Probleemoplossing en die onderrig en leer van wiskunde in graad 4
The objective with this research was to establish the correlation between problem solving and the teaching and learning of mathematics in grade 4. The results of the Third International Mathematics and Science Study (TIMSS) showed that South Africa is behind other countries in terms of the teaching and learning of mathematics, especially with regard to problem solving. Because problem solving is an integral part of the teaching and learning of mathematics, a literature study was conducted (1) to investigate the learning of school mathematics and (2) to describe the manner in which problem solving can take place in the classroom. The learning of school mathematics was studied by focusing on different approaches to the learning of mathematics. The constructionist approach to learning was identified as the appropriate approach towards learning, which correlates with outcomes-based education (OBE) and with the approach currently taught in South African schools. Factors which contribute towards the meaningful learning of school mathematics, namely mathematical knowledge and skills, meta-cognition, learning strategies and tasks and assignments in mathematics, have been discussed. The role of problem solving in the learning of mathematics was studied by means of a possible problem-solving model which may be developed together with the learners. The teaching of problem solving was investigated by referring to the planning of a problem-based lesson and attention was paid to the learning content of the lesson and the planning of the teaching-learning activities. Together with the learners a problem-solving model was developed for the teaching of problem solving. The implementation of the teaching of problem solving was described with reference to the use of big-group presentations as well as problem solving in small groups. Attention was also paid to problem solving, and the use of different assessment techniques was discussed. The empirical investigation was done by means of a case study, and the focus was firstly on the influence of problem solving on the learning of mathematics, and secondly on the manner in which problem solving may be taught. Information was collected during the qualitative investigation by using a questionnaire which was completed by the learners, as well as an interview and observation schedule. The class work, homework and group work books of the learners were studied and transcribed. Video recordings were made of the learners' participation in the big group, small groups and written work, and the transcribed information was used to make deductions about the teaching of problem solving to the learners. From the empirical investigation it became clear that there is a correlation between problem solving and the teaching and learning of mathematics. Problem solving may be taught to learners by means of a problem-solving model, although this does not necessarily result in successful problem solving by all learners. While learners are solving problems, they are also learning mathematical concepts and acquiring and applying mathematical skills.
- ETD@PUK