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How Do Children Learn Maths?

Concepts such as measurement, addition, subtraction and shape may seem like simple common sense to us, but everyone has to learn them at some point. So, how do young children begin their mathematical learning, and how can you support it at home?



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First of all, what counts as ‘Maths’?

When somebody says the word ‘maths’, your mind probably goes straight to multiplication tables and finding the angles of a triangle. In fact, maths covers a pretty broad range of concepts, all of which find their bases in early years learning. Concepts that will be explored by little ones include:

  • Counting (both forwards and backwards).
  • Understanding size.
  • Understanding quantities and mass.
  • Recognising shapes.
  • Understanding patterns.
  • Classifying (sorting things into groups).
  • Exploring dynamics (putting things together, pulling them apart, throwing, throwing, flipping and spinning).
  • Investigating spatial relationships (talking about directions or where things are in relation to other things).

Exploring these concepts early on will give children a strong foundation upon which to build more formal mathematical learning.

It’s also important to remember that young children are learning all the time, and do not differentiate between the different ‘subjects’ they are learning about throughout the day. Whether it’s a new word or the knowledge that a square has four equal sides, it’s all just new information!


But how do they actually learn these things?

Being able to recite numbers 1-100 and actually having an understanding of why each number goes where it does are two different things (the latter will make addition and subtraction much easier!). Similarly, knowing that the shape on your block toy is called a triangle is not the same as knowing that every shape with three sides, no matter their lengths, is also a triangle. 

For effective future learning to take place, children need to have a working understanding of mathematical concepts, rather than simply reciting what their parent or teacher told them. For example, to begin to understand how π (pi) works, you first need to understand that a circle will always have the same width, no matter which direction you measure it in. The complex maths we learn at secondary school and beyond is all based on concepts we learn in our very first years.


So, how can we build understanding?

Well, there are several key theories on the best way to do this, but all of them follow a similar structure. Let’s look at two of them.

Bruner’s Three Phases

Jerome Bruner was an American psychologist specialising in Learning Theory. He believed that, in order to learn anything, children went through three phases:

1: Enactive.
Children engage with something concrete, allowing them to explore and test out ideas. A good example is block play.

2: Iconic
This is when children begin to explore a concept ‘on paper’, using diagrams or images rather than physical objects. They might use a picture of four oranges, or a drawing of a tower.

3: Symbolic
Once children have a full grasp of the concept, they can begin to represent it through abstract symbols. For example, they can write the number ‘4’ without needing to draw 4 of anything.


Liebeck’s ELPS

British mathematician, Pamela Liebeck, built on Bruner’s theory to create her own four-step learning process for mathematics:

Experience
Gaining experience of the concept in the ‘real world’, such as counting items, building blocks or measuring ingredients.

Language
Learning to use language that can describe the experiences of step one. This includes mathematical language such as ‘bigger’, ‘smaller’, ‘more’, ‘less’, and the names of numbers and shapes. Parents and teachers are of particular importance at this stage, as they can say the names of things while children explore them.

Pictures
Much the same as Bruner, this stage involves learning to use images and diagrams to represent maths.

Symbols
At this stage, children can use abstract symbols and language to explain mathematical concepts, such as number digits.


You may have noticed that both processes began in the physical world, giving children the opportunity to explore concepts kinaesthetically. Not only do young children learn best by using their own senses and bodies to explore, but physical experiences are required for children to give meaning to later abstract concepts. They will not be able to solve 1+4 if they have never held five items in their hands and counted them out. From here, you can begin to attach words to numbers, before eventually growing the abstract understanding of numbers and addition.


Scaffolding

Another important aspect of learning is called ‘scaffolding’, or ‘the zone of proximal development’. Essentially, this is the idea that if a child explores a concept with someone who already understands it, they will be able to learn more than if they explored alone. 

It is key to note however, that scaffolding involves ‘exploring together’ not ‘teaching’. As the person-in-the-know, you are there to provide hints and ask questions, whilst still giving the child the space to explore and create their own understanding.

For example, if a child said that a circle is always bigger than a square, you might ask them if they can draw lots of different sizes of each, then cut them out and see if the small circles can fit inside the big squares. They are still actively exploring, you just gave them a nudge in the right direction.

For true understanding to develop, children need to be active in their own learning, and confident that they are able to learn! Simply telling them the answers or saying they’re wrong could both limit their learning and damage their self-confidence as a learner.


Maths at Home

So, now that you have an understanding of how children learn, what can you do at home to support their mathematical learning?

Luckily, most of it is pretty intuitive, and you’re probably already doing more than you think! The key is to use the things your little one is interested in in daily life, and draw their attention to the mathematics at play.

Here are a few ideas:

  • Counting
How many plates do we need? There are two on the table, how many more do we need? How many flowers can you count? How many toys?
Counting and addition can easily be worked into many activities throughout the day!


  • Understanding size.
    Try getting your little one to compare toys to one another (is the cow bigger or smaller than the sheep? Is this tower taller or shorter than that one?). Encourage them to work out whose clothes in the laundry belong to who based on their size, or plant sunflowers and measure their growth.


  • Understanding quantities and mass.
    Cook! Try making meals together, encouraging your little one to weigh and measure. Draw their attention to the fact that, if they move water from a jug to a glass, the amount of water doesn’t change, and encourage them to tell you how much or little they want to eat and drink.


  • Recognising shapes.
    Toys are great for this. You can make all sorts of different shapes out of blocks, toy roads and fences. You can also get those craft materials out and draw, paint, cut and stick!


  • Understanding patterns.
    Why not make necklaces or bracelets, or play some clapping games? The rhythms in simple songs are great for picking up patterns!


  • Classifying (sorting things into groups).
    Get your little one involved in sorting the laundry! Pair socks, separate lights and darks, and group all the clothes belonging to one person together. You can also get them to help in putting away the washing up after dinner, by grouping together cutlery or bowls and plates.


  • Exploring dynamics (putting things together, pulling them apart, throwing, flipping and spinning).
    Squash balls of play-dough (or real dough!), play ball games and build things with blocks. Dynamics are an important part of daily life, so there are plenty of opportunities to draw your little one’s attention to them.


  • Investigating spatial relationships (talking about directions or where things are in relation to other things).
    Use your full vocabulary when playing and going about your daily activities. Should the pan be inside the oven, or on top of the stove? Is the doll’s sofa in front of the TV or beside the door? Can you put the oranges inside the bag?


All in all, mathematical learning in the early years is pretty intuitive, and in no way limited to particular activities. Your little one’s natural interest in exploration and love for learning will lead them to make plenty of their own discoveries! But, by gaining an understanding of how mathematical learning takes place, you can properly scaffold their exploration, and give them a helping hand.

So, I hope this helps, and happy exploring! If you have any questions, or want to share your maths journey with us, drop us a message on our Instagram.

Lizzie
Content Creator at MEplace

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