Investigating the beliefs about problem-solving of mathematics teachers at independent secondary schools in South Africa

[摘要] ENGLISH ABSTRACT : The South African National Curriculum Statement (NCS) for Mathematics calls for teachingthat facilitates and promotes problem-solving as a routine activity and which promoteslearning and teaching from a constructivist paradigm. This is in line with internationalcurricula. However, teachers have found it difficult to incorporate problem-solving into theirteaching and to include problem-solving questions in their school-based assessments, even inprivileged school environments.Researchers argue that teachers' beliefs about the nature of Mathematics and the teaching andlearning of Mathematics significantly influence their teaching practices. Teachers who hold aconstructivist belief about the teaching and learning of Mathematics have been shown toincorporate problem-solving in their teaching more readily. However, those with traditionalistbeliefs find it difficult to include the reformed practices called for by the reformed curricula.This research therefore investigated the beliefs of practising secondary Mathematics teachersabout problem-solving, the nature of Mathematics, and the teaching and learning ofMathematics, and how their beliefs related to their implementation of problem-solvingactivities 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 predominantlyprivileged secondary schools in South Africa. As these schools offer a positive teaching andlearning environment with qualified and experienced teaching staff, a reasonable expectationwould be that the aims and objectives of the reformed curriculum would be met. Data wascollected through the use of questionnaires with further data collection taking place in theform of semi-structured interviews. The data from 95 completed questionnaires wereanalysed, followed by the semi-structured interviews that were used only for the purposes ofinforming future research, as only two interviews could be completed. The theoretical framework used for the study is based on the three belief dimensions ofMathematics 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 toa constructivist belief within these three dimensions. In addition, teachers' beliefs whereinvestigated in relation to their teacher-training qualifications and their academicqualifications in Mathematics. Both these aspects have been shown in prior research to havean influence on a teacher's beliefs.The research indicated that:(i) the participants hold traditionalist beliefs in general about the nature ofMathematics, while they hold constructivist beliefs about the teaching andlearning of Mathematics;(ii) the participants with post-reform qualifications are more likely to holdconstructivist beliefs in general than their colleagues with pre-reformqualifications;(iii) the participants with only a Mathematics 1 qualification, and who haveboth pre- and post-reform professional qualifications, are more likely tohave traditionalist beliefs;(iv) the participants (most of whom are qualified and experienced educators)struggle to describe adequately aspects of teaching and learning thatinvolve problem-solving.The study therefore informs schools and teacher-training institutions regarding aspects ofteachers' professional development – that the focus should be on the development ofconstructivist beliefs which will encourage problem-solving as a routine activity in classroompractice.

[发布机构] Stellenbosch University