On Doing Maths in Chinese
I knew, of course, that maths as taught in Asia is some way ahead of the UK (and, for that matter, most of the West).
I had vaguely suspected that maths as taught in mainland China might also be some way ahead of maths as taught in the rest of Asia.
But I’d expected that Chinese 11-year-olds would do the sort of maths bright students cover in the UK at age 13-14, or possibly age 15.
Maths isn’t a strong suit of mine, but I did study it at the advanced level until the point when I could stop, and got the top grade in our age-16 exams.
So, while I realised I might have to refresh my memory of various topics when required to “help” with the homework, I did, at least, expect to be vaguely familiar with whatever Zac was learning in his Chinese school.
Further, because in unschooling Zac’s covered quite a bit of advanced maths, however patchily, I figured he’d have a reasonable start at doing maths in Chinese.
Given this is the no-calculator test that our brightest and best 11 year olds sit when they finish primary school, I wasn’t entirely wrong about this.
But nor, honestly, was I right.
After accompanying Zac on his 7am bus, which brings him in at the frankly ungodly hour of 7.45am – and that still, horrifyingly, makes him late for class – I repair home for a scheduled class with Huaze, wondering all the while whether the school would actually bother to call me if Zac were, say, found sobbing hysterically in the bathroom.
I figure that, if there’s one subject apart from English – which, obviously, doesn’t count, given he’s a native speaker – in which Zac can ever hope not to be bottom in his Chinese school, it’s going to be maths.
And, therefore, that that’s the area where we need to get his literacy up first and foremost.
So Huaze and I plough through what I understand to be his maths textbook and endeavour to break it down into manageable keywords.
By which I mean identify as many high-frequency keywords as possible that share characters in common, so that he’s building key vocab without being overwhelmed by too many new characters.
This takes a lot of time because — well, because Chinese uses an awful lot of technical maths vocabulary, whose dictionary translations I don’t understand in English.
I had only expected to have to learn the Chinese words for English words that both of us already knew. Or at the worst for English words that I already knew.
So it comes as a very, very rude shock to my system that, in his first week of Chinese school, poor Zac is studying rational numbers, the definition of rational numbers, and specifically a) something intuitive called “opposite number” and b) something rather less intuitive called “absolute value”, a concept that, prior to Google and Twitter assistance, I had firmly assumed was some sort of “Chinese thing”.
Absolute value, for the record, is not a Chinese thing. It’s an international thing.
But I hadn’t heard of it because we don’t introduce it in the UK until advanced, and optional, post-16 maths.
In case you care, absolute value is represented by these special line brackets – | |. It expresses the distance from zero and it’s always positive.
Zac is required to operate with this doing sums and word problems involving negatives, positives, “non-negatives”, “non-positives”, fractions, decimals, and multiple series of interlocking brackets, all at the same time, with answers including ±, and lots of explanations using algebra which he finds helpful but I do not.
Well, I think brightly, after more Googling. At least they’re not doing equations with it. Because equations with absolute value typically produce multiple possible answers, not all of the simple ± variety either.
I mean, there’s no way they can expect 11-12-year-olds to do equations using absolute value, can they? That would just be insanely difficult…
There are certain linguistic peculiarities about doing maths in Chinese that make it, well, not exactly easy. (Research suggests that the Chinese use a different part of the brain to do maths from English speakers, which could be one reason why doing maths in Chinese gives me a headache.)
On the plus side, China uses Arabic numerals, just like we do, except when problems are written out as word problems, and Roman letters for the variables in equations, just as we do.
Chinese geometric terms are often pleasingly logical (three-angle-shape, long-square-shape, equal-side-three-angle-shape, six-angle-shape…) — because the roots of Chinese are, well, Chinese, you don’t have to mess with Graeco-Roman terminology like you do in English.
Further, the Chinese use Western measurements in the standard Roman abbreviations, except when problems are written out as word problems. Chinese measurements are relatively intuitive – “thousand-metre” is a kilometre, even if “part-metre” is a decimetre, not a centimetre.
It is helpful, rather than unhelpful, that the character for “metre” is also the character for “rice”, because it means we don’t need to learn yet another bloody character and (not always a given in Chinese) both sense of the character are pronounced the same way.
On the down side? Well….
Fractions, while written the same way, are enunciated as “four under three”, rather than “three over four”.
Chinese does not say “two to the power of three” but “two-of three-times-square”.
Whether a number is increasing or decreasing by a percentage, it always “increases”, though when it decreases, it “increases” by a negative percentage. When reading numbers out, you have to express “zeroes” that we leave silent.
And then there’s the whole 10,000 thing. Whereas we count big numbers in thousands and multiples of thousands, Chinese counts in “tenthousands”.
So a million (1000×1000) is not a million but “one-hundred-tenthousand”, two hundred thousand is “two-ten-tenthousand” and their big number is neither a million nor a billion but 亿 (10,000 x 10,000, or hundredmillion).
