Ship of Fools: Shanghai Maths

Thread: Shanghai Maths Board: Oblivion / Ship of Fools.

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Posted by Hairy Biker (# 12086) on :

On World Maths Day, does the UK have anything to learn from the Shanghai experience of teaching maths? Do shipmates have any experience of Asian teaching, and maths teaching in particular? Is it really different from the western approach, and if so, is it better and could it work in the UK?

Posted by Og, King of Bashan (# 9562) on :

I have no idea what the difference is, although I know that a number of different systems (including something called the "Singapore System") are used by the various middle schools in and around my neighborhood. If we ever have a kid, I will have to figure out what it is all about, and I wonder if I will be able to be of any assistance when it comes time to study for a test.

I do agree that intimidation by numbers and math is a problem. I know a number of people who will not touch a Sudoku puzzle simply because they see numbers and assume that it is beyond their grasp. Never mind that the puzzle itself requires no math and wouldn't be any different if the numbers were replaced with the letters a-i, they see numbers and run. That isn't good.

I will note that I have never had a particularly positive experience with a visiting instructor or professor. Small differences between what the student is normally expected to do and what the visiting teacher normally expects a student to do can lead to a lot of frustration. To cite an example, my mother remembers hearing an American professor talking about failing Chinese students for not citing sources in papers, which just wasn't something they were ever taught or expected to do. I'd be a little worried if my kid was going into a classroom with a teacher who had never taught in the UK before.

Posted by que sais-je (# 17185) on :

quote:
Originally posted by Hairy Biker:
does the UK have anything to learn from the Shanghai experience of teaching maths?

Technologically developing countries put a lot of emphasis on science and engineering which means a high priority for maths. Britain does performing arts, financial services etc. I'm rather cynical about our commitment to science (outside some prestige areas).

The history of the Fields Medal is interesting. If you look at the table, the most successful European country is France - and most French recipients were at a French institution. Winners from the Pacific area mostly were based in the USA. I imagine that will start to change in about 20 years as Chinese, Japanese and, no doubt, Malaysian and Indonesian Universities get better.

A random thought: maths is cheap. Famously a mathematician is some one who lies down, turns off the light and starts work. Coffee is needed but no expensive kit as required by physics, chemistry, or biology for example. It would be interesting to see how poorer countries do in those subjects.

Posted by IngoB (# 8700) on :

quote:
Originally posted by que sais-je:
The history of the Fields Medal is interesting. If you look at the table, the most successful European country is France - and most French recipients were at a French institution. Winners from the Pacific area mostly were based in the USA. I imagine that will start to change in about 20 years as Chinese, Japanese and, no doubt, Malaysian and Indonesian Universities get better.

There are ten winners of the Fields medal from France, six from the UK, but only one from Germany. Are we to conclude from that that the UK is six times ahead of Germany in science and technology, and France ten times? Hardly. Perhaps we should rather conclude that the Fields medal, and "pure math" in general, is really pretty damn useless as indicator of science and technology success...

quote:
Originally posted by que sais-je:
A random thought: maths is cheap. Famously a mathematician is some one who lies down, turns off the light and starts work. Coffee is needed but no expensive kit as required by physics, chemistry, or biology for example. It would be interesting to see how poorer countries do in those subjects.

Most "real" maths is somewhat less useful than philosophy, frankly. The truth is that what is pushing science and technology ahead is applied maths. And that is largely developed in the physics and engineering departments of the world, and yes, also by official "applied maths" departments (groups in maths departments) where they exist. "Trickle down" effects from pure maths are rare. I just thought to myself "what pure maths have I ever found useful in two decades of doing science?" I thought I had a good candidate, pulled out Kuznetsov's book on bifurcation theory - and it is published in the series "Applied Mathematical Sciences". Oh well. Anyway, as it happens applied maths is not that cheap. Certainly cheaper than a lot of experimental stuff, but most supercomputer cycles of this world are being burned through by applied maths in one way or the other. And staff costs are anyhow the main expenditure of any research organisation.

Posted by que sais-je (# 17185) on :

quote:
Originally posted by IngoB:
There are ten winners of the Fields medal from France, six from the UK, but only one from Germany. Are we to conclude from that that the UK is six times ahead of Germany in science and technology, and France ten times? Hardly. Perhaps we should rather conclude that the Fields medal, and "pure math" in general, is really pretty damn useless as indicator of science and technology success...

Very possibly. I just found the distribution interesting. After all, there has only ever been one German among the the World Maths Day's gold medallists. Perhaps Germans aren't so competitive. Who knows?

quote:
Most "real" maths is somewhat less useful than philosophy, frankly.
... I just thought to myself "what pure maths have I ever found useful in two decades of doing science?"

If I'd posted that I'm sure you'd make the obvious reply.

However one might mention: non-Euclidean geometries Riemannian geometry, group theory, topology, number theory, linear algebra, algebraic geometry, Hilbert spaces - to say nothing of the 19th century's setting maths on a reliable foundation though their work of continuity. The Euler-Lagrange equations are debatable, but without them we shouldn't have Lagrangians/Hamiltonians and the physicists could all go home. Which reminds me: had Emily Noether's background not been in abstract algebra would she have produced her famous theorem?

And there's the Google PageRank algorithm.

But I don't know if the OP was only concerned about "what is pushing science and technology ahead". It's not what I did maths for nor is it necessarily what the 4-18 year old kids in World Maths Day did it for. May be they did it because they found it exciting, exhilarating or whatever and the question is why don't British kids have that enthusiasm?

But if that is what counts we could get rid of pure maths and philosophy, also history, literature, theology, archaeology (except forensic), computer science (keeping the applied bits), art, music, classics, certainly theoretical cosmology.

Posted by Horseman Bree (# 5290) on :

No subject of any sort is valuable for everyone. Some subjects are incredibly valuable to some.

My son-in-law works in a mathematical field known as Category theory, which has significance in the study of Quantum supercomputing - but he claims that only about 200 people in the world really understand him.

Fortunately, the kind of people who give grants consider that this extremely abstruse field is worth spending the money.

Should we cancel the study because the field is limited to "those who know"?

Or could we open up the study of math (or other subjects) so that more people might have an inkling?

Basic subjects are taught to everyone in school because we don't know at an early age which students will be good at particular studies/work. If we cater to the limited range of interests of certain people, then we will get what is now all too common: a large crowd of people who can't do anything but video games in their parents basement for the rest of their lives.

Maybe a bit more insistence on actually knowing something, anything at all, might be more productive than whining about how something you learned in school didn't apply to your particular career.

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