[LINK] On Doing Maths in Chinese

[stephen at melbpc.org.au]

6th MAY 2013

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 that 
bright students cover in the UK at the age of 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.

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Comments
Yvette says:
May 6, 2013 at 11:59 am

This sounds fun! No really, what I’ve learned more about your foray into 
Chinese math education is not so much how much further ahead they are but 
rather how far behind many Western nations are. I have a somewhat weird 
idea of what kids should be learning at what age (especially if they’re 
science geek kids like I was) because I was in a similarly academically 
rigorous school… in the honors math section to boot. So thus far I’ve just 
been nodding my head in the “of course a kid who is on a technical track 
would do absolute values- now when are they tackling logarithms?” kind of 
way.

(By the way, the reason I ended up in said school with said program was my 
Hungarian immigrant math teacher mother was basically looking for a school 
which had a similar curriculum to what she remembered- and when she taught 
there Hungary was always leading those “which country is the best at X 
subjects” surveys in math. Similarly a “10 hours a week” nation, so I had 
no chance at normalcy.)

Perhaps rambling now, but one of the reasons I find this all interesting as 
well is because one constant thing you read about math literacy is even 
though kids in say the USA do worse they far and away seem to think that 
they’re “pretty good at math”- most people just don’t know what they’re 
missing and what they need to succeed until it’s too late. Frankly one of 
the biggest reasons the retention rate is so low in first year 
physics/engineering in my experience is people enter without sufficient 
skills on the very basic things you need to know cold- sorta like how at 
Zac’s level now he needs to know multiplication tables without thinking, 
because if you’re worrying about that now it’s impossible to ALSO keep 
abreast with the new stuff. Only so many hours in the day and all that.

Ok I’m done now!

--

Cheers,
Stephen

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