What is Singapore Math?

What is the Singapore Math Method?

The Singapore Math method is founded on the constructivist research pioneered by Jerome Bruner in the United States in the 1960s. The Singapore Math pedagogy is based on the Concrete-Pictorial-Abstract Sequence.

The Concrete–Pictorial–Abstract (CPA) Approach
The CPA approach guides students from hands-on learning to abstract thinking. They first explore math with real objects, then visualize with pictures, then represent ideas with bar models, and finally use numbers to show what they’ve learned. This step-by-step progression makes learning math clear, engaging, and lasting.

In this approach, students’ learning experiences are situated in a meaningful context that begins with explorations of concrete objects and virtual manipulatives and is followed by pictorial and abstract representations of these situations.

Mathematical concepts are abstract. Elementary school age children are entering the developmental phase where they can understand abstractions. It is important to create a bridge to understanding abstractions in a concrete and relevant context using common objects.

Examples of common objects are apples, crayons, toy cars, etc. Examples of manipulatives include counters, connected cubes and others. The use of common objects and manipulatives corresponds to the concrete state. The pictures of these objects correspond to the pictorial representations of the objects. Subsequent calculations and equations correspond to the abstract stage.

What is the Singapore Math Pedagogy?

The Singapore Math pedagogy for teaching math is based primarily on the five learning theories that were developed by leading European and American educators, mathematicians and psychologists of the 19th and 20th century: Jean Piaget, Jerome Bruner, Zoltan Diens, Lev Vigotsky, and Richard Skemp.

Jean Piaget, psychologist and educator, suggested that students should have ample learning time to accommodate new ideas. That’s why Singapore Math programs contain anchor tasks which are designed to be dealt with for a long time over the course of a unit. According to Piaget, children need to continually construct their understanding and then reconstruct prior ideas as they mature.

Jerome Bruner, an educator and a student of Jean Piaget, advocated for children to engage in concrete activities prior to moving to abstract learning. Bruner, believed that a student could learn almost anything, provided that instruction would go through appropriate stages. Each level in the instructional sequence should become more abstract.

Zoltan Diens, mathematician and educator, advocated that informal learning through exploration should take place before structured learning. He noticed that in trying to solve a problem, most people would engage in a random search for a solution. He called this stage “Free Play” and suggested that all learning should begin at this stage.

Lev Vigotsky, psychologist and educator, advocated cooperative learning in the zone of proximal development (ZPD). ZPD is the distance between a student’s independent problem-solving level and the potential level of problem solving under the guidance of an adult/expert.

Richard Skemp, mathematician and educator, suggested that it is important for students to develop a relational understanding of conceptual ideas. He believed that even elementary school children could create complex and complete conceptual frameworks and, as a result, they are capable of learning with deep understanding.

What is Bar Modeling?

Bar Modeling or model drawing is an ingenious problem-solving strategy built into the Singapore Math curriculum. Bar Modeling is a pictorial representation of mathematical quantities and their relationships. It helps students visualize abstract mathematical concepts to gain deeper understanding of the operations they need to use in order to solve word problems.

Bar Modeling improves student problem solving abilities because visual representations of word problems allow students to grasp them in their entirety (wholes) with minimum effort (law of Pragnanz). Bar Modeling allows students to organize textual information and then restructure it visually in a model. It helps students think holistically, gain insight and then solve the problem.

Bar Modeling is a term that was coined in the United States. The original term is the Model Method or Model Drawing that was developed in Singapore in the 1980s. Bar Models are also called Tape Diagrams or Strip Diagrams in the Common Core State Standards in Mathematics, New York State Modules, Eureka Math and some other elementary mathematics programs used in the United States.

What is the Authentic Singapore Math Curriculum?

The authentic Singapore Math curriculum is developed and tested in Singapore based on the curriculum approved by the Singapore Ministry of Education. The authentic program is focused on a few important topics and teaching problem-solving strategies in each grade. The small number of topics are explored in greater depth during the school year. Focusing on learning a few important topics in each grade reveals the main purpose of Singapore Math, which is to allow students to spend more time learning the most important concepts in elementary mathematics, deepen their understanding, and achieve mastery.

Due to its long-standing successful track record, interest in the Singapore Math curriculum has grown steadily over the last 10 years. Larger publishing houses began to notice the popularity of the Singapore Math curriculum and borrowed some elements of the program, such as model drawing and number bonds to incorporate into their programs. Some of these publishers even market their programs as Singapore Math. However, most of the programs that imitate the authentic curriculum lack the coherence and focus of the original materials from Singapore.

• Mastery over coverage – Fewer topics taught in greater depth, with cumulative review to ensure lasting understanding.
• Concrete–Pictorial–Abstract learning reinforced with bar modeling – Students progress step-by-step from hands-on exploration to visual and symbolic reasoning, building strong problem-solving and algebraic thinking skills.
• Ongoing assessment and placement guidance – Students begin at the right level, track growth through chapter reviews and checks, and receive feedback that supports continuous improvement.
• Built-in differentiation and scaffolding – Anchor tasks, guided practice, and extension challenges meet every learner’s needs—from support to enrichment.
• Aligned with Singapore’s Ministry of Education design principles – Developed and validated against the same standards that have made Singapore Math a world leader in mathematics education.
• Blended-learning ready – Works seamlessly with print materials or online tools such as video tutorials, interactive games, and knowledge checks for flexible learning at home or in school.