The ability to intuitively estimate the number objects you can see is known as automatic number sense and has been widely studied in the scientific literature, but is usually thought to be separate from the formal and precise maths abilities we learn at school.

A new study just published online in Nature suggests that these abilities are more intertwined than we might think, as the better the number sense of 14 year-olds, the better their formal maths ability.

The researchers, led by psychologist Justin Halberda, flashed up a series of dot patterns to a group of 14 year-old students. Just like the one in the picture.

The kids were asked to indicate the ratio of blue and yellow dots but because the patterns flashed up so quickly, for only one fifth of a second, the kids didn’t have time to count them. They had to rely on a guestimate – their number sense – to give their answer.

After a whole set of these, the researchers calculated each kid’s accuracy, to give a measure of their overall number sense ability.

This in itself isn’t particularly interesting, as number sense has been widely tested and researched in the scientific literature. However, in the past, it’s often been considered a fuzzy, perhaps more ‘primitive’, ability unrelated to formal maths skills.

Owing to the fact that the researchers had access to the children’s maths achievement test scores, all the way back to kindergarten, they tested whether number sense and maths skills were related.

It turns out they were, and automatic number sense accounted for almost a third of the scores on formal maths tests.

This was even after controlling for the fact that some children were generally brighter or quicker than others.

What is not clear is whether just being better at maths means you develop a better number sense, or whether a better number sense encourages better maths skills.

The fact that they are related at all is interesting, however, as it suggest that intuition plays a part in the practice of mathematics – the most logical of pursuits.

Link to scientific paper.

Link to PubMed entry.

Link to write-up from ScienceNow.