06May2013

On Doing Maths in Chinese

Fractal created by Kacey.

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.

9 Comments

  1. Yvette says:

    This sounds fun! :P

    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/math 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 things 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!

    • Theodora says:

      I actually agree that we’re pitifully far behind. Did you look at our 11-year-old exam? That’s for the most able students finishing primary. You would think if they were going to split it, they’d have a harder maths option than that available — a technical track, as they say.

      You would think that on the top track in the UK by age 16 we would have covered everything that Chinese 11-year-olds do. But, no…

      There’s a small thesis to be written on why communist (let’s leave the question of whether China is currently in any meaningful sense communist out of it) countries do / have done better at maths.

      • Yvette says:

        For sure. My mother always says that a big part of it was that in Hungary you never have/had enough university spots for everyone who wanted to go, and back in the day the issue was exaggerated because unless you had Party connections or had parents classified as laborers you frankly would never get a spot for an “easy” course in humanities. So while in the West you’d probably not worry about university spots in terms of your future as much, in Hungary she frankly could never go for her first love (history) and ended up studying to be a math teacher. Pretty much all her friends were in the same boat and became engineers or doctors or what not.

        These days in Hungary I know it’s still similar to the old system in that there aren’t enough spots at university, but BY FAR the most coveted spots (based on the number of points at your exit exam) is comp sci/ electrical engineering. This is because that’s now the best way to get money/ have skills to leave and go abroad. :)

        And yeah I looked at the test you linked and wasn’t particularly impressed- it reminds me of how I had to take standardized tests every year and never thought they were supposed to be difficult. I think another difference in the two systems though is I think in the US (what I know best) there’s an emphasis that kids should “like” math and no one ever fails anything, but frankly there are things in life you have to get through even if you don’t like them (I always think it’s a question of how much you like the other stuff that makes you put up with the non-enjoyable parts), and frankly I have failed my fair share of tests but suffered through them. The latter always freaks people out because I’m pretty open in how I NEVER got an A in math from middle school on (I was always in the B- range to be honest), cause I’d fail stuff along the way and get a great final exam score. So I feel like I learned a lot and had great math skills going to university, but most people I know would’ve shied away from such a baptism by fire.

        Ok once again I’ll stop, as I’m sure I could keep going on on this. :)

        • Theodora says:

          I think there’s a lot to be said for failing, actually. We keep moving the goal posts so more people can pass, and, quelle surprise, things get easier and easier.

          What amazes me about China is that they don’t seem to have a two-tier track. Every Chinese child, of every ability, does absolute value at age 11-12. Parents get them tutors if they can’t cope, and, if they really can’t cope, they go to special school (though there’s also a market in bribing teachers).

          There’s a lot of elements to the Chinese system that I do not like, of course, and I’d think that the way the language works makes a lot of aspects of maths actually easier (in particular, the way they use the visual side of the brain — saw a very interesting visual expression of 1/2^n where they were given the problem as squares, and then had to redo it as triangles).

          But Chinese students can’t be born more able than American and British students, can they?

          • Yvette says:

            Yeah prolly no more than Hungarian kids I should admit. ;-) (Though interesting detail, one of my mom’s big complaints about American vs Eastern European math was the fact that there are different tracks too!)

            I have read that one reason Chinese students do well as well is, as you’ve said, language-based and visual in the sense that the language is just better structured because the words for counting are shorter so you can do it more quickly (I think it was in “Outliers”). Granted I think that might be something that sounds more impressive to a lay person than someone actually familiar with maths and sciences- sounds stupid but after a point you stop using numbers!- but there are certainly various differences in visualizations and such.

            In defense of the American system however, when it comes to graduate admissions in the USA in physics (one I know best, but any science/engineering program) there are literally different piles in admission for domestic versus international students (mainly China/Korea/Taiwan/Asia) as the Asian systems does have serious problems teaching students research and experimental initiative- most people just have no idea how to do this when applying for a PhD, and need to be taught. That and the cheating and plagiarism is insane from what I’ve gathered, so you just assume everyone’s standardized scores are fake and an applicant is “ethical” if they show a professor who is “writing” them a letter of recommendation said letter before signing their name…

          • Theodora says:

            Interesting. I’d say as a native speaker the maths vocab is easier and more intuitive, and, yes, the counting words are shorter. The way the language is structured also naturally makes hard concepts sound easier and makes the connections between them clearer, where English jumps around wildly between Greek, Latin and, well, English: abstract ideas are typically structured using very simple building blocks.

            As regards cheating — bribing teachers to pass failing students is a not uncommon alternative to tuition. Zac says cheating in tests is pretty standard (a 16-y-o on his CFL class was copying answers on a test from an older student), because it’s less about the knowledge and more about the results, or appearance of results. I’d imagine people can also bribe professors if the family’s rich enough. Which, if they’re headed to the US, the family will be, of course.

  2. Alex says:

    I teach English as a Foreign Language at a private boarding school in a tiny city in China. It’s amazing how advanced the students are—I come into class, and see the second grader’s board covered in decimals and fractions!

    In other classes, at least, there is a high reliance on rote learning (endlessly repeating and copying words in English or Chinese). Unfortunately, this means that my students can answer basic questions about themselves as long as they are always asked in the exact same way (even down to tone of voice and emphasis).

    There is less of an emphasis on creativity (there is only one right answer!), like you mentioned in a later blog entry where Zac worried that he “got the essay wrong” since he didn’t write down what the teacher told them before verbatim. It’s an interesting school system!

    I wish you and Zac the best of luck!

    • Theodora says:

      Well, he didn’t “worry”, exactly. He just noticed that he’d done it wrong for China because they were required, as you say, to parrot word-for-word, not paraphrase, and of course his natural instinct was to write in his own words.

      This is a huge issue with English (and for that matter Chinese) language teaching all the way through. Zac’s native speaker Chinese classes are listening comprehensions and “fill in the right word” type questions, or “which of these sentences is grammatically correct” multiple choice. None of the fun stuff we do, like writing poetry, for example.

      I think one reason it happens is that the ONLY way to become literate in Chinese is to write the bloody characters out over, and over, and over, and over, and another is that, in my limited experience, Chinese sentence structures need to, simply, be learned by repetition.

      But I have a friend who does EFL examinations in China of Chinese kids hoping to go to Western universities. And even though she explains to both the institutions and the teachers that their students will be marked down for parroting and rote speeches, and marked up for creativity, they simply do not get it.

      It’s crazy. Foreign language teaching in every other culture I’m familiar with uses lots of role play, improvised conversations, etc. And, as you say, in China it is from the script. When I talk English with Chinese children I start with the script and then try and expand a little, speaking slowly and clearly, but even if I veer only slightly from the script, I need to switch back to Chinese.

      Interestingly, Zac’s considered extremely good at art in the school, because he draws things that he has imagined, typically sci-fi landscapes and rockets, which Chinese children don’t really do.

  3. Lashunda says:

    I do not even know how I ended up here, but I thought this post
    was great. I don’t know who you are but certainly you are going to a famous blogger if you are not already ;) Cheers!

Post a Comment

Your email is kept private. Required fields are marked *

*
*

You may use these HTML tags and attributes: <a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <strike> <strong>