Lecture
Notes
for
Chapter 1
Chapter Title: “Problem Solving”
Read pages 1 – 45
Review the Errata Sheet: (http://cis.edcc.edu)
Textbook: Computer Math by Charles
Reeder
Special Instructions: The
homework for this chapter requires the use of a word processing application and
the IPO worksheet format.
Problem
solving becomes easier the more we do it—practice and more practice! I think it’s interesting to consider all the
ways we solve problems of various sorts.
What type of problem have you solved—one that when you first confronted
it there appeared to no solution? Or,
after considering it for a time, you were able to come up with a solution that
didn’t initially occur to you?
Problem
solving works best during the practice stages when you make the time available
to do it. (Note: don’t wait until the last minute to do the
homework.)
Can you
think of a problem you solved in your own life that was unrelated to math? For example, did you repair the garage door when
there was no one else to help—but you did it anyway? Were you able to meet a work deadline without
the resources that were promised—but you made it happen? We encounter tons of situations requiring our
ability to solve problems—the more we do it the better we become at solving
problems.
Section 1-2
Problem Solving Concepts:
Pages 4-6
in our textbook reveal two individuals who’ve provided some helpful points to
consider when identifying problem solving techniques.
First, Polya writes about four phases involved in the solution of
a problem. As you read his four steps
(understand the problem, devise a plan, implement the plan, review
the solution) be sure to consider the questions he poses. These questions are but a few that have been
taken from Polya’s book mentioned in the first
paragraph. So much of our ability to
solve problems is merely added onto the knowledge we’ve gained from solving
earlier problems.
Second, we
read bout Rubinstein’s anatomy of a problem.
His approach is much more general since it applies to professional,
social, political, and mathematical problems.
It’s interesting to note that we each see a situation differently. That is, it may be an “unsolvable” problem
for one person, while for another it’s “easy” to solve!
Practice
Problems, p. 6:--Consider the three aspects to the problems presented. Using the example as a guide, merely identify
the data, condition, and unknown in
problems 1-2.2, .4, .6. Then compare your response to those presented
in the Student Solution Manual. These
three parts of problem solving are important to recognize.
Now for
some brainstorming problems! (see pages 7-8) Answer the following problems: 1-2.11 and 1-2.13—spend ample time to arrive
at a solution and send your response using the Discussion Board where you’ll
see some directions for completing this part.
Be sure to
read the entire chapter—even those pages not mentioned in these notes. Now, let’s move on to the next section.
Section 1-3 The IPO Method:
Many of you
have already taken CIS 100 Introduction to Business Computing—in that class you
discussed the Information Processing Cycle (Input, Processing, Output, and
Storage). This Information Processing
Cycle is the basis for the IPO Method discussed in this section and in
developing the IPO worksheet that you’ll be using.
Compare the
IPO Worksheet that appears on page 14 (prepared as a Word table) with the IPO
Worksheet that’s shown on page 44 (prepared using paragraph indentions). You’ll be completing your homework using the
IPO worksheet—it can be presented in either one of the forms shown on page 14
or page 44.
Back on
pages 14-33—study the sections of the worksheet as well as the type of
information each section should contain.
(Be sure to know these sections!)
Points to
consider about the sections on the IPO worksheet!
Problem Statement: The
problem should be written exactly as stated—even if you don’t agree with the
wording. If you are working for a firm
that does consulting work for a vendor and the two firms have agreed to the
problem statement, you cannot then change it at a later date.
Output: Merely
state what you are trying to find. Don’t
embellish it.
Input: Be sure to include all of the data.
Process:
Notation: If you are using formulas, identify the elements of the formula
here. If there is no data for this
section, write None Needed.
Additional Information: If you need to obtain information from another source, you can list the
information here. BUT if the data has
been provided in the problem statement, then it needs to be listed in the Input
section. If there is no data for this
section, write None Needed.
Diagram: Some problems don’t require a diagram in order to solve it. If there is no data for this section, write None Needed.
Approach: This fourth sub-section of the Process section must explain in words
what is to be done in the Solution section that follows. Do not show any calculations in the Approach
section. (Example: “divide the numerator by the denominator to
obtain the percent.”)
Solution: This is the section where the actual
arithmetic/math will be apparent. This
is where you will add, subtract, multiply or divide. (Example:
2 / 4 = .50 or 50%)
Check: See page 33 regarding the Check
section. Always include a check for the
problem. Always aim at Step 6!
Prepared by Judy Forth
Winter 2009