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A sense of number is, to some extent, innate. How do we know? How can we ask babies to demonstrate counting skills without language skills to match? The answer is a fascinating delve into early development: researchers measure the length of time infants stare at dots on a screen. Why? Because, just like adults, their gaze time is longer if they look at new information, and shorter if it's the same old thing they've just seen. Turns out, you can show six-month-olds changing arrays of ten dots and they rapidly get bored of them, even if they're in different groups- but change the number to twenty and you'll surprise them into looking for longer.
It is likely that tiny babies can also add and subtract, too - and we know this because they look for longer at surprising (wrong) results of sums. For example if you put two objects behind a curtain, then add a third, they look for much longer if the curtain raises to reveal two or four than three. One explanation - that the babies can already count - is called the violation-of-expectations paradigm, and the effect appears to be present in babies as young as five months old, even when controlling for other factors like the objects used.
The first study cited here also suggests a correlation between infants' ability to somehow nonverbally 'count' (or at least compare) small numbers (called one's ANS - approximate number system) and their later maths scores, giving a tantalising glimpse into a predestined mathematical future for some almost from birth .This effect is not completely explanatory and most noticeable, as you'd expect, at very high and very low abilities.
It's understandable why this early number concept is important; being able to judge who has the most food, count one's offspring, or even compare armies seems crucial to survival. So it makes sense also that some animals (such as lemurs ) appear to have a very similar sense of non-verbal number.
So what can we do to help very young children improve their ANS - their 'gut' number sense?
First, if you have spare ten minutes, try out this fun comparative dots test for adults - it will give you a breakdown of your performance in accuracy and speed compared to others in your age group. This will give you some insight as to the way that ANS 'feels' for pupils. Now consider what made that task harder - the time element, the different sizes of the dots, the way they were scattered, and most importantly the ratio of yellow to blue dots as compared to the total size of the set. This is an example of a principle called Weber's law, and formalises the intuitive mathematical idea that it is easy to differentiate which is larger in a set of 4:6 yellow:blue dots, but a great deal harder if there are 44:46.
Secondly, imagine how difficult it would be to understand numbers if this sense was impaired in some way. Some experts, like Brian Butterworth, suggest that this is one way to describe dyscalculia - a type of learning disability likened to number blindness. Other symptoms include difficulty placing numbers in order or distinguishing place value. The good news is that all pupils can be helped, whatever their ability, with the kind of games and visualisation activities Butterworth and his team have created to help maths learners of all ages.
Finally, if you teach young children or have some of your own, take every opportunity to explore and play with ANS whenever it comes up. Compare sets, add and subtract one and ask what is different, ask children to draw two things that are different sizes or point to 'bigger' and 'smaller' - remember that the best evidence we have at present suggests their brains are computing, counting and comparing long before they can express this in words.