Making sense of number sense…
…and its implications in the classroom.
Hello and welcome to the 37th edition of our fortnightly newsletter, Things in Education.
Can you imagine 100 dolphins? Even if you close your eyes and think about it, you won’t be able to. What you are imagining is many dolphins. To actually get a sense of how many dolphins is 100 dolphins, one could imagine trying to fit 100 dolphins in an empty passenger airplane that flies from Delhi to Bangalore, or at least what volume 100 dolphins may take up. So, an adult’s number sense comes from multiple faculties. In the example above, you would need more than just counting. You would need spatial skills and cognition to imagine the unlikely scenario of having 100 dolphins in an airplane.
Look at the cards above. Even without really counting, you could say that the two cards have different number of dots on them. Similarly, with the two cards below – do they have the same or different number of dots?
Without counting, can you say if the two cards below have the same number of dots?
Number sense is the innate ability to recognize and understand the numerical quantity of a group of objects without the use of symbols or formal language. As we discovered, our basic number sense works till 3 objects. We can tell apart 1 object from 2 objects, 2 objects from 3 objects, and 1 object from 3 objects easily. But as the number goes higher, our ability to differentiate between the number of objects goes down. That is why it was not easy to say how many dots there were on the two cards above – it was difficult to say whether there were the same number of dots or not and how different the number of dots was.
Surprisingly (or not), this ability to tell apart 1, 2 and 3 objects is evolutionarily engraved in our brains. Studies have shown that various animals are able to do exactly this. It stands to reason then that babies (less than 1 year of age) should also be able to differentiate between 1, 2 and 3 objects – and that is what studies have shown us. Studies in babies and animals have also shown that beyond 3, it becomes difficult for them to decipher the difference between the number of objects.
Do you think that it is just a co-incidence that in number notations of different languages, the numbers 1, 2 and 3 are represented by those number of dots or lines? And almost universally it changes with the notation for 4!
As we saw earlier, it was difficult to differentiate between 7 and 8 dots on the two cards. However, if you notice, it gets much easier if the dots are somewhat ordered.
Even without counting, you do know that the number of dots is different.
Do you need to count the number of circles to know how many there are on the card below?
So what do all these cards tell us? Our number sense is good up to 3 objects, and we can almost intuitively differentiate the number of objects. And as we share this trait with other animals and babies, it seems to be a trait that is not learned. As the number of objects goes higher, our ability to differentiate between the number of objects falls. If we order the objects, the ability to tell apart the number of objects is somewhat increased. This suggests that our number sense also comes from visual cues and spatial awareness. So, our number sense comes from evolutionarily conserved cognitive mechanisms.
So, what are the different cognitive mechanisms involved in number sense?
Subitizing - This is the ability to recognize the number of objects in a group without counting them. It is thought to be based on the visual recognition of patterns or configurations of objects. This is what we did with the dot cards.
Approximation - This is the ability to estimate the number of objects in a group based on their overall size or volume. It is thought to be based on our sense of spatial awareness and the relationship between objects in physical space. This is what we did with imagining 100 dolphins in an airplane.
Discrimination - This is the ability to differentiate between two quantities of objects. It is thought to be based on our ability to detect differences in the spatial arrangement or pattern of objects. You could discriminate between 7 and 8 dots when they were arranged in a particular way. Most of us may not have been able to tell that there were 3 concentric circles, and would have had to count them.
As a preschool teacher or an early childhood curriculum creator, how can you leverage this limited number sense to extend the sense of numbers?
By using manipulatives
Manipulatives, such as blocks, allow students to practise subitizing by recognizing patterns or configurations of objects. They may also provide a tactile and visual representation of quantity, supporting approximation.
By engaging in spatial awareness activities
Spatial awareness activities, such as arranging blocks or objects in a certain order, help children develop their sense of discrimination by requiring them to distinguish between different patterns or configurations of objects.
By encouraging estimation
This helps children develop their approximation skills by providing opportunities to practise judging the size or volume of a group of objects without counting them.
Developing number sense beyond 3 is a challenging mission for a child’s modular brain. Educators must ensure that their learning activities help with making connections between different areas of the brain. We will go into more detail of the different cognitive mechanisms and how to help students fine-tune them through learning activities in the upcoming editions.
If you found this newsletter useful, please share it.
If you received this newsletter from someone and you would like to subscribe to us, please click here.