### Abstract:

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.