What are Math Heuristics?

Curious about what are math heuristics, continue reading the article we prepare for you.

What Are Math Heuristics?

Have you ever wondered why the PSLE Examination Board sets a chunk of rather challenging sums today, ending up in us complaining that it is not fair for our kids? Another common statement is ‘PSLE math sums have become so hard unlike when we were kids.’ We are stumped by some of the upper primary Math questions set today and want to give our kids an edge by making them more procedurally fluent and by expecting them to memorize procedures and formulae hoping this will enable them to score in their math paper. But this is not to be. Others will say, ‘How can my kid do math heuristics? They are for the math geniuses.’

Basically, math sums set in PSLE exam are meant to test critical thinking and math logic. Our 12-year-old kids will need to interpret, understand, reason and analyse information and use appropriate strategies for the problem sums in the math paper. So, the varying ways to solve math sums has always been there but the exposure to such math heuristic methods have not been tapped as much as it is today in Singapore. Primary school children are now expected to conceptually understand the varied problem-solving paths to aid them in their solving of complex math questions.

To answer the question: ‘What are Math Heuristics?’, one has to know the root word and its origin. The word ‘heuristic’ comes from the Greek ‘heuretikos’, meaning “inventive” which in turn relates to ‘heuriskein’, meaning “to find”. In other words, heuristics serves as a way to discover, or to find a solution to a said problem, in a way by trial and error or experiment.

Hence, math heuristics are proven strategies that our children can employ to solve math problems efficiently and effectively. These steps are systematic, and applicable to math problem-solving in primary school.

Singapore Math syllabuses identified 12 math heuristics which are applicable to problem solving in the upper primary level.

  • 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
What are Math Heuristics?

 According to characteristics of each heuristic type above, plus how and when they can be applied in the process of mathematical problem solving, they can be grouped into four main categories:

  • To give a representation: Draw a diagram/model, draw a table, make a systematic list
  • To make a calculated guess: Look for pattern(s), guess and check, make suppositions
  • To go through the process: Act it out, work backwards, use before-after concept
  • To change the problem: Restate the problem in another way, simplify the problem, solve part of the problem

So, by definition, heuristics carries the following characteristics:

  1. Math heuristics merely point us towards possible ways in which one might be able to find a solution to a math sum.
  1. Such heuristics methods do not come with specific procedures that can be mechanically applied. One has to make some judgement calls as to how to proceed or continue in the problem-solving steps.

If one has to compare the types listed, there are the types which are more general in approach, such as ‘restate the problem in another way’ which only offers a general direction as to what and how we should do versus the ‘draw a diagram’ method where its diagrammatic or model representation will give a more specific instruction and hence facilitate in the problem-solving.

What is the Problem-Solving Process in Math Heuristics?

Another important point to note is that Singapore Math adopts Polya’s four-step problem-solving process as expressed below:

1. Understand the problem: What to find? What is known and unknown?
2. Devise a plan: Choose the most suitable heuristic
3. Carry out the plan: Solve the problem
4. Look back: Check the answer

Because the steps are easy to follow and generalizes well, it has become a fine approach for solving math problems. 

The very first step of ‘Understanding the Problem’ is vitally important. This ensures the understanding of the vocabulary words in the question, what the problem is asking for, and what information is given in the question which will help solve the problem. 

From here the math heuristics come into the picture, whether to draw a diagram, look for a pattern, make suppositions, use a before-after concept or to restate the problem in another way and so on.  From the decision to attempt though a particular method, this will lead us to step two: devise a plan, then step three: carrying out that plan. Finally, it is always good to look back and to double check the answer to see if the answer is reasonable. 

maths sam worksheet


We hope that by finding a satisfactory explanation of the definition or meaning of ‘what are math heuristics’, this will help parents understand the world of heuristics and how these can help your child solve mathematical problems. When used correctly, they can make mathematics much easier and more manageable for students to answer problem sums in the math paper.

At S.A.M. Hougang, we are always ready to answer any queries and to help guide your child to the right path of learning and discovering mathematics the fun and meaningful way. We offer a comprehensive Singapore Math curriculum while incorporating the 12 math heuristics and Polya’s four-step problem-solving process over the full eight odd years leading up to PSLE. Our programme starts as early as four years old. 

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