Sounds like an ad for Singapore's tourism ministry, eh?
Singapore's math methods are my latest interest for a couple of reasons:
1. They're simple
2. They make sense
3. They work
Singapore has a very comprehensive way of looking at math education as illustrated by their pentagonal framework graphic below. This graphic is courtesy of a detailed article on their approach Problem Solving in Singapore.
The U.S. isn't the only country to be unhappy with its math scores and try to make efforts to change that. Singapore did exactly that to much greater success than we can for many reasons. With a centralized education system that's small and has designated leaders, they can do more in terms of continuity. We may not be able to do that but we can learn from their techniques, which are wonderful in their simplicity and clarity. For example, they have a well balanced focus (not just procedural skills). They consider the role of attitude and metacognition in learning. Plus, they regularly give students non-routine problems and the resources to solve them. Their approach isn't a magic bullet but it's certainly something to consider.
This is one of the single best articles I've read that will give you a taste of their method and how it can work: Singapore Math: Simple or Complex? In it, you can see an example of their bar model method. It's a terrific visual that boils the problem down into something a student can see clearly. But more than that, the operations needed to complete the problem can be seen. Want to take 3/5 of 40 but have no idea how to do that because you can't remember the rule? That's no longer an issue because they're not teaching rules; they're teaching understanding. Since many students learn by doing and seeing, their method takes an abstract subject like mathematics, especially algebra, and makes it concrete.
I've ordered some of their textbooks since they're available in the U.S. and some schools and homeschoolers are trying them. Deceptively simplistic looking and small, they pack a punch. My main critique would be the contrived nature of the problems but that's probably one of the few weaknesses. For K-5, that's not really the worst thing anyway. Kids at that age aren't so jaded about math and don't expect everything to be realistic.
A refreshing, simple, and effective way to approach math. I guess the old K.I.S.S. method really does work after all. Keep it simple and all.