Box clever: Singapore’s magic formula for maths success

Singaporean classrooms are noisy places where children learn maths by folding
paper, constructing models and re-arranging pieces of fruit or lollipop
sticks. And it is this method devised by the ministry of education that the
city-state says has led to its rapid rise up the international tables.

In the last Timms survey of maths and science standards in 49 countries,
Singapore came first for science and second for maths. Since the scheme
known as Singapore Maths was introduced in the 1990s, the nation has not
only moved to the top but no longer has a tail of low achievers. It was also
ranked first for the quality of its education system by the Global
Competitiveness Report 2007?2008.

As Singapore moved away from traditional methods to Western-style creativity
and discovery learning, England moved in the opposite direction, bringing
back compulsory times tables and tests for mental arithmetic. England, too,
has improved its standing from 25th place in 1995 to seventh in the 2008
Timms survey published last December, but still more than one-fifth of
children fail to pass the national curriculum maths tests. Last year, only
78 per cent of 11-year-olds and 77 per cent of 14-year-olds reached the
standard expected for their age.

Now the Singapore system is being brought to Britain by the publisher Marshall
Cavendish and Maths ? No Problem, an organisation promoting good materials
for home and school. But is it the method which makes the difference, or are
children in Singapore more diligent and better supported at home?

Ling Yuan, head of maths at the Catholic High School in Singapore, was in
Britain last week conducting seminars for home educators and maths teachers
and visiting schools. She says the content of what is taught in primary
maths differs very little to what is in the national curriculum in England,
except that children in this country are expected to learn some areas of
geometry that are taught to secondary-age children in Singapore.

There is more emphasis in Singapore maths, however, on gaining a good
understanding of the basics before moving on, she says. This provides a
strong foundation. Key to the programme is the insistence that children
learn by sequence, first by manipulating objects in the real world, then by
drawing pictorial representations before using the mathematical symbols.

“The concrete, pictorial, abstract method is very powerful because it
helps children to visualise number and proportion. There is a huge emphasis
on problem solving,” she told a seminar in London. “The children
form a mental picture and a deeper understanding using beans or pieces of
pasta and then they might draw a box with green beans in it and for every 10
green beans you get a red one.”

The simple task of folding paper can help children visualise division, she
said, adding: “We don’t get our children to memorise times tables. We
are not into rote learning. We get the children to calculate 12 times six by
breaking it into two times six and 10 times six and they soon get the answer
into their brains.”

Children in Singapore start school later, at the age of seven, and classes are
larger ? about 40 pupils. Whereas many maths classes are set by ability in
England, Singaporean primary schools have mixed ability classes and rely on
scaffolded questions to provide more challenging work for the most able.
There is also an emphasis on children learning from each other.

“You would be shocked if you walked into one of our classrooms. Where is
the teacher? He or she will not be at the front but working with one of the
groups and there will be a lot of noise, we encourage children to work out
the problems together,” explains Ling. “Sometimes parents come to
us worried because their children say they have been playing in maths, but
when they see the mid-year test scores, they are satisfied.”

Teachers are provided with examples of practical exercises and ways of
illustrating mathematical concepts through pictures, using rectangles
divided into parts or with blocks in which the children draw different
numbers of objects. This helps primary teachers in Singapore who, like those
in England, teach across the curriculum and are not usually maths
specialists, adds Ling. The system has already been adopted at schools
serving disadvantaged pupils in parts of America and a study by the US
Department of Education found they had made very significant progress. “Singaporean
students are more successful in mathematics than their US counterparts
because Singapore has a world-class mathematics system with quality
components aligned to produce students who learn mathematics to mastery,”
the researchers concluded. Some UK schools are adopting the scheme, among
them Northwood Preparatory School in Rickmansworth, Hertfordshire. Bernie
Westacott, its head of maths, says pupils were already doing well but after
just a year of Singapore Maths are a year ahead of where they would have

“I have been teaching since 1973 and have never been happy with UK
textbooks nor the way we have taught maths,” he says. “I have
continually searched for something that would be closer to what I felt was a
better way so that this could be given to teachers as a ready-made resource,
along with a reasonable amount of training. A few years ago I came across
Singapore Maths which seemed a perfect fit.

“Pupils focus intensely on a handful of ‘real maths’ topics, whereas in
the UK the maths curriculum is a mile wide and an inch deep, making it
difficult for students to master the most important skills. Rather than
teaching pupils to memorise facts and routines, the focus is on maths
concepts which are born out of practical experience. We have seen a large
improvement in their problem-solving ability because they are manipulating
objects as opposed to learning routines.”

Stephan Cook, the head of St Faith’s CofE school in Wandsworth, south-west
London, says aspects of the Singapore method are already in place in
Britain, but less systematically. he says: “The books for teachers
giving examples of how maths problems can be portrayed pictorially would be
useful, but the most important thing in any method is that the teacher
understands the concepts before trying to pass them on.”

New versions of the Primary Mathematics and My Pals Are Here series of
textbooks, published by Marshall Cavendish under curriculum guidelines from
the Singapore Ministry of Education, will be available in Britain later this

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