The Singapore Math Method: Benefits and Principles

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The Singapore Method is an educational approach to teaching mathematics that is recognized worldwide for its effectiveness. It is characterized by a systematic progression from the concrete to the abstract, enabling children to gain a deep understanding of mathematical concepts rather than simply memorizing procedures. Used in more than 10,000 schools across 160 countries, this method offers significant learning benefits: it fosters critical thinking, improves problem-solving skills, and builds a positive relationship with mathematics from an early age.

Key points about the Singapore Method:

A three-step progression: concrete → pictorial → abstract

Developing deep understanding rather than rote memorization

Significant improvement in problem-solving skills

Proven results in the PISA international assessments

An approach consistent with Montessori principles for young children

What is the Singapore Math method?

The Singapore Method is an approach to teaching mathematics developed in Singapore in the 1980s. Faced with disappointing results from their students, the educational authorities in this small country completely overhauled their approach to teaching mathematics, resulting in a system that has propelled their students to the top of global rankings in international assessments such as PISA.

The Core Principles of the Singapore Method

The method is based on a few fundamental principles that set it apart from traditional approaches:

The CPA (Concrete-Pictorial-Abstract) progression: This three-step sequence allows students to first manipulate concrete objects, then visually represent concepts, and finally move on to mathematical abstraction.
Deep understanding: The focus is on understanding concepts rather than memorizing procedures.
Problem-solving: At the heart of the method lies the ability to solve complex problems by employing a variety of strategies.
Bar modeling: A distinctive visual technique for representing and solving problems.
Mastering the basics: A limited number of concepts are taught each year, but in depth.

This approach, used at the Boulogne-Billancourt Private Bilingual Elementary School, has proven effective in helping students develop a solid understanding of mathematics and build a positive relationship with the subject.

The Benefits of the Singapore Method for Learning

A deep understanding rather than superficial memorization

Unlike traditional methods, which often emphasize memorizing algorithms and formulas, the Singapore Method encourages students to understand why these procedures work. This deep understanding offers several advantages:

Better long-term retention of knowledge
An increased ability to apply concepts in new contexts
A reduction in math anxiety, as students understand what they are doing
The development of mathematical intuition that facilitates the learning of new concepts

Development of critical thinking and problem-solving skills

The Singapore Method emphasizes problem-solving as the primary vehicle for learning. Students are regularly presented with situations that require them to:

Analyze complex information
Develop problem-solving strategies
Justify their reasoning
Assess the suitability of their solutions

These skills go far beyond the realm of mathematics and prepare students to tackle the challenges of the 21st century, where critical thinking is valued more highly than simply memorizing facts.

A visual and hands-on approach that promotes inclusion

Moving from concrete to abstract concepts helps engage all students, regardless of their learning styles. Visualizing problems through bar graphs is particularly beneficial for:

Students who have difficulty with abstract mathematical language
Visual learners who need to "see" problems in order to understand them
Students with specific learning disabilities

This inclusive approach enables more students to succeed in mathematics, thereby reducing learning disparities.

The progression from concrete to pictorial to abstract: the core of the method

Step 1: Hands-on learning through hands-on activities

In the first phase, students manipulate physical objects (cubes, counters, rulers, etc.) to explore mathematical concepts. This stage is fundamental because it allows children to:

Creating a hands-on, sensory experience of concepts
Building strong neural connections
Discover mathematical properties on their own

For example, to understand addition, students will first use concrete objects to visualize the combination of two quantities.

Step 2: Pictorial Representation

Once students are comfortable with hands-on manipulation, they move on to representing concepts visually. It is at this stage that the well-known bar modeling technique—a distinctive visual method of the Singapore approach—comes into play. This representation allows students to:

Visualizing Mathematical Problems
Establishing relationships between quantities
Identify the steps needed to solve the problem

This intermediate step serves as a bridge between the concrete and the abstract, greatly facilitating the transition.

Step 3: Mathematical Abstraction

In the final phase, students move on to mathematical symbols and abstract procedures. Thanks to the previous steps, they approach this abstraction with a solid understanding of what the symbols represent. Students can then:

Using Mathematical Notation Effectively
Apply procedures with understanding
Solve complex problems with confidence

This natural progression supports children’s cognitive development and facilitates a smooth transition to abstract thinking.

