The Singapore mathematics syllabuses, developed by the Curriculum Planning and Developing Division (CPDD) within the Ministry of Education Singapore (MOE), has identified 13 heuristics that are applicable to mathematical problem solving.
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
(Heuristics 12 and 13 are in the secondary syllabus.)
These 13 heuristics can be grouped into four categories based on how they can be used:
To give a representation e.g. draw a diagram, make a list, use equations
To make a calculated guess e.g. guess and check, look for patterns, make suppositions
To go through the process e.g. act it out, work backwards, before-after
To change the problem e.g. restate the problem, simplify the problem, solve part of the problem
The following are examples of some of the heuristics mentioned above and how they can be applied to solving simple non-routine problems. It also demonstrates how a problem might be solved by using different heuristics strategy and how another problem needs more than one heuristics strategy to solve.
For more non-routine questions and worked solutions, check out PSLE Maths Strategise and Score.