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7 Av 5766 - August 1, 2006 | Mordecai Plaut, director Published Weekly










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Mathematics, The Queen of Sciences
by A. Ross

"I hate Math; it's my worst subject." "I can't do arithmetic." "I seem to have a mental block about numbers." "Math is so boring."

Mathematics, sometimes called the Queen of all sciences, is more often disliked by children of all ages than any other subject they learn at school. There are those who love numbers, with their absolute logic, and can wax positively lyrical about the subject; e.g. "Mathematics possesses not only truth, but supreme beauty; a beauty cold and austere."

What is the cause of this general distaste for numbers among children — a dislike which they often carry with them into adulthood, and then almost invariably make their feelings known to the next generation? Why do more people, intelligent successful people, seem to fail in this subject, which is so rational and consistent, than in any other area of study?

Very small children do not know anything about liking or disliking a subject. Preparation for mathematics begins a long time before a child goes to school. Children from the age of two begin counting objects and learn how to identify large and small, more and less, halves and quarters. It is a very small child indeed who can be fobbed off with the myth that he now has two biscuits instead of one, when he complains that his is broken.

By the time he goes to school, he should be familiar with the above terms and several more, like before and after (else how will he understand the idea of `what number comes before 2'), a lot and a little, few and many. Mathematical concepts and the understanding of them are built like a wall: brick by brick, one after the other. If a child comes to school with the basic numerical concepts fixed firmly in his mind, he should have no difficulty in building from there.

Naturally, experienced teachers will not take this knowledge for granted, and will spend the first few weeks of the term consolidating the verbal ideas. However, if a child is ill for a few days and misses some lessons, one or two of the bricks in this wall are missing. There will be a hole in the wall. As with so many other learning disabilities, it boils down to a language problem. If this happens later on the child's school career, the problem becomes even more complicated.

An example of language difficulty, is that the terms `add' and `subtract,' are not always clear to a child. We might say `less than,' or `take it away from,' and the child will understand it differently from the way we expect.

Teachers ask children to tell a story about numbers. One child read an exercise on 6-3, and instead of the expected `six candies on a plate and I ate three,' or something similar, she said, "My Mummy was supposed to fetch me from Shanni's house at six, but she fetched me at three instead." A teacher hearing this will realize immediately that the concept has been misunderstood, and will spend time on putting that particular brick into its place.

Another important part of language training is grouping. A doll, a ball and a jigsaw puzzle are all toys, in the same way as cows, cats and dogs are all animals, and apples oranges and pears are all fruit.

Another major cause of difficulty in the understanding of mathematics is the way it is taught. It might be that an inexperienced teacher is at fault. S/he will think that s/he has explained a concept sufficiently and that the class understands it well. Perhaps the explanation was sufficient for the top five percent of the class, but the other 95 percent will be left with only a vague understanding of how to apply the idea. Furthermore, some people to whom number concepts have never been a problem, as the ideas are so obvious and self understood, are not fit to teach mathematics to the younger classes. Once a child loses the thread and decides that he is `not good at' math, the damage is done.

Let us take some further examples of language which can mislead children when they are trying to solve a problem. When the question is put: `Yanky has 7 apples, and Shmuli has four, how many more does Yanky have?' many children will catch onto the word `more,' when actually the process is subtraction. These children will need to do dozens of exercises, all in the same vein, till they have really internalized the idea and before they can move on to the next step.

As someone who was taught by a brilliant man, and consequently suffered for years thinking I `couldn't do math,' I find teaching the subjects to infant classes and early juniors stimulating and exciting year after year. When a little boy suddenly makes the discovery that 8 plus 6 is exactly the same as 6 plus 8, always, and he shouts it out in triumph as if he were Archimedes, it is the greatest gift he could give me. The same applies to multiplication tables at a later stage.

If a child works out for himself that five times three is the same as three times five, he will have no trouble at all with more complicated ideas. Learning by rote is not encouraged nowadays, and gone are the days when every school child could say their tables almost in their sleep (after all, who needs it, we all have pocket calculators!), yet children who have been trained to learn the tables by heart have a great advantage over the others. They can do multiplication and division in their heads.

Many children do not have a very good memory and have to learn a fact several times until they understand it clearly. The child has to learn and revise, and revise again, until finally he has grasped the point and remembers it well enough the next day. Then he has to do numerous exercises on this point, long after the teacher thinks he will never forget it. This is called `overlearning,' and is one of the most effective teaching tools for the less-than-average child.

Another cause for lack of success in number work is lack of organization. If a child has attention deficit (ADHD) he is very likely to be disorganized as well. As a result, he may well read plus signs for minus and vice versa. He will also not align the numerals in their correct places, thus 38 plus 56 will be very difficult for him.

Most schools nowadays let the children write inside expensive text books instead of copying out the sums, so for these children the alignment problem is eliminated. But the difficulty of misreading of signs still remains. Thus the child might get most of the sums wrong — not because he did not know how to solve them but because he did not follow instructions.

In every other subject, half answers are often awarded half marks. But in math, a sum is either right or wrong. I am discussing arithmetic rather than solving geometry or algebra problems. In consequence of the need for perfection which they might never achieve, some children begin to feel that they cannot do math at a very early age indeed. They do not like to see crosses on their page. (I personally only put ticks and leave the wrong ones unmarked.)

In an average class, there will always be a few children who dislike frequent revision and repetition. They grasp concepts quickly, even before the teacher has finished explaining to the class, and then become bored which is a recipe for class disturbance. In this age of computers and easy printouts, it is quite easy for teachers to make interesting work sheets with numerous different examples. There are also workbooks on the market which cater to the above average child. It is up to each teacher to make math exciting for the slower students but also for the quicker ones, so that we can reverse this trend of people not enjoying math.


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