Comparison with traditional mathematics education in France

Differences in teaching approaches

Traditional mathematics instruction in France differs from the Singapore method in several notable ways:

Emphasis on procedures: The French approach has long prioritized the learning of algorithms and procedures, sometimes at the expense of understanding.
Faster pace: French curricula generally cover more topics each year, but in less depth.
Less visual support: Visual representations, such as bar charts, are used less frequently.
A more abrupt transition to abstraction: The shift from the concrete to the abstract is often more rapid, which can leave some students struggling.

These differences may partly explain the concerning results of French students in international assessments, where 29% of students struggle with mathematics, compared with only 7% who achieve a high level of performance, according to the latest PISA results.

Comparison of results

Countries that have adopted the Singapore method or similar approaches (Singapore, Hong Kong, South Korea, Japan) consistently rank at the top of international mathematics assessments:

Singapore consistently tops the PISA rankings in mathematics
Students in these countries demonstrate a better conceptual understanding
They are particularly skilled at solving complex problems
The gap between the highest-performing students and the lowest-performing students is generally smaller there

In light of these results, many countries, including France, are showing increasing interest in this method, and the Ministry of Education is gradually encouraging its adoption.

Implementing the Singapore Method in the Classroom

A concrete example: learning subtraction

To illustrate the Singapore Method in action, let’s take the example of learning subtraction:

Hands-on phase: Students use blocks or counters to represent a number, then physically remove a quantity to understand the concept of “subtraction.”
Visual phase: They draw bars to represent the quantities, then cross out or circle the part to be subtracted, thereby visualizing the operation.
Abstract phase: Once they have grasped the concept, they move on to standard mathematical notation (8 – 3 = 5) with a solid understanding of what these symbols represent.

This step-by-step approach allows students to develop an intuitive understanding of subtraction, going far beyond simply following a procedure.

The structure of a typical lesson

A math lesson using the Singapore Method generally follows this structure:

Foundation: Review of prior knowledge needed for the new lesson
Guided discovery: Exploring a real-world problem that introduces the new concept
Modeling: A clear demonstration of how to represent and solve the problem
Guided practice: Similar exercises completed with the teacher’s assistance
Independent practice: Working independently on a variety of problems
Reflection: Discussion of the strategies used and lessons learned

This balanced approach allows students to gradually build their understanding and confidence.

The necessary tools and resources

To effectively implement the Singapore Method, several resources are needed:

Manipulatives: Stacking blocks, counters, rulers, etc.
Textbooks and workbooks: Several publishers offer French adaptations of Singaporean textbooks
Teacher training: Specific training is recommended to understand the philosophy and techniques of the method
Visual aids: Posters, mind maps, and other tools to help illustrate concepts

The investment in these resources is more than offset by the progress students make.

The Singapore Method in the French School System

The gradual adoption in French schools

In recent years, the Singapore Method has been gaining ground in French schools:

Official trials have been conducted in several school districts
Many private schools have adopted it as their primary approach
Resources tailored to the French curriculum are now available
The Ministry of Education is encouraging its use in light of disappointing results on international assessments

This initiative is part of an effort to revamp mathematics education in France in order to improve student performance.

Compatibility with official programs

The Singapore Method fits well within the framework of French curricula:

It covers all the concepts required by the Common Core of Competencies
His progress is in line with the expectations for each cycle
It is fully in line with recent recommendations on explicit instruction and hands-on learning
It aligns with the emphasis on problem-solving in current curricula

Schools like 123 mon école that adopt this approach can do so while still meeting institutional requirements.

The challenges of transitioning to this method

Despite its advantages, adopting the Singapore approach presents certain challenges:

The need to train teachers in a different approach
The need to adapt certain cultural aspects specific to Singapore
The initial investment in educational resources
Potential resistance to change from various stakeholders

However, these challenges are not insurmountable, as demonstrated by the successful experience of many schools that have made this transition.

The connections between the Singapore Method and Montessori education

Although they have different origins, the Singapore Method and the Montessori approach share several common features that make them particularly compatible.

Complementary philosophies

Both educational approaches share fundamental values:

The Importance of Hands-On Learning: Both methods recognize that children learn best by handling concrete objects
Respecting the child's pace: They emphasize individual progress and mastery of concepts before moving on to the next step
A focus on deep understanding: Both approaches prioritize conceptual understanding over rote memorization
Learner autonomy: They encourage children to discover things on their own and develop their independence

These philosophical similarities explain why many Montessori-inspired schools naturally adopt the Singapore method for mathematics.