Adding to the joy of nations, 亿, like “one” （一）, is pronounced “yi” (the two words sometimes also have the same tone, though not when pronounced together).
When it comes to decimal places, these are expressed logically enough as fractional parts — albeit fractional parts that count in tenthousands rather than thousands. The first decimal place is a “ten-part”, the second decimal place is a “hundred-part”, the fourth decimal place a “tenthousand-part”, the fifth decimal place a “ten-tenthousand-part”, and so on.
All of this is the sort of thing that makes it quite difficult to follow along in class. But it isn’t the half of it.
Chinese maths is taught rigorously by concept, and the concept drummed in by true-false word problems about the concepts being introduced, which are not dumbed down.
It’s not, actually, a bad approach for any child who’d like to study sciences at university. But it’s an incredibly hard one to catch up on, because it requires a lot of technical terms to have been learnt already. Some of these use common characters. Others don’t.
Chinese children are expected to be competent in arithmetic and number bonds, again drilled into them over years of practice, with numbers up to 17, the first few powers of the most common numbers, the most common decimals and fractions, and how the decimals relate to the fractions. It means they’re very good at computation.
A Chinese child will know – that is to say will have learned through repeated drilling – not only how many millimetres in a centimetre and how many centimetres in a metre but how many millimetres in a metre and how many decimetres in a kilometre, etc.
At least 10 hours of the 50 hour school week that Chinese middle schoolers undergo is devoted to maths.
And, further, quite a lot of the maths involves copying down word problems using Chinese characters from the board and then solving them.
Which is easy if you can write Chinese characters as fast as a Chinese middle school child. Rather less easy if you can’t.
Still, by his third day of school, Zac’s actually copying sums down from the board into his notebook, and doing some of them.
Meanwhile, Huaze and I are sweating blood over Skype trying to find a way to chunk down the impenetrable wall of characters Zac faces on a daily basis into a manageable list of words.
A Chinese middle school Year 1 maths textbook doesn’t use the baby syntax that Chinese as a Foreign Language texts use. It’s horrible stacks of clauses, generally without either endings, word breaks or pronouns to give you a clue as to how they fit together, just the odd 的 or 得 – and fewer of those than you’d hear in speech because it’s written, and formal writing at that.
We spend an excruciating half-hour on a problem to which we both know the answer, trying to establish why it means what it does (a word meaning “explain/show” has been used in two senses: first as a request to “explain” and secondly in reference to the placement of a point on a number line “the point representing X on the number line…”).
There’s an absolute heap of maths vocab that we haven’t thought to cover in Zac’s patchy preparation for this massive endeavour. Whole stacks of words for “correct”, “explain”, “demonstrate”, “if…then…”, “in … the case of”, “let it be…”, “work out”, “calculate”, “solve”, “statement”, “proposition”. And I do mean stacks of words.
It takes us at least an hour per page, often longer.
And then I grab a taxi, and head off to collect my spawn. And every time I take the taxi, I wonder if I’m going to find a bloody, tearful puddle at the other end. And, amazingly, I don’t.
“Mum,” Zac says, as we plough through yet more maths vocab. “You realise we don’t actually use that book much in class?”
“WHAT?” I say. “What do you mean?”
“Well,” he says. “The impression I get from the kids in class is that this is basically a posh boarding school that’s quite hard to get into.”
At the time, the significance of what he’s saying doesn’t register. All I really know about the school is that it’s a good school, that takes foreign students, teaches English in English and has some foreign language support.
It takes, literally, weeks for me to, well, do the maths, to work out from reactions when talking to locals and from the attitudes of the kids in school, that this is probably one of the top five schools, certainly one of the top ten schools, in Harbin.
That’s a city bigger than London, the capital of a province with over 40 million people, or roughly double the population of all Australia – and able students from all over the province are shipped into Harbin to board at the best schools.
By the very fact that it gets any children at all into Shanghai Jiaotong and Beijing Tsinghua universities, two of the top universities in a country of 1.6 billion people, this is an academic elite school. (The Ivy League, by contrast, serve a population less than 20% of that.)
The maths in any Chinese school is going to be difficult for any Western child, not only because the literacy required is high, and the teaching style is different, but because the maths itself is harder.
The maths in an academic elite school? The maths that’s taught to some of the most able children out of a population of over forty million, in a society that thrives on academic achievement and takes maths very seriously?…
“I think the book’s kind of easy,” Zac says. “I think that’s the standard textbook all schools use. But they all seem to do different, harder worksheets. And what we’re doing in class is a lot harder than what’s in the book.”
To my eternal discredit, I ignore this. It CAN’T be much harder than what’s in the book. He must just think it’s harder, because it’s in Chinese.
Ignorance, as they say, is bliss.
Picture credit: Kacey 97007.