Cognitive Process Instruction: Research on Teaching Thinking Skills

By Jack Lochhead; John Clement | Go to book overview

Can Heuristics Be Taught?

The Elements of a Theory and a Report on the Teaching of General Mathematical Problem-Solving Skills1

Alan H. Schoenfeld
INTRODUCTION
Can students be taught general strategies that truly enhance their abilities to solve mathematical problems? Or are the heuristics described by Polya and others merely a description of the actions of accomplished problem solvers? Are they essentially valueless as prescriptions for problem solving? While many mathematicians are convinced that they employ heuristics, there is little evidence that general problem-solving skills can be taught.I offered a course based on the applications of heuristics to mathematics majors at the University of California, Berkeley. This article presents the rationale for heuristics and notes some questions about their effectiveness in the teaching of problem solving. I offer some suggestions regarding these questions, and describe the course I used to implement these suggestions. I discuss what we can and cannot expect students to assimilate--heuristics they can learn to use and obstacles that prevent them from employing others effectively.
SECTION 1. Problem Solving in Perspective: Theory and Practice
George Polya How to Solve It was published in 1945. That and his subsequent work laid the foundations for the study of general strategies for problem solving in mathematics, focusing on the broad strategies he called "heuristics." Definitions vary, but the following is compatible with Polya's usage:

A heuristic is a general suggestion or strategy, independent of subject matter, that helps problem solvers approach, understand, and/or efficiently marshal their resources in solving problems.

Examples of heuristics are: "draw a diagram if possible," "try to establish subgoals," and "exploit analogous problems"; a more complete list is given in Section 3. A rationale for the study and teaching of heuristics is the following:
1. Through the course of his career, a problem solver develops an idiosyncratic style and method of problem solving. A systematic use of these strategies may take years to develop fully.
2. In spite of these idiosyncracies, there is a surprising degree of homogeneity in the approaches of expert problem solvers.
____________________
1
Revised version of a paper to appear in Applied Problem Solving, edited by R. ERIC Lesh, 1979.

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