Maths is one of those things that you’re either good at or not, right? That’s what people seem to tell you anyway. More so than any other school subject, maths is something that is surrounded by negativity. In fact, 3 in 10 UK adults claim “they are not a numbers person” (Research reveals how poor maths skills are holding the UK back, 2019), and “I can’t do maths” is said so frequently that it doesn’t seem a strange thing to say (Kowsun, 2008 as cited in Attitudes Towards Maths: Research and Approach Overview, n.d.) Moreover, we seem to hold a common belief that strong mathematical abilities are a genetic gift possessed only by a rare few.

Why do we seem to have this collective opinion? Is there any actual truth behind the idea that we are “born good at maths”? What does the science say about all that?

**Why do we think maths skills are genetic?**

First, let’s note that the human need to find an external reason for events is actually very relevant here. Basically, a lot of us like to think that the events in our lives are actually out of our own control. In some events (like whether it’s going to rain tomorrow), this is almost certainly true, but in others (like whether you get a new job) it’s often just a belief rather than fact.

This notion is known as having an external locus of control and it’s been proven to have a number of negative effects on things such as health, career development and even learning ability. Very few people have a fully internal locus of control, hence it is unsurprising that so many of us apply the same principle to mathematical ability and claim that we are either good at maths or not.

Another reason for the widespread belief that mathematical ability is decided by your genetics is that many other things involving brain function have been linked to genetics. These include psychiatric disorders, temperament, and even the ability to empathise with others. Thus, it is logical to suggest that other brain functions, such as performing mathematical calculations may also be determined by genetics to some extent. But logic alone is not enough to prove this connection; well-designed scientific studies are required. Let’s take a look at a few…

**The Panamath test**

In many of the studies we’ll discuss, the subjects’ non-verbal approximation skills were assessed using the Panamath test. This test measures both accuracy and response time of estimating “Which colour dots are there more of?” using 160 various images. The dots can be of various sizes (see the images below), but the subject is asked to focus on comparing the quantities of them. To understand more about this test, I actually decided to take it myself to see if having a maths degree meant that I was actually good at non-verbal approximation.

As one would hope, my results did actually show that I’m pretty good at non-verbal approximation. I came almost within the 90% percentile for my age group, with high accuracy but a slow response time (see results below).

According to some studies like Halberda, Mazzocco, and Ferguson’s, this should indicate that I performed well at in-school mathematics tests, which would be true. So, to some extent, my own results would support the conclusion that non-verbal approximation skills are linked to mathematics ability. Take the test yourself and see how you rank at:

https://panamath.org/test/consent.php

**Studies on older children**

In comparison to studies on younger children, there is an abundance of studies on children aged 5 and over. This is likely because it is often easier to use older children in experiments; they can better understand tasks etc.

One of the key studies on older children is a study of 14-year-old children, which found that the subjects’ ‘Approximate Number System’ correlated with their past scores on standardised mathematics achievement tests (Halberda, Mazzocco and Feigenson, 2008). The Approximate Number System (ANS) can be defined as the cognitive system that supports animals in processing quantity information without the aid of language or symbols to guide a variety of everyday life decisions (Li, Zhou, and Lindskog, 2019). For example, elephants use Approximate Number Systems when deciding which source of food to eat from (Szkudlarek and Brannon, 2017).

In this 2008 study, it was found that there were large differences in the non-verbal approximation skills between the 14-year-olds. In fact, these differences correlated with the individuals’ past scores on mathematics tests, even from all the way back to just 5 years old. The correlation also remained when other cognitive and performance factors were controlled. This study, therefore, supports the idea that our mathematical ability is linked to our unlearned, evolutionary ability to approximate quantities.

Another study also discovered that children’s “non-symbolic numerical abilities” are correlated to their achievement in in-school mathematics tests (Gilmore, McCarthy, and Spelke, 2010). One’s non-symbolic numerical abilities can be defined in a similar way to their ANS acuity; the ability to process quantity information and perform operations without the aid of symbols. This particular study was conducted on children who were younger than those in the study detailed above – all children were between 5 and 6 years old and attended a public kindergarten. Gilmore et al. tested the children’s non-symbolic numerical abilities using a similar method as the Panamath test, with the added complication of adding quantities before deciding which is larger (see below). The subjects were also assessed for achievement in literacy and mathematics two months after completing their non-symbolic numerical ability tests.

From their experiments, Gilmore et al. concluded three things: the literacy and mathematics test results were strongly correlated, children’s performance of non-symbolic addition correlated significantly with their performance on the mathematics test, and did not do so with performance on the literacy test. This, once more, reinforces the idea that mathematical ability, in particular, is linked to one’s non-symbolic numerical abilities.

**Studies on younger children**

Only one major study of this kind has been conducted on children younger than 5 (before beginning formal education). This was a study of 200 children between the ages of 3 and 5 (with a mean age of 4) by the John Hopkins University, which was published in 2011 (Libertus, Feigenson and Halberda, 2011).

Just like in the studies above, Libertus, Feigenson and Halberda used the quantifying dots method to measure the acuity of the children’s Approximate Number Systems. Each child completed 60 test trials, where the maximum number of each colour of dots in each trial was 15 and dot size varied in 30 of the trials.

The children’s mathematical ability was measured using a test called TEMA-3 which involved verbally counting, comparing spoken number words, reading Arabic numerals, and solving addition and subtraction problems among other things.

