[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.