## What is Singapore Math?

Singapore Math is a teaching method used in Singaporean schools across first through sixth grade. It prioritizes conceptual understanding over rote memorization through a three-step learning process: concrete (using physical objects), pictorial (using visual representations), and abstract (using symbols for problem-solving).

## History and International Success of Singapore Math

Primary Mathematics 1–6, the first Singapore Math program, was published in 1982 by Singapore Math Inc. In 1992, a revised second edition included more problem-solving techniques, with a focus on model drawing for approaching solutions.

In 1995, Singaporean students ranked first among 60+ countries that participated in the Trends in International Mathematics and Science Study (TIMSS). This study, conducted every four years, provides reliable and timely trend data on the mathematics and science achievement across various countries. Since 1995, Singaporean students have consistently ranked among the top, placing first in 10 out of 13 instances up to 2019.

## What is the Singapore Math Method?

Singapore Math is a holistic and multilayered math teaching system used in Singaporean schools to build students’ problem solving abilities, utilizing math textbooks effectively. Its effectiveness lies in its three pillars of math learning: building deep conceptual understanding, procedural fluency, and real-world application.

Conceptual understanding deals with the “why” behind mathematical concepts. Procedural fluency deals with the “how” in solving mathematical problems. Real-world application deals with the “where” and “when” of using mathematical concepts and skills.

The Singapore math approach also includes the CPA (Concrete, Pictorial, Abstract) progression, number bonds, bar modeling, and mental math. These tools help students grasp concepts thoroughly and improve their problem-solving skills.

### The Heart of the Singapore Math Approach

The central concept of the Singapore Math curriculum revolves around Mathematical Problem-Solving, supported by five key components: Attitudes, Metacognition, Processes, Concepts, and Skills. These are interrelated and collectively contribute to the overall goal of developing a student’s ability to solve mathematical problems effectively.

This holistic approach ensures that students are not only proficient in performing mathematical operations but also in understanding the underlying concepts and applying them in various contexts.

## The CPA (concrete-pictorial-abstract) Sequence

The Concrete to Pictorial to Abstract sequence introduces math concepts in a simple way and progresses to increasing levels of abstraction.

### Concrete

The learning journey begins with the concrete approach, often involving manipulative tools. Where students engage with tangible objects to model problems. This hands-on method makes abstract concepts more relatable and easier to understand. Unlike traditional methods where teachers demonstrate how to solve a problem, the CPA approach brings concepts to life through hands-on experiences.

For instance, if a problem involves adding pencils, students first handle actual pencils, then progress to abstract counters or cubes representing the pencils.

### Pictorial

Next, students move to the pictorial stage, often using a manipulative to bridge the gap between concrete and abstract. Children utilize visual representations to model problems. This stage bridges the gap between hands-on experiences and abstract ideas through diagrams and illustrations, offering visual learning benefits.

For instance, creating models or diagrams of fractions helps make abstract concepts more accessible and easier to understand. Key Singapore Math models include number bonds and bar modeling.

### Abstract

Finally, the abstract phase introduces symbols and notation to represent word problems. This symbolic approach is implemented once students have a firm grasp of the concrete and pictorial stages. Here, teachers introduce mathematical symbols (+, –, x, ÷), allowing children to solve problems using numbers and notation.

### Number bonds

A number bond in math is a simple addition fact that a child can instantly recognize and complete, similar to a multiplication fact. It helps children understand part-part-whole relationships and is often used in primary school education to build a foundation for arithmetic skills.

For example, the number bond for 5 can be shown as 2 and 3 in separate circles connected to a circle with 5. This method helps early elementary students work towards addition and subtraction, illustrating strategies to solve expressions mentally. Using number bonds fosters a solid number sense that serves students throughout their math education, helping them to easily decompose and recompose numbers for more complex calculations.

### What is Bar Modeling

A bar model, also known as a model drawing, is a pictorial representation in math that uses bars to show known and unknown quantities. This method helps students solve problems in addition, subtraction, multiplication, and division by using proportional rectangles to represent numbers.

For example, to find the sum of 5 and 3, a student can draw a bar representing 5, and another representing 3, and combine them to see the total of 8. This method enhances mathematical fluency and number sense, making it easier for students to tackle complex problems.

