Education.com
Try
Brainzy
Try
Plus

# What Does Problem Solving Involve? (page 2)

By Pearson Allyn Bacon Prentice Hall
Updated on Jul 20, 2010

### Types of Problems

In general, problems can be classified as either real-world application or process problems. The former refers to the type of problems that require adaptive reasoning in authentic, everyday situations (Silver, Kilpatrick, & Schlesinger, 1990). An example is the following:

Nate and Matt are friends at school. Nate likes to play at Matt’s house in the afternoon. Matt lives nine miles from the school. How far does Nate travel back to his house when he goes from school to Matt’s house and then back to his house, if he lives five miles on the other side of the school?

In contrast, a process problem is considered nontraditional. It describes a situation in which the solution path is not as readily discernable from the story as the application problem presents. Examples include:

1. If an 8-inch pizza serves two people, how many should two 12-inch pizzas serve?
2. Find two consecutive numbers whose product is an even number.

3. Arrange the digits 1–6 in six slots on the perimeter of a triangle so that all three sides add up to the same sum. 3

### Using Heuristics

Both types of problems require the solver to apply some type of heuristic. The word heuristic derives from the Greek word for discover and means a general strategy used to guide the problem solver in finding a solution (Charles & Lester, 1982). Typical heuristics include:

• drawing a picture
• using manipulatives
• working backward
• acting it out
• making a table or list
• using smaller numbers
• looking for a pattern
• guessing and checking

Unlike algorithms, which prescribe specific procedures that yield a result, the application of heuristics does not guarantee career solutions. One could draw a diagram or construct a table, for example, and not necessarily arrive at a logical or correct result. However in the absence of knowledge of exactly what to do, a heuristic helps students begin to solve the problem—the more heuristics with which students are familiar, the greater the likelihood of finding a solution.