Singapore Math

Since the Trends in International Mathematics and Science Study (TIMSS) started ranking countries’ competitiveness in math literacy in 1995, Singaporean students have consistently ranked among the best students in mathematics in the world. TIMSS 2019 ranked both Singaporean fourth-graders and eighth-graders first in the world in mathematics.

Another international study, the Program for International Student Assessment, shows Singapore’s 15-year-olds are among the best at problem solving - the ability to solve unstructured problems in unfamiliar contexts.

The Singaporean curriculum, which the country’s Ministry of Education created, generally focuses on fewer topics but in greater depth. Students don’t just learn equations to reach an answer; they learn how the equations work.

Learning math begins with the concrete: blocks, cards, buttons, whatever. Most curriculums then jump to abstract equations, like 2 + 3 = 5. But Singapore Math introduces the “pictorial” phase — a bridge between concrete and abstract.

Based on the work of American psychologist Jerome Bruner, the Singaporean curriculum begins with hands-on group activities with objects like buttons or dice. Next, students move onto the pictorial phase — drawing representations of concrete objects before moving on to abstract equations. It is precisely this visual approach that helps drive Singapore Math’s success.

When the Common Core standards were developed, policymakers looked to the success of other high-performing countries, such as Singapore. Therefore, the Common Core standards mirror several Singaporean approaches, including a narrower focus with greater depth. And to further align with Common Core, Singapore Math Inc. introduced new Common Core textbooks in 2014. 

As a doctoral student at Northeastern University, Kevin Mahoney published the first study examining the effects of Singaporean teaching techniques on American students.

“Across the board in every case, all of these students were able to make substantial gains,” Mahoney said. In June, a study released in the United Kingdom reached a similar conclusion: teaching Singapore math in the west can drive a small gain in students’ math skills. After one academic year of Singapore math education, gains were equivalent to about one extra month of instruction, according to the study.

The Singapore math method is a highly effective teaching approach originally developed by Singapore’s Ministry of Education for Singapore’s public schools. The method has been widely adopted in various forms around the world over the past twenty years following the curriculum’s introduction to the U.S. in 1998. It is a method 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.

The Concrete, Pictorial, Abstract (CPA) approach develops a deep understanding of math through building on existing knowledge. This highly effective framework introduces concepts in a tangible way and progresses through increasing levels of abstraction. In the concrete phase, students interact with physical objects (apples, buttons, manipulatives, etc.) to model problems. In the pictorial phase, they make a mental connection between the objects they just handled and visual representations of those objects. For example, real oranges (or counters standing in for oranges) are now represented as drawings of oranges. Only in the abstract phase do students use symbolic modeling of problems using numbers and math symbols (+, −, ×, ÷).

In typical U.S. math classrooms, 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. 

Also, 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.