English Mathematician, Author, Mathematics Professor and Head of Mathematics Department at University of Ghana

# W. W. Sawyer, fully Walter Warwick Sawyer

English Mathematician, Author, Mathematics Professor and Head of Mathematics Department at University of Ghana

## Author Quotes

Education is essentially the direction of mental energy. Children have abundant energy looking for an outlet. If adult society provides a satisfactory outlet, hobbies develop into professions and adults find life in their work. If adult society fails in providing an outlet, a double disaster occurs. The child has no energy or enthusiasm for work; and the child's energies are left to find an outlet at random. Society has then abdicated its duty to educate.

Only by providing satisfactory activities for citizens can delinquency, vandalism, crime and violence become exceptional rather than normal

Energy then is morally neutral, it is good or bad depending on the direction it takes. Our task is to provide legitimate outlets for it. The provision of such outlets is important in three ways - for society, for the individual and for the learning of subjects. For any society that wishes to remain civilized this is the highest priority; only by providing satisfactory activities for all citizens can delinquency, vandalism, crime and violence become exceptional rather than normal. This is a priority of which our dominant institutions seem totally unaware. For the individual, finding a satisfactory outlet for energy means a sense of fulfillment and escape from frustration. For the learning of subjects it is the driving force without which little will be learned.

The aim of scientific education, as I see it, is to produce workers in all departments of knowledge in their due proportions; to encourage communication between workers in different fields, and also between them and the general community; to raise the intellectual standards and intellectual interests of the whole country.

I enjoyed the mathematics that I had time to learn. If I ever need or want to learn some more, I shall not be afraid to do so.

The appeal of arithmetic to infants is usually self-evident and recognising unusual mathematical maturity is not difficult. The unjustified fears of some educationists about allowing children to forge ahead, needs discussion and recognition of the need for young mathematicians to work in depth and at speed.

I have for a long time believed that the thought processes of very young children closely resembled the thought processes of genius.

The best way to learn geometry is to follow the road which the human race originally followed: Do things, make things, notice things, arrange things, and only then reason about things.

I would like to emphasize that the activity approach does not mean every lesson must take place in the playground. All that is necessary is that there should be enough activity to make the mathematical work meaningful and purposive.

The commonest complaint from the abler pupils is that if they finish a set of exercises ahead of the rest of the class they are simply given more of the same kind, which they find very boring.

In discovering something for ourselves, we have a sense of freedom and conquest. In memorizing something that another person tells us and that we do not understand, we are slaves.

The effectiveness of education depends on adaptability to individual differences. Rigid syllabuses and lock-step teaching ignore the real forces in the mind that make for development and learning and the resentment of the gifted when drill continues after a skill has been learned is very often evident. The problem is how to get practice of necessary skills without causing such resentment, a problem often neglected by some modern mathematics' reformers.

In mathematics, if a pattern occurs, we can go on to ask, ‘Why does it occur? What does it signify?’ And we can find answers to these questions. In fact, for every pattern that appears, a mathematician feels he ought to know why it appears.

The essential quality for a mathematician is the habit of thinking things out for oneself. That habit is usually acquired in childhood. It is hard to acquire it later.

In the rhythm of rote learning all the emphasis is on the answer. In the rhythm of research, the emphasis is on the two items: understand what the problem is and solve the problem.

The first duty of a teacher is not to talk but to listen; to try to understand the direction the energies of each pupil are taking and not to expect activity in places that Energy has yet to reach.

It is clear that a great increase in the quality of life would occur if we could improve the teacher-pupil ratio. In the present economic climate of the world, such an aspiration appears hopeless. However, most official economic thinking relates to an age long dead. It is concerned with greater efficiency of production. But it was evident in 1930, and is still more evident in the age of the micro-chip, that the problem is not to produce but to distribute. The main social problem is to keep people occupied; the main economic problem is to spread incomes so that people who need things can afford to buy them.

The main task of any teacher is to make a subject interesting.

It is quite natural that if a child of limited intelligence can only do one subject, that subject should be arithmetic. The judgments involved in thinking, "Is this the right block? No, that one's too long," and later associating the various blocks with 0, 1, 2, ...., and 9 are much simpler than those required to learn the 26 letters of the alphabet and the eccentricities of English and American spelling.

The practical value of mathematics lies in the fact that a single mathematical truth has a multitude of applications. If children can handle numbers with confidence and enthusiasm, they will be able to apply arithmetic to any situation that later life may bring.

It is well known that there exists a mathematical theory of musical sounds. Very few people know that music has made a contribution to mathematics. In fact a suggestion made by a musician led to a total revolution in the way mathematicians approach their subject. No doubt, mathematicians would have made this step forward sooner or later if the musician had not given this hint, but as a matter of historical record, that was how it happened.

The topics and treatment of the mathematics syllabus should be determined by the following principles: a. The course must be enjoyable and generate steadily increasing enthusiasm in the pupils, b. It should develop independence and activity of mind, curiosity, observation, and confidence, c. It should make pupils familiar with the basic ideas and processes of mathematics.

It is widely recognized that the weakest students can be very unhappy if their special needs are not met. It is often not recognized that the ablest too can suffer acutely, if they are captive in a lockstep class and have to work, at what seems to them a snail's pace, through material they could have disposed of quickly when they were several years younger. The root of the trouble lies in the concept that education is something done to a pupil by a teacher. This is entirely untrue, at any rate for mathematics. Young mathematicians are hungry for knowledge and nothing delights them more than to be given the opportunity to read ahead on their own. The strongest students will then reach topics far beyond anything that a school curriculum could possibly contain or a school teacher be expected to expound. Even those, who are slightly above the level the curriculum envisages, will benefit from the relief of boredom and the extra knowledge acquired.

To master anything from football to relativity requires effort. But it does not require unpleasant efforts, drudgery. The main task of any teacher is to make a subject interesting.

Mathematicians, it is often said, tend to be musical. It is less well known that problems arising from music have played an important role in the discovery of fundamental mathematical ideas. Questions about the vibrations of a piano string led to a fierce controversy that forced mathematicians to clarify their ideas about area, continuity, and the convergence of series.