Counting is easily taken for granted but there’s a lot of fascinating research into how we learn to count – and there’s more to it than you may think.
The Mathematical Brain
It’s first worth considering where our capacity to do mathematics comes from. Neuropsychologist Brian Butterworth in his book “The Mathematical Brain” suggests we’re born with an innate sense of number hard wired into our brain and he attributes this to a small region of the brain behind the left ear he calls “the number module”. He compares this idea to colour – in the same way we perceive the “greenness” of a leaf we can also perceive the “twoness” or “threeness” of a group of objects. Take counting. Like times tables and algebra, we tend to think it’s something kids have to be taught. Wrong, says Butterworth – it’s an instinct. Sure, we have to learn the names and symbols of numbers to develop that instinct, but, because the number module is hard wired into the brain, basic counting comes naturally. Remote tribes can count even when they have no words for numbers. In maths as in language he believes, “kids start off with little starter kits” And their maths starter kit is the number module. There are other theories too – such as maths being an extension of our spatial awareness – but there’s something nice in the idea of a “little maths starter kit”. A Word of warning - All this doesn’t mean a child is predestined to be either good at maths or not. Far from it, we’re all born ready to learn maths – and it’s what happens in the first 10 years or so that sets us up.
Counting With Toddlers
Research suggest that toddlers – even as young as 12 months – have a sense of how many there are in a set – up to around three objects. This comes from their innate sense of number. Counting is learned when the toddler starts making the connection between this innate sense of “how many there are” and the language we use to count “one, two, buckle my shoe”. This is the first stage in learning maths and it’s the building block for many early concepts. Should parents count with their toddlers? Absolutely, using a variety of real objects. And since counting and language are interlinked reading to your toddlers is equally if not more important.
Counting – early learning milestones
Here are some stages of learning to count that you may notice your child going through at ages 3 to 5:
- Recognising how many objects are in a small set without counting. So if you show your child four apples they won’t have to count them to tell you there’s four.
- Knowing the “number words” from one to ten and their order.
- Know the sequence regardless of which number they start on. So if you say “start counting at four” they will count “four, five . .” as opposed to always counting from one.
- Conservation of quantity – This is where children realise that the number of objects in a set stays the same unless any are added or removed. So if they count six cans of beans in a straight line, then you rearrange the beans ( in front of their eyes ) into say two stacks of three – they will realise there’s still six without recounting.
- Counting non-visible objects – your child will realise they can count things they can’t touch or even see – such as sounds, members of someone else’s family, or even ideas.
- Cardinality, not to be confused with carnality - This is knowing that the last number counted is equal to the quantity of the set. If your child counts six oranges 1,2,3,4,5,6 and then you ask “how many oranges are there”? and they count them again then they haven’t grasped “cardinality”.
Counting on – as a step towards adding
Learning to add comes as an extension of counting. Here are some stages a child goes through to make this connection:
- Counting all – For 3 + 5, children will count “one, two, three” and then “one, two, three, four, five” to establish the quantity of the sets to be added – for example, three fingers on one hand and five fingers on the other. The child will then count all the objects “one, two, three, four, five, six, seven, eight”
- Counting on from the first number – Some children come to realise that it is not necessary to count the first number to add. They can start with three, and then count on another five to get the solution. Using finger counting, the child will no longer count out the first set, but start with the word ‘Three’, and then use a hand to count on the second addend: ‘Four, five, six, seven, eight’.
- Counting on from the larger number – It’s more efficient when the smaller of the two numbers is counted. The child now selects the biggest number to start with which is “five”, and then counts on “six, seven, eight”.
- The final stage isn’t really counting – it’s where learners know their number facts and skip the time consuming counting altogether.
Beyond basic counting
Counting is the first mathematical pattern learners encounter. From here they soon begin to count backwards which is a step towards subtraction and they’ll also count in twos, fives and tens which is a foundation for multiplication. The next big step is the idea of place value and counting to base 10. Learners often make this leap simply because it’s an obvious and efficient way to count large numbers. In Komodo we use practice examples like this to help learners make the connection to counting in tens and ones.
It’s easy to forget that counting is a key concept in maths with many stages before it’s mastered. There’s certainly a lot more to it than one, two, three!
I’m Ged McBreen, Co-Founder of Komodo and a qualified Maths teacher. If you found this article interesting sign up to our email list.