“What is the secret to Asia’s attainment in maths—and can Britain learn it?”
© Mark Bowden/ istock
In a series of international mathematics tests in 2012, British teens reached only the average score. Shanghai’s school children came top of the list, with results that showed them to be the equivalent of three years of schooling ahead of Britain’s children. The UK government is now bringing over 60 maths teachers from Shanghai to introduce Chinese teaching methods to Britain, in the hope that this will raise standards.
But why are the Chinese better at learning maths, at least in the Chinese cities that took part in the tests? And can that success be learned, or transplanted into British schools? The signs are that some of it can, but there are limits.
The cultural differences between the two countries have an immediate impact on maths. The learning of maths in Chinese is significantly different from learning the subject in English and some of the differences may not be easily transferable.
For example, number names in Chinese clearly relate directly to place value. Where we count “eight, nine, ten, eleven, twelve…”, the Chinese equivalent translates into “eight, nine, ten, ten-one, ten-two…” While our words “eleven” and “twelve” relate to the 10 fingers on our hands using the old English “ei lief on” meaning “one left over” and “twe lief” (two left), few people know this or use it to support the meaning of place value. Research shows that English-speaking children learning early arithmetic are often a year or so behind those learning in Chinese.
A second difference is the length of the spoken words, which are shorter in Mandarin Chinese than in English. “Seven” is “qi,” for example, and “one hundred” is simply “bai.” Even with single syllable words—“one, two, three” is “yi, er, san” in Chinese—there are subtle differences, such as the long “thr” in “three,” that mean they take longer to say. Travelling around Taiwan speaking about learning maths, I used to challenge my translator to count to 10 in Chinese as I counted in English. I could only reach around six by the time my translator finished.
This difference affects our mental processing power. As people continuously process ideas in their minds, they are deploying a part of their short-term memory function referred to by scientists as the “phonological loop.” This function relates to written and spoken information and, because of the difference in word length, while westerners can remember about seven digits (plus or minus two), Chinese speakers can cope with around 10. As a consequence, mental arithmetic in Chinese is easier than in English because the simpler numbers are easier to remember. Arithmetic in other languages, such as Arabic or Hebrew, both of which have even longer number words, is inherently more difficult. So there are certain advantages to learning maths in Chinese.
But can this alone account for the substantial gap in attainment between Asian and western countries when it comes to maths? The table below shows a selection of results from the OECD’s 2012 Programme for International Student Assessment (Pisa) survey. Millions of 15 year olds from 65 countries took the same tests, to compare attainment levels in maths, reading and science. Shanghai came top, and Peru last.
The top seven places were taken by Asian countries or cities. The highest European nation, Liechtenstein, was placed eighth, followed by Switzerland and the Netherlands. The UK and French scores were at the OECD average. The USA was just below average.
There are a large number of factors affecting these scores—which are the subject of some controversy. American commentators have said that judging Chinese cities against entire countries gives an unfair result, though the enormity of China and the structure of its education system makes participating in such tests difficult. The Shanghai sample also excludes a significant percentage of migrant workers of lower social status, which pushes its score upwards. But these criticisms still cannot explain the wide differences between Asia and the rest. What’s the secret—and can Britain learn it?
In Shanghai, maths teachers are specialists with a degree in mathematics, whereas UK primary teachers teach all subjects. Roughly twice as much time is devoted to maths in Shanghai, and it is taught first thing in the morning so that teachers can mark work during the day. Children who are less successful stay behind for extra classes, and maths homework is given daily. Whereas British teachers teach by themselves most of the time, Chinese teachers work in teams, planning and observing each other’s lessons.
It has long been observed that Asian Tiger economies make huge demands on their children’s learning with extended practice of arithmetic. But although this can lead to increased scores and standards, it can also impose huge pressure on children, which causes anxiety and a limited degree of flexibility in solving problems; the outcome can be the exact opposite of what is intended.
