculum would be met. Data was collected through the use of questionnaires with further data collection taking place in the form of semi-structured interviews. The data from 95 completed questionnaires were analysed, followed by the semi-structured interviews that were used only for the purposes of informing future research, as only two interviews could be completed. The theoretical framework used for the study is based on the three belief dimensions of Mathematics teachers: (i) the nature of the discipline of Mathematics; (ii) the teaching of school Mathematics; (iii) the learning of school Mathematics. Teachers’ beliefs were further categorised on a continuum moving from a traditional belief to a constructivist belief within these three dimensions. In addition, teachers’ beliefs where investigated in relation to their teacher-training qualifications and their academic qualifications in Mathematics. Both these aspects have been shown in prior research to have an influence on a teacher’s beliefs. The research indicated that: (i) the participants hold traditionalist beliefs in general about the nature of Mathematics, while they hold constructivist beliefs about the teaching and learning of Mathematics; (ii) the participants with post-reform qualifications are more likely to hold constructivist beliefs in general than their colleagues with pre-reform qualifications; (iii) the participants with only a Mathematics 1 qualification, and who have both pre- and post-reform professional qualifications, are more likely to have traditionalist beliefs; (iv) the participants (most of whom are qualified and experienced educators) struggle to describe adequately aspects of teaching and learning that involve problem-solving. The study therefore informs schools and teacher-training institutions regarding aspects of teachers’ professional development – that the focus should be on the development of constructivist beliefs which will encourage problem-solving as a routine activity in classroom practice.