What Is the “Singapore Math” Method and What Makes It Effective?

The Singapore Math® method is a dynamic and proven teaching approach that’s upheld Singapore’s leading global position in math education for years. In the US, it inspired the development of Math in Focus®: Singapore Math® by Marshall Cavendish®—a core math program that has driven success in our nation’s classrooms for well over a decade. 

What exactly makes Singapore’s approach to math instruction and Math in Focus so effective? Here are three elements of the methodology that show its resounding impact:

1. Concrete-pictorial-abstract (CPA) approach

The foundation of Math in Focus is an emphasis on hands-on learning, which is enacted through a progression through concrete, pictorial, and abstract (or CPA) applications of each concept. This approach first invites students to physically engage with concrete objects (the C of CPA) to introduce the math. The idea is that tactile experiences help students form stronger connections to what they’re learning.

From there, students transition to pictorial representations (the P of CPA) of those same concepts, such as drawing diagrams, graphs, or tables that reflect their understanding. The goal of this stage is to deepen thinking while encouraging students to visualize the mathematical connections they made in the concrete phase. 

Then comes the A of CPA: abstract. In this final stage, students use abstract reasoning to identify patterns and principles that apply across different contexts. An example of this might be using algebraic reasoning to identify multiplicative patterns—like linear growth—as they present in a word problem, an equation, and a visual. The ability to grasp a concept conceptually is a powerful indicator that students not only understand it but would also be able to draw their own conclusions based on what they already know as lessons progress.

2. Metacognitive thinking

Metacognitive thinking, or thinking about one’s own thinking, has wide-ranging benefits on student achievement in math. A 2025 meta-analysis summarized that “metacognitive instruction on math achievement has large and statistically significant effects.” This is a powerful tool for evaluating one's attitudes about a problem and persevering towards a solution. Students who practice metacognition as a core learning habit are also far less likely to rush into premature generalizations—both in math and in life. 

Metacognition is woven into every lesson of Math in Focus. The program regularly encourages students to consider their own problem-solving strategies, identify misconceptions, and adjust their reasoning. They learn to self-reflect: Why did I approach the problem this way? Where in my thinking process did I misunderstand? These opportunities to pause, think, and ask meaningful questions naturally deter students from feeling discouraged by their mistakes. Instead of feeling dejected, they develop resilience and an inclination to view errors as opportunities for growth. Students ultimately develop not only math proficiency but also general critical thinking skills.

3. Depth and rigor in conceptual understanding 

Many math programs pride themselves on the simplicity they offer. For certain program elements, like teacher materials or digital student workbooks, simpler is better. However, math itself is not always simple. The Singapore Math® approach celebrates this by encouraging thinking that goes beyond surface-level answers to develop conceptual understanding. The methodology teaches students to approach complexity with curiosity rather than avoiding it, which promotes rigorous exploration of mathematical concepts. Indeed, much of Math in Focus’ prestige is tied to the deep understanding it enables in this way, which leads to students wanting to analyze problems and find their solutions.

Alongside developing positive attitudes, this practice also effectively accelerates students’ learning. They learn to generalize mathematical principles and identify connections between different ideas. Fractions are seen not just as numbers, for example, but as expressions of proportional reasoning. In Math in Focus, mathematical mastery comes from a rigorous pursuit of understanding the “why.”

Problem-solving that’s fueled by curiosity

In mathematics, there is often a hyper-focus on solutions at the cost of truly understanding why they’re solutions in the first place. This is why Math in Focus shines; it’s a program whose teachings reach a depth that’s rarely achieved through other curricula. For students, this means they develop a drive to know the reason behind why different math concepts work. For example, students not only learn that all numbers multiplied by zero equal zero, they learn why, too. Students become motivated to develop enduring mathematical competence. In Math in Focus, discovery fueled by curiosity lies at the heart of problem-solving.