## Number sense

Number sense is considered as an innate numeracy skill, which not only humans but also some animals, such as fish and birds have. As the name says, it refers to sense of numbers. Number sense enables us to estimate the number of cars on the parking lot without counting them on-by-one, or to tell whether there are more people queueing in one line or in the other one.

APPROXIMATE NUMBER SYSTEM (ANS)

It has been proposed that we use a system called approximate number system, ANS, when estimating magnitudes (e.g. object or dots) approximately, or making comparisons of numbers (1).

When testing what kind of number sense an individual has, researchers often use tasks, in which you need to compare a number of dots or number symbols. Those who have a good number sense often respond quicker and more accurately in these tasks compared to those with weaker number sense.

Look at the pictures.

Can you quickly estimate which of the pictures has more dots?

Can you quickly say which of the numbers is bigger?

How far apart the numbers are from each other may also affect the performance in this type of task. This is called a distance effect. It takes less time to judge that 9 is bigger than 2, compared to judging that 9 is bigger than 7, as 9 and 2 has a bigger distance between them compared to 9 and 7.

SUBITIZING

Another innate ability related to number sense is subitizing. Subitizing means a rapid and accurate judging of small numbers (1–4) presented as objects.

Look at the picture.

Can you quickly say how many dots there are, without counting the dots one by one?

GROUPITIZING

When children start to develop in their addition skills, that is to add collections of objects together, they can also start using their subitizing skills in order to count larger collections of grouped objects without counting one by one (2). This is called groupitizing. For example, a child may see two groups of threes in a picture, then add threes together, and quite quickly get an answer of six.

Look at the picture.

Can you count the dots by groupitizing? Do you come up with more than one solution how to group the dots and getting the same answer?

RELATION TO OTHER MATHEMATICAL SKILLS

The latest research is consistent in its findings that symbolic number sense (e.g., measured using number comparison tasks) seems to relate to mathematics achievement. Those children with weak symbolic number sense skills seem to perform weak in mathematics in general, or showing mathematical learning difficulties (3, 4). The research results concerning non-symbolic number sense (e.g., measured using dot comparison tasks) have been more mixed, which partly can be explained by using different methodological approaches in studies. Some studies have found a relation between non-symbolic number sense and mathematics achievement, some not. Children having mathematical learning difficulties often have problems in subitizing tasks, and they are slower and more inaccurate in comparing the dots and numbers compared to their age peers. In everyday situations it might be difficult for these children to estimate the number of objects, for example saying that there are 20 sweets on the table if there are actually 8.

IN OUR PROJECT

In our project, we will assess children's symbolic number sense. In the number sense tasks the child needs to compare 1- and 2-digit numbers (e.g., which is bigger 2 or 7).

REFERENCES

(1) Dehaene, S. (2011). Number sense. How the mind creates mathematics. New York: Oxford University Press.

(2) Gilmore, C., Göbel, S. M., & Inglis, M. (2018). An Introduction to Mathematical Cognition. Routledge.

(3) De Smedt, B., Noël, M.-P., Gilmore, C. & Ansari, D. (2013). How do symbolic and non-symbolic numerical magnitude processing skills relate to individual differences in children’s mathematical skills? A review of evidence from brain and behaviour. Trends in Neuroscience and Education, 2(2), 48–55.

(4) Schwenk, C., Sasanguie, D., Kuhn, J.-T., Kempe, S. Doebler, P. & Holling, H. (2017). Non-symbolic magnitude processing in children with mathematical difficulties: A meta- analysis. Research in Developmental Disabilities, 64, 152–167.