"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.
