Problem solving

Hiroki Okubo

1 Introduction

How do you solve problems that arise in your rela-tionships with other people? We consider the pro-cess of solving problems, as well as some of thehindrances and aids to problem solving, an effort toovercome obstacles obstructing the path to a solu-tion.

The focus is on individual problem solving. Itis worth remembering, however, that working ingroups often facilitates problem solving. The solu-tions reached by groups often are better than thosereached by individuals. We engage in problem solv-ing when we need to overcome obstacles to answera question or to achieve a goal. If we quickly canretrieve an answer from memory, we do not have aproblem. If we cannot retrieve an immediate an-swer, then we have a problem to be solved.

How people solve problems depends partly onhow they understand the problem. Consider anexample of how understanding the nature of theproblem matters.

2 The problem-solving cycle

The problem-solving cycle includes: problem iden-tification, problem definition, strategy formulation,organization of information, allocation of resources,monitoring, and evaluation.

In considering the steps, remember also the im-portance of flexibility in following the various stepsof the cycle. Successful problem solving may in-volve occasionally tolerating some ambiguity re-garding how best to proceed. Rarely can we solveproblems by following any one optimal sequence ofproblem-solving steps. We may go back and forththrough the steps. We can change their order, oreven skip or add steps when it seems appropri-ate. Following is a description of each part of theproblem-solving cycle.

1. Problem identification: Do we actually have aproblem?

2. Problem definition and representation: Whatexactly is our problem?

3. Strategy formulation: How can we solve theproblem? The strategy may involve analy-

sis — breaking down the whole of a complexproblem into manageable elements. Instead, orperhaps in addition, it may involve the comple-mentary process of synthesis — putting to-gether various elements to arrange them intosomething useful. Another pair of complemen-tary strategies involves divergent and conver-gent thinking. In divergent thinking, youtry to generate a diverse assortment of possiblealternative solutions to a problem. Once youhave considered a variety of possibilities, how-ever, you must engage in convergent think-

ing to narrow down the multiple possibilitiesto converge on a single best answer.

4. Organization of information: How do the var-ious pieces of information in the problem fittogether?

5. Resource allocation: How much time, effort,money, etc., should I put into this problem?

6. Monitoring: Am I on track as I proceed tosolve the problem?

7. Evaluation: Did I solve the problem correctly?

3 Types of problems

Problems can be categorized according to whetherthey have clear paths to a solution. Well-

structured problems have clear paths to solu-tions. These problems also are termed well-defined

problems. An example would be, “How do youfind the area of a parallelogram?” Ill-structured

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problems lack clear paths to solutions. Theseproblems are also termed ill-defined problems.

Cognitive psychologists often have studied a par-ticular type of well-structured problem: the class ofmove problems, so termed because such problemsrequire a series of moves to reach a final goal state.Perhaps the most well known of the move problemsis one involving two antagonistic parties.

• Three hobbits and three orcs are on a riverbank. The hobbits and orcs need to cross overto the other side of the river. They have forthis purpose a small rowboat that will holdjust two people. If the number of orcs on eitherriver bank exceeds the number of hobbits onthat bank, the orcs will eat the hobbits on thatbank. How can six creatures get across to theother side of the river.

Here are examples of ill-structured problems.

• A woman who lived in a small town married 20different men in that same town. All of themare still living, and she never divorced any ofthem. Yet she broke no laws. How could shedo this?

• You have loose black and brown socks in adrawer, mixed in a ratio of five black socksfor every brown one. How many socks do youhave to take out of that drawer to be assuredof having a pair of the same color?

4 Negative and positive trans-

fer

People have particular mental sets that promptthem to fixate on one aspect of a problem or onestrategy for problem solving to the exclusion ofother possible relevant ones. They are carryingknowledge and strategies for solving one kind ofproblem to a different kind of problem. Transfer isany carryover of knowledge or skills from one prob-lem situation to another. Transfer can be eithernegative or positive. Negative transfer occurswhen solving an earlier problem makes it harder tosolve a later one. Positive transfer occurs whenthe solution of an earlier problem makes it easierto solve a new problem.

Radiation problem is one of the result of positivetransfer.

• The radiation problem: Imagine that you area doctor treating a patient with a malignantstomach tumor. You cannot operate on the pa-tient because of the severity of the cancer. Butunless you destroy the tumor somehow, the pa-tient will die. You could use high-intensity X-rays to destroy the tumor. Unfortunately, theintensity of X-rays needed to destroy the tu-mor also will destroy healthy tissue throughwhich the rays must pass. X-rays of lesser in-tensity will spare the healthy tissue, but theywill be insufficiently powerful to destroy thetumor. What kind of procedure could you em-ploy that will destroy the tumor without alsodestroying the healthy tissue surrounding thetumor?

• The military problem: A general wishes tocapture a fortress located in the center of acountry. There are many roads radiating out-ward from the fortress. All have been mined.Although small groups of men can pass overthe roads safely, any large force will detonatethe mines. A full-scale direct attack is there-fore impossible. What should the general do?

References

[1] R. J. Sternberg and K. Sternberg, (2009) Cog-nition, 6th edition, Wadsworth

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