Think of problem solving as working your way through a maze. In negotiating a maze, you make your way toward your goal step by step, making some false moves but gradually moving closer to the intended end point. What guides your choices? Heuristics, or rules of thumb. It is a strategy that is powerful and general, but not absolutely guaranteed to work. Heuristics are crucial because they are the tools by which problems are solved.
Each learner must know what heuristics are and must be aware of their power. Also, each learner must have both general and specific heuristics. General heuristics are cognitive "rules of thumb" that are useful in solving a great variety of problems. They are usually content-free and apply across many different situations. Specific heuristics are used in specialized areas, often specific subject domains or professions.
Probably the most powerful general heuristic is "means-ends analysis." Essentially, the heuristic is this: form a subgoal to reduce the discrepancy between your present state and your ultimate goal state. Phrased more colloquially: do something to get a little closer to your goal.
Problems defy one-shot solutions; they must be broken down. Means-ends analysis accepts incremental advancement toward a goal. You apply it again and again, trying to reduce the discrepancy further. By means of this less-than-direct path, you find your way to the ends you seek. Such a search is not simply a process of trial and error, because the steps taken are not blind or random. Rather, the application of a series of tactical steps leads you ever closer to the goal. Mistakes made along the way must be accepted as inextricable from the problem solving process.
The benefits conferred by means-ends analysis may be as emotional as intellectual. If a large and complex problem seems daunting as a whole, perhaps one can summon the will to accomplish a small piece of it. And that success can motivate one to persist. Thus starting a task can make the effort self-sustaining. "Just do it!" is not solely a great marketing slogan; it can also be seen as a directive to disregard the ominous hulking problem that looms ahead and simply take the first step.
What are some other heuristics? One goes by the name of "working backward." First, consider your ultimate goal. From there, decide what would constitute a reasonable step just prior to reaching that goal. Then ask yourself, What would be the step just prior to that? Beginning with the end, you build a strategic bridge backward and eventually reach the initial conditions of the problem. Working backward makes "next steps" plainer than simply wishing and hoping that dreams will materialize.
A third heuristic seeks to solve problems by "successive approximation." Initial tries at solving a problem may result in a product that is less than satisfying. Writing is a good example. Few accomplished writers attempt to write perfect prose the first time they set pen to paper (or fingertips to keyboard). Rather, the initial goal is a rough draft or an outline or a list of ideas. Over time, a manuscript is gradually molded into form. New ideas are added. Old ones are removed. The organization of the piece is reshaped to make it flow better. Eventually, a polished form emerges that finally approximates the effect that the author intended. Successive approximation accepts the design process as problem solving, a series of zigs and zags toward something better. Not only is such a process compatible with human information processing, but awareness of the principle can sustain a half-baked idea that initially seems raw, wild, and foolish but is just possible the germ of an eventual marvel.
A fourth and final example of a heuristic involves portraying the problem at hand in an explicit "external representation." List, describe, diagram, or otherwise render the main features of the problem. This heuristic has several important features. First, it allows us to represent more complexity than we can hold in mind at once. Depicting a problem on paper, whiteboard, or computer screen relieves short-term memory of the burden of representing the problem and allows the processing capacity of our brains to be directed toward solving it. An incidental benefit is that often the very attempt to represent the problem explicitly forces a problem solver to be clear about what it is he or she is trying to do and about what stands in the way. Another benefit of external representation is that the medium chosen to portray a problem may help the solver see the problem in a new way. Finally, an external representation is potentially a public document. The fact that other people can see it might help a group reach consensus about the nature of a problem.
All heuristics help break down a problem into pieces. The problem as a whole is thus transformed. It is no longer a chaotic mass. Rather, through the creation of various subgoals, each of the pieces becomes manageable. The importance of monitoring subgoals is an example of a more general phenomenon: one common feature of problem solving is the capacity to examine and control one’s own thoughts. This self-monitoring is known as metacognition. The mind exercising metacognition asks itself, What am I doing? and How am I doing? These self-directed questions are assumed in the application of all heuristics.
Problem solving requires both the vigilant monitoring and the flexibility permitted by metacognition. When solving problems, means shift continually depending on one’s position relative to desired goals. Even goals change as old goals are superseded by new and better ones. Maintaining flexibility is essential. Too often we feel wedded to a chosen strategy and continue to apply that strategy even if it leads us wildly astray. When this happens, it is usually wrong to conclude that we must start over. The important question is always "What do I do now, given my goal, my current position, and the resources available to me?" Getting off course along the way is fully expected. Cool-headed reappraisal is the best response – not mindless consistency, panic, or surrender.
Perhaps more powerful than any heuristic is an understanding that, by its very nature, problem solving involves error and uncertainty. Even if success is achieved, it will not be found by following an unerring path. The possibilities of failure and of making less-than-optimal moves are inseparable from problem solving. The willingness to suspend judgment – to accept temporary uncertainty – is an important aspect of thinking in general. John Dewey linked tolerance of uncertainty to reflective thinking:
"Reflective thought involves an initial state of doubt or perplexity….To many persons both suspense of judgement and intellectual search are disagreeable; they want to get them ended as soon as possible….To be genuinely thoughtful, we must be willing to sustain and protract the state of doubt, which is the stimulus to thorough inquiry."
How then is it possible to improve problem-solving ability? First, we need to recognize when we are engaged in problem solving and accept as natural, normal, and expected the stepwise and discursive path toward a goal through the application of general and specific heuristics. Second, we must not let anxiety take hold. Anxiety is a spoiler in the problem-solving process. It stalks right behind uncertainty, ready to pounce. Demanding and uncertain environments, the seedbeds of all problem solving, are fertile ground for anxiety. Uncertainty is an integral part of the business of solving problems. Those who cannot bear situations in which it is impossible to see the way clearly to the end are emotionally ill-prepared to solve problems.
* Excerpts from "What is problem solving?" by Martinez, M.E. Phi Delta Kappan, April 1998, pp. 605 – 609.