Preliminary tests found that dot size and gender had no effect on the accuracy and response time measurements of ANS acuity. The results of the study itself showed that the subjects’ ANS accuracy was positively correlated to their TEMA-3 score and that their response time was negatively correlated to their TEMA-3 score (see graphs below). Hence, this study suggests that the link between ANS acuity and mathematics ability is present before formal education but does not delve into why this link exists.

**Nature or nurture?**

Despite the findings in the studies above, it should be noted that one’s ANS or non-verbal approximation skills develop throughout life. This means that during the years prior to being studied, the subjects’ development in this area may have been influenced by external factors, like their time spent watching TV or their toys. Of course, it’s not possible to hand a newborn baby the Panamath test and ask them which colour of dots is greater. And so, we are left with the problem of determining what is nature and what is nurture.

In this context, proving that a skill is entirely the result of either nature or nurture is near impossible. Imagine your dad is Euclid or your mum is Emmy Noether. It’s likely that you’re going to be pretty good at maths, right? But is that because you have ‘inherited’ your parents’ mathematical abilities? Or is that because, as a result of your parents’ interests, you’ve been surrounded by mathematics materials from childhood? Truthfully, it’s probably a mixture of the two, but no one can be certain.

**General attitudes towards learning**

So why do so many people claim to be inherently good or not good at mathematics? Well, maybe we should actually broaden the scope and think about attitudes towards learning in general.

At the start of this article, we noted that many people like to think that their life is actually mostly out of their individual control. This principle can be extended to learning (and learning mathematics, in particular) and we see that many people do not feel that their ability to learn is in their own control. Hence, the belief that one’s mathematical ability cannot change becomes a self-fulfilling prophecy.

**Quantification in mathematics**

Whilst the basis of mathematics is undoubtedly assessing quantities and the studies above suggest that this skill is linked to mathematics achievement, it’s questionable how much of mathematics (especially in later education) relies on quantification.

University-style problems may involve algebraic integration, solving matrices, or finding the standard deviation of a data set – how much of this actually requires quantification skills? Likely very little. Even with everyday mathematics such as calculating how much flour is needed to make three of a given recipe or finding out how much a 20% discount will actually save you; quantification isn’t really the issue. Performing operations on quantities is what’s necessary for a lot of instances.

So, although a connection between non-verbal approximation skills and mathematics achievement has been established, it would be foolish to imply that each guarantees success at the other. Scored highly on the Panamath test? Great, but it doesn’t necessarily mean that you could get a first-class mathematics degree (and vice-versa).

**Maybe she’s born with it. Maybe it’s… Something else.**

So, what can we actually conclude from all of this? Well, yes, your genetic makeup may have some impact on your mathematical ability, but there’s a heck of a lot of other things that certainly do as well. Sorry, but claiming that your ability is entirely down to your luck in the Mathematics Skills-related Genetics Lottery (sounds a bit less exciting than most) isn’t likely to cut it with many people.

## References

Gilmore, C., McCarthy, S. and Spelke, E., 2010. Non-symbolic arithmetic abilities and mathematics achievement in the first year of formal schooling. *Cognition*, [online] 115(3), pp.394-406. Available at: https://www.harvardlds.org/wp-content/uploads/2017/01/Gilmore-McCarthy-Spelke-2010-1.pdf [Accessed 22 June 2021].

Halberda, J., Mazzocco, M. and Feigenson, L., 2008. Individual differences in non-verbal number acuity correlate with maths achievement. *Nature*, [online] 455(7213), pp.665-668. Available at: https://www.nature.com/articles/nature07246 [Accessed 22 June 2021].

Kcl.ac.uk. 2019. *Research reveals how poor maths skills are holding the UK back*. [online] Available at: https://www.kcl.ac.uk/news/research-reveals-how-poor-maths-skills-are-holding-the-uk-back [Accessed 22 June 2021].

Li, J., Zhou, X. and Lindskog, M., 2019. Editorial: Approximate Number System and Mathematics. *Frontiers in Psychology*, [online] 10. Available at: https://www.frontiersin.org/articles/10.3389/fpsyg.2019.02084/full [Accessed 22 June 2021].

Libertus, M., Feigenson, L. and Halberda, J., 2011. Preschool acuity of the approximate number system correlates with school math ability. *Developmental Science*, [online] 14(6), pp.1292-1300. Available at: https://onlinelibrary.wiley.com/doi/epdf/10.1111/j.1467-7687.2011.01080.x [Accessed 22 June 2021].

n.d. *Attitudes Towards Maths: Research and Approach Overview*. [ebook] Lewes: National Numeracy, p.1. Available at: https://www.nationalnumeracy.org.uk/sites/default/files/documents/attitudes_towards_maths/attitudes_towards_maths_-_updated_branding.pdf [Accessed 22 June 2021].

Szkudlarek, E. and Brannon, E., 2017. Does the Approximate Number System Serve as a Foundation for Symbolic Mathematics?. *Language Learning and Development*, [online] 13(2), pp.171-190. Available at: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5362122/ [Accessed 22 June 2021].

Emilia is a UEA Mathematics graduate, Norwich local, and incoming Consulting Development Analyst at Accenture. Maths-wise, she is particularly interested in statistics and computing, as well as their respective applications to the finance industry. Outside of spending hours of her life puzzling over numbers, she also enjoys a good ol’ pub quiz, shopping, and traveling with her mates.