Is Mathematics That Difficult?

Many dread Mathematics at school. Many drop the subject as soon as they can do so. 

But we need people with some knowledge or understanding of Mathematics in practically all fields of the development process, be it in engineering, the environment, science, administration – perhaps in all areas of the national development agenda. 

Administrations or governments have realised this and some therefore try to vigorously promote the study of Mathematics at school and college.

Often administrations look at the structures for the learning or study of mathematics and they take action, often a feeble one.  They consider class-size, text-books, teachers and other defects in the system. 

Meanwhile some measures are taken by schools and teachers, examiners try to make the subject more relevant and interesting by attractive syllabuses and meaningful examinations. Still the subject is not liked by many students. The Mathematical Association is keen on changing the image of Mathematics in the country and it should be encouraged by being resourced to carry out this most useful endeavour.

Meanwhile we may survey attitudes to Mathematics in this and other countries over the years. Some scholars have observed that early human communities passed through tortuous processes before evolving procedures for systems of counting.

It is suggested by some that Mathematics developed in the few areas with developed urban civilisation and well-organised economics.  But perhaps apart from Japan, China and India, students do not do that well in Mathematics in many developed countries. 

I am inclined to think that apart from the obvious effects of genetic inheritance, attitude to Mathematics is more influenced by attributes of culture.

The Ghanaian does not generally like adherence to a system. Sentiment peace and tranquillity generally impact greatly on the logical system. A story will illustrate this.

A niece with a spare garage was entrusted by an uncle with the safe keeping of a car.  A week or two later a son of the uncle appeared and asked to use the car.  The niece released the car which was subsequently smashed.  When queried the niece answered “But it is his father’s car? How can I refuse him the use of his father’s property?”

The niece would not understand that she had no authority to release the car.  Her justification was based on sentiments and the desire for peace.

It is the same majority type who find elementary arithmetic analysis a bore and not exciting.  You try to dissociate the number ‘1’ from the discrete object used in counting. You have two empty bowls, two oranges and two heaps of salt. You put the oranges in one bowl and the two heaps of salt into the other. You have two oranges in one bowl but only one heap of salt in the other. 

We refuse to believe that when we say one plus one equals two, we are thinking of discrete objects like oranges. We therefore try to bring weight and other concepts in.  But in the case of oranges, we never consider size.  Two oranges are two oranges irrespective of size and colour.

Such basic difficulties in the thinking process hinders the thrill in defining “number”.  In such circumstances teachers are constrained to tread the familiar path in addition to add 135 to 200 and 311.  You arrange the figures thus:

135
206
311
——
652
–––– 
5 + 6 + 1 equals 12.  Therefore you put 2 down and carry 1.  You add it to 3 and 1 and you obtain 5 and so on.

In the computer age, we do not do such additions “mentally”, but the process is important even though many experts today may not call it Mathematics.  But if we are to understand and enjoy the subject we should know what Mathematics is all about.

A great Mathematician once described Mathematics as a “meaningless game, played with meaningless symbols” while another said “Mathematics is the science in which we do not know what we are talking about and do not care whether what we say is true or not”

No teacher should therefore give up in trying to define “number” with his young college students. The definition has occupied great minds and Bertrand Russell and Alfred North Whitehead tried to establish the foundations of Mathematics in the three volumes of “Principia Mathematics”

We should introduce the rigours of Mathematics to the young. We should not deny them the beauty and joy of reasoning and abstract thought. Meanwhile we should make sure that they have enough knowledge of Mathematics to promote economic and social development wherever they find themselves.

Mathematics is not that difficult. It is mainly our character which refuses to accept uncomfortable conclusions which is the problem.

Mathematics is not that difficult. Often we do not like it because it introduces an alien culture to our way of thinking. We do not like the unpleasant conclusions of the thoughtful mind and Mathematics leads inexorably to conclusions set by the original postulate. It should help us to take correct positions on evidence, facts and figures.

We should not become part of “the talk before you think” population. We should insist on high level grades in Mathematics for our students in tertiary institutions no matter their area of learning.

If you do not achieve a good grade in Mathematics and you are working at a high level in any institution you should not oppose the promotion of excellence in Mathematics. Perhaps you did not get a good chance. But you can improve yourself by reading and studying and you will enjoy that Mathematics challenges your thoughts.