Heuristic Mathematics.

In this article, Michelle Choo, Associate Lecturer at Marshall Cavendish Institute and established author of several Mathematics books, demystifies heuristics for parents.

If you ask parents what heuristics are, the most common answers you would get will be:

• “Heuristics are difficult Maths questions”

• “Heuristics are those Maths word problems with the * ”

No doubt, some Maths word problems can be slightly challenging, but that’s not what heuristics is all about. As a result of this misconception, many parents of school-going children are often terrorised by today’s Maths syllabus.

Over time, the goals and aims for learning Mathematics have evolved, and inevitably so have the teaching and learning methods.

For those who are intimidated just by the word heuristics, Michelle Choo, Associate Lecturer at Marshall Cavendish Institute and established author of several Mathematics books, demystifies heuristics for parents

What are heuristics?

The word heuristics originates from the Latin word heuristicus, which is equivalent to Greek heur (ískein) + Latin –isticus –istic and means to find out or to discover.

To put it simply, heuristics are a set of problem-solving rules that help us discover the best and most practical ways to solve problems.

Mathematics is more than the study of number and patterns. The learning outcome is to develop one’s logical thinking and ability to solve complex problems.

Singapore Mathematics, a problem-solving curriculum

With problem solving as the core of our Mathematics framework, the use of heuristics is inevitable. Of course, heuristics are not used independently, but supported by the five inter-related components:

• Attitudes

• Metacognition

• Skills

• Processes

• Concepts

The Singapore Mathematics syllabuses, developed by Curriculum Planning and Development Division (CPDD), Ministry of Education Singapore (MOE), have identified 13 heuristics that are applicable to mathematical problem solving. These are:

1. Act it out

2. Draw a diagram / model

3. Use guess-and-check

4. Make a systematic list

5. Look for patterns

6. Work backwards

7. Use before-after concept

8. Make suppositions

9. Restate the problem in another way

10. Simplify the problem

11. Solve part of the problem

12. Think of a related problem*

13. Use equations*

(*Covered in the secondary syllabus.)

These 13 heuristics can be grouped into four categories based on their applicability. They are:

• To give a representation. Draw a diagram, make a list, use equations.

• To make a calculated guess. Guess and check, look for patterns, make suppositions.

• To go through the process. Act it out, work backwards, before-after.

• To change the problem. Restate the problem, simplify the problem, solve part of the problem.

As such, heuristics play a very important role in mathematical problem solving, which is fundamental to mathematics learning.