Die ontwikkeling van wiskunde-onderrigstrategieë vir probleemgesentreerde leer in Graad 2

Abstract

The poor mathematics achievement of South African learners is often ascribed to a flawed foundation for mathematics in the foundation phase. This hinders meaningful learning, which should be founded in proper comprehension. Literature emphasises the important role of a problem solving approach to mathematics teaching to enhance mathematics understanding. My own concern about the disharmony between theory and practice, with specific reference to the almost exclusive use of direct teaching strategies at the cost of problem solving approaches to mathematics teaching, motivated this study. The literature in this field reports on different types of problem solving approaches to mathematics teaching. However, research clearly indicates that a problem-centred approach to mathematics teaching is suitable for the foundation phase as these young learners are in the process of mastering basic mathematics concepts and problem solving techniques. The research aim of this study was to develop meaningful strategies to support problem-centred learning in mathematics in Grade 2 by way of action research. In an effort to reach this aim, the study included a literature review and action research. Die literature study firstly confirms the importance attributed nationally and internationally to problem solving for meaningful learning of mathematics. Secondly, the literature study reveals the determinants that should be considered in the development of such teaching strategies, namely teacher-related factors and factors related to the teaching context. Thirdly, the principles of problem-centred learning are identified from the literature to serve as a framework for the development of the teaching strategies for problem-centred learning. The principles of problem-centred learning as identified from the literature include a constructivist approach to teaching and learning, with a specific focus on social-constructivist learning, metacognition, cooperative learning, reflection and the facilitation of learning. Four Grade 2 teachers at a South African double medium school in the North West province participated voluntarily in the action research. Participation involved the development of teaching strategies for the problem-centred teaching of mathematics. This qualitative study followed an interpretivist-constructivist research approach to find answers to the research question. The meaningfulness of the developed teaching strategy for problem-centred learning was examined by interpreting the participants' experience of the cyclical development and implementation of the teaching strategies. The teaching strategies developed by the participants are related to the problem-centred learning principles: A constructivist approach to the teaching-learning of mathematics forms the basis of problem-cenred learning teaching strategies. The construction of understanding is enhanced when learners are confronted with a problem that is at their level of development and that links with their pre-knowledge. The problems should gradually become more challenging as the learners' knowledge and skills develop. Die learners should receive the opportunity to be actively involved with their own learning by using concrete learning material and solving problems that are relevant to their world to construct knowledge networks. Teaching strategies should be founded in social constructivism where learners solve problems cooperatively by communicating their methods and solutions. Problem solving in homogeneous pairs is useful since both learners receive an equal opportunity to solve the problem at their own level of development. Learner reflection is also regarded as a valuable strategy during cooperative learning in homogeneous pairs. Reflection contributes to the promotion of metacognition among foundation phase learners. The teacher should play a facilitating role by creating a learning environment that promotes problem-centred learning. This facilitating role requires thorough planning and suitable problems to guide learners to independent mathematical problem solving by means of questions. The findings confirm the teacher as the main determinant of the way in which problem-centred learning is implemented in the classroom. The realisation of the problem-centred learning principle of facilitating problem solving requires the teacher to have the necessary knowledge of mathematics, to know the learners, and to have pedagogical knowledge and skills. This would enable them to accommodate any hindering factors related to the teaching context. The role of action research, where participants work together as a community of professional teachers in the development of teaching strategies, is critically evaluated with an eye to the value of action research for teaching practice in South Africa.