7 Impactful ways to nurture Counting and Cardinality
Why is counting and cardinality important in early maths?
Infants have demonstrated the ability to make judgements about quantity within the first months of life (e.g., Antell & Keating, 1983; Starkey & Cooper, 1980).
"We are born with a core sense of cardinal number", says neuropsychologist Brian Butterworth, author of The mathematical brain, reviewed in this issue of Plus. "We understand that sets have a cardinality, that is, that collections have a number associated with them and it doesn't really matter what the members of that set are."
However, research suggests that these earliest abilities may be based on an approximate sense of number (Huttenlocher, Jordan & Levine, 1994) It is not until their toddler years that children develop the ability to perceive, describe, and reason about exact quantities using the process of subitising and later, through counting (Clements & Sarama, 2014).
Children practice several skills as they learn to count:
The CARDINAL PRINCIPLE which typically develops between 3 and 5 years of age, is a developmental milestone that provides a foundation for early numeracy. Yet, the development of an understanding of cardinality is an element of counting that can be overlooked but plays a crucial part in linking counting skills to calculation.
A child who understands the 'howmanyness' or Cardinal concept will count a set once and not need to count it again. They will automatically remember and know how many are represented. Currently, children are not always given access to the cardinal significance of counting until they have established the ability to recite the numbers, and this limits understanding that can emerge from learning to count. We need to make understanding cardinality a central part of counting, and include many opportunities for children to create sets of a given number as well as count all of a set.
As Gattegno (1964) observed, it has always been difficult for young children to distinguish clearly between:
1. the last object counted as five and
2. the whole group of objects as five.
This is crucial to cardinality; understanding that a number represents a set of items and that once you have the number label for a set there is no need to count the separate items in order to know how many there are. In the context of counting on. Fuson (1982)
It takes children 3- 4 years to fully develop their understanding of the all the connections between quantities and numbers. Many and varied experiences in a wide range of contexts (outside, role play, dice games etc.) need to be provided over time for children to explore to cement their understanding. For example: a wide range of opportunities to count out a small number of discrete physical objects from a larger quantity, varying these in type, size and colour, (counting items on a worksheet or PPT slide just won’t do), counting movements, counting sounds (eg coins dropping into a piggy bank), counting continuous quantities (eg spoonfuls of sand); and so on. We cannot assume that if children can count reliably to 10, they can count above 10. The ‘teen’ numbers are the hardest to learn in English, as they are irregular.
Here, Barbara Sarnecka, a professor of Cognitive Sciences at the University of California-Irvine, talks of the importance of cardinality as a critical preschool concept. This key understanding is important for children’s learning and seems to be a prerequisite for accurate assessment of their number knowledge. She recommends a focus on spoken number words along with many opportunities to practice counting and subitising in order for uound children to learn about cardinality.
Here are 7 impactful ways of nurturing Counting and Cardinality:
Our Super dotty and spotty subitising spots are a powerful and playful way to nurture COUNTING & CARDINALITY. Subitising Spots is built to grow with your child, teaching critical skills in subitising, counting, number bonds and logic along the way.
Conceptual and perceptual subitising has been well researched for many years and yet subitising with young learners has yet to find its way into many early years’ settings and classrooms. Subitising is too often a neglected quantifier in educational practice. You can easily encourage quick daily practice to help build critical early number sense and build number fluency! Use Subitising Spots for joyful and playful maths like this:
Viv Lloyd’s article explains subitising here: You will find many ideas for developing young children’s conceptual subitising on the Erikson site.
3. Research points to the following as helpful in supporting young children's number sense:
3.. Research by Paliwal and Baroody (2017) stresses the importance of:
- Labelling the total number of items then counting them (Label-first). For example, on a page with 3 elephants, saying, “Look there are 3 elephants. Let’s count them.” And counted them as, “one, two,three.” or
- Counting the items, then emphasising and repeat the last word (Count-first). For example, on a page with 3 elephants, say, “One, two, three, t-h-r-e-e. There are three elephants.”
- Researchers indicate that the latter is the preferred method of modelling, suggesting that the first did make a difference compared to Counting Only, where the total number of items was not emphasised.
4. Counting REAL OBJECTS that can be moved, rather than pictures or objects on a screen. COUNTING COLLECTIONS and ESTIMATION STATIONS.
6. READING SYMBOLS
Ruth Trundley and Helen J Williams explore how small changes in the use of resources can impact children's learning:
7. NUMBER PATHS/ TRACK GAMES
My particular favourite is called 'Get The Animals Home'
Did you use this in your classroom or at home? How impactful was it? Don't forget to post in the comments. Math IS Visual. Let’s teach it that way.
Thank you for all you do to support your children's number journey. Thank you for watching and listening.
Love, Janey x