On Monday I was required to monitor at the Tokyo University undergraduate entrance exams. I shepherded 60 terrified 17 year olds through a 2.5 hour Japanese language test and then a 100 minute maths test. These tests were part of a two day examination process for those want to enter the humanities faculty of Tokyo University. About the Japanese test I can say nothing, but the maths test interested me, and can be found online (in Japanese) at the Mainichi Shinbun newspaper. In order, based on my feeble attempts at translating the exam, the four questions were:

- A straightforward but nasty calculation of the properties of a line intersecting with a cubic function, including elucidation of all minima and maxima of the products of the lengths of two line segments
- A geometry question with two proofs
- A constrained linear programming problem
- A simple Markov model with a slight twist

The students had 100 minutes, and to their credit quite a few of the students managed all four, though a lot also stumbled and didn’t get past two. I would say that for a well-trained student with good maths skills, these four questions can all be done inside their allotted 25 minutes, but it’s a pretty risky process – even a small error at the start, or misconception of how to do the problem, and you have basically lost the whole question because you only have time to attack the problem once. And these problems are probably about the same level of difficulty as the questions on a standard year 12 maths exam in Australia – where usually we would have three hours.

But these questions were for the *Humanities Faculty* of this university. If you want to study Japanese literature at Tokyo University, you first have to get through that 100 minutes of high level mathematics. It says something, I think, about the attitude of Japanese people towards mathematics, and towards education in general, that they would even set a mathematics test for access to a Humanities Faculty; and it says even more about the national aptitude for maths that the students could tackle this exam.

At about the same time as these exams were being held, *the Guardian* and the *Sydney Morning Herald* released articles slamming the mathematical and science abilities of the average student in the UK and Australia, respectively. *The Guardian* reported on a new study that found English star students were two years behind their Asian counterparts in mathematics, with 16 year old English students at the same level as 14 year old Chinese. The study also found that

The research also found England’s most able youngsters make less progress generally than those of similar abilities across the 12 other countries studied. The other countries studied were Singapore, Hong Kong, Taiwan, Japan, Australia, Slovenia, Norway, Scotland, the US, Italy, Lithuania and Russia.

Meanwhile, the *Sydney Morning Herald* reported on a new study showing that the proportion of students doing mathematics is falling fast, with apparently only 19% of students studying maths, science or technology in their final year of school, and a rapid fall in mathematics enrollments amongst girls especially. The corresponding figure in Japan in 2002 was 64%.

So is this a problem, why is it common to the English speaking world and viewed so differently in Asia, and what can be done about it? Obviously as a statistician I think this is woeful[1], and it certainly is my personal opinion that understanding mathematics is a good thing, but is it bad for a society as a whole to neglect mathematics education? I don’t know if that’s objectively verifiable. So let’s skip that question, assume for now that improving the number of people taking mathematics is good, and just jump onto the question of why it is unpopular in Australia, and why the British are so bad at it.

First, I would like to dispute the possible explanation provided in *the Guardian* article by “the researchers”:

In east Asian cultures education has historically been highly valued. This can be seen not only in teachers’ high salaries, but also in the heavy investment of families in private tutoring services

While it may be true that “social and cultural factors” affect maths achievement, the idea that Asians are better at maths because they value education more highly is a very weak one. If this were the case, would it not also be the case that Japanese would universally be better at foreign languages than the British or Australians? Japanese get a long exposure to English teaching but are generally woeful at it, despite all the money they sink into private tutoring services. No, there’s something else going on here, something about the Asian approach to maths and the way it is taught that is important.

It is certainly the case that private tutoring services need to be considered in the mix. When comparing a 16 year old English student to a 14 year old Japanese student, for example, you are comparing someone who does a 9 – 5 study day with very long winter and summer holidays against someone who does an 8 – 8 study day with two-week holidays, and who gets 2-on-1 or small group tutoring in key subjects for up to 3 hours a day, and on weekends. This process starts at age 10 and really ramps up at about age 15-16, just when the linked article finds the biggest gap between English and Asian students. It’s also the kind of process that benefits the “brightest” students most, and would explain the gap very nicely.

It may be that if the UK wants to compete with the sleeping giants of Asia on basic educational outcomes, it’s just going to have to face up to a simple fact: British students need to study harder. A lot harder.

There are some more nebulous cultural factors that come into play, however, and I am going to go out on a limb here and name a few factors in Japanese society (the part of Asia I am familiar with) that I believe make Japanese so much better at maths than their western counterparts.

