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 the totality of their maths performance? Sound too good to be true? We tend to agree, but some scientists don’t think so. They think they may have found that key ... *number sense*.

**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, they believe 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 approximate sense 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 are strong in number sense (i.e. approximation ability) will also be strong in the rest of their mathematical abilities (since number sense is the core). It follows then that if children were trained to develop their approximation abilities, they should see an overall improvement in their maths performance. A software game, *The Number Race,* has in fact been designed for just this purpose; however, so far, performance improvement in the game has not been shown to translate into overall mathematics performance improvement^{5}.

**Where are numbers stored in the brain?**

We decided to explore one particular aspect of this model ... that all numbers are stored in one central *number sense *area. We brought in young adult participants and had them answer simple addition problems for us. The task was designed in such a way that the participants had to memorise a number which could either be a digit or a written number word. They then had to retrieve the number from memory to add it to another number. We measured how long it took for them to see the second number, add it to the first number (which they had to retrieve from memory), and then verify whether a third number which was shown to them was the correct sum or not.^{1 2}

Here’s what we were looking for. If all numbers are stored in a central *number sense *area, then there shouldn’t been a difference in the amount of time that it takes to retrieve a number from that area, since the same brain process will be used to retrieve a memory from the same area. However, if numbers 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 much faster to retrieve the number from memory when it had first been shown as a digit. What this seems to show is that numbers are not all 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. This seems to lead us toward the idea that *number sense* may not be at the core of mathematical ability but rather may simply be one of many mathematical abilities.

**References**

1) Myers, T., & Szűcs. D. (2015). Arithmetic memory is modality specific. *PLOS ONE*,* 10*(12), e0145614. https://doi.org.10.1371/journal.pone.0145614

2) Szucs, D., & Csépe, V. (2004). Access to numerical information is dependent on the modality of stimulus presentation in mental addition: a combined ERP and behavioral study. *Brain research Cognitive Brain Research*, *19*(1), 10-27. https://doi.org/10.1016/j.cogbrainres.2003.11.002

3) McCloskey, M., Caramazza, A., & Basili, A. (1985). Cognitive mechanisms in number processing and calculation: Evidence from dyscalculia. *Brain and Cognition*, *4*(2), 171-196. https://doi.org/10.1016/0278-2626(85)90069-7

4) Dehaene, S., Piazza, M., Pinel, P., & Cohen, L. (2003). Three parietal circuits for number processing. *Cognitive Neuropsychology*, *20*(3), 487-506. https://doi.org/10.1080/02643290244000239

5) Wilson, A. J., Dehaene, S., Dubois, O., & Fayol, M. (2009). Effects of an adaptive game intervention on accessing number sense in low-socioeconomic-status kindergarten children. *Mind, Brain, and Education, 3*(4), 224–234. https://doi.org/10.1111/j.1751-228X.2009.01075.x