A friend of mine is Chinese and when he discovered that I produce mathematics educational software, he told me not to try to sell it to the Chinese as there is nothing we can teach them about arithmetic.
This started me thinking. I have heard many times that Chinese children are much better than western children at arithmetic and I couldn't believe it was just that they practised more or were drilled more efficiently. Then one day I discovered what I think is the main reason - the way they describe their numbers is a great deal easier than the way we describe ours and this gives them a great advantage.
(I should point out that I may be mistaken in one or two of the technical details, but that won't make any difference to the argument, so if you are Chinese and you spot a tiny error, please don't worry about it.)
Think of the number 3457, for instance. We say ‘three thousand, four hundred and fifty seven', of course. We say exactly how many thousand there are and exactly how many hundreds there are. But when it comes to the tens, we don't say ‘five tens'. Instead, we say ‘fifty', a word that does not tell us how many tens it contains.
It is even worse if teens are involved. For instance, the number 8413 is read as ‘eight thousand, four hundred and thirteen'. Again the thousands and hundreds are self explanatory, but the word ‘thirteen' does not tell us how many tens it contains. This has to be learnt as a separate concept.
Not so in the Chinese number system! Their system reads the second number as ‘eight thousand, four hundred, one ten and three' and the first as ‘three thousand, four hundred, five tens and seven'.
So, what's the big deal? I hear you ask. Well, the point is that the extra layers of confusion we have in our number system are introduced just at the point when children are learning to add, subtract, multiply and divide small numbers, i.e. those up to about 99, mentally. By the time they get to the hundreds and thousands, they have mastered the four operations.
Let's see how this affects the learning process. Suppose we want to add 57 and 18. The first thing our children have to do is to recognise that 57 is really ‘five tens and 7' and that 18 is ‘one ten and eight'. Then they add the seven and eight, which they will say as ‘fifteen'. They then have to remember that this is one ten and five, so they write down the five and carry the one.
Next comes fifty plus ten, which they have to remember is five tens plus one ten (or they may know that the answer is sixty straight away) and add the carry digit from the previous column. They write this digit down. Lastly they need to read the answer as ‘seventy five', remembering as they do so that seven in the tens column is ‘seventy'.
Now let's try it the Chinese way.
57 + 18. They read this as ‘five tens and seven plus one ten and eight'. Seven plus eight is one ten and five, so write down the five and carry the one. Now five tens plus one ten plus one ten is seven tens. Write seven in the tens column. The answer is ‘seven tens and five'.
Our children have to make about four conversions from the numbers they are given to separate them into tens and units (and vice versa) that Chinese children do not have to do.
So, if we abandoned saying the ‘teen' numbers, calling them ‘one ten and one' etc and stopped using words such as ‘twenty', ‘thirty' etc and called them ‘two tens', ‘three tens' etc, would our children be much better at mental arithmetic? I certainly think so.
What about other languages? Well, these can be even more difficult. In French, for example, ‘seventy eight' is ‘sixty - eighteen' etc. In German they swap the early numbers around, so 28, for example, is ‘eight and twenty'. They must have a lot of trouble too!
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