Teaching General Problem-Solving Skills Is Not a Substitutefor, or a Viable Addition to, Teaching Mathematics

摘要

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 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 fascinating, and his influence probably can be sourced, at least in part, to those examples. Nevertheless, in overa half century, no systematic body of evidence demonstrating the effectiveness of any general problem-solving strategies has emerged. It is pos-sible to teach learners to use general strategies such as those suggested by POlya (Schoenfeld, 1985), but that is insufficient. There is no body of research based on randomized, controlled experiments indicating that such teaching leads to better problem solving.