Thursday, 26 March 2015

Problem-solving Heuristics

Apply logic to solve puzzles – that’s all it is. And there’s a systematic science to it.

Most children love activity books. This proves their innate need to be challenged and mentally stimulated. Maths puzzles tap into this instinctive desire to stretch children’s minds.

Challenging Maths questions challenge them to find and apply faster, more creative solutions. This trains them in higher-order thinking and decision-making skills on top of subject knowledge.

Now, don’t we all apply these skills at home, at work and at play? Therefore, heuristics practically take children beyond school, right through their lives.

Heuristics in PSLE Maths

More than half of PSLE Maths marks go to heuristics-related questions.

Approximately 55% of PSLE Maths marks are dedicated to long, open-ended questions that necessitate problem-solving. Several are routine questions, easily solved using the four basic operations of addition, subtraction, multiplication and division. Many are non-routine questions, requiring the four basic operations AND problem-solving heuristics.

The Ministry of Education has identified 11 heuristics for primary-level Maths, and two more for secondary-level Maths.

 1. Use Diagrams / Models 2. Act it Out 3. Use Before & After 4. Use Systematic Listing 5. Look for Patterns 6. Work Backwards 7. Use Guess & Check 8. Simplify the Problem 9. Make Supposition 10. Solve Part of the Problem 11. Paraphrase the Problem 12. Think of a Related Problem 13. Use Equation Source: Ministry of Education of Singapore (2007). Mathematical Syllabus Primary. Singapore: Curriculum Planning and Development Division.
Opening Hearts & Minds
• Accertation
We teach students problem-solving heuristics. Students simply add this new information (heuristics) into their existing mindset.
• Tunning
We guide students in heuristics application. Students begin to realise the limitations of their existing mindset. They begin to modify their existing mindset to incorporate heuristics.
• Restructuring
We expose students to the variety of challenging Maths problems that necessitates heuristics application. Students begin to address the inconsistencies between their existing mindset and heuristics. They begin to recreate their existing mindset to feature heuristics.
Habituating the Process
• Understanding the problem
Students will be trained to look for, visualise, organise and connect information. They will also develop Maths language proficiency.
• Choose an appropriate heuristics
Students will learn how to select, and combine where necessary, the most appropriate heuristics for different problems.
• Perform the chosen heuristics
Students will develop computational skills, geometrical skills and logical reasoning.
• Reflect
Finally, students will be trained to check their solutions, to improve on the methods used, to seek alternative solutions, and to extend the methods to other problems.