The ideal transition from preschool to elementary school

The Singapore Method provides a smooth transition for students who have been educated using the Montessori method in preschool:

Montessori students are already accustomed to using hands-on materials to understand mathematical concepts
They have developed independent learning skills that prepare them well for the Singapore method
Their experience of progressing from the concrete to the abstract using Montessori materials (number rods, golden beads) is reflected in the CPA approach in Singapore
Their ability to work at their own pace aligns with the mastery-based philosophy promoted by the Singapore Method

This educational continuity allows students to build on what they have learned while adapting to the increasing demands of elementary school.

Applying the Singapore Method at 123 mon école

In schools 123 mon école, the Singapore Method is rigorously implemented and adapted to the French context.

An integrated approach to the elementary school curriculum

To 123 mon école, the Singapore Method is fully integrated into the elementary school curriculum (grades 1–5) at our schools in Courbevoie and Boulogne-Billancourt. It is part of a program that meets the requirements of the French Ministry of Education while enriching it:

Math using the Singapore method takes about 5 hours a week
The curriculum is supplemented by other subjects taught in accordance with French and international standards
Teachers receive specialized training in this method to ensure its effectiveness

Results observable among students

The use of the Singapore method at 123 mon école produces tangible results:

Students develop a positive relationship with mathematics
They demonstrate a thorough understanding of the fundamental concepts
Their ability to solve complex problems is improving significantly
They demonstrate greater independence in their work

These observations confirm the effectiveness of the method and its suitability in the context of a bilingual school with high academic standards.

Continuity with the Montessori approach in preschool

123 mon école ensures a smooth transition between the Montessori approach used in preschool and the Singapore method used in elementary school:

The mathematical skills developed using Montessori materials in preschool (sense of quantity, counting, concrete operations) serve as a solid foundation
The progression from the concrete to the abstract, which is central to both approaches, ensures methodological continuity
The independence and confidence developed in preschool are valued and reinforced by the Singapore Method

This educational continuity ensures that students get the most out of their school experience at 123 mon école, with a solid foundation that effectively prepares them for the next stage of their education.

Frequently asked questions

At what age does 123 mon école begin using the Singapore Method 123 mon école

The Singapore Method is used in elementary school (grades 1–5) at 123 mon école, starting at age 6. It is implemented at our schools in Courbevoie and Boulogne-Billancourt. This method accounts for approximately 5 hours per week in our math curriculum.

Does the Singapore Method completely replace the national curriculum?

No, the Singapore Method does not replace the national curriculum; rather, it enriches it. Our elementary program follows the official national curriculum while upholding the values of Montessori education. The Singapore Method is used as a teaching approach for mathematics, while adhering to the objectives of the Common Core Standards.

How does the Singapore Method fit in with the bilingual program at 123 mon école

To 123 mon école, instruction is 100% bilingual starting in first grade, with an equal balance between French (12 hours per week) and English (12 hours per week). The Singapore method for mathematics is taught primarily in French (5 hours per week), while mathematics based on Cambridge standards is also taught in English (4.5 hours per week). This dual approach strengthens students’ understanding of mathematical concepts in both languages.

What is the difference between the Montessori method and the Singapore method for teaching math?

The Montessori method and the Singapore method share similar principles, such as the importance of hands-on learning and the progression from concrete to abstract concepts. However, the Montessori method is a holistic approach that addresses all aspects of a child’s development and uses specific materials (number rods, golden beads). The Singapore Method is more specifically focused on teaching mathematics, with a structured sequence and characteristic bar modeling. At 123 mon école, we use the Montessori method in preschool (ages 3–6) and then the Singapore method in elementary school (ages 6–11) for mathematics.

Should parents be familiar with the Singapore Method to help their children?

Parents don’t need to be experts in the Singapore Method to support their children. At 123 mon école, we hold regular meetings with families and open houses to explain our educational approach. We also provide resources and advice to parents who wish to learn more about this method. The teaching staff is always available to answer parents’ questions and guide them in supporting their child.

How do you assess students' progress using the Singapore Method?

To 123 mon école, we prioritize ongoing assessment over one-time evaluations. Teachers regularly monitor students’ progress and adapt their instruction based on identified needs. We use formative assessments to identify potential challenges and adjust our teaching approaches. This method allows us to track each child’s development and provide academic support when necessary, while respecting each child’s individual pace.

The Singapore Math Method: Benefits and Principles