The many ways we use numbers - are we confusing our young children?

Over the last two years Midlothian Early Years Team have been running an Early Level Numeracy project funded by #STEMnation. Over the time we have delved deep into how numeracy progression looks for some of our youngest learners, looked at the skills they are born with and what as practitioners we can do to help them develop and refine these skills.

As a group of ELC and P1 practitioners we had a number of “light bulb” moments during our discussions based on reading materials. My colleague Jane ( Jane Cunningham PT Mauricewood Primary School) and myself went onto explore these in more depth and work out ways to ensure all practitioners had a chance to think about and questions these ideas.

One of the concepts that caused “light bulbs” was the idea of using numbers as identifiers. In Early Level we are often encouraged to find maths in everyday routines, life and community. Rightly so. However, it did become apparent that while this message enabled maths to be real to children, to help them see from an early age that maths is a hugely important part of life and understanding our world, it could also create confusion in relation to understanding of number.

Numbers, written symbols, were predominantly created to explain an amount, the cardinality of group or set. 4 is a symbol we use as a society to explain the quantity 4. We have also evolved to use numbers as identifiers, a way to name or tag an object but this doesn’t necessarily link to cardinality, it isn’t always explicit. If you have toilet stall named No.3 in your school, when you look in it are their 3 toilets? If you have a 4 on a chair at the snack table – are there 4 chairs, or is it meant to be the fourth in a row, and if so is it still placed like this? Even if it is, again this is number as position ( like no. 12 door) not as quantity. Telephone numbers, bus routes all use numbers as identifiers. In this way children are being exposed to numbers that don’t represent amounts, at the same time as we are trying to help them understand that they do! Let’s count the teddy bears, 1,2,3! Yes, there are 3 teddy bears. 3 means there are three things. But yet it doesn’t if it is a number 3 bus!

It seems so simple when you say it. Yet as a group we discovered it wasn’t that simple and that there were many times when we had discussed numbers with children and had potentially given out confusing messages about the importance of cardinality.

We spent time considering whether children needed to understand this difference, and even whether practitioners did. Discussions continue! We do think practitioners and parents/carers need to be aware of the different ways numbers are now used in society to ensure that we don’t confuse our children. They are used as identifiers (as discussed), in a referential way ( e.g. time) ordinal (positional eg. 2^nd in the race) and cardinal – the all important quantity.

We agreed that is important for children to see numbers in use in a variety of ways but that our focus had to be on helping them develop their understanding of the Number-ness of number otherwise known as Number Sense. The importance of knowing 4 is made up of 4 things shone through all our professional reading and research very clearly and could easily make another blog post!

Dr Sue Gifford sums it up in the following quote “This dual meaning of numbers…..can be confusing for children, particularly if they do not have an understanding of cardinal values like the Threeness of three” P, 82 Gifford Teaching Mathematics 3-5

We decided therefore to start to question and think about all the numbers we displayed or pointed out in our ELCs, classrooms and communities and ask ourselves first if they help build Number Sense and understanding, or were they just a little bit confusing and at this important early stage and perhaps unnecessary.

The journey and discussion continues!

Further reading on Number Sense and Numbers as Identifiers

Big Ideas of Early Mathematics – Erikson Institute The Early Maths Collaborative

Teaching Mathematics 3-5 Developing learning in the Foundation Stage - Dr Sue Gifford

Early Number Sense Jeni Black – Nrich Website Early Number Sense Nrich - https://nrich.maths.org/10737

Teaching and Learning Early Number edited Ian Thompson

Realising the Ambition - Education Scotland 2020