Relevance Of Teaching/learning Maths W.r.t. Its Application (part 2)

Part 2

It is of the nature of mathematics that its field of operation is very narrow, but that within this field one is tied by a strict logical regime the forms of reasoning encountered in mathematics are rarely applicable in a wider context. Certainly learning mathematics gives practice in analysing the meaning of statements, marshalling evidence, discarding what is irrelevant, and so on.

Mathematics may exhibit the purest form of reasoning, but from an educational point of view this can be regarded as its weakness as well as its strength.

Survival mathematics is important, but conventional mathematics teaching does little to develop it. Only a minority of students will make substantial use of mathematics in their careers, and even for them there is little in the way of a common mathematical requirement. Mathematicians` mathematics can give pleasure and satisfaction but however inspired the teaching some students are left unmoved by it.

There is no question of the importance of mathematics as a human intellectual achievement, or of its essential role in technological progress. There will always be students who want to continue to study mathematics for these reasons. Some are motivated by their hopes of following careers in which they know mathematics will be necessary.

Some just enjoy doing mathematics, and the experience of personal challenge and success that it affords and its independence of literary ability can be an additional attraction. In these terms the discipline of mathematics will clearly continue to flourish, as it has done for centuries past.

It is a curious paradox that the world is becoming simultaneously both a more mathematical and a less mathematical place to live in. At the level of personal skill, the demands made on us are less than those made on our parents and grandparents. Goods increasingly come packaged in convenient standard sizes. Filling the car with petrol requires no knowledge of litres or gallons: the pump will register the cost directly. The shopkeeper need not add up the prices of his customers` purchases: he has a calculator to do that, and the newest ones will keep a check on tax and stock levels at the same time and ma y even enter the prices automatically! The navigator of a modern tanker does nothing so crude as drawing triangles on a chart: he enters his data on the keyboard, and the computer does the rest for him more accurately in a fraction of the time. Different societies are at different distances along the road to this `ready-made revolution` but we can all see the signs of its advance.

What is important is to know in any particular situation what calculation needs to be performed, and to be able to have a rough idea of what the answer should be and, if one is in the position of having to do the calculation, to know how to use the machine that will do it.

But on the other hand, many of the achievements of the modern world would have been impossible without mathematics. The builders of the great temples, mosques and cathedrals, of the nineteenth-century bridges and tunnels, of the first iron ships and aircraft, used little mathematics but to design a modern tower block, jumbo jet or motorway calls for all the resources of modern computers and sophisticated mathematical models. Our economic life, too, is now a days controlled by mathematics as is evident from the mass of numerical data carried by the media in their business and industrial reports.

This shift of emphasis must surely be reflected in the mathematics that is taught in school. Already there are signs in a number of countries of a greater interest amongst educators in the applications of mathematics. But we must not make the mistake of trying to take children at school the first one-hundredth of the route towards a Ph.D. in aeronautical engineering or computer technology.

For most students, what is important is not to develop techniques (beyond the survival level) but to gain some insight into the ways in which mathematics can extend our ability to understand, control and enrich the world we live in: not mathematics for use, but appreciation of mathematics in use.