
Singapore employs a mathematics teaching method called productive failure - ocjo
http://qz.com/535443/the-best-way-to-understand-math-is-learning-how-to-fail-productively/?linkId=18512366
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dstyrb
This sounds extremely similar to the way I was personally taught trigonometry,
calculus, linear algebra, and tensor calculus.

First you are asked to work out some monstrous 4 page problem by hand. Then
you have a lecture on the specific tricks in each of those courses (SOC-CAH-
TOA, differentiation by dropping the power, linear algebra by matrices, tensor
calculus by superscript-subscript interaction). Then you are asked to do the
same problem again in 3 lines... Perhaps it's not outright failure, but you
are forced to "discover" an advanced concept for yourself before being given
the proper tool.

I feel perhaps the author is too bold with: "Singapore, the land of many math
geniuses, may have discovered the secret to learning mathematics (pdf). It
employs a teaching method called productive failure (pdf), pioneered by Manu
Kapur, head of the Learning Sciences Lab at the National Institute of
Education of Singapore."

I feel a bit more research will show that this is an extremely well
established teaching methodology. I mean, who _wasn't_ taught integration in
this manner?

["Given the curve f(x), find the area under the curve from x=0 to x=10" so you
pick a bunch of random points, find the value of f(x) at those points,
multiply by however far you chose to put the points apart, go in with the
wrong-but-kind-of-close answer "Oh, by the way, there's this thing called
integrating, sit down for a sec kids"]

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pkinsky
Interesting, sounds like another instance of problem solution ordering:
[http://mkremins.github.io/blog/doors-headaches-
intellectual-...](http://mkremins.github.io/blog/doors-headaches-intellectual-
need/).

>Think of yourself as someone who sells aspirin. And realize that the best
customer for your aspirin is someone who is in pain. Not a lot of pain. Not a
migraine. Just a little.

>One of the worst things you can do is force people who don’t feel pain to
take your aspirin. They may oblige you if you have some particular kind of
authority in their lives but that aspirin will feel pointless. It’ll undermine
their respect for medicine in general.

>Math shouldn’t feel pointless. Math isn’t pointless. It may not have a point
in job [y] or [z] but math has a point in math. We invented new math to
resolve the limitations of old math. My challenge to all of us here is, before
you offer students the new, more powerful math, put them in a place to
experience the limitations of the older, less powerful math.

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hellofunk
Singapore gets a lot of attention for having good schools, high-achieving
students, novel teaching methods (sometimes), and in a sense, all of these
things are true.

But there is always a cost. The enormous pressure that minors have to perform
well in school in Singapore has led it to having one of the highest teen
suicide rates in the world. In the short time I lived there, I knew 2
highschoolers who committed suicide.

There is nothing wrong with challenging a child, but I hope Singapore's
culture eventually evolves to be a little easier on kids in general.

~~~
cLeEOGPw
Spoken like a true american.

Given 8.5/100000 suicide rate in US and 10.27/100000 in Singapore, what would
you choose, 999989 well educated, well developed in mathematical and
analytical thinking, highly proficient in solving unknown problems
individuals, or 999991 lower than average (US has notoriously low education
standards), highly afraid of math, often leaning towards social and gender
"sciences", overconfident and self important, yet having very little skill
practice or general knowledge, individuals? The answer is pretty obvious.

~~~
hellofunk
I'm specifically talking about teen suicide rates, not whole-population
suicide stats.

Additionally, your stereotyping of the rest of the world as self-important is
not the right attitude.

p.s. I do not live in the U.S.

~~~
oddx
Do you have any stats for this claim?

I found only this link and look like rate isn't really high
[http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1414751/table/T1...](http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1414751/table/T1/)

>Suicide numbers and rates per 100,000 young persons aged 15-19 - Canada 10.8,
Singapore 8.5, USA 8.0

~~~
hellofunk
I've seen that before as well, but it is based on real old data. Many of the
numbers are from over a decade ago.

My claim for this statement is a bit less formal; within Singapore, where I
lived, it is common word-of-mouth that the teen suicide rate needs serious
attention, and they often say there that it is much worse than in most other
places. But I can't point you to a specific study.

Also, regarding formal stats: Singaporeans are (rightly so) quite skeptical of
any official figures released by the government. Singapore's leaders tend to
keep private any stats that are unfavorable (much of the recent haze-related
details the last couple of years were promptly removed from public media if
they were too critical; and if anyone there writes articles, even on a
personal blog, that are critical of the culture, its policies, or raise
serious questions, they often get severely fined or imprisoned).

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Asbostos
This sounds a lot like the well established - but poorly implemented - idea of
constructivist learning [1]. A difference seems to be that it would be much
easier to design an activity in the Singapore method since it's OK if the
student never actually discovers the proper method and in the end the teacher
will simply tells them the answer.

[1]
[https://en.wikipedia.org/wiki/Constructivist_teaching_method...](https://en.wikipedia.org/wiki/Constructivist_teaching_methods)

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shoo
this seems naively similar to the "problem-solution ordering issues" post that
was on here a few days ago:

[https://news.ycombinator.com/item?id=10483695](https://news.ycombinator.com/item?id=10483695)

face people with the problem first, let them struggle on their own for a bit
and try to figure it out, then show them a way of solving it.

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geebee
This is a good idea, though we shouldn't act like it's completely novel. I
received most of my math education in the US (I was a math major in college as
well), and my high school calculus textbook (this was in the US) was very open
about how some of the problems were there to be _tackled_ rather than solved.
There were almost always a few problems at the end of the chapter that weren't
easily solvable without the principles and techniques that would be introduced
in the next chapter. You might be able to estimate it, brute force it, various
other things… who knows, maybe you'd discover the next chapter for yourself.

Personally, I think it's an excellent approach. It does sound like Singapore
is doing this much earlier in math education than I encountered it in the US.

In spite of all this, I don't see the technique as being especially promising
in the US. Not because I think it's a bad approach - I think it is an
excellent one. But because people in the US seem to think that they need to
copy a _process_ from Singapore or Finland or whatever. Oh, see, what we need
to do is teach _productive failure_. Let's get it into the textbooks!

What we need to do is to start drawing our math teachers from the top tier of
math graduates who are inclined to teach and show talent. A lot of these
processes that we try to copy from other countries come naturally to people
who really understand math and are good at teaching it. I'm not saying there
should be no agreed on curriculum, but these success stories, I think, are
more the outcome of talented teachers than a curriculum created and imposed
from above.

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rikibro
Didn't know this was a thing but normally (it requires time) I learn like that
- often being scorned by more experienced people, saying it is inefficient
and/or I I'm rude not to hear their advises.

In the long run, this actually builds confidence to attack any (engineering
and more) problem you face and being relatively independent from a teacher.

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tome
The current Prime Minister of Singapore was the best mathematician in his year
at Cambridge:

[https://en.wikipedia.org/wiki/Lee_Hsien_Loong#Background_and...](https://en.wikipedia.org/wiki/Lee_Hsien_Loong#Background_and_education)

~~~
Frqy3
It is fitting then that Singapore is teaching its students to wrangle with
mathematics.

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SixSigma
> They recognize that the approach is good but they worry about efficiency and
> standardized tests

"We know the students learn better but that's not our personal performance
metric"

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crdoconnor
This sounds a little like test driven development.

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boothead
This is definitely the way I learned Haskell. I spent ages trying to learn by
reading and didn't really start making progress until I learned to just write
some code and figure it out as I went.

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guai898
This might be suitable for motivated students. I don't think it will work for
everyone.

