The process of problem solving                          3/1
Problem Statement
The
first
obstacle









Obstacle gone
The problem statement itself sometimes discourages us from attempting to solve a problem. A large number of words, multiple conditions and puzzling sentences are a few of the factors that can, and do, give rise to confusion when we read the problem statement. This confusion results from the fact that a persons working memory cannot embrace the entire problem at once. This is a consequence of how we are built, not a measure of intelligence.

Since reading the problem causes confusion, do the obvious and avoid reading the problem. Instead scan the problem, looking only for what the problem asks for. All the details, the if's, and's and but's should be ignored. Try this on the problem statement below. If you do this honestly, you will not be aware of anything about the problem except what the problem asks for.

SureMath Problem Solving
SureMath Problem Solving
SureMath Problem Solving
Figure 3.1
Respond
to
what
is
asked
for
Having identified what is asked for, How many mints were originally in the bowl?, your next chore is to respond to what is asked for. Return to the problem to see if it tells you how to respond. Don't look at the nitty-gritty detail. Look for the big picture.

The big picture is that the original number of mints is the sum of the number left and the number taken.

SureMath Problem Solving
SureMath Problem Solving
SureMath Problem Solving
SureMath Problem Solving
Figure 3.2
Start
simple










Respond to
what the
equation
asks for
Note the simple and obvious nature of the response. A problem solution is best started using a true statement that is independent of the details of the problem. The tendency of the novice problem solver is to try to get all the details into the starting point. Avoid doing this and you will solve problems easily and reliably.

This equation requests information about left and took. Go back to the problem statement to see if it tells us anything about these things. Indeed it does. It tells us the left is 17 and that there are three people taking mints. This provides the information needed to respond to the request made by the current requesting equation.

SureMath Problem Solving
SureMath Problem Solving
SureMath Problem Solving
SureMath Problem Solving
SureMath Problem Solving
Figure 3.3
Respond
to what
the equation
asks for.
The new requesting equation wants information about the mints taken by the individuals involved. We now get to use the details in the problem statement. These describe the mints taken by each person. First is Sean and the appropriate response can be written from the problem statement.
SureMath Problem Solving
SureMath Problem Solving
SureMath Problem Solving
SureMath Problem Solving
SureMath Problem Solving
SureMath Problem Solving
Figure 3.4
Continuing to identify the information about the mints taken by the other two individuals takes you to the answer to the problem using appropriate algebra as needed. To see the complete solution click here. Use the Back capability of your browser to return to this page.
What
have we
learned
about
problem
statements?
A problem statement is a source of information much like a dictionary, telephone book or reference book. It is a place to look up things when an equation requests information. Don't try to understand the problem statement. Trying to understand a problem statement can quickly lead to confusion, which results in flailing at the problem rather than solving it. The understanding of a problem evolves as it is solved.
In a
nutshell
Starting a problem solution is the simplest, least time consuming step in solving a problem.

Problems solve themselves.


A problem is understood by solving it, not by pondering it.
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