Chapter 1: Problem Solving

The following quote from the National Council of Teachers of Mathematics (1989) relates to the emphasis and focus of problem solving in the Saskatchewan math curriculums.

In coming to an understanding of what problem solving as the “central focus of a mathematics curriculum” could be, we need to consider three different ways of thinking about problem solving.

First, there is problem solving as an art, where to know mathematics is to be able to do mathematics. According to Polya (1985), one learns the practical art of problem solving by imitation and practice. The teacher is the key. Polya developed a series of heuristics of problem solving strategies, which can be learned as a separate set of skills, and then implemented in novel steps to be developed sequentially or through textbooks emphasizing these heuristics. It was not Polya’s attempt to systematically apply the strategies or heuristic, because for non-routine problems, which are the type that require art in their solution, there is no systematic approach. Certain heuristics work in certain problems and expert problem solvers are able to select the strategies most likely to work, but there are no guarantees when dealing with non-routine problems.