## Pros and Cons of Singapore Math

Singapore Math is known for its unique approach to teaching mathematics, emphasizing problem-solving and conceptual understanding. Here are the key pros and cons:

Pros of Using Singapore Math

- Focus on Problem-Solving:
- Encourages students to deeply understand concepts rather than memorize formulas, fostering critical thinking skills.

- In-Depth Learning:
- Covers fewer topics each year but in greater depth, ensuring a strong foundation for advanced learning.

- Clear and Concise Materials:
- Textbooks and workbooks are easy to read with clear graphics, enhancing student comprehension in grade 1 and beyond.

- Proven Success:
- Students using Singapore Math consistently perform well in international assessments, demonstrating its effectiveness.

Cons of Using Singapore Math

- Implementation Challenges:
- Requires extensive teacher training, which can be costly and time-consuming.

- Parental Involvement:
- Parents may find it challenging to help their children with homework because they might not be familiar with the Singapore Math method, having learned math through traditional approaches.

- Initial Adjustment Period:
- Schools and students transitioning from traditional math programs to Singapore Math may experience an adjustment period where they might initially struggle with the new methods and expectations.

## Which Singapore Math Curriculum Do We Recommend?

**Primary Mathematics U.S. Edition**

- Primary Mathematics is the curriculum that initially propelled Singapore to the top of international math tests. The U.S. Edition is almost identical to the original Singapore program but adapted with U.S. measurements and currency. It embodies the Singapore math approach, including the Concrete, Pictorial, Abstract (CPA) progression, number bonds, bar modeling, and a strong focus on mental math.

**Intensive Practice U.S. Edition**

- Intensive Practice U.S. Edition offers challenging supplementary material for primary level mathematics. It is designed to offer rigorous practice and extend students’ mathematical thinking.

**Dimensions Math**

- Dimensions Math 6–8 extends the Singapore math approach to middle school. This program emphasizes problem-solving and encourages students to think mathematically in various contexts. It covers pre-algebra, algebra, geometry, data analysis, probability, and some advanced math topics, following the CPA approach and incorporating bar modeling and other key principles from the Singapore mathematics framework.

## How Is Singapore Math Different?

Singapore Math stands out from traditional U.S. math programs by focusing on understanding concepts and solving problems instead of just memorizing steps. In U.S. programs, students often repeat the same steps with different numbers. Singapore Math, however, makes students think through problems from the beginning, which helps them engage more deeply and think critically. This approach also connects new lessons to past learning, making it easier to understand how everything fits together.

Additionally, Singapore Math covers fewer topics each year but goes into each one in greater detail. This way, students master each concept before moving on to the next. This method helps build a strong foundation and boosts students’ confidence in their math skills. By encouraging innovative problem-solving, Singapore Math prepares students well for more advanced math and real-world applications.

## Singapore Math Placement Test

Taking a Singapore Math placement test is a pivotal step in ensuring your child receives the most effective and personalized math instruction. Our test helps to accurately assess what your child knows and identify any areas where they might need additional support. This targeted approach prevents future learning gaps and lays a solid foundation for success in math.

By understanding your child’s specific strengths and weaknesses, you can make informed decisions about enrolling them in group or private tutoring sessions, possibly using different math strategies. These tailored tutoring programs are designed to support individual growth and accelerate their learning, helping your child to excel in their mathematical journey. Proper placement ensures your child is grouped with peers of similar abilities, fostering a positive and supportive learning environment

To take the first step in providing your child with a tailored math learning experience, schedule a free placement test consultation with us today. This call will help us understand your child’s needs and ensure they are placed in the optimal learning environment. Schedule a consultation now.

## Final Thoughts

Singapore Math is an educational approach for grades one through six that fosters a deep understanding of mathematical concepts. By using a three-step process—concrete, pictorial, and abstract—it emphasizes mastery over memorization, building strong problem-solving skills and critical thinking. This method ensures continuity in learning, preparing students for advanced math and real-world applications, making them confident and capable problem solvers. Through this comprehensive approach, Singapore Math equips students with the tools they need for academic success and beyond.