More recently the Council endorsed this recommendation (NCTM, 1989) with the statement that problem solving should underly all aspects of mathematics teaching in order to give students experience of the power of mathematics in the world around them.
They see problem solving as a vehicle for students to construct, evaluate and refine their own theories about mathematics and the theories of others. National Council of Teachers of Mathematics (NCTM) (1980).
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.
As the emphasis has shifted from teaching problem solving to teaching via problem solving (Lester, Masingila, Mau, Lambdin, dos Santon and Raymond, 1994), many writers have attempted to clarify what is meant by a problem-solving approach to teaching mathematics.
The focus is on teaching mathematical topics through problem-solving contexts and enquiry-oriented environments which are characterised by the teacher 'helping students construct a deep understanding of mathematical ideas and processes by engaging them in doing mathematics: creating, conjecturing, exploring, testing, and verifying' (Lester et al., 1994, p.154).
Problem solving is, however, more than a vehicle for teaching and reinforcing mathematical knowledge and helping to meet everyday challenges.
It is also a skill which can enhance logical reasoning.
For these reasons problem solving can be developed as a valuable skill in itself, a way of thinking (NCTM, 1989), rather than just as the means to an end of finding the correct answer.
Many writers have emphasised the importance of problem solving as a means of developing the logical thinking aspect of mathematics.