Basic Principles of Problem Solving
These are purposely kept short here to aid you in keeping the basic
principles in your memory. They are also useful for class or group discussion
Problem solving is also decision making. Decision making
is essentially a problem process.
There is one best guide to problem solving. Centuries
of experience have shown that the scientific method or guide is the best
method for problem solving.
There are stages of mental activity to problem solving.
They have been recognized. SM-14 is a formula for them that is neither
too short nor too long. The stages are subject neutral. You must apply
techniques or action methods at the various stages to accomplish results.
The stages are used in a flexible manner. You may skip,
backtrack, stall, loop ahead or back, combine two or more ingredients,
use various combinations.
Break complex problems into sub-problems. Complex problems
should be broken down into sub-problems and sub-sub-problems. Follow SM-14
in solving sub-problems if they are complex.
Creative, non-logical, logical, and technical methods or techniques.
These are the supporting action techniques actually used in trying to
solve problems. What are often called “scientific methods”
are really the technical methods often used.
Procedural Principles and Theories. In problem solving
over the centuries a supporting culture and norms developed. They are
not standardized and are often controversial. Some are embodied in government
regulations for grant holders. Codes of ethics have often been assembled.
Much remains to be done to clearly present them to problem solvers.
Attributes and Thinking Skills. These are necessary
supporting ingredients required by problem solvers. The personal attribute
of honesty is of supreme importance. A wide variety of thinking skills
must be employed.
Skepticism. A healthy and practical skepticism is needed
– a questioning, challenging doubt of ideas and concepts, a mind
definitely open to new ideas. Because of past and present misunderstandings
about the scientific method, be skeptical of parts of existing literature
on problem solving.
Truth. Since it is so difficult or impossible to obtain
truth, our objective is “on the evidence available today the balance
of probability favors the view that . . .”
The theory of multiple working hypotheses. In most cases
in the use of the scientific method you end up with one educated guess
or hypothesis at stage 7 of SM-14. However, T.C. Chamberlin, in a famous
essay of 1892 [reprinted in Physical Science: Men and Concepts edited
by Omer, Knowles et al. (1962)], calls attention to the fact that there
are times when you must have more than one hypothesis, as in geology.
This may also happen in the social sciences and in decision making in
Falsification of the Hypothesis. Once a researcher arrives
at a hypothesis, there is a human tendency to seek evidence supporting
it. However, it must be challenged, and practical attempts to falsify
it should be included. There is much ignoring of contrary evidence, especially
in the social sciences.
Creativity Is Needed. Logical reasoning is essential,
but many problems are so complex that creative thinking must be used.
Learn to Abstract Basic Principles from what you read
Read a Variety of Publications. Extensive reading will
find you knowledge and trigger your imagination.
Assumptions are often necessary to speed progress, but
Decision Making. In problem solving you must make many
decisions. Learn to be a good decision maker.
Authoritative Opinions can often be wrong. Challenge
them if they don’t agree with your research.
Most Thinking Is Problem-Solving Thinking. If you analyze
your thinking, you will find that most of it concerns simple and complex
Critical Thinking is really problem-solving thinking.
Ask Questions. Ask what, why, which, where, when, who,
Don’t Ignore Contrary Evidence. This is one of
the major faults of untrained problem solvers.
Cost vs. Benefits. Always keep this in mind.
Look Back after you finish.
Think Aloud. Sometimes this helps in solving problems.
Use Sketches and Diagrams. Visual aids can be helpful.