*It isn’t about native talent*: A pet hate of mine about western approaches to mathematics is the idea that some people are talented at it, and most people aren’t. I don’t think this is true at all, and I think it’s not something that Japanese believe very strongly. The reality is that getting good at maths is a long, hard slog that involves a huge amount of repetition of basic skills (things like completing the square, substitution, differentiation, interpreting graphs, sign diagrams, etc.) – just like learning a language. Sure, solving maths problems requires creativity and intuition, but these are only of any value if you know the tools you can apply them to, and are familiar enough with those tools to recognize when and how to use them. Mathematics – and especially high school mathematics – is a process of drilling, drilling, drilling, and I think that Japanese recognize this. In Japan the default assumption is that if you pay attention at school and do your homework, you will be good at maths. Sure, they recognize that advanced maths requires extra commitment and talent, but there is a fundamental assumption here that the broad body of maths (up to and including differentiation, integration, limits, and basic probability theory) are things that anyone can learn.*The teacher is important*: the flip side of the idea that education is important is an increased stress on the value of the teacher, and their role as a guide. The role of the guide is also viewed very differently if they are teaching something that they believe anyone can do, compared to if they are teaching a subject that everyone believes is impossible for most mortals to comprehend. Find me a westerner under the age of 30 who is “terrible at maths” and I will show you someone who was humiliated by an arrogant maths teacher at a crucial time in high school, usually around when they were 14. I was in the bottom class in mathematics when I was 14, expecting to drop out as soon as possible, until a good teacher put some time into teaching me, and I found that I really loved it. In Japan, teachers can be bullies and they can be cold and hard, but I would also argue that they have a much greater burden of personal care and responsibility placed on them compared to western teachers, and the failure of their students is treated more like a professional failure (rather than due to the student’s personal talents) than it is in the west. I think this is especially important with mathematics, because when you don’t get it it really hurts – like a kind of itching in the back of your brain – and the failures pile up rapidly. Just a single year between 12 and 14 in which you give up on maths is enough to make all the subsequent years ever more challenging, meaning the damage and the attendant confidence failures compound.*Being nerdy is cool*: In Japan, it’s okay to be a nerd, and being good at mathematics is admired and respected. It’s virtually unheard of to find someone here who looks down on a man who can do maths, or thinks that it is beyond the female brain, or thinks that being interested in mathematics is weird. Furthermore, the nerd world in Japan is much more gender neutral than in the west, so there’s nothing unusual about girls doing maths. Good mathematics skill – up to and including being able to rearrange equations or solve systems of equations, for example – is not seen as a weird foible, but as an admirable sign that you are a rounded human being.*There is a social expectation of mathematical skill*: In addition to nerdiness being much more acceptable, the range of mathematical abilities that qualify you as a nerd in Japan is much more esoteric and advanced than in the west. There is a general expectation that ordinary people can solve maths problems, that they understand the basic language of mathematics so that even if they can’t solve a problem they know roughly what it is and where it sits in the pantheon. Parents assume that their kids will learn mathematics, and don’t dismiss it as the too hard subject that only the special or the weird get ahead in. Whereas in Australia having a kid who is good at maths is unusual, in Japan it is unusual (and*embarrassing*!) to have a kid who is not good at maths.

I think these properties add up to a society in which mathematical achievement is encouraged and widespread. I think that Australia and the UK need to change some cultural factors so that the intellectual and educational landscape is closer to that in Asia if they want to keep up on mathematics and technology achievement – especially since China’s education system is maturing, and other Asian nations like Vietnam, Singapore and India are getting wealthier, with all the educational gains that implies. So what should Australia do?

