PHYS1010 - 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 for 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 picture's 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. Fourth, 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 that 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 equations that 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 that 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. 

The previous was excerpted from "The Competent Problem Solver, A Strategy for Solving Problems in Physics", University of Minnesota, School of Physics & Astronomy, 1994. It was transcribed by David DeMuth 

Copies of this workbook are available at the CU Bookstore. Several copies are also on reserve in the Math-Physics Library.