Word problem (mathematics education)

In science education, a word problem is a mathematical exercise (such as in a textbook, worksheet, or exam) where significant background information on the problem is presented in ordinary language rather than in mathematical notation. As most word problems involve a narrative of some sort, they are sometimes referred to as story problems and may vary in the amount of technical language used.

A typical word problem:

Tess paints two boards of a fence every four minutes, but Allie can paint three boards every two minutes. If there are 240 boards total, how many hours will it take them to paint the fence, working together?

Word problems such as the above can be examined through five stages:

The linguistic properties of a word problem need to be addressed first. To begin the solution process, one must first understand what the problem is asking and what type of solution the answer will be. In the problem above, the words "minutes", "total", "hours", and "together" need to be examined.

The next step is to visualize what the solution to this problem might mean. For our stated problem, the solution might be visualized by examining if the total number of hours will be greater or smaller than if it were stated in minutes. Also, it must be determined whether or not the two girls will finish at a faster or slower rate if they are working together.

After this, one must plan a solution method using mathematical terms. One scheme to analyze the mathematical properties is to classify the numerical quantities in the problem into known quantities (values given in the text), wanted quantities (values to be found), and auxiliary quantities (values found as intermediate stages of the problem). This is found in the "Variables" and "Equations" sections above.

Next, the mathematical processes must be applied to the formulated solution process. This is done solely in the mathematical context for now.