What is Singapore Math?
The Singapore math method is a highly effective teaching approach originally developed by Singapore’s Ministry of Education in the 1980s for Singapore public schools.
The method has been widely adopted in various forms around the world over the past 25 years following our introduction of the curriculum to the U.S. in 1998. Read our story here.
Singapore consistently ranks at the top in international math testing. The intentional progression of concepts in the Singapore math approach instills a deep understanding of mathematics.
Two international tests, the TIMSS (Trends in International Mathematics and Science Study) and the PISA (Programme for International Student Assessment), assess math and science competency in countries around the world. Singapore students consistently rank among the top on both tests.
The Singapore math method is focused on mastery, which is achieved through intentional sequencing of concepts.
Some of the key features of the approach include the CPA (Concrete, Pictorial, Abstract) progression, number bonds, bar modeling, and mental math.
Instead of pushing through rote memorization, students learn to think mathematically and rely on the depth of knowledge gained in previous lessons.
An attitude that math is important and approachable is also essential. Students perform at a higher level when their potential for understanding and success is assumed.
In typical U.S. math programs, students get a worked example, then solve problems that very closely follow that example, repeating all the same steps with different numbers. In Singapore math, students must think through concepts and apply them in new ways from the very start. Since they can’t rely on simple replication, students are pushed to greater engagement and broader thinking. In U.S. math programs, concepts and skills are more compartmentalized within and across grade levels than in Singapore math, where a strong sense of connectivity to past learning is woven throughout.
Singapore math not only helps students become more successful problem solvers, it helps them gain a sense of confidence and resourcefulness because it insists on conceptual depth. This naturally prepares students to excel in more advanced math
CPA (Concrete Pictorial Abstract) Approach: Introduces concepts in a tangible way and progresses to increasing levels of abstraction.
Number Bonds: Shows the part-whole relationship between numbers.
Bar Modeling: Helps students visualize a range of math concepts, such as fractions, ratios, and percentages. Allows students to determine the knowns and unknowns in a given situation.
Mental Math: Helps students develop number sense and flexibility in thinking about numbers.
CPA Approach STEP-BY-STEP
Let's take a closer look at the CPA approach through this addition problem from Dimensions Math Textbook 1A.
Concrete: ACTIVITY & Manipulatives
This is the introduction to the problem. In this stage, teachers lead a classroom activity where students represent birds and act out the story problem. The interaction introduces students to the problem in a tangible way.
Students may also use linking cube manipulatives to model the problem in a concrete way.
Pictorial: Number Bonds
Students then work on a visual representation of the problem by showing the two parts and the whole in the form of a number bond.
Students move to the final stage of the sequence, an equation that represents the story problem.
Number bonds are a pictorial technique that show the part-whole relationship between numbers. Initially, the whole number is written in one circle, and the parts of the number are written in adjoining circles connected by lines to the first circle. This method helps early elementary students work towards addition and subtraction, and illustrates strategies to solve expressions mentally. Using number bonds fosters a solid number sense that serves students throughout their math education.
Bar models are a versatile and transferable tool that students can use to visualize a range of math concepts, such as fractions, ratios, percentages, and more. Drawing bar models for word problems allows students to determine the knowns and unknowns in a given situation. It extends the CPA approach, especially the pictorial phase, as it allows students to illustrate the mathematical information given in problems. It prepares them to understand more complex math on a conceptual level. This method is most effective when used frequently throughout the program.
The Singapore Math approach teaches techniques and skills to easily and accurately perform mental math. These strategies help students develop number sense and flexibility in thinking about numbers. Many mental math strategies involve factoring numbers into parts, then performing operations on them in a different order from the original expression. The thought processes involved in mental math are often illustrated by number bonds.
Some mental math strategies are taught as early as grade 1. As students progress, they learn to apply new mental math strategies to specific types of problems and adapt ones they already know. Students are encouraged to develop their own strategies, and to use their discernment in deciding when and where to use them.
We started Singapore Math Inc. 25 years ago because we thought everyone should have access to this effective teaching approach. All of our programs preserve the techniques, sequencing, and rigor that define Singapore math. We continue to provide the original curriculum that put Singapore math on the map, while evolving the Singapore math approach through new series to better serve today’s students and educators.