*Ditch the nerd-baiting*: there’s something really wrong with the way the English-speaking world treats people who do nerdy things. I’m sure it’s mellowed a lot since I was a kid but it’s still there, the kind of ugly-four-eyes assumption about anyone who is interested in anything that isn’t sport or fashion. Until this weird attitude dissipates – and until the nerd world becomes more gender-balanced, to boot – it’s going to be hard to encourage the kind of cultural changes needed to make maths achievement standard across the board*Less intuition and initiative, more drills*: I think it’s very sweet that maths teachers want to encourage their charges to think about the broader world of maths, about creative problem-solving, about applying maths to the real world, etc. But I think those are natural talents all humans possess, that cannot be unlocked without a robust background in the basic skills that make mathematics work. So leave the creativity for people who need it, and stuff kids’ heads full of “useless” rote learning of techniques and drills. It’s boring, but it’s essential to the bigger stuff. If you aren’t able to immediately see when and how to complete a square, then any problem which requires this basic technique is going to be beyond you, no matter how intuitive you are. Maths, possibly more than any other discipline, is built from the ground up, tiny block by tiny block, and all those blocks are essential. So ram them down every kid’s throat, and make every kid think that knowing the quadratic formula is not a test of some kind of obscure talent, but a basic expectation of every 12 year old*Force mathematics at higher school levels*: When I finished school our balance of subjects had to include at least one science/technology subject, but it didn’t have to include maths. This is wrong, and part of the reason that so many students in Japan do mathematics is that you can’t get into a good university if you take this approach: every one of the better universities includes mathematics in its entrance exam. My personal belief is that completion of higher school certificates should require one foreign language, mathematics, and English. That leaves two other subjects to choose from, and guarantees that you have to do some kind of mathematics to the end of school. Not only will this very quickly lead to a society where entire generations of people are generally familiar with mathematics, it will also put a real focus on the quality of teaching at the earlier years, since any student who is doing badly in years 8 – 10 is going to fail their higher school certificate. [Probably this suggestion for a national curriculum is completely unreasonable, but at the very least students could be forced to do mathematics up until year 11, for example].*Make school more robust*: The Japanese school system is about to shift to a “tougher” system that will include Saturday morning classes, because the previous system was considered “relaxed” compared to earlier years. This is, frankly, ridiculous, but so is the attitude towards education of most of the English-speaking world. Summer holidays are way too long and relaxed, there is a real lack of extension classes and tutoring, and expectations are altogether too low. Education isn’t valued enough, and until this changes anyone who wants their child to do better is going to be swimming against a strong current. Educational achievement is partly supported through the shared goals of a whole society, not just through the targets of individual families, and the expectations we hold for education are primarily set through the school system. So toughen it up – not in the sense of making teachers scarier or bringing back outdated “three Rs” educational styles, but by increasing the amount of time students spend at school, setting tougher standards for graduation and university entrance, making schools compete with each other (as Japanese schools partly do) and forcing parents to take greater responsibility for and involvement in their children’s education. This change isn’t specific to mathematics, but it would certainly help.

I don’t think there’s anything special about Asian students, or about Asian culture, that we can’t adopt. Asians’ mathematics achievements aren’t some kind of native or racial talent. It’s just a collection of attitudes towards education, mathematics and nerdiness that we can adopt if we want. Obviously there will be (potentially challenging) institutional changes required as well, and many people may judge it not worth the effort, but I personally think a world where everyone is good at mathematics is a better world, and we should be aiming for it. With these cultural changes maybe one day everyone will know the obvious thrill of being able to complete a challenging mathematics exam … and enjoying it!

—

fn1: Though obviously, the less people doing maths, the longer I will remain competitive in the marketplace …

February 28, 2013 at 1:39 pm

Firstly, I don’t think I even understood your description of the problems confidently, let alone being able to solve them. The first one sounds like simultaneous equations would be involved to find the intersection point, but my memory of a max and min points on curves is gone. And I don’t know if I’ve ever heard of a Markov model before [1].

Secondly, good for Japan (and other Asian nations) for considering whether a humanities student is a well rounded individual in their entrance exams. In Australia, anyone in science/technology gets told that they’re missing a well rounded education while the arts crowd pats themselves on the back about how broad their range of topics is. [2]

” figure in Japan in 2002 was 64%”Seriously? They quoted stats that are a decade out of date? Were they also going to reference how many people though science looked fun based on Ghost Busters?

”is it bad for a society as a whole to neglect mathematics education”I’ll take a stab at this one.

Yes.

Modern society rests on a basis of technology and science. If we forgot everything we’d ever learnt about art, our world in 50 years would be indistinguishable from where it would be if we did not forget. The same is not true of science nor the mathematical basis it rests on.

Forgetting all we know about economics would probably result in repeating the same 50 years of economic history again. But that’ll happen away.

“Sure, solving maths problems requires creativity and intuition”I think you underestimate how little value most Westerners would put on creativity or intuition with regards to maths. I’m a fan [5], but I didn’t see much creativity in the maths I did at school/uni. I just took a set of numbers and metaphorically bashed them they went away. Most (Western) people would assume that’s all there is.

” With these cultural changes maybe one day everyone will know the obvious thrill of being able to complete a challenging mathematics exam … and enjoying it!”Yeah. Now you’re dreaming. Enjoying a maths exam is going to take a rare (and slightly deranged) mind. Ask the kids walking out of the university exam you monitored.

“Though obviously, the less people doing maths, the longer I will remain competitive in the marketplace”I’m not sure maths employment works like that. At least not compared to other industries. It’s not like the old maths falls out of fashion and the new maths is what everyone is hiring for, except for a supporting legacy maths, so you have to remain cutting edge while abandoning older maths. Whereas that statement is absolutely accurate applies to technology. Probably untrue for accounting too. Maybe I’m just in a field that does a terrible job of retaining any value from older work….

