MAT109 Assignment 2: Mathematical Problem Solving
The goal of any mathematics course is to introduce you to a
variety of methods used to solve real-world problems. In this way, you are able
to practice solving problems and, along the way, improve your critical thinking
skills.
It may seem that solving a mathematical problem involves
nothing more than knowing the right formula and the following the correct
steps. However, that is only part of the process. Solving problems is more of
an art than a science which means that human intuition and imagination
play an extremely important role in the process. Through
these human abilities, we link experience to knowledge and skills resulting in
a synergy that leads to a solution.
In 1945, mathematician George Polya (1887-1985) published a
book titled How To Solve It in which he demonstrated his approach to solving
problems. Here are his principles of problem solving:
Polya’s First Principle: Understand the Problem
To solve a problem, you have to understand the problem.
Do you understand all the words used in stating the problem?
What is the problem looking for?
What data or information has been provided in the problem?
Are there any special conditions mentioned in the problem
that we need to consider in the solution?
Can you restate the problem in your own words?
Can you draw a picture or make a diagram that could help you
solve the problem?
Is there enough information in the problem to help you find
a solution?
Polya’s Second Principle: Devise A Plan
There are many different ways to solve a problem. The way you choose is based upon your own
creativity, level of knowledge, and skills. Basically, solving the problem
involves finding the connections that exist between the data you’ve been
provided and the unknown you need to find.
Here is the assignment:
Think of a problem that involved several steps that you had
to follow to reach a solution. If you
can’t think of a problem, look at any of the problems in Chapter 1 in the book
and pick one that you can explore here.
Prepare a 200-300 word multiple paragraph response defining
the problem and the steps need to reach a solution.
Then in your responses to at least two classmates, address
the following items:
Comment on the problems they demonstrated and the steps they
employed to reach solutions.
What would you have done the same or different?
Do you agree with the solution?
Can you suggest a different approach to solving the same
problem?
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