John Sweller, Richard Clark, and Paul Kirschner
Problem solving is central to mathematics. Yet problem-solving skill is not what it seems. Indeed, the field of problem solving has recently under- gone a surge in research interest and insight, but many of the results of this research are both counterintuitive and contrary to many widely held views. For example, many educators assume that general problem-solving strategies are not only learnable and teachable but are a critical adjunct to mathematical knowledge. The best known exposi- tion of this view was provided by Pólya (1957). He discussed a range of general problem-solving strat- egies, such as encouraging mathematics students to think of a related problem and then solve the current problem by analogy or to think of a sim- pler problem and then extrapolate to the current problem. The examples Pólya used to demonstrate his problem-solving strategies are fascinating, and his influence probably can be sourced, at least in part, to those examples. Nevertheless, in over
