Centre for Neuroscience in Education

Studying at Cambridge

What if there were a key to unlock mathematical abilities? What if we could train children in just one focused area and then see improvements in all aspects of their maths performance? Sound too good to be true? Some scientists believe they have found that key—number sense. However, our latest research seems to show otherwise.

What is number sense?

Have you ever looked at a crowd and estimated how many people were there? This ability to approximate, i.e. have a sense of the quantity (how many) or magnitude (how much) of objects without having to count, is in essence what we mean by number sense. Most agree that humans have the ability to estimate in this way. Where scientists differ on this issue is whether number sense is at the core of mathematical abilities.

Is number sense at the core of mathematical abilities?

Some scientists have proposed that all numbers are stored in the brain in the “approximation area”.3, 4 In other words, that if you were to see a digit, such as “7”, then your brain would translate the digit “7” to an approximate sense of that number and store it in an area of the brain specifically reserved for remembering approximations. Likewise, the same would happen if you saw a written number word, such as “seven” or if you heard a number word spoken aloud. According to this model, all numbers would be translated into an approximation and they would all be stored in the number sense area of the brain (which some believe is the Horizontal Intraparietal Sulcus).4

Proponents of this model also believe that people who have strongnumber sense (i.e. approximation ability) will also be strong in the rest of their mathematical abilities. It follows that if children were trained to develop their approximation abilities, they should see an overall improvement in their maths performance.

Where are numbers stored in the brain?

We decided to explore the idea that all numbers are stored in one central number sense area. We had young adult participants answer simple addition problems for us. Participants had to memorise either an Arabic digit (e.g., 8) or a written number word (e.g., eight). They then had to retrieve the number from memory to add it to add it to an second presented number which was always an Arabic digit. We measured how long it took for our participants to see the second number, add it to the first number (which they had to retrieve from memory), and verify whether a third number which was shown to them was the correct sum.1 2

Here’s what we were looking for: if all numbers are stored in a central number sense area, then the amount of time that it takes to retrieve a number from that area should be the same regardless of whether the retrieved number was presented as an Arabic digit or written number word (since the number will have been stored in the same form and area of the brain). However, if different types of number are stored in different areas of the brain (e.g. digits are stored in one area and written number words in another), then you would expect to see different retrieval times.

What did we find?

We found that participants were faster to retrieve the number from memory when it had first been shown as a digit than when it was shown as a number word. What this seems to show is that numbers are not translated into a central number sense area but rather digits are stored as digits and written number words are stored as written number words, etc. If there is no central number sense area where numbers of all forms are stored, then it raised the question concerning whether number sense could be the foundation of mathematical abilities. Rather than being the core, number sense (or approximation ability) may simply be one of many mathematical abilities.