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Math Heuristics Made Simple

– The Ultimate Guide for Parents

Math Heuristics? Heuristics Math? You might have seen or heard these terms being used in primary school Math, but what exactly are they? Why should you learn them?

What does "Math Heuristics" mean to you?
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If you are looking for the answers, you’re in the right place!

This in-depth guide will cover the following:

After reading it, you’ll have a crystal-clear idea of what Math Heuristics are and become a better problem solver. Ready to pick up these exciting new skills?

What are Math Heuristics?

Before we dive into that, we’ll first need to understand what a heuristic is.

Put simply, heuristics are just simple rules and mental shortcuts that we have created based on our past experiences. Ever heard of the phrases “rule of thumb”, “estimate”, or “stereotyping”? If you did, that’s what it is.

So what about heuristics in Math?

Math Heuristics are simple problem-solving strategies that can be applied to Math questions. 

These are often tried-and-tested strategies that many Mathematicians before our time had invented to solve new Math problems that they encountered.

Why use Math Heuristics in problem-solving?

If you are familiar with Singapore Math, you’ll notice that the curriculum focuses on Problem Solving.

Thinking skills and heuristics as part of the Singapore Mathematics Framework

By right, Math Problem Solving can be a fun and rewarding experience. However, many children find it difficult and lose marks in this area. Why? This is because where problem sums are concerned, the approaches and the solution may not be obvious.

Ask any child studying the upper primary levels such as Primary 5 and Primary 6 and they’ll most likely agree. Unlike Primary 4 where problem sums are more straight forward, Primary 5 and Primary 6 problem sums are much more complex and demand higher order thinking.

This is where Math heuristics can come in handy.


Math heuristics improve problem-solving performance

It’s like equipping yourself with a valuable toolbox to help you solve these challenging problem sums.

Knowing a set of Math heuristics can dramatically increase your chances of solving any Math problem. Not only does it help to get you started, but it also provides a guide to your thinking processes.

For example, if you have had the experience of solving simpler questions that are related to this particular challenging problem that you are trying to solve, you could apply the same method of solving it.

That is an example of a heuristic known as “Simplifying the Problem”. We’ll see some more other examples soon.


They also reduce effort and save time

Since Math heuristics are mostly tried and tested strategies, you don’t really have to spend as much time thinking of a newer, unique solution from scratch.

On top of that, using certain Math heuristic allows you to solve certain types of problems in a more systematic way. Hence, it’s a faster and more accurate problem-solving strategy.

What types of Math heuristics are there in Primary School Mathematics?

According to the Singapore Mathematics framework developed by the Curriculum Planning and Development Division (CPDD) team at the Ministry of Education Singapore (MOE), there are 11 types of heuristics in Mathematics that can be applied to Primary School level Math problems.

  1. Draw a diagram
  2. Make a systematic list
  3. Guess and Check
  4. Make a supposition/Assumption
  5. Look for patterns
  6. Act it out
  7. Work backwards
  8. Use the Before-and-After Concept
  9. Simplify the problem
  10. Solve part of the problem
  11. Consider special cases

These 11 Math heuristics can be further categorized into 4 groups based on how they are used:

To Give a Representation Draw a diagram Make a systematic list
To Make a Calculated Guess Guess and Check Make a supposition/Assumption Look for patterns
To Walk through the Process Act it out Work backwards Use the before and after concept
To Rephrase the Problem in Another Way Simplify the problem Solve part of the problem Consider special cases

What are some Math heuristics examples?

Here are some heuristic Math problems and an example of how to use each heuristic method to solve them.

Example of the Draw a Diagram Math Heuristic
Example of the Make a list Math Heuristic
Example of the Guess and Check Math Heuristic
Example of the supposition method
Example of the look for pattern Math Heuristic
Example of the working backwards Math heuristic
Example of the Before and After Math Heuristic

Conclusion – Practice Makes Perfect!

Thinking skills and heuristics are essential for mathematical problem-solving.

Now that you have a better picture of what Math Heuristics are and how they work, try them out with a variety of Math questions!

As you are doing the questions, don’t forget to think about which Math Heuristics is the best-fitting for each particular scenario.

If you continue to hone your problem-solving skills over the next few weeks with these heuristics mentioned above, you will be able to see questions in new perspectives and increase your efficiency in solving Math problems!

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