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"]

Interesting, sounds like another instance of problem solution ordering: http://mkremins.github.io/blog/doors-headaches-intellectual-....

>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.

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.

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...

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

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.

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.

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.

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...

> 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"

This sounds a little like test driven development.

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.

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