A Logical Problem Solving Strategy
Introduction
At one level, problem solving is just that, solving problems. Presented with
a problem you try to solve it. If you have seen the problem before and you
already know its solution, you can solve the problem by recall. Solving
physics problems is not very different from solving any kind of problem. In
your personal and professional life, however, you will encounter new and
complex problems. The skillful problem solver is able to invent good solutions
for these new problem situations. But how does the skillful problem solver
create a solution to a new problem? And how do you learn to be a more skillful
problem solver?
Research in the nature of problem solving has been done in a variety of
disciplines such as physics, medical diagnosis, engineering, project design and
computer programming. There are many similarities in the way experts in these
disciplines solve problems. The most important result is that experts follow a
general strategy for solving all complex problems. If you practice
and learn this general strategy you will be successful in this course. In
addition, you will become familiar with a general strategy fro solving problems
that will be useful in your chosen profession.
A Logical Problem-Solving Strategy
Experts solve real problems in several steps. Getting started is the most
difficult step. In the first and most important step, you must accurately
visualize the situation, identify the actual problem, and comprehend
the problem. At first you must deal with both the qualitative and
quantitative aspects of the problem. You must interpret the problem in light
of your own knowledge and experience; ie. Understanding. This enables
you to decide what information is important, what information can be ignored,
and what additional information may be needed, even though it was not
explicitly provided. In this step it is also important to draw a picture of
the problem situation. A picture is worth a thousand words if, of course,
it is the right picture. (If a picture is worth a thousand words, and words
are a dime a dozen, then what is a pictures monetary value?) In the second
step, you must represent the problem in terms of formal concepts and
principles, whether these are concepts of architectural design, concepts of
medicine, or concepts of physics. These formal concepts and principles enable
you to simplify a complex problem to its essential parts, making the search for
a solution easier. Third, you must use your representation of the problem to
plan a solution. Planning results in an outline of the logical steps
required to obtain a solution. In many cases the logical steps are
conveniently expressed as mathematics. Forth, you must determine a solution by
actually executing the logical steps outlined in your plan. Finally,
you must evaluate how well the solution resolves the original problem.
The general strategy can be summarized in terms of five steps:
- (1) Comprehend the problem.
- (2) Represent the problem in formal terms.
- (3) Plan a solution.
- (4) Execute the plan.
- (5) Interpret and evaluate the solution.
The strategy begins with the qualitative aspects of a problem and progresses
toward the quantitative aspects of a problem. Each step uses information
gathered in the previous step to translate the problem into more quantitative
terms. These steps should make sense to you. You have probably used a
similar strategy when you have solved problems before.
A Physics-Specific Strategy
Each profession has its own specialized knowledge and patterns of thought. The
knowledge and thought processes that you use in each of the steps will depend
on the discipline in which you operate. Taking into account the specific
nature of physics, we choose to label and interpret the five steps of the
general problem solving strategy as follows:
Focus the Problem:
In this step you develop a qualitative
description of the problem. First, visualize the events described in the
problem using a sketch. Write down a simple statement of what you want to find
out. Write down the physics ideas which might be useful in the problem and
describe the approach you will use.
Describe the Physics:
In this step you use your qualitative
understanding of the problem to prepare for the quantitative solution. First,
simplify the problem situation by describing it with a diagram in terms of
simple physical objects and essential physical quantities. Restate what you
want to find by naming specific mathematical variables. Using the physics
ideas assembled in step 1, write down equation which specify how these physical
quantities are related according to the principles of physics or mathematics.
Plan the Solution:
In this step you translate the physics
description into a set of equations which represent the problem mathematically
by using the equations assembled in step 2. Write down an outline of how you
will solve these equations to see if they will yield a solution, before you go
through the effort of actually doing any mathematics.
Execute the Plan:
In this step you actually execute the solution you
have planned. Combine the equations as planned to first determine an algebraic
solution. Then plug in all of the known quantities into the algebraic solution
to determine a numerical value for the desired unknown (target) quantity.
Evaluate the Answer:
Finally, check your work to see that it is
properly stated, reasonable, and that you have actually answered the question
asked.
Consider each step as a translation of the previous step into a slightly
different language. You begin with the full complexity of real objects
interacting in the real world and through a series of steps arrive at a simple
and precise mathematical expression.
The five-step strategy represents an effective way to organize your
thinking to produce a solution based on your best understanding of physics.
The quality of the solution depends on the knowledge that you use in obtaining
the solution. Your use of the strategy also makes it easier to look back
through your solution to check for incorrect knowledge and assumptions. That
makes it an important tool for learning physics. If you learn to use the
strategy effectively, you will find it a valuable tool to use for solving new
and complex problems. After all, those are the ones that you will be hired
to solve in your chosen profession.
Excerpted from "The Competent Problem Solver, A
Strategy for Solving Problems in Physics", University of Minnesota, School of
Physics & Astronomy, 1994.