How Important Is Teaching Of Mathematics

It is a remarkable fact that, in almost every country, mathematics occupies a central place in the school curriculum.

At the level of primary school, there is general agreement on what mathematics should be taught. But when we turn to secondary schools, we note a remarkable variety in the content of the courses. In fact, it is possible to find countries in which the secondary mathematics curricula have almost nothing in common. And this must make us ask: `Is Mathematics really as important as is claimed?`

However, there is often much confusion about the sense in which the word `mathematics` is used. So perhaps we should begin by attempting to clarify our thoughts about this.

It may be helpful to distinguish three categories of mathematics.

1. Survival mathematics

That is, the mathematics that we need in order to go about our daily business and make good use of our leisure time. Some people refer to this as `the basics` or `the core curriculum` but this seems to imply that these needs are the same for everybody, which is clearly not true. City dwellers use different mathematics from those who live in a village a lawyer`s mathematical needs are different from those of a housewife) if your hobby is photography, you want different mathematics from a person who plays football. Survival mathematics is a reflection of our personal life-style.

And yet it has certain common features for all of us. First, we almost always have to use it in a situation that requires an immediate response: paying a bus fare, deciding where a tree is going to fall, estimating the date for the completion of a contract, getting each dish in the oven at the right time, choosing the right camera exposure, positioning oneself to intercept an attack by the opposing forwards.

Second, it is rarely carried out with paper and pencil (or even with a pocket calculator). Third, one is hardly aware that one is using mathematics at all. And this means that survival mathematics has little to do with formal mathematical instruction.

The very process of taking a problem out of a textbook in a lesson called mathematics, and writing the answer in an exercise book in one`s own time, makes it largely an irrelevance as far as survival mathematics is concerned.

This does not mean that mathematics teachers cannot help children to acquire the mathematics they need. But it is an illusion to suppose that this can be left to mathematics teachers alone. Other teachers, parents, elder brothers and sisters all have a part to play. In this sense, every teacher must expect to be a teacher of mathematics.

2. Mathematics for use

Next, much of the mathematics in the school curriculum is mathematics for use. This extends from quite simple skills, such as decimal arithmetic, up to advanced topics such as the use of differential calculus to find maximum and minimum values. It describes all the mathematics that some people need in order to do their work successfully.

The difficulty with most of the mathematics in this category is that it is job-specific only a minority of people will ever use any particular piece of mathematics. For example, engineers need to know some trigonometry, a subject that is of no use whatsoever for pharmacists and bank employees. Economists need to understand statistics, but not electricians. And, of course, few children at school can be sure what work they will do in later life.

This presents us with a curricular problem: should we try to teach every mathematical topic that might be needed later by some learners?

How important is learning mathematics?

Within a class of 30 students, we may find a wide variety of career possibilities this would be a sure recipe for an overloaded curriculum. Or should we restrict ourselves to some general topics such as proportion, the properties of some common geometrical figures, and substitution in formulae with which many of the students will need to learn?

If we adopt this latter course, we may find ourselves left with rather a small mathematics curriculum.

Of course, mathematics is also an essential tool for the scientist, and this has often been used to justify the inclusion of particular mathematical topics in the curriculum. The usual assumption is that students should first learn the mathematics, and then apply it in the science lesson. However, if this means that they are expected to learn it in an abstract form, they may well fail to master it and the failure in mathematics can lead to frustration in the science lesson as well. Much science teaching in schools is too dependent on mathematical skills and for many students these can get in the way of learning the science.

We also need to recognize that mathematics for use is something which changes with time. Use of basic to advanced calculator is an obvious evidence of such trend.

3. Mathematicians` mathematics

And this is about `Real` mathematics proof and abstract structures. Most curricula contain something of this kind of mathematics: for example prime numbers, geometrical theorems, sets. We might call it mathematicians` mathematics.

It would be wrong to imagine that a hard line should be drawn between this and the mathematics referred to previously. These is certainly a place for logical reasoning in teaching mathematics from a practical point of view for much of the power of mathematics lies in the connection between facts, so that a little remembered knowledge can produce a large amount of derived knowledge. If mathematics is worth its place in the curriculum, it should certainly be learnt in such a way as to bring out these relations.

There are also other aspects of mathematicians` mathematics.

Think of the pleasure which many people get from solving mathematical puzzles and playing games with a mathematical structure or the sense of personal achievement which can result from investigating number patterns. Then there are parts of mathematics which can only be described as `delightful`. This kind of mathematics may `teaches one to think`.

End of Part 1