Purpose of Word Problems

< 14.6 Math as a Language 2 | Topic Index | 15.2 Understanding Word Problems 1 >

Word Problems are universally considered as a difficult aspect of mathematics. Before considering the difficulties, let us see the objectives or reasons why word problems are an important part of the math curriculum.

Some of the objectives are easily apparent to most teachers.

Word problems describe situations in life where math can be used to analyse the situation, find alternatives and find a solution. This enables students to understand the relevance of math to their lives and possibly reinforces their motivation to learn the subject. But teachers usually have a simplistic understanding of life situations. Teaching of &ldquo;operation metaphors&rdquo; are not explicitly a part of the math curriculum. Teachers do not even realise that these are one of the sources of the difficulties students face while doing word problems. We will deal with this issue in detail in the next chapter. Word problems present a variety of mathematical computations and procedures, in contexts relevant to life. Hence, they enable students to practice the computations &amp; procedures with an understanding of their relevance. This enables learning at a deeper level. Understanding a word problem, writing its solution in logical steps and interpreting the solution in terms of the rea-life context, enhance appreciation of the precise nature of math vocabulary &amp; syntax. A math student has to be as careful with language as a lawyer!
 * 1) Applications of Math to real life situations
 * 1) Fluency with computations &amp; procedures
 * 1) Precise use math-related vocabulary &amp; syntax

Critical Thinking

The most important objective of solving word problems is to develop critical thinking. Most teachers may not be aware of this aspect. We will see this in detail in Chapter 29.7 &ldquo;Types of Thinking&rdquo;

Let us now look at several other objectives which may also not be apparent to teachers.

Using a familiar life situation or a story reveals its relevance. It kindles interest of the students and increases motivation to learn the topic. History of math has many such stories of how new ideas were thought of. For example, before introducing the idea of exponents, introduce and discuss with students a problem which needs the use of exponents. The famous chess story where a king is requested to place 1 grain of rice in the 1stsquare and keep on doubling the number of grains in the subsequent squares could be used. Let the students arrive at the idea of &ldquo;repeated&rdquo; multiplication before introducing the notation as a short cut to represent such operations. Using a story from history of math can also reveal its connection with the previous topics. When doing decimal numbers (which are usually done after fractions) use a problem which uses both representations thus emphasising their equivalence and interchangeability. Here the social conventions of using these representations in certain fields can be brought out. For example teachers give fractional marks to questions in answer papers in rational number format, whereas all prices are denoted in decimal notations.
 * 1) Introducing a new topic
 * 1) Connecting a topic to previous topics

Developing Logical &amp; Structured Thinking

Teachers also need to realise that most applications of math in real life, which are understandable to students would be from arithmetic and elementary geometry. Most other applications in science &amp; engineering use more complex topics like calculus, trigonometry &amp; differential equations. It will be difficult for both the teachers &amp; students to provide easy to understand examples.

But what needs to be emphasized at all levels of schooling is that the basic purpose of learning math is to &ldquo;develop logical &amp; structured thinking&rdquo;. At every level of school from K to 12, math provides ample opportunities for developing these skills. The tragedy is that instead of doing the above, math has been reduced to memorizing computations &amp; procedures. This has been a major reason for the development of math anxiety &amp; phobia among students.

We give a few explorations for developing logical thinking in K-5 level.

In the next chapter, we will deal with some of the difficulties students face in understanding &amp; solving word problems.
 * 1) Given any number, we can always provide a bigger number. Hence there is no &ldquo;biggest&rdquo; number
 * 2) Visualise the difference between odd, even, composite &amp; prime numbers
 * 3) Visualise number 324. Write it in Base 8 number system.
 * 4) Why is ODD + ODD = EVEN whereas ODD X ODD = ODD?
 * 5) What exactly is &ldquo;Carry over&rdquo; in addition?
 * 6) Give an example in life where it makes no sense to &ldquo;put together&rdquo; 2 numbers stated in the same unit of measurement.
 * 7) Why do we take LCM while adding 2 fractions?

< 14.6 Math as a Language 2 | Topic Index | 15.2 Understanding Word Problems 1 >