Experts (teachers) in a particular field are often so fluent in solving problems from that field that they can find it difficult to articulate the problem solving principles and strategies they use to novices (students) in their field because these principles and strategies are second nature to the expert. To teach students problem solving skills, a teacher should be aware of principles and strategies of good problem solving in his or her discipline.
The mathematician George Polya captured the problem solving principles and strategies he used in his discipline in the book How to Solve It: A New Aspect of Mathematical Method(Princeton University Press, 1957). The book includes a summary of Polya’s problem solving heuristic as well as advice on the teaching of problem solving.
Novices in a particular field typically have not yet developed effective problem solving principles and strategies. Helping students identify their own problem solving errors is part of helping them develop effective problem solving skills. Beverly Black and Elizabeth Axelson’s list of common problem solving errors, adapted from Arthur Whimbey and Jack Lochhead’s book Problem Solving and Comprehension (Lawrence Erlbaum, 1999), provides useful insight into the mindset of a novice problem solver.
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The CFT has prepared guides to a variety of teaching topics with summaries of best practices, links to other online resources, and information about local Vanderbilt resources.
