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Math Heuristics

A Handy Parents’ Guide

Math Heuristics, heuristics math, whaaattt?!

If you have a  primary school-going child, you might have seen these terms appearing on their worksheets or heard them being used at some parents’ workshop. Do you know what they mean?

What does "Math Heuristics" mean to you?
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Regardless of whether you are feeling confused about what Math Heuristics are or simply curious about it, this simple and comprehensive guide is written especially for you!

The difficulty of Primary School Math problem sums has increased dramatically over the years. Some might link the cause to Math Heuristics, but do you know: the Heuristics are in fact on our side?

In order to understand why, let’s take a look at what a heuristic is.

What is a

Heuristic?

The term “heuristics” may sound fancy pancy, but it’s not as complicated as we think. Put simply, heuristics are just simple rules and mental shortcuts that we have created based on our past experiences. Having them helps us make quicker decisions on everyday problems.

Ever heard of the phrases “rule of thumb”, “estimate”, or “stereotyping”? If you did, you would already have some basic idea of what a heuristic is!

Heuristics – Rule of thumb strategies that helps us solve problems faster and more efficiently

Let’s look at a couple of more concrete examples.

Every morning, we face the same problem of deciding what to wear for the day. So, if you wanted to save time, you might come up with a set of default outfits to wear on specific days, based on your past experience and the rules of your workplace or school.

Other times, when you find yourself looking at a menu with a great variety of food options, you might have ended up choosing your favourite dish that you have enjoyed elsewhere in the past.

These concepts of “default outfits” and “favourite foods” are simple problem-solving strategies that we use to help us make these decisions more easily. Coincidentally, they are just what we have been talking about: “heuristics”! Because of the numerous decisions that we have to make everyday, using these “rule of thumb” strategies allows us to solve our problems faster and more efficiently!

What are

Math Heuristics then?

Where Math problems are concerned, there are usually many approaches that can be taken to solve them.

math-heuristics

At first glance, the approaches and their solutions are usually not obvious, especially for the more complex problem sum questions. In these cases, we can often use a couple of “Math Heuristics”. When these simple problem-solving strategies are applied to Math questions, they help us get started and provide a guide.

In other words, Math Heuristics are tried-and-tested strategies that many Mathematicians before our time had invented to solve new Math problems that they encountered. Of course, certain Math Heuristics are more useful in certain questions or situations, just like our “default outfits” and “favourite foods” strategies, as we shall see later.

Although Math Heuristics may not be explicitly taught during our time, as long as you have solved a Math question before, you definitely would have used some form of heuristics!

Why do we want to learn

Math Heuristics?

Firstly, using Math Heuristics increases the chance of solving a Math problem. If you have had the experience of solving simpler questions that are related to the more complex question that you are trying to solve, you could apply the same method of solving it.

Next, it reduces the amount of effort needed to think of a solution. Using a Math Heuristic allows you a systematic way to solve certain types of problems, and lets you save much more time than thinking of a newer, unique solution from scratch. Since they have also been tried and tested, they are also usually faster and more accurate.

What kind of Math Heuristics are there in

Primary School Mathematics?

There are 11 Math Heuristics that can be applied to Primary School Math problems in Singapore. These 11 heuristics can be categorized into 4 main groups:

Using a Representation
  1. Drawing a diagram
  2. Making a systematic list
Making a Calculated Guess
  1. Guess and Check
  2. Making a supposition/Assumption
  3. Look for patterns
Walking through the Process
  1. Acting it out
  2. Working backwards
  3. Use the before and after concept
Restating the Problem in Another Way
  1. Simplifying the problem
  2. Solve part of the problem
  3. Considering special cases

Usually, more than one Math Heuristics can be applied to solve any Math problem. Using Math Heuristics to solve Math problems is not about finding the perfect solution, but of finding a solution relatively quickly. As with everything else, practice makes perfect! To increase the efficiency of solving Math problems, one must keep practicing and consciously think about using the best-fitting Math Heuristics for each particular scenario.

 

Some Points To Take Note:

Although heuristics may help to make our lives easier in solving Math problems, it is also important for us to be mindful of how heuristics work. This is largely due to the potential of cognitive biases.
Some students might be overly used to them and tend to overlook relevant information, assuming that the method of partially similar looking problem sums to be the same, thus creating stereotypes. Being aware of these pitfalls help us make better and more accurate decisions.

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