# PROCESSES

Mathematical processes refer to the process skills involved in the process of acquiring and applying mathematical knowledge.

At the primary level, children develop these process skills through problem solving in all 3 content strands. Real-life context should be provided as situations in the problem. Through solving problems in real-world context, children see the relevance of mathematics in everyday situations.

Below is a list of mathematical processes. Examples of the usage of these processes in specific content strands are provided in Worksheets section. Source: “Chapter 4 Primary Mathematics Syllabus,” Primary Mathematics Teaching and Learning Syllabus, 2012, 31-32.

‘Concrete-Pictorial-Abstract’ (CPA) approach is one common approach used by Singapore mathematics teachers in the process of leading children to acquire and apply mathematical knowledge. This approach derives from Jerome Bruner’s three stages of cognitive representation. Read more about Bruner’s work here.

CPA approach put information in 3 stages of representation. Together with process skills, children are lead to understand the problem and eventually solving the problem.

• Concrete stage of representation
The usage of a tangible object, such as mathematical manipulative, role-play, etc.
• Pictorial stage of representation
The usage of visual to understand the problem.
• Abstract stage of representation
The usage of Mathematical symbols, such as ‘+’, ‘-‘, ‘x’ or ‘÷’ to represent the problem.

Watch this video for further explanation on the ‘Concrete-Pictorial-Abstract’ approach. Concrete Stage – The usage of concrete materials to aid understanding of Mathematical concepts Pictorial – Transfering of understanding from concrete materials to pictorial form Abstract – Using Mathematical symbols to express understanding of Mathematical concepts Bar Modelling is a technique used in the ‘pictorial’ stage of CPA approach to help children visualise Mathematical concepts. Bar Modelling is incredibly useful for problem solving where children will go through a structured thought process and reasoning in attempt to solve questions.

A bar model is made up of rectangles, which is also known as units. Depending on the questions, different types of bar models are used in different context.

The unit (rectangle) represents an amount. Using the diagram above as an example, an unit represents 3. It could be 3 apples, 3 girls, 3 pens… Depend on the context of the question. As the question is asking for the answer of two units (indicated by the question mark and bracket arrow), so simply, 2 x 3 = 6, (2 times of 3)

Bar Modelling comes in various forms. More examples are shown in my Article Category ‘Problem Solving‘.