Singapore Maths: Symbolism To Abstract Thought

Maths isn’t something that I typically associate with illustration but is often used with younger children for Maths text books and tests.

Whilst exploring these resources I came across a method of teaching called Singapore Maths. As the title suggests, this is the method used in Singapore when introducing children to the concept of numbers and groups.


Instead of introducing symbols straight away, the children are given objects instead. The objects are used to demonstrate numbers and groups and simple age appropriate concepts. This is called the CPA method (Concrete, Pictorial, Abstract). At the concrete stage, children model the problems by handling objects. Pictorial is where they’ll use pictorial reference or representation to help them deal with the problem. This could be by drawing or building to help them ‘see’ the problem and start bridging the gap between the concrete and abstract stage. Abstract is where mathematical symbols and numbers are used. This isn’t a linear concept and teachers tend to repeat the process as new concepts are introduced. Only once they understand the concept of numbers and groups by visual representation are they introduced to actual symbols.

This method is becoming popular because Singapore is consistently ranked top in international assessments (Cvencek, Kapur & Melzoff, 2015).

This is noteworthy in relation to my studies as it is looking at how context given through interaction and pictorial representation before explanation aids development. Pictures and interaction are laying foundations for better comprehension by providing symbolic assistance.

The concrete, in the context of how a child could form a narrative from looking at my images, would be their own life experiences so far. They would have a certain level of understanding of particular situations. An example could be their experience of darkness. Which emotions are tied to it. Would that be a signifier of danger ahead, or would their view contradict that assumption and the narrative take a different turn for them. The pictorial¬†is my representation of the elements within an illustration, this is where my involvement starts. This is how the story I’m telling occurs to me. The abstract is what the individual viewer’s mind does with the illustration once they’ve taken it in. How much detail they look for and where they seek to find meaning will all have an impact on the story they choose to build around the pictures.

CVENCEK, D., KAPUR, M. & MELTZOFF, A.N. (2015) ‘Math achievement, stereotypes, and math self-concepts among elementary-school students in Singapore.’¬†Learning and Instruction.¬†39. p. 1-10.

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