The approximate number system – building a foundation for maths

From birth, we all have the ability to recognise differences in quantity, thanks to something known as the approximate number system. This ability develops with age and experience. So what do we know about how your toddler understands quantity?  

What exactly is the approximate number system? 

From the moment we’re born, we have an intuitive sense of quantity – in one experiment, newborn babies were played a number of sounds and were then shown a group of items. They looked for longer at the group that had the same quantity of items as the number of sounds they heard. So, if they heard four sounds, they would look at a group of four items for longer than they’d look at a group of 16 items.^[1]  

This ability to recognise and compare differences in quantity uses the approximate number system – as its name implies this is a rough system – so not as accurate with larger quantities or when the difference in quantities in two groups is smaller.  

The accuracy of the approximate number system improves with age and has been linked to maths achievement in older children.^[2] 

Younger children need a greater difference in quantity than adults to be able to say accurately which of two groups has more items.^[3] 

The approximate number system becomes more accurate with practice. 

You can support the development of your toddler’s sense of quantity by taking about numbers when you play. 

This might include counting stairs, or blocks in a tower, but could also be simply talking about having more blocks, lots of cars, or who’s collected more leaves.  

And when you think about it, there are lots of chances to chat about quantity in daily life too – how many fish fingers you have, or which queue has more people in it. 

You don’t need to plan to talk about quantity or get them to count all the time, just know that your everyday chats will be supporting your toddler’s number sense.  

References: 

[1] Izard, V., Sann, C., Spelke, E.S., & Streri, A. (2009). Newborn infants perceive abstract numbers. Proceedings of the National Academy of Sciences of the United States of America, 106, 10382-10385. 

[2]  Chen, Q., & Li, J. (2014). Association between individual differences in non-symbolic number acuity and math performance: A meta-analysis. Acta Psychologica, 148, 163-172.  

[3] Navarro, M.G., Braham, E.J., & Libertus, M.E. (2018). Intergenerational associations of the approximate number system in toddlers and their parents. British Journal of Developmental Psychology, 36, 521-539.