Do you understand Mathematics?

Beniel Seka

If somebody asks you what mathematics is how would you reply? I raise this question because many people do not like mathematics. Some of you fear mathematics for a number of reasons. Some students perform well but others perform poorly. A number of people think mathematics is a jargon of numbers and calculations.

 Mathematics involves a lot of fields such as Arithmetic, Algebra, Geometry, Trigonometry and Calculus. The list increases as you go up in the level of study. I will restrict this presentation to primary school level which is the background of learning mathematics in other levels. Quite often people fail to cope with mathematics because they did not understand mathematics in primary school. They just memorized or crammed what their teachers told them.

Mathematics is a subject which is learnt by understanding rather than by blind memorisation. It also has structure. Among the subjects taught at school, mathematics is probably the most hierarchical because it has a logical order to it. You cannot expect to understand any part unless you understand the parts that came before. One of the many criticisms about mathematics teaching in schools is that the structure of the subject is neglected. Too often it is presented as a collection of bits of information and techniques with no connection to each other. Learners are forced to know them. This may create distaste and hence develop lack of interest among the learners.

Some topics are taught before the learners are ready for them. For example, you can see addition and subtraction being taught before the children have mastered counting. This is because some teachers take for granted that counting is easy. It has been realised that some children can rehearse the counting and you may be deceived that they know how to count. Also manipulation of metres, centimetres and millimetres is taught in situations where the children have no clear understanding of the concept of length. The list of things is long and perhaps is one of pupils’ major causes of lack of understanding of mathematics in primary schools.

It is very clear that such an approach is not successful for the majority of learners. For example, many pupils in primary schools have too many things to memorise and cannot relate one part of the subject to another. The attraction of memorisation without proper understanding is that it seems to give a short-cut to getting the correct answer. Unfortunately it creates a very narrow and shallow view of the subject. It eventually creates more problems than it solves. Mathematics is more than getting the correct answer since it is concerned in developing in pupils a logical and creative way of thinking that is powerful skill for solving new and related problems. Just knowing how to get the correct answer in one particular situation does not always help in solving a new problem. The pupil must know how to solve problems of similar nature.

Most of you will argue that teaching for understanding consumes time and requires patience. However, you will agree that it creates a much more worthwhile result and is rewarding. It makes mathematics learning a more enjoyable activity. It creates in pupils a much more positive attitude to learning in general and mathematics in particular. It also creates the opportunity for all pupils to experience a measure of success and progress in mathematics. In this way, they gain confidence and are better equipped for future learning.
It is therefore important that the learning environment of the pupil is made as friendly to allow conducive interaction. The environment outside the classroom, including their homes should also assist the learning of mathematics. Opportunities should be sought to use the immediate environment of the pupils to create their interest in learning mathematics. The more this happens, the more likely it will be that pupils are able to understand the mathematics they are taught and use the knowledge acquired in their daily life. So insist on learning mathematics by understanding the process instead of just memorising formulae and facts without understanding them.

Mathematics teachers should guard against assuming that the pupils understand what they are teaching. They need to include assessment and evaluation strategies that will give an indication. If the teacher merely asks, “Have you understood?” and the pupils reply, “Yes,” may not be sufficient.

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