Singapore Math is neither a spiral program or mastery. It is designed to focus on basic ideas to a point where the math is naturally understood.
It has characteristics of a spiral program in that each year it returns to aligned concepts and topics (even sometimes at the same points in the school year), and it includes reviews and problems that integrate higher order thinking throughout the year. However, it doesn’t focus on frequent repetition of problems of the same level. Not like you would find in a program like Saxon math.
Singapore Math is also not a program that is designed specifically mastery. Mastery comes from the way that the program is used. For example, a student who struggles in a particular topic area can get additional resources ot help with their struggle, especially outside of school or within a self-paced Singapore math program such as a homeschool program. Singapore math uses a CPA (concrete pictorial abstract) approach that progresses in a natural way thus helping students to understand the concepts more deeply and enhances their ability to master the math. However, it is not focused on reaching mastery before moving on. Because it progresses through specific topics, students are focused on understanding of each topic before moving on.
It would probably be best be defined as a scaffolded curriculum. Singapore math has a clear process by which students start from more accessible points in the topic to the most advanced problems. The material is set up in a way that allows for a natural progression, even if the student hasn’t seen the material before, they will be able to work on developing cognitive leaps that connect that concepts together and make it easy to build upon.
In other words, Singapore math could be described as a program with elements of spiral learning and mastery but which focuses on helping the student learn through clear step by step methodology that builds upon each step so that students can have the skills to move from easy to rigorous problems.
