Why Singapore Math Works
What Is Singapore Math?
Singapore Math is a mathematics curriculum developed by Singapore's Ministry of Education in the 1980s. Since its introduction, Singapore has consistently ranked among the top nations in international math and science assessments (TIMSS). Impressed by these results, many U.S. school districts and gifted education programs have adopted it.
The guiding philosophy is 'Teach Less, Learn More.' Rather than rushing through a wide range of topics, Singapore Math focuses deeply on fewer core concepts, ensuring students truly understand each idea before advancing.
The CPA Approach: Concrete, Pictorial, and Abstract
Singapore Math's signature teaching method is the CPA (Concrete-Pictorial-Abstract) progression. Students first explore concepts using physical objects, then represent them as pictures or diagrams, and finally work with abstract numbers and symbols.
For example, when learning fractions, students first split physical objects (blocks, pizza), then draw diagrams of divided shapes, and only then write '1/2.' This ensures the abstract symbol is always tied to a real, understood concept.
The Bar Model for Visual Problem Solving
Another hallmark of Singapore Math is the Bar Model: a technique for drawing complex word problems as rectangular bars to make their structure visible.
For example, 'Min has 12 more candies than Young, and together they have 48. How many does Min have?' can be solved visually with bars without any algebra. This method also builds the conceptual foundation for algebraic thinking in later grades.
How It Differs from Traditional U.S. Math
Traditional U.S. math instruction often prioritizes procedure first, teaching formulas and having students drill many repetitions. Students can become fast calculators without understanding why the methods work.
Singapore Math inverts this. Students who deeply understand division can reconstruct the concept even if they forget a formula. This is why Singapore Math students tend to perform well on reasoning-based tests like CogAT and NNAT, and in competitions like AMC 8.
The Connection to Beast Academy
Beast Academy is a gifted math series for grades 2–5 created by Art of Problem Solving (AoPS), built on Singapore Math's foundational philosophy. It consists of comic-book-style Guide books and companion Practice workbooks that develop creative problem solving and mathematical discussion.
If Singapore Math builds deep conceptual roots, Beast Academy grows creative reasoning on top of them. The two programs complement each other, which is why using them together produces the strongest results.