Age group: Pre-school, Kindergarten
Target readers: Parents of young children, primary school teachers, educators
Last year, after playing with the blocks and while putting the toys back to its place, I asked my 3-year old daughter to give me ‘three’ pieces. She has understood small counts like 1, 2, 3, and so I presumed she would give me ‘three’ pieces. She looked at all the pieces and replied, “There is no ‘3’.”
I told her that I was not looking for ‘3’ but for one, two, three. She once again replied that she didn’t see a ‘1, 2 and 3’. I gave her three pieces and counted – “one, two, three”. She said, “No, this is not three (by looking at the piece)…this is 4 (because it had the numeral 4 in it)”.
I understood that she was looking at the form and not the count that I was referring to. It was cute to see her innocent face look at me with a big question mark probably thinking, ‘What’s wrong with this guy? Can’t he see it is not 3 but it is a 4?’
Finding a way through the abstraction of numbers isn’t very easy. Yet, we expect kids to learn and understand the concept with a few repetitions. Once we see them parroting numbers, many of us think they have understood the connection between number representation and counting.
Learning to count might look like a very simple idea to adults because we have forgotten how we struggled to learn it ourselves! So, I would like to throw some light on how complex this process is from a child’s perspective.
Learning to count involves a lot of procedural skills and underlying concepts which are interlinked.
Children first need to learn to chant the number words like 1,2,3.. They do not understand the meaning initially, but often learn it like a play or a social experience along with parents or other kids. Initially they tend to skip numbers or swap the order of numbers. But kids love repetition and they learn the sequence eventually.
They need to understand that the numbers don’t represent the object and understand that we are using the number as a concept of quantity.
They need to keep the chant of 1, 2, 3 going at the same pace as their finger touches every object to be counted. And to realise the one-to-one correspondence that every object has to be counted exactly once.
They need to connect the sound two with the written representation of 2 that we are showing as a number, and associate it with the idea of quantity.
Most often, we use our fingers to show them the count. This adds another layer of understanding to learn to correlate the fingers in our hand with the sound and the symbol and the concept. While doing this, we may start counting from our thumb (counted as 1), then the index finger as 2, and so on until we reach 5 on our little finger. Initially, most children think that each of these fingers represent the count. So, if you count 1 from the index finger, they may not agree because they think the index finger represents 2. Don’t you now see why!
They need to understand the concept of cardinality – to correlate that if you count from 1 to 5 touching 5 objects, there are a total of 5 objects.
They need to understand that irrespective of the order of counting (left to right, random fashion) or how the objects are placed (on top of each other, side by side), it is the same as long as every object receives one count.
They need to be able to extend the concept and be able to abstract and generalize.
When we point and say two balls or three dolls, they need to understand that the two and three are words denoting the concept of quantity that can apply to dolls, balls or any object. They learn that it does not matter what we count (objects of the same or different type), the process of counting is the same. And apply it to non physical entities like ‘the number of family members’.
Children observe and learn, and it is best if the children get introduced to this new skill through fun and play. Learning about numbers and how to count is a very slow process which cannot be mastered just in a few months time. We need to give lots of opportunities for children to explore, experiment and generalize this learning. Every child will learn these ideas by making mistakes.
As we become aware of the complexity of this learning, we are likely to be less impatient and create a rich environment that facilitates this. It is fun to watch when children learn something as subtle as numbers that human species took years to get a grip on. And how silly we, as parents, assume that children have learnt numbers once they have memorized the numbers in the correct sequence!
Editor: Gayathri V.
Author: A two times TEDx speaker, Vinay Nair is one of the co-founders of Raising A Mathematician Foundation. He is a mathematics educator and is passionate about gifted education, history of Indian mathematics and working with students who are passionate about mathematics. He often speaks on forums both online and offline. He can be reached at firstname.lastname@example.org.