Why do Far Eastern pupils do better at maths? Because their language for word counting is more logical, says Ian Thompson.
The Third International Mathematics and Science Study (TIMSS) is currently being carried out in more than 50 countries, including Japan, the United States and the European Union. The National Foundation for Educational Research has organised the testing in this country using a sample of 300 randomly selected schools: 150 with nine-year old children and 150 with thirteen-year olds.
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In 1964 and 1981 comparisons of the mathematical attainment of secondary school pupils were carried out in 15 and 25 countries respectively by the International Association for the Evaluation of Educational Achievement. In both of these studies Japanese students outperformed their English and American peers. In the first International Assessment of Educational Progress, which took place in 1988 and which involved six countries, Korean 13-year-olds consistently performed better than their counterparts from elsewhere.
Several writers have argued against a simplistic interpretation of such data, and various criticisms have been levelled at the measuring instruments and general methodology used in these studies. However, despite these concerns, there is no doubt that, for whatever reasons, Japanese, Korean and Chinese teenagers have produced consistently higher standards of performance on these tests. Other researchers have shown that at the age of six the mathematical performance of American children is significantly lower than that of Japanese and Taiwanese children, and that Chinese four-year-olds are able to count to a significantly higher limit than their American peers.
Various reasons are given in the literature for this superior performance by Asian children: the time spent on the study of mathematics (approximately 20 per cent more than here); the high status accorded to academic achievement; the great respect for teachers; a highly competitive educational system; the existence of juku (cramming schools) and also of abacus schools. But another possible explanation may lie in the greater regularity that exists in the structure of the counting word system of Asian languages compared with that which is to be found in the English system.
Place value is accepted as being an extremely important mathematical idea in that a lack of understanding of the concept will almost inevitably lead to later difficulties with mental or written computation. This subtle and powerful concept involves the use of just 10 different symbols, and yet, by ascribing a different value to a numeral dependent on its position in relation to other numerals, it allows the writing of numbers of any size. As soon as children begin to operate with two-digit numbers they are working with place value.
In the following discussion English words will be used to provide a literal translation of the Asian way of verbalising and reading numbers.
Oral counting in Japanese and Chinese begins as in English by proceeding from one to ten. However, this is then followed, not by eleven, but by ten one, ten two, ten three . . . ten nine, two ten, two ten one, two ten two, etc. After two ten nine comes three ten, and the decade numbers (30, 40, etc) continue this pattern up to nine ten. Within this system the number which is one less than a hundred, for example, is nine ten nine. The structure can therefore be seen to be highly regular, logical and systematic, and this regularity must surely facilitate the appreciation and absorption of the recurring pattern that underlies this counting system.
The English counting word system, on the other hand, contains several idiosyncratic words which are likely to conceal the basic tens and ones pattern of the system. For example, the teens contain words which reverse the underlying tens and ones pattern: we say fourteen and sixteen, but twenty-six, thirty-six and ninety-six. This problem is further exacerbated when we express numbers in symbolic form, because the reversal is not extended to the written representations of these numbers: fourteen is written as 14 and not 41. Or, looked at another way, 14 is read as fourteen not as ten-four as it is in Chinese.
English also possesses the two idiosyncratic number words eleven and twelve which give no indication whatsoever of the fact that they mean ten and one and ten and two respectively. Even when children come to appreciate the "pattern" which dictates that after twelve the teens are spoken in reverse order with the tens appearing in the second half of the number word, there are further irregularities to be found in that thirteen and fifteen, with their idiosyncratic pronunciations of three and five, tend to interfere with the regularity of the established "digit-teen" pattern of numbers after twelve.
Whereas in Japanese the teens and the decade words all involve the conspicuous presence of the word jxu (ten) to describe numbers such as ten-two (12), three-ten (30) or nine-ten (90), English uses two differently spelled and differently pronounced variations of the basic word ten, namely -teen in the second decade and -ty in successive decades - neither of which is likely make it obvious to a young mind searching for pattern that the concept of ten is involved.
In fact, a close scrutiny of Asian languages shows that because of the completely logical structure of the number word system the word jxu (ten) is used in ninety of the numbers below one hundred (all except the first nine numbers), thereby helping to reinforce the basic underlying regularity of the number word system. In contrast the English word ten appears only once in those same ninety-nine numbers. A further potential source of confusion in young children's minds is the irregular pronunciation of the decade words twenty, thirty and fifty. Because they do not have the regular form two-ty, three-ty and five-ty these particular words do not make it easy for children to see the way in which the words two, three, and so on, are re-used in the naming of the decades. They have the potential to conceal the relationship between these decade names and the first nine numbers - a connection which is more clearly observed in the decade names of larger numbers such as sixty, seventy, eighty and ninety. This relationship is heavily emphasised in the highly logical structure of the counting word sequence found in Asian languages.
It is also unfortunate that these irregularities occur in the early teens and decade names (twelve, fifteen, twenty, thirty) - just the numbers that young children are experiencing and coming to terms with in their early number work at home and at school. This also means that English-speaking children have to memorise a long sequence of seemingly unrelated number names before the patterns become visible. The x-ty one to x-ty nine sequence does settle down after twenty, but the relationship between the numbers one to nine and the decade words is not particularly obvious.
Indeed research does exist to show that there is a long period of months, extending to years in some cases, during which young children continue to learn the teen and decade names. In addition to this, English-speaking children have been found to make more errors in reciting the counting word sequence than do their peers operating with the the Chinese regularly-named sequence.
Various reasons have been given for the inferior performance of English and American children on international tests and for the repeated success of Asian children. Given the general acceptance of the importance of the first few years of life for learning, is it not feasible that something as basic as the irregularity of the English counting word sequence and the inevitable ensuing obfuscation of the tens and ones structure of two-digit numbers may well disadvantage English speaking children early in their development, and thereby make some contribution towards their later inferior performance?
Ian Thompson is senior lecturer in the department of education at the University of Newcastle upon Tyne