In the digital age, learning is no longer what it used to be. Gone are the days when memorizing formulas and mechanically solving problems sufficed. Today, international school students must grasp the essence of mathematics, develop logical thinking, and hone problem-solving skills. More importantly, they need to learn how to apply these concepts in real-life situations. This modern approach does more than just prepare students for exams—it builds a solid foundation for holistic development. Mathematical thinking transcends rote learning, equipping children with confidence to face diverse challenges in the future.
So, how can children not only excel in math but also develop a genuine love for it, while exploring its deeper aspects? This question frequently concerns parents of international and bilingual school students. In this article, we’ll explore innovative approaches that aim to transform the fear of math into an appreciation of it as a powerful tool to understand the world. Additionally, we’ll delve into the role of modern educational methods, such as Singapore Math and CPA (Concrete-Pictorial-Abstract), widely adopted in international schools.
Singapore Math is a globally recognized and advanced teaching method. This method widely implemented in international schools and various educational systems worldwide. Its unique feature lies in not just simplifying math concepts. It is also building a strong and lasting foundation of logical thinking. At its core is the CPA (Concrete-Pictorial-Abstract) framework, which takes students step by step from tangible experiences to abstract reasoning.
The CPA model begins with the use of visual materials to help students familiarize themselves with mathematical concepts. Then transitions to pictorial representations such as diagrams, and finally moves to abstract symbols like numbers and formulas. This approach not only helps students master the subject. Also, this fosters critical thinking, problem-solving skills, and the ability to apply mathematics to real-world situations.
To gain a deeper understanding of this method and discover how students can naturally develop a love for math, we invite parents to join this journey and explore ways to help their children not only excel in numbers but also build essential 21st-century problem-solving skills.
1. Learning Math for Understanding, Not Memorization
Math today is more than numbers and formulas
It’s a foundation for systematic thinking and creative problem-solving across diverse fields. When students truly grasp mathematical concepts, they don’t just solve problems; they analyze, think critically, and innovate solutions.
However, traditional teaching methods often fall short. Many students memorize formulas without understanding why they exist, leading to difficulty in applying them practically. This creates frustration, disinterest, and even fear of math. The lack of conceptual clarity prevents children from fully engaging with the subject, resulting in shallow learning experiences that don’t last.
Modern educational practices, like Singapore Math, address these gaps. By focusing on understanding and application, they nurture a deeper engagement with the subject, replacing fear with curiosity and mastery.
2. Singapore Math and the CPA Method: Learning to Understand from the Root
Singapore Math has long been recognized as one of the most effective approaches to teaching mathematics, particularly for international students. What sets this method apart is its focus not only on solving problems correctly but also on helping students deeply understand the core concepts. This is a critical factor in building a strong mathematical foundation, rather than relying solely on rote memorization of formulas.
At the heart of Singapore Math lies the CPA method (Concrete – Pictorial – Abstract), which is considered the international gold standard for mathematics instruction. According to Singapore’s Ministry of Education, all math curricula in the country must integrate the CPA method to gain approval and official implementation. This ensures a consistently high standard of education nationwide. Reports from Singapore’s National Institute of Education (NIE) reveal that over 90% of schools in the country rigorously apply CPA, demonstrating its outstanding effectiveness in enhancing students’ mathematical abilities.
With its scientifically designed process, the CPA method offers a comprehensive, step-by-step approach that enables students not only to master but also to deeply understand mathematical concepts. Specifically, the CPA process includes:
Concrete: In the initial stage, students engage with tangible objects such as blocks, coins, or marbles to illustrate mathematical concepts. For instance, students may group blocks to perform addition or subtraction or use coins to represent fractions. By manipulating physical objects, students can easily grasp complex ideas like division, measurement, or comparison. This stage not only establishes clear connections between real-world experiences and mathematical concepts but also sparks a curiosity to explore more about the subject.
Pictorial: Once students are comfortable using physical objects to illustrate mathematical ideas, they move on to using pictures and diagrams to represent problems. For example, students might draw diagrams to show the division of objects or use bar models to compare quantities. This stage serves as a crucial bridge, helping students transition from concrete understanding to abstract thinking. It also supports students in visualizing the relationships between real-world scenarios and more advanced mathematical concepts. Additionally, using visual representations enhances students’ ability to communicate ideas effectively, laying a foundation for more efficient learning in the future.
