Word problem (mathematics education)

In science education, a word problem is a mathematical exercise where significant background information on the problem is presented as text rather than in mathematical notation. As word problems often involve a narrative of some sort, they are occasionally also referred to as story problems and may vary in the amount of language used.

Here is a mathematical problem in mathematical notation:

The same problem might be presented in the form of a word problem as follows:

The answer to the word problem is that John is 15 years old, while the answer to the mathematical problem is that J equals 15 (and A equals 35).

Word problems can be examined on three levels:

Linguistic properties can include such variables as the number of words in the problem or the mean sentence length. The logico-mathematical properties can be classified in numerous ways, but one such scheme is to classify the quantities in the problem (assuming the word problem is primarily numerical) into known quantities (the values given in the text of the problem), wanted quantities (the values that need to be found) and auxiliary quantities (values that may need to be found as intermediate stages of the problem).

The most common types of word problems are distance problems, age problems, work problems, percentage problems, mixtures problems and numbers problems.

Word problems commonly include mathematical modelling questions, where data and information about a certain system is given and a student is required to develop a model. For example:

These examples are not only intended to force the students into developing mathematical models on their own, but may also be used to promote mathematical interest and understanding by relating the subject to real-life situations. The relevance of these situations to the students is varying. The situation in the first example is well-known to most people and may be useful in helping primary school students to understand the concept of subtraction. The second example, however, does not necessarily have to be "real-life" to a high school student, who may find that it is easier to handle the following problem:

Word problems are a common way to train and test understanding of underlying concepts within a descriptive problem, instead of solely testing the student's capability to perform algebraic manipulation or other "mechanical" skills.

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