Singapore Primary Math Explained sc-math

Primary math problem solving heuristics

Updated: 14 January, 2005

Singapore's Primary Mathematics Syllabus focuses on mathematical problem solving with emphasis on the development of concepts, skills and its underlying processes. As part of the process of problem solving, the syllabus listed some heuristics for problem solving at the primary level. "Heuristics" can be defined as guidelines or strategies intended to increase the probability of solving a problem.

Different heuristics serves different purposes such as helping the child to:

  • understand the problem;
  • simplify the task;
  • identify possible causes;
  • identify possible solutions;
  • think or reason.
They are often used in combinations to solve the problem.

A brief description of the listed heuristics is given below.

Act it out

Take on the role of people, things or process in the problem and try to do what they do. It may sometimes be helpful to make use of objects to represent the situation or problem.

Use a diagram / model

Draw a diagram / model to create a pictorial description of the problem. This helps the child to visualise and understand the problem. Drawing also enables the child to "manipulate" the data.

Make a systematic list

Organise the data such as numbers or type of objects logically into tables or lists. This helps the child identify and spot missing data asked for in the problem. Organised tabulation of data also helps the child perceive trends or patterns in the data.

Look for pattern(s)

Examine the available data for patterns or relationships. Having perceived a pattern, the child can then predict the missing data or answer.

Work backwards

Look at the end results and work backwards towards the beginning. This strategy can be useful in problems involving a series of steps or computations. It is also useful when the problem gives more data about the end condition and little data about its beginning.

Use before after concept

Compare the situation before and after the problem is solved. Sometimes the differences (or a specific difference) can shed light on the cause and lead to a possible solution.

Use guess and check

Make an educated guess of the answer and check to see if it is correct. Use the knowledge gained from testing an incorrect guess to improve the next guess. It is important to avoid making wild guesses. Track the guesses made and look for patterns to improve the next guess.

Make suppositions

Study the data given and make suppositions (assumptions without proof) about some aspects of the problem to form the basis for further thinking. This reduces the number of possibilities and makes it easier to explore the problem further.

Restate the problem in another way

Read the problem carefully and restate it in the child's own words. This helps the child understand the problem and identify important factors of the problem.

Simplify the problem

Make a difficult problem simpler. This can be done by changing complex numbers to simple numbers or by reducing the number of things in the problem. The solution to the simplified problem may help the child solve the original problem.

Solve part of the problem

Split a complex problem into smaller parts and solve the simpler part first.

The Singapore primary mathematics syllabus suggested the above eleven problem solving heuristics for primary students. It is important to expose your child to the various problem solving heuristics. Besides knowing the heuristics, they should also know when to use them.

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