Abstract: The final stage of the CPA method involves teaching students to use mathematical symbols, formulas, and numbers to solve problems logically and efficiently. At this stage, students are encouraged to tackle more challenging problems, such as analyzing data or performing multi-step calculations. The abstract stage goes beyond problem-solving; it also encourages students to explore multiple solutions, fostering creative and critical thinking. These exercises help students realize that mathematics is not just a subject but a powerful tool for addressing real-world challenges.By following this structured approach, Singapore Math equips students with both a deep understanding of mathematical concepts and essential problem-solving skills for the 21st century.
3. Turning Math into a Problem-Solving Tool
When students learn math by understanding its principles rather than merely memorizing formulas, the benefits go beyond academic results. This approach unlocks opportunities for developing essential skills for the future. Mathematics is not just about calculations; it is a powerful tool for solving real-world problems in everyday life.
For example, students can apply their math knowledge to analyze data from charts, understand how to manage personal budgets, or make sound decisions based on logical reasoning. These foundational skills not only support their academic success but also prepare them for future careers, especially in fields like technology, finance, and science.
Research from the National Institute of Education (NIE) in Singapore has shown that the CPA method not only helps students achieve higher scores on exams but also enhances critical thinking, creativity, and confidence when tackling challenging questions. These skills are particularly valuable for students aiming to take international exams such as the IB, SAT, or assessments within international school curricula, providing a solid foundation for studying abroad.
The positive transformation in students is evident when modern math teaching methods are applied. Students not only grasp concepts but also learn to apply mathematics to real-world problems, such as measuring, analyzing situations, or solving group project tasks. This represents a significant step forward in fostering holistic development and preparing them to navigate an increasingly fast-changing world.
4. Fostering Problem-Solving Skills Through Singapore Math with Everest Education
At Everest Education, math is more than numbers and formulas—it’s a journey of discovery and innovation. Through interactive, hands-on activities, our students explore the true essence of mathematical concepts and their relevance in the real world. For us, math isn’t just another subject; it’s a cornerstone for cultivating critical skills that empower students to thrive in the 21st century. That’s why our Singapore Math programs are thoughtfully designed to ignite a passion for learning while fostering excellence in mathematics.
Take a real-life math lesson at E2, where students explored the “Take Away” method to calculate areas. Using paper cutouts and tangible shapes like squares and circles, teachers demonstrated how to find the remaining area by subtracting the circle’s area from the square’s. This multi-step process followed the celebrated CPA (Concrete-Pictorial-Abstract) approach, ensuring a deeper grasp of the concept:
Concrete: Students kick-started their learning by engaging with real materials—paper, blocks, and tools. These tangible models bridged abstract ideas, allowing students to see, touch, and experiment with mathematical principles in action.
Pictorial: Once students were comfortable with hands-on practice, they transitioned to drawing diagrams and sketches. These visual representations, like “Area = Square – Circle,” encouraged collaborative discussions and strengthened their ability to connect visuals with theoretical concepts.
Abstract: Finally, students translated their understanding into formulas, solving problems that reflected real-life scenarios. This stage solidified their confidence and equipped them with practical problem-solving skills.
Under the dedicated guidance of our educators, Everest Education students leave each math class with more than just solutions:
Enhanced Logical Thinking: By experimenting and discovering patterns themselves, students move beyond rote learning to truly understand the “why” behind every solution.
Boosted Creativity: Math lessons become an exciting playground for creativity, with activities like cutting, crafting, and designing models.
A Lifelong Love for Math: A supportive and engaging environment helps students feel excited and inspired to learn.
At Everest Education, every lesson is a stepping stone toward building a better future. Students not only master mathematical concepts but also develop patience, teamwork, and systematic thinking—skills essential for success in a rapidly changing world. With us, math is not just a subject; it’s a launchpad for lifelong growth.
5. Conclusion
In a rapidly changing world, preparing students with a solid foundation is not only a responsibility but also a wise investment. By approaching Mathematics through the CPA method and Singapore Math programs, parents are equipping their children with the tools not only to solve problems but also to solve life’s challenges. Let Everest Education open the door for your child to discover their passion for learning, develop critical thinking, and be ready to face the future full of potential.
By following this structured approach, Singapore Math equips students with both a deep understanding of mathematical concepts and essential problem-solving skills for the 21st century.
