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?