Subitizable Symbolic and Non-Symbolic Number Processing in Developmental Science (Jane Hutchison & Ian Lyons)

July 12, 2019 – Graduate student Jane Hutchison and Professor Ian Lyons, in collaboration with researchers at the Toronto District School Board and the University of Western Ontario, have had a paper published in Developmental Science.

Description of study findings

Basic numerical skills at the outset of formal schooling, such as the ability to count or say which of two numbers is the greater quantity, are strong predictors not just of future math skills, but also of academic achievement in general. So what basic skills are useful for children to have when, for instance, they enter kindergarten? Researchers have differed in their answer to this question, based in part on a debate about whether it is better for children to learn how to work with non-verbal, perceptual quantities (such as knowing at a glance which of two sets of objects contains more objects), or whether it is better to just jump straight to understanding number symbols, such as Arabic numerals. Previous work we conducted (Lyons et al, 2018, Developmental Psychology; OSF link) showed that children who entered kindergarten with strong symbolic number skills got better at working not only with number symbols but also with nonverbal, perceptual quantities by the end  of the kindergarten year. However, the opposite was not true: children with strong perceptual quantity skills at the beginning of kindergarten got a little better at working with perceptual quantities by the end of the school year, but these skills did not predict improvements in symbolic number skills. One take-away from this study is that students who came to kindergarten with solid symbolic number skills were equipped to improve across the board; those who arrived with strong perceptual quantity skills, but weak symbolic number skills, struggled by contrast.

However, our most recent study (Hutchison et al., 2019, Developmental Science; OSF link) demonstrated that this was only part of the story. It turns out that not all perceptual quantities are the same. Researchers have long known that perceptual quantities ●, ●●, ●●●, and ●●●● (i.e., 1 to 4) operate a bit differently from larger quantities. Humans – even young children – have the ability to rapidly recognize the exact value of these small perceptual quantities (a process referred to as subitizing), but they can only approximate the value of larger perceptual quantity. Given that exact representation is a key property of symbolic numbers, one might expect the development of symbolic number skills to be more strongly related to the development of small quantities, whose exact value can be immediately recognized, but not large quantities, whose value can only be approximated. This is exactly what we found. For small, subitizable quantities (1 to 4 and ● to ●●●●), the relation between symbolic and perceptual numerical skills was bidirectional over the course of kindergarten. This means that strong symbolic number skills at the beginning of kindergarten predicted improvement in perceptual quantity skills by the end of kindergarten and vice versa:  strong perceptual quantity skills at the start of kindergarten predicted improvement in symbolic number skills by the end of kindergarten. Crucially however, this bidirectional relation was only found for small, subitizable quantities. Quantities outside this range (5+) followed the pattern we saw in our previous paper: symbolic number skills predicted improvements in perceptual quantity skills over the course of the kindergarten year, but not the other way around. 

So what does this mean for kindergarten children? Based on our results, entering kindergarten with strong symbolic number skills is beneficial for the further development of both symbolic and perceptual numerical abilities. On the other hand,  coming to the table with strong perceptual quantity skills appears to primarily benefit the further development of perceptual, but not symbolic, quantity skills, with the important exception of smaller quantities (1-4). Working with these ‘subitizable’ quantities may help to improve symbolic number skills as well, albeit still within this more limited range.

On a theoretical level, it’s worth noting that perceptual quantity processing is something that is present from a very young age – as early as infancy – and it is shared across many other non-human species. In contrast, number symbols were invented only a few thousand years ago, and children must learn these through cultural means (i.e., parents and educators). Our work suggests that, for the most part, thinking with cultural numbers early in the education process in fact shapes our thinking with biologically ancient, perceptual quantities, and not the other way around. The quantities 1 to 4 (or ● to ●●●●) are potentially crucial exceptions to this rule though. Number symbols have to be learned somehow, and researchers have proposed this happens primarily by linking symbolic and perceptual quantities specifically in the subitizing range. Our results provide support for this view.