#254 from R&D
Innovator Volume 6, Number 1
Do Creative Solutions Come From?
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,
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
the problem in a different way.
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.
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).
at the problem in a different way.
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
What is the length of x?
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.
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.
the conventional uses of objects.
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
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.
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.
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.
the problem into subgoals.
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
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.
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