Singapore Math is successful because of key ingredients:

What makes "Singapore Math" so effective? 

1. Focus on the use of the Concrete - Pictorial - Abstract Cycle. And not as just a remediation tool. As students move through these stages of understanding they build important strategy connections and move to generalization of concepts.  CPA is a cycle not a linear progression.

2. Focus on Visualization and the Use of Heuristics. Visualization comes from the process of building and drawing. It is that magic moment when the concrete or pictorial have suddenly moved to an image in your mind. You no longer have to build or draw it. For me, this happens in multi- digit multiplication now. I  finally have lost the visual of stacking for multiplication in my mind. Breaking apart the numbers is what I see now. For instance, I see 314 x 7 as  (300 x 7) + (10 x 7) + (4 x 7). No regrouping for me. 
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Heuristics are structures that students create to make meaning for themselves. One heuristic I like is: What do you know, what do you need to know, what can you draw, what can you do. Another is bar models. Neither have a "right" way to do them. It is like writing a paper in high school, if it makes sense to me and to my reader, it makes sense. 

3. Focus on the Use of Mathematical and Perceptual Variation. Every problem has a purpose in developing student understanding. Problem strings vary by mathematical complexity or by the visual models used to represent them. Learning occurs in the bridges between the problems. 

4. Focus on Problem Solving as the Heart of Mathematics. The goal of mathematics is to solve real world problems. Notice I didn't say WORD problems but real-world problems. There is a difference. No longer is the role of the mathematician calculating endless strings. Mathematical modeling and application of mathematics to solve problems in the world around us is the goal. Doing this in a way that is collaborative, flexible, able to be communicated and justified is not a bonus but the whole purpose.

All of this occurs with the support of the readiness, engagement and mastery cycles and a three part lesson structure that helps students move through exploration, guided practice and independent practice.