Learning
Mathematics by heart is a thing of the past. Nowadays, children are expected to
work out calculations using creative problem-solving skills

It is without
a doubt that primary school maths is no longer limited to simple arithmetic
sums. By the end of Primary one, children are expected to tackle problem sums
involving topics on money, measurements, fractions and graphs (to name a few) -
on top of basic addition, subtraction, multiplication and division. The key is
to develop an understanding of mathematical concepts, and to acquire analytical
skills that will enable the children to apply the mathematical concepts to
problem-solving scenarios.

With a growing
emphasis on encouraging creative thinking and problem-solving abilities in our
school curriculum, it is not surprising that children need to be exposed to
more challenging approaches to learning mathematics – and parents feel an increasing
pressure to keep up with the latest trends.

One of the
latest teaching methods, adopted in many primary schools, is the use of
learning centres in lower primary classroom, as part of the Strategies for
Effective and Engaged Development (SEED) programme. In brief, the SEED
programme intends to integrate learning between mathematics, science and the
English language, through a thematic approach. Such integration across the
curriculum should give rise to fun learning activities in primary schools, while
at the same time developing language skills with mathematic and scientific
knowledge.

Other than the
efforts made to improve the curriculum in our primary schools, what can parents
do to help advance the learning of our children? With jargons like “analytical
skills” and “problem-solving techniques”, coupled with various teaching methods
involving models and its variants, parents are often at a lost as to how best
introduce mathematics to their pre-schooler and subsequently to sustain an
active interest in mathematics.

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Need For Creative Learning

In this
current knowledge-based economy, where the emphasis is on creative and
independent learning for children, the traditional method of spoon-feeding
students with information and grading them based on the knowledge they have
retained is irrelevant. What the new economy requires are students with nimble,
innovative and analytical thinking skills, to challenge problems that are new
and unknown. Parents need to nurture problem-solving skills in their children and
not merely train them to perform like calculators.

With the
Ministry of Education announcing the changes to the A-level “thinking”
examination in 2000, students can expect more questions intended to test their
understanding and application of concepts across topics, instead of merely
applying well-memorised formulae.

Nowadays, most
enrichment centres have designed their mathematic classes to keep pace with
teaching trends in primary schools. Through a series of carefully crafted
questions, students are gently steered into discovering for themselves a
magical and lively world of numbers. It is certainly more meaningful to acquire
knowledge and upgrade abilities by way of self-exploration, than by a purely
teacher-orientated approach. Active learning is the trend for modern education.
Children can build up self-confidence and gain knowledge at the same time, in
the learning process.

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Importance of understanding concepts

Most people
know how to count from 1 to 10,000. Although they may not have done it before,
they know that they are able to do so because they understand that 1+1=2,
2+1=3…., and so forth. This means that they understand the

**Concept**and**Method**needed to count up to 10,000.
Parents should
try not to intimidate their children with big numerals, as it is more important
to understand the concepts and models necessary to solve a problem, instead of
blindly applying the same well-used method. Counting and calculation skills are
by no means the only measure of a child’s mathematics ability. Several more
fundamental skills need to be developed to boost mathematical learning and
understanding.

**Multiplication Table – Beyond Mere Memory**

Despite
earnest efforts to memorize the multiplication table, it is not unusual for
children (even adults) to forget portions of it. The accumulation of knowledge
and abilities are best achieved by way of thorough understanding of the subject
matter, instead of relying solely on memory. New teaching methods in
mathematics aim to replace sole reliance on memory work with real
comprehension, so that knowledge can be recollected whenever necessary.

To replace the traditional ways of memorisation and drills in Maths
learning, the current Mathematics syllabus features lively maths sums to help
captivate and equip children with the initiative to think, and therefore rely
on their own strengths to solve problems.

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Different strategies in solving Mathematics problems

Primary school children are taught a variety of ways
or strategies to work out their problem sums. They can use any method they are
comfortable with, as long as they end up with the correct answer. Children’s
mind needs to be simulated to think in a multi-model manner. A likely scenario
is where a child, out shopping with his mother, is asked, “If you have $17 and
you buy an item worth $9.90, how much change are you left with?” Before the mum
could elaborate, he answered, “Mummy, I can take $10 to minus $9.90; then add
the balance 10 cents to the $7. Or I can take $1 to minus 90 cents and $16 to
minus $9; and then you add the 2 answers together!” Such a scenario would imply
that the child has learnt many ways to derive a solution from a problem,
instead of relying on a fixed way or method. The child is also able to relate
and apply his mathematics skills in his daily life. Every child should be
encouraged to develop similar abilities, with the appropriate exposure to
different mathematical reasoning.

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Calculation skills verses Problem-Solving skills

During the 19

^{th}century, when Carl Friedrich Gauss (a mathematical genius) was ten years old, he was asked to add up every numeral from 1 to 100 (ie.1 + 2 + 3 +..100 = ? ). He instantly scribbled “5050” on his slate and laid it down with the proud declaration, “There it lies.” When the other students turned in their slates after painstakingly adding the numerals one at a time, no one except Gauss had the correct answer!
How did Gauss
do it? He had observed that each pair of numerals - 1 and 100; 2 and 99; 3 and
98; and so on up to 50 and 51 - added up to “101”. From the resultant 50 pairs
of numerals, he deduced the mathematical statement: 50 x 101 = 5050. What Gauss
had exhibited was problem-solving skill, and not just calculation skill!

1 + 2 + 3 +
…50 + 51 +…99 + 100 = ?

Therefore, problem-solving skills are much more
important than calculation skills.

Young students are encouraged to acquire a real
comprehension of Maths, not simply memorise formulae. From as young as K1,
young minds should be coached to think creatively and independently for more
complicated Maths concepts which they will encounter as they grow older.

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