A Review of the Effectiveness of Math Heuristics in Singapore Mathematics

Looking to understand about the effectiveness of Math Heuristics? Well, then parents, you have come to the right place. Now, in the realm of education, the methodology used to teach various subjects plays a crucial role in a child’s academic development. One such methodology that has gained popularity is the Singapore Math approach, known for its focus on problem-solving, critical thinking, and strong foundation in mathematical concepts.

As a parent, it’s important to understand the core principles of this approach and its potential benefits for your child’s learning journey. In this informal review, we will explore the key features of Singapore Math and its heuristics, offering insights into why it might be a great choice for your child’s math education.

What is Singapore Math?

Singapore Math, also referred to as the “Singapore Model Method,” is an educational approach that originated in Singapore and has garnered international recognition for its effectiveness in teaching mathematics. The approach emphasizes the development of a deep understanding of mathematical concepts rather than rote memorization of formulas. It encourages students to think critically, solve complex problems, and apply mathematical principles to classroom maths sums and also to real-world situations.

Heuristics in Singapore Math

Math heuristics is defined as problem-solving strategies that encourage students to approach complex math problems in a systematic manner. Singapore Math introduces several powerful heuristics that equip students with tools to tackle a wide range of mathematical challenges.

Effectiveness in Problem-Solving

One of the standout features of Singapore Math is its emphasis on problem-solving. Rather than solely focusing on solving equations or performing arithmetic operations, this approach encourages students to explore various ways of arriving at solutions. Through the use of visual aids, students learn to represent problems graphically, making abstract concepts more tangible. This visual approach and other heuristic strategies not only enhances comprehension but also nurtures the creative thinking skills required to tackle diverse mathematical challenges.

Concrete-Pictorial-Abstract (CPA) Approach

The Concrete-Pictorial-Abstract (CPA) approach is at the heart of Singapore Math. This three-step learning process helps students gradually transition from concrete experiences to abstract mathematical concepts.

Students start by using physical objects to understand mathematical concepts. This hands-on approach makes abstract ideas more relatable and easier to grasp.

Visual representations, such as diagrams and bar models, bridge the gap between the concrete and abstract stages. These visual aids helps the student visualize relationships and solve problems more intuitively.

Once a solid foundation is built through the concrete and pictorial stages, the student is able to progress to solving problems using symbols and mathematical notation. The transition to abstract thinking becomes smoother and more effective.

The Benefit of Building Strong Number Sense

Number sense refers to a deep understanding of numbers and their relationships. Singapore Math places a strong emphasis on developing number sense through activities that help a student understand the properties and operations of numbers. By focusing on number bonds, place value, and mental calculations, the student not only improves his computational skills but also enhances his ability to apply math strategies in everyday situations.

Conceptual Understanding over Procedural Fluency

Procedural knowledge involves understanding the rules and routines of mathematics while conceptual knowledge involves an understanding of mathematical relationships While procedural knowledge is a series of steps that must be followed to solve mathematical problems, students with conceptual understanding of mathematics can apply and adapt prior knowledge to new sums, in effect making math applicable beyond solving just a single math problem.

12 Math Heuristic Strategies

Singapore Math syllabuses identified 12 math heuristics which are applicable to problem solving in the upper primary level. (See our blog on Heuristic Methods to Help Solve Mathematics Sums.

  • Draw a diagram/model
  • Draw a table
  • Make a systematic list
  • Look for pattern(s),
  • Guess and check,
  • Make suppositions
  • Act it out,
  • Work backwards,
  • Use before-after concept
  • Restate the problem in another way,
  • Simplify the problem,
  • Solve part of the problem

Let me just discuss the first five strategies. More strategies can be viewed in our blogs.

Model Drawing
Model drawing involves creating visual representations of word problems using bar models or diagrams. This approach helps students break down complex problems into simpler components and visualize the relationships between quantities.

Draw A Table
Students organize information in a table format to analyze different variables and their relationships. This heuristic enhances logical reasoning and data organization skills.

Make a Systematic Listing
Involves listing all possible outcomes systematically to identify patterns and make informed decisions. This heuristic is particularly useful for combinatorics and probability problems.

Look for Patterns
Identifying patterns is crucial for developing algebraic thinking. Encourage your child to analyze the numbers, shapes, or operations involved in the problem to discover underlying patterns that can lead to the solution.

Guess and Check
Encourages students to make educated guesses, test their solutions, and refine their approaches based on the outcomes. This heuristic promotes critical thinking and the ability to adapt strategies.

Effectiveness of Math Heuristics


In the realm of math education, the Singapore Math approach stands out for its problem-solving focus, concrete-pictorial-abstract methodology, and powerful heuristics.

By nurturing critical thinking, fostering deep comprehension, and developing strong number sense, this approach equips students with essential skills for success in mathematics and beyond. As parents, understanding the principles behind Singapore Math can help you make informed decisions about your child’s education, setting them on a path towards mathematical proficiency and confident problem-solving abilities.

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