I was recently introduced to Professor Hamesh Sharma by Judy Hornigold and to Chris Woodin  through my own research.

I have always been an advocate for the importance of subitising as a foundation for number sense and mathematical thinking. Are Sharma’s visual clustering and Woodin’s icon cards related to subitising, or not! That’s what I was interested in exploring.

What is subitising?

As I’ve previously posted, subitising is a term that was introduced by the Swiss psychologist Piaget. It’s the ability to look at a small number of objects and instantly recognise how many objects there are without needing to count.

There are two types of subitising: perceptual and conceptual. Our brains can only easily subitise objects up to five – this is perceptual subitising. Conceptual subitising is anything above five objects requires the brain to beginning counting on or adding groups of objects together. 

Why is it important?

Subitising is essential for children’s mathematical development for many reasons as it:

• helps children to understand what numbers mean or how many ‘things’ a number refers to.
• can develop children’s pattern recognition.
• prevents children becoming over-reliant on counting by ones.
• develops children’s understanding of whole to part relationships, e.g. 3 and 3 is 6, 2 and 4 is 6. By separating and combining numbers through subitising, children lay the foundations for addition and subtraction
• enables children to develop an understanding of the commutative law of addition, i.e. it doesn’t matter in what order you add numbers together – you always get the same answer! For example, 2 + 3 = 5 and 3 + 2 = 5

Visual Clustering – Icon Cards

In contrast, Sharma and Woodin emphasise the importance of patterning within the objects.  They explain that it is important for children to visualise numbers as images. When children are able to construct and deconstruct the image they are identifying the subordinate parts, the precursor to addition and subtraction.

Sharma provides an explanation on clustering and cluster cards here. While more information on Woodin’s use of icon cards can be found here.

Both approaches rely on subitising as a foundation. More importantly, they use the same arrangement of objects so that the image and associated number are anchored in the child’s memory. For students who have difficulty with counting and comparing, even small numbers of objects, this relationship is imperative to establishing basic foundational maths skills.

I’ve created a set of cards here.

Until next time,

Carole