#254 from R&D Innovator Volume 6, Number 1          January 1997

Where Do Creative Solutions Come From?
by Richard E. Mayer, Ph.D.

Dr. Mayer is professor of psychology at the University of California, Santa Barbara.  He is the author of Thinking, Problem Solving, Cognition (W.H. Freeman & Co., New York, 1992).

A problem exists when a person has a goal but doesnít know how to achieve it.  Thus, a problem consists of a given state, a goal state, and obstacles between them.  Creative problem solving occurs when a person invents a novel solution to a problem.  In short, a creative problem solver must find a path between the given state and goal state of the problem. 

Where does a creative solution come from?  When confronted with a problem, what do successful problem solvers do?  What can you do when you don't know what to do?  Based on research and theory in the cognitive psychology of problem solving, I can offer six basic suggestions for stimulating creative thinking.

Restate the problem in a different way. 

Sometimes, the most difficult part of problem solving is understanding the problem.  It can be useful to describe the given state and goal state of the problem in words, symbols, diagrams, concrete objects or any other format available to you.  Then, you should try to restate the givens or goals in a different way.

For example, suppose your problem is to destroy an inoperable tumor without destroying the healthy surrounding tissue by using rays that, at sufficient intensity, can destroy anything in their path.  One way to restate this problem is to ask how you can use the rays so that the intensity is high at the tumor but low in the surrounding tissue.  By reformulating the problem in this way, it is easier to invent the solution of having many weak rays all converge on the tumor.

Many weak rays (arrows) converge on the tumor (dot in middle) but remain weak while passing through the healthy tissue (oval).

Look at the problem in a different way. 

Sometimes the process of problem understanding occurs visually.  In this case you may experience a sudden reorganization when you are looking at a visual representation of the problem.  In short, you literally can look at the problem situation in a new way.

For example, in the geometry problem shown below you are asked to find the length of a line x, and are told that the radius of the circle is 3 inches.  If you see the line as a hypotenuse of a right triangle, you are unlikely to find the solution.  However, if you can see the line as a diagonal inside a rectangle, you are on the road to a solution because the other diagonal is the radius of
the circle.  (Answer:  3 inches.  Determined from the other diagonal in the rectangle.)  

What is the length of x?

Remove mental blocks. 

People often impose constraints on the problem-solving situation that are really not necessary.  These self-imposed obstacles can be called mental blocks.  It is useful to detect and eliminate any unwarranted assumptions that limit the range of solution possibilities.

For example, suppose that your problem is to make four identical equilateral triangles using six equally-sized match sticks.  Many problem solvers approach this problem with the self-imposed constraint that the sticks can be arranged in only two dimensions, so they lay the sticks out and move them around on the surface of a table.  In contrast, a solution becomes more apparent when you remove the mental block of thinking only in two-dimensional space and realize that the solution could involve a three-dimensional approach.  You can build a three-sided pyramid such that each side and the base are equilateral triangles.

Six sticks make four equilateral triangles in this pyramid.

Ignore the conventional uses of objects. 

Sometimes your past experience can limit the way you think about how to use objects in a problem.  You can be so accustomed to using an object in a certain way that itís almost impossible to conceive of using it for a different function.  In those cases, you need to ignore the conventional function of objects.            

For example, suppose you are given a large paper square, four smaller paper squares, and some paper clips, and you are asked to attach the squares together and then hang your creation from an eyelet that is screwed in overhead.  Many problem solvers will use the paper clips in their conventional function--that is, to connect the paper squares together--but will have difficulty in using them in an unconventional function--that is, bending one paper clip into a hook.  To solve this problem, you have to suppress the conventional way of thinking about how to use paper clips. 

Find a related problem. 

If you cannot solve the problem thatís facing you, think of a related problem that you do know how to solve.  Try to use the solution procedure of the related problem as a way of solving the new problem.  This process of thinking by analogy involves finding a related problem in your memory, abstracting the solution principle or method from that problem, and applying that principle or method to the new problem. 

For example, suppose that you were asked to improve a standard radar system so that you could increase the area under surveillance.  Because the earth is curved and radar waves travel in straight lines itís not possible to pick up objects that are beyond the horizon.  To solve this problem, you can think of an analogous situation, such as throwing a ball so that it will hit a remote object and then bounce back to you.  This will work as long as the remote object can be reached by a straight line.  However, if you have a ceiling overhead, you could throw the ball at the ceiling at such an angle so that it would bounce off the ceiling and hit the remote object; then it would bounce off the object to the ceiling and off the ceiling back to you.  This principle can be applied to radar by installing satellites for reflecting radar waves. 

Radar pulse (from black box) reflects off satellite (circle) to remote object (plane), and then bounces back along the same path.

Break the problem into subgoals. 

When youíre faced with a large problem, a reasonable approach is to break it into a collection of smaller problems.  You can then work on methods for solving each part of the problem.

For example, in writing a computer program for an automated telephone ticket selling system for an airline, you can break the goal into more manageable subgoals.  These may include writing program modules to accommodate each possible option available to the end user.

These six techniques represent general approaches to creative solutions that have been studied by researchers in the field of problem solving.  These general heuristics should help you figure out what to do when you don't know what to do.     

Copyright 1997 by Richard E. Mayer

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