摘要 : Problem solving is central to mathematics. Yet prob-lem-solving skill is not what it seems. Indeed, the field of problem solving has recently undergone a surge in research interest and insight but many of the results of this resea... 展开 Problem solving is central to mathematics. Yet prob-lem-solving skill is not what it seems. Indeed, the field of problem solving has recently undergone 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 exposition of this view was provided by Polya (1957). He discussed a range of general problem-solving strategies, such as encouraging mathematics students to think of a related problem and then solve the current problem by analogy, or to think of a simpler problem and then extrapolate to the current problem. The examples Polya used to demonstrate his problem-solving strategies are fascinat-ing and his influence can probably be sourced, at least in part, to those examples. Nevertheless, in over half a century, no systematic body of evidence demonstrating the effectiveness of any general problem-solving strate-gies has emerged. It is possible to teach learners to use general strategies such as those suggested by Polya (Sch-oenfeld, 1985) but that is insufficient. There is no body of research based on randomised, controlled experiments indicating that such teaching leads to better problem solving. 收起