The process of problem solving                          4/1

Starting

Where
to
start
Start a problem solution by responding to what the problem asks for.
How
to
do it
To start a problem solution the only thing you are interested in is what the problem asks for. In order to not get confused or wrapped up in all the details of the problem ignore the details. Scan, do not read, the problem looking for such words as when, how much, where, how far, how long, find, show that and the like. The words connected to these key words will define what the problem asks for.

With what is asked for identified the next step in getting started is to answer the question asked as simply and directly as possible. The first place to look for the answer to the question asked is the problem statement. Figure 4.1 is an example in which the answer is in the problem statement.

SureMath Problem Solving
Figure 4.1
Keep
it
simple
The problem asks for the number of brake liners produced in Cleveland. To find out we proceeded to read the problem statement to see if it tells us. Indeed it does. In the first sentence it tells us that the number produced in Cleveland is twice the number produced in Sarasota. We stop reading and write this as the starting equation.

At this point ignore the rest of the problem statement. All we are after is an answer to what the problem asks for. We found it in the first sentence. The rest of the problem statement is of no interest to us. All we want to do is to write a starting equation that responds simply and directly to what the problem asks for.

If
it's not
in the
problem
statement
The answer to what the problem asks for is frequently in the problem statement in elementary and middle school. As you move on to more advanced work the answer to what the problem asks for is less likely to be in the problem statement. Indeed in subject matter courses like physics or chemistry the answer to what is asked for will rarely be in the problem statement.

If the answer to what the problem asks for is not in the problem statement you will have to use knowledge. Knowledge consists of what you know or can find out. Thus the response to what the problem asks for is available to you from your own experience, text books, reference books, the world wide web, teachers, friend, encyclopedia, dictionaries and many other sources. The response to what the problem asks for will frequently be a concept from the particular course you are studying.

Figure 4.2 provides and example in which knowledge is used to respond to what the problem asks for.

SureMath Problem Solving
Figure 4.2
Starting the solution required use of knowledge namely the meaning of the word average. This knowledge may not yet be present in the internal knowlege base of the younger student. The problem would then be used to introduce the student to the meaning of average to help make it a part of the student's internal knowledge. Note that the student's internal knowledge is a small part of the knowledge available to the student.

Though the problem statement did not explicitly answer the question asked it did so implicitly through the presence of the word average. Learn to use the problem statement as a source of information. The problem statement is not an object to be understood. Instead it is simply a source of information and should be used in the same way as a telephone book, dictionary, text book and similar reference material. It is a place to look up information. In starting a problem you want to know what the problem statement tells you about how to respond to what the problem asks for. It will tell you either explicitly or implicitly. If it is not explicit then you abandon the problem statement and look for the answer in the knowledge pointed to by the implications of the problem. This is further illustrated in Figure 4.3.

SureMath Problem Solving
Figure 4.3
Respond
to what
the problem
asks for.
Even those who have no experience in physics could surmise that they need to know something about falling objects to respond to what the problem asks for. Those familiar with some elementary physics would have the knowledge needed to write the initial equation.

Once the starting equation and the meaning of the symbols are known anyone with even modest algebraic skill can obtain the answer to the problem.

Starting a problem solution is the simplest, least time-consuming step in solving a problem.
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