Through a problem-solving approach, this aspect of mathematics can be developed.
Presenting a problem and developing the skills needed to solve that problem is more motivational than teaching the skills without a context.
The National Council of Teachers of Mathematics (NCTM, 1980) recommended that problem solving be the focus of mathematics teaching because, they say, it encompasses skills and functions which are an important part of everyday life.
Furthermore it can help people to adapt to changes and unexpected problems in their careers and other aspects of their lives.
As was pointed out earlier, standard mathematics, with the emphasis on the acquisition of knowledge, does not necessarily cater for these needs.
Resnick (1987) described the discrepancies which exist between the algorithmic approaches taught in schools and the 'invented' strategies which most people use in the workforce in order to solve practical problems which do not always fit neatly into a taught algorithm.
Individuals can no longer function optimally in society by just knowing the rules to follow to obtain a correct answer.
They also need to be able to decide through a process of logical deduction what algorithm, if any, a situation requires, and sometimes need to be able to develop their own rules in a situation where an algorithm cannot be directly applied.
A further reason why a problem-solving approach is valuable is as an aesthetic form.
Problem solving allows the student to experience a range of emotions associated with various stages in the solution process.