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4.2
Applying the Problem Solving Methodology
P
urpose
The role this topic plays in quantitative reasoning
There is a strong interdependence between quantitative reasoning and problem solving. While steps
1 through 5 of the Problem Solving Methodology (PSM) are applicable to quantitative and qualita-
tive problem solving, steps 6 through 8 are very quantitative and use quantitative reasoning skills. In
quantitative disciplines, professionals use common terms like problems, problem definition, solutions,
validation, and a mathematical model to communicate across disciplines. As you make stronger connec-
tion with mathematical language, your learning process, the problem solving process, and quantitative
reasoning, your quantitative expertise performance will become stronger.
L
earning Goals
What you should learn while completing this activity
1. Gain a better understanding of the Problem Solving Methodology and its usefulness for solving a
complex problem.
2. Strengthen step 6 of PSM by producing effective mathematical models
3. Strengthen step 7 of PSM by effectively integrating sub-solutions (mathematical models)
4. Validate the model’s results for reasonableness and appropriateness (step 8 of the PSM)
D
iscovery
Finding out for yourself
Think back over some of the larger problems you have solved over the last few years. When have
you stopped to figure out a solution mathematically? List at least three problems where finding the
solutions required the use of mathematics. What was it about the problem that made you decide to use
mathematics? What role did the mathematics play or what value did it have?
W
hat Do You Already Know?
Tapping into your existing knowledge
1. How do you choose what kind of mathematics to use to solve a problem?
2. How do you narrow the description of a problem so that it is one that you can solve?
3. How do you divide a problem into sub-problems you know how to solve?
4. What is the difference between validating a sub-problem and validating the whole problem?
I
nformation
What you need to know
R
eadings