[1] A quick Google check doesn’t show Markov model appearing on RussianBrides.com, therefore I’m pretty confident I haven’t.

[2] I’m still a little hurt by an aunt’s suggestion that my Commerce/Computing degree was narrow/vocational compared to an Arts degree. [3] I concede that accounting is useful compared to Modern Communist Thought, but I don’t accept moral value judgements being made on intellectual snobbery.

[3] The study of economics taught me vastly more about being a dogged contrarian debater than anything else save 1) the university pub and 2) internet flame wars. I reckon I could take Socrates in a debate. [4]

[4] Mostly cause he wore a toga and my opening move would be trying to kick him in the balls. Togas are garbage for dodging.

[5] The same way I’m a fan of physical exercise – mostly at a distance while drinking a beer.

February 28, 2013 at 2:06 pm

I don’t think we learn them in year 12 in Australia. I’m surprised you didn’t touch on it in economics (it’s a very popular thing for decision modeling and cost-effectiveness analysis). The correct western approach here should be to say “Don’t worry, you aren’t missing anything.” But I should really say, “Sucker!!!”

I remember from the day I entered uni to just a few days before I left Australia at the age of 32, people from humanities backgrounds going on about how poorly rounded science/tech education is. So let me share this conversation I had with a humanities academic, in 2006:

Cancer Wardhas an older engineer make that same point about modern engineers vs. pre-revolutionary engineers in Russia. I think he was trying to suggest that the Soviet system didn’t appreciate its scientists being renaissance men. But you’re suggesting the same thing about modern Australia – could it be that you’re overstating things, or could it be that every generation sees the same problem?This conversation happened in front of a few other people, and I think the academic quite beautifully destroyed her own case there. So don’t ever let them diss your well-rounded curves! And on the same note, don’t ever let them tell you

Dragonlanceis not literature!I must apologize here for giving you a misconception. The SMH article quoted figures 10 years out of date, but showed the figures for 2002 and 2012 in Australia only. The figure for Australia in 2002 was 3% higher than it is now. So whatever the dubious motivations of schoolkids in Japan in 2002, unless there has been a radical change, the comparison is probably still viable [subject to the usual caveats]. The original report may have contained better figures, but the SMH didn’t show them and I couldn’t be bothered chasing down, let alone reading, the original study[1].

I could also be placing too much reliance on stated educational goals vs. grubby educational practice. I’m pretty sure it’s common for educationalists in the West to talk about encouraging these things, but at the coal-face when the teachers are faced with the actual snotty-faced ingrates in question, they probably wig out on fully implementing the theory. Also, I’m partially arguing here against something I didn’t mention in the article: there is a common stereotype of Asian education that it is all rote learning with no education in creative, intuitive thinking or exchanging ideas. I doubt this is true, but to the extent it is true it has a positive flipside: more intensive drilling makes better mathematicians.

Finally, just as a quibble:

Not really, since there’d be no pictures or stories by which to compare different societies, so we’d have no clue if they were indistinguishable or not. Which is why we need the humanities despite their narrow and blinkered education.

—

fn1: As part of its media reform laws, the Government should make a law requiring journalists to put a link to any study they report on so that the reader can a) see what lying shitbags journalists really are and b) not get so angry about the deliberate burying of data that journalists continually engage in.

February 28, 2013 at 7:55 pm

“don’t ever let them tell you Dragonlance is not literature!”There are two statements that rebut that sort of elitism mentality for me:

1. Jeremy Bentham’s “push-pin is as good as poetry”, and

2. http://www.oglaf.com/ statement “I think erotica just means porn that works for me” This site is NSFW

Clearly, I’m more likely to use the second line of attack when I only have time for one.

“Not really, since there’d be no pictures or stories by which to compare different societies, so we’d have no clue if they were indistinguishable or not.”I didn’t say we could tell the difference, I said there would be no observable difference. This posits an un-involved neutral observer, such as Uatu the Watcher or God. Such an observer would probably just be relieved to dodge the bullet that is the next decade of Tracey Emin exhibitions.

February 28, 2013 at 11:32 pm

I’m definitely of the opinion that porn is what other people read, erotica is what I read. It’s a completely bullshit distinction. Also, burlesque is just dancing for people who couldn’t get into ballet, and nipple tassels don’t suddenly make you not a stripper. So get off my lawn!

Let me fix that for you:

Agree about Tracey Emin, though!