Number Sense is ….
“… good intuition about numbers and their relationships.
It develops gradually as a result of exploring numbers, visually them in a variety of contexts, and relating them in ways that are not limited by traditional algorithms.” (Howden, 1989)
“Research indicates that early number Sense predicts school success more than other measures of cognition, such as verbal, spatial, or memory skills or reading ability.” (Watts, Greg, Duncan, Siegler, & Davis-Kean, 2014)
Jo Boaler, a professor at Stanford University explains it in this way:
Van de Walle and others (2018) suggest Four Early Numeracy Concepts and Four Number Sense Relationships necessary for the development of Number Sense, something we will continue to explore.
Early Number Concepts
- Verbal Counting – to say the numerals in the correct order
- Object Counting – 1 to 1 correspondence
- Cardinality – the last object counted in a set tells how many
- Subitising – the ability to see how many without having to count
Number Sense Relationships
- Spatial relationships – having a visual to go with a number
- One or Two More & Less – instantly knowing the amount that is one or two more & less
- Benchmarks of 5 and 10 – knowing how a number relates to 5 and 10
- Part-Part-Whole – understanding how a whole can be broken into parts
Counting is fundamental to later maths development. Early counting predicts later mathematical success (Clements and Sarama, 2014) and even later reading fluency (Koponen, Salmi, Eklund and Aro, 2013).
Many children begin school with the ability to differentiate between sets of certain ratios (in particular, 2:1 and 3:2) enabling them to tell the difference between sets just by looking at them. However, they are unable to tell the difference between sets that are close in number (for example, 10 and 9). It should be noted, that this does not apply to all children, in particular, those that may suffer from Dyscalculia. A term referring to a wide range of life-long learning disabilities involving maths. It includes all types of maths problems ranging from an inability to understand the meaning of numbers, to an inability to apply mathematical principles to solve problems.
Those who study children’s mathematical development explain that counting involves five principles (Gelman and Gallistel, 1978):
- One-to-one correspondence
- Stable number word order
- Order irrelevance
Sound complicated? It is! Something we adults take for granted as “simple” is actually quite complex developmentally. Although we will explore each principle in future posts the following by the National Center on Intensive Intervention is a brief introduction.
Verbal Counting – Stable Number Word Order
As children engage with nursery rhymes, songs and role-play opportunities they often develop the order of number words. However, just because children are able to rote recite the number words it does not mean that they understand one-to-one correspondence nor the knowledge of differences in the magnitude or size of numbers (for example, knowing that 7 comes after 6 doesn’t mean that the child knows that 7 is more than 6).
Counting rhymes, books and videos are ways of supporting children in developing Verbal Counting. An enabled adult who is able to support and intervene when a child experiences difficulty is significant at this stage.
I usually add the counting rhymes to the classroom library and make activities (available in the counting rhymes section) so that students can retell the rhymes. This assists with developing the rhythm of counting.
What strategies/ideas do you use for Verbal Counting? Please feel free to comment.
Until next time,