This article is an extract for teachers on teaching methods.

LONDON, July 2 — One country teaches children to recite their times tables and drills them in mental arithmetic. The other bans rote learning and encourages pupils to manipulate real objects and share ideas as they work in groups.

 Which one is Singapore, which consistently comes first or second in the international league tables for mathematics, and which is England? The answer may come as a surprise.

For despite the reputation of Pacific Rim countries for traditional chalk and talk, it is Singapore that uses the so-called trendy modern methods whereby children learn by doing in noisy classrooms. Times tables are frowned upon, just as they once were in England before the advent of the national curriculum.

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 been.

 “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.” — The Independent