Some Asian countries have set out to improve this weakness in problem-solving ability. The Japanese have a long-established technique called Lesson Study designed to instil just this ability in the young. The method uses carefully designed lessons to encourage cooperation and class discussion. This involves not only making lessons stimulating so that the children enjoy them, but also very careful design of lesson sequences to build to a significant idea.
Of the top Asian economies, Singapore stands out—not only does it come second in the Pisa rankings, but maths is taught in English. Why does Singapore score so highly compared with the UK? Since the 1980s, the goals of maths education in Singapore have changed from the highly-efficient learning of necessary skills—typical of Asian mathematics—to focus on the development of creative thinking. The Singaporeans use ideas that they have gleaned from around the world, including the translation of Japanese Lesson Study books into English. In primary schools the curriculum is designed to encourage children to focus on deep understanding of a smaller number of fundamental ideas. Secondary education separates students into academic and technical schools, according to their skills. Singapore’s curriculum is not overloaded with detail; the intention is that children should be encouraged to make sense of maths rather than simply accept statements by teachers. The child’s creativity is more central in this approach than in the traditional western method, the aim being to encourage children to make sense of new ideas while still developing their fluency in carrying out mathematical operations.
Innovations like this are impeded when rigid curriculum requirements cause teaching to focus on immediate, set goals. In the Netherlands, which scores higher than the UK in the OECD tests, there is a perception that students starting college are not achieving the desired levels of fluency in maths. During a project to introduce Lesson Study to the Netherlands—for which I was an advisor—we found that teachers were so fixed on the need to satisfy immediate curriculum requirements that they struggled to encourage any flexible thinking. There were also cultural differences. The Dutch participants were keen to be good solo teachers and took some time to learn to work together. This contrasted sharply with Asian teachers, who were more attuned to being part of a team.
In Britain the government’s concern is not only with the mathematical limitations of the more able, but also with the lack of mathematical competency in the adult population. This can have substantial economic consequences.
It is not simply that some people don’t like maths. My book, How Humans Learn to Think Mathematically, studies the long-term development from the new-born child, through school and on to university and beyond. Successive shifts in subject matter, say from whole number arithmetic to fractions, or introducing negative numbers, involve subtle changes in meaning. Pleasure comes from making sense of ideas and fitting them together in meaningful ways.
Anxiety will develop if the student cannot cope with increasingly sophisticated ideas. The consequence is a division between those who build ideas coherently, developing the intellectual resilience to tackle new problems based on previous success, and those who attempt to learn a collection of increasingly complex procedures to use in ever-more sophisticated problems. This second group is prone to disaffection. If Britain is to improve the quality of teaching and learning in maths, teachers must consider the fundamental issues behind disaffection.
Over recent years, the UK’s performance in maths in the OECD’s tests has not changed. Attempts to drive long-term improvement are not helped by inconsistent teaching policies, as successive governments seek to make their mark on the way maths is taught. To improve the learning of maths over the longer term requires a fundamental grasp of how learners make sense of maths. Only in this way can everyone make the best of their talents. This includes both stretching the high achievers and supporting the wider population, and ensuring that as few people as possible experience the sort of excessive pressure that inhibits their ability to learn.
The UK government is making some moves in the right direction. It is shifting the criterion for success away from insisting that children achieve grades A-C at GCSE, which has led to resources being focused on that goal. A greater emphasis is now put on improvement at all levels, and there is a desire to encourage the performance of higher attainers.
The teachers from Shanghai will take part in “maths hubs,” based around UK schools rated highly for the quality of their maths teaching, to help develop improvements that can be implemeted at a network of partner schools. The hope is that some of our teachers and policymakers can grasp how to encourage better performance.
However, we also need a better understanding of the underlying mechanisms involved in mathematical learning. This will enable us to distinguish between advantages in Chinese mathematics that cannot be incorporated into our ways of working and those that may be of more lasting value.
