Well-Structured Versus Ill-Structured Problems
Mathematicians and cognitive psychologists often distinguish between "well structured" and "ill-structured" problems.
Definition
A well-structured problem yields a right answer through the application of an appropriate algorithm. Most textbook problem sets in mathematics, science, engineering, or business feature well-structured problems that have right answers.
In contrast, an ill-structured problem (sometimes called an "ill-defined" problem or a "messy" problem) doesn't yield a particular, certain answer. Ill-structured problems mirror real world problems where data are conflicting or inclusive, where disputants disagree about appropriate assumptions or theories, or where values are in conflict. Disputants may propose different solutions to the problem, each with particular strengths and weaknesses. In approaching an ill-structured problem, the thinker must attend to alternative points of view and create arguments justifying the proposed solution.
In other words, one responds to a well-structured problem with a right answer but to an ill-structured problem with a claim and a justifying argument.
Examples
King and Kitchener, 1994 p. 11 provide the following examples to distinguish between well-structured and ill-structured problems:
Examples of well-structured problems:
- Converting a unit of measure between its English and metric equivalents
- Solving for X in an algebraic equation
- Calculating the trajectory of a rocket's flight
Examples of ill-structured problems:
- Determining what really happened at the Hue massacre in Vietnam
- Judging the adequacy of a theoretical proposition
- Predicting how to dispose of nuclear waste safely
