How do children begin to understand Maths

Observational research record

To help us understand how to design digital maths games for Early Years children we need to understand how young children begin to comprehend maths as a concept and the steps they take to gain a foundation of understanding.

This requires that we work with the experts! Children and the teachers who support their learning.

On this blog I will post my observations from ethnographic research carried out with a number of primary schools.  I am particularly interested in building my understanding of the learning environment, how teachers encourage learning through play, the communication used to introduce maths, and how teachers affirm reflection and self awareness in the child and the activity they have experienced, “meaning-making”.

Visit 1 - Wyborne Primary School, New Eltham, London

“Securing emotional confidence is the key to children's progression from Early Years to Key Stage 1” EYFS Lead teacher, Wyborne Primary School."

During my visit to Wyborne I was able to observe teaching methods for two groups; Reception where the children are 4 or 5  years old, and Early Years Foundations Stage (EYFS) where children are 3 or 4 years old. In both settings I was able to observe children learning through freeplay, indoors and outdoors and carpet time teaching activities.


The morning began with a carpet based teaching session where children followed the teacher creating cursive text. The teacher worked directly on the smart board and children sitting in front of the board copied as instructed on individual A4 whiteboards. The lesson continued with phonetic sounding of 'igh' and progressed to questioning how 'igh' becomes 'sigh etc.  

This session was followed by Freeplay activities on structured stations.  The teacher was clear to introduce the Freeplay activities, explaining the children need to take turns and share the activities.  Each station had a card with basic written instructions.

Sorting Exercise - Sort the trains by colour

The children were given a large basket of toy trains and they were asked to sort the trains into groups by colour and count how many of each colour.

As well as counting how many, they also considered which line of trains was the longest, shortest, biggest etc, were there more or fewer in the comparative lines of trains.  These terms were discussed in conversation by adults with the children playing with the trains.

Ob 1
Children were confident in the task and keen to show off their understanding and mastering of the activity.  Children demonstrated what was described as ‘alongside playing’ where they copied others but showed caution in verbalising the number of trains - peer learning first to ascertain understanding then trying it out for themselves.
Count the Bears

Count the Bears

Number and pattern - Count the Bears

Collect a group of bears, count them and write the number on the card, then draw the bears next to the number

Size and Capacity - Filling pots with oats and lentils

How many scoops filled each pot? Children were encouraged to estimate / guess, then find out through filling the pots - trying out. They were free to work with others or on their own, again in this activity I could see alongside play where children were modeling their approach by watching other children engage with the oats and pots

Filling pots with oats and lentils

Filling pots with oats and lentils

Putting snakes in order of length

Putting snakes in order of length

Longest, shortest - Putting snakes in order of length

Children were asked to line the snakes in order of size, shortest to longest. No children played with this activity; the teacher noticed that the activity was not popular and tested the activity out with the group later in the afternoon during a carpet activity, many children found this difficult which she concluded was the reason that the activity had not been engaged with.

Ob 2

Children show their understanding of a topic by participating with the activity that has been set up, watching then trying out, learning through experience.

Discussion with Reception Teacher

How does mark making happen in Maths?

“Children do this when its relevant to them - it's most likely to happen in role play”

How do children make meaning of a task?

“This is adult driven through language, using words like How many? etc they use questions and discuss with the children” see Sorting trains notes."

“Adults observe if and when children show in play, through words, or actions, understanding of a task - this is then logged in the child's profile."  

Ob 3
I saw this in action later in the day.  While watching the children set up a circle game outside, which involved children holding hands in a circle; they talked about making the circle bigger by adding people to the circle. They also stacked tyres and got in the tyres, building it higher and using words like ‘make it taller’.

How do you use digital tools like iPads and the Smart Screen?

“The large Smart Screen is good for showing a concept or idea at carpet time. Videos or animations reaffirm a topic that has been introduced - the visual and audible nature of the animations and films are very engaging”

“The large Smart Screen is not reliable for interaction as hotspots are not always where they should be and this can affect the affirmation of learning if the selection area is giving the wrong feedback”.

Children were invited back to the carpet for group activities

What's missing - Mr Caterpillar - number sequences

The teacher held up to the class a picture of a Caterpillar on a board. Each segment of the caterpillar had a number on it which is held by velcro, the teacher takes away a number or swaps a number and children are invited up to put the numbers in the right order.  The numbers are reordered again and children are asked which number is missing - they are asked to write the number in the air then write it on their friends back

Draw and count

On the Smart Board the teacher draws a snowman and talks about seasons and the weather, while doing this she continually interacts with the children, asking them to tell her how many eyes to draw how many buttons etc.  The Children count out loud.

Youtube films

Children practice counting along to the songs played on videos, they then count in different languages.  Children who can speak more than one language are asked to show the class.

Ob 4

The teacher was careful to ensure that all children demonstrated understanding, which was important to gauge learning and allow the children to show they understood.

Forest School and Outdoor play

Forest School

Forest School

An area next to Reception and Nursery is set up for Forest school learning.

I was given an introduction to the Forest School and outdoor play areas, the teachers explained how important outdoor play or outdoor learning was for the children in particular the Forest School program of learning.  


Some of the main principles are written below

  • Forest school needs to be a long-term process of regular sessions, rather than a one-off or infrequent visits; the cycle of planning, observation, adaptation and review, links each session.

  • It uses a range of learner-centred processes to create a community for being, development and learning.

  • It takes place in a woodland or natural environment to support the development of a relationship between the learner and the natural world.

  • Promote the holistic development of all those involved, fostering resilient, confident, independent and creative learners.

  • It offers learners the opportunity to take supported risks appropriate to the environment and to themselves.

  • It is run by qualified Forest School practitioners who continuously maintain and develop their professional practice.

There is also other outdoor play areas directly outside the Nursery and Reception classes, this enables freeflow activities to be set up and children chose if they want stay in or go outside.

20180226_104030 2.jpg

Above is the outdoor play area next to reception classes - teachers reported that children make marks on the blackboard.  Below are the large scale blocks for outdoor use in the Nursery, these are very popular.

Ob 5
It was evident that children felt more liberated in the outdoor environment and enjoyed playing out the concepts they had been introduced to during the learning sessions (see notes in Ob 3).


The afternoon began with a carpet activity which was a Maths Focus Session

Counting claps

Children sat on the carpet in front of the Smart Screen - Youtube video Super Simple Songs plays a counting song, children watched the video.  The teacher asks the children to Clap as they say the numbers 1-20, counting claps and relating the number to the action.

On the wall next to the carpet is a numberline, children use a pointer stick to count and move forward and backwards making sure not to miss a number.

Listen only and count

The teacher held a metal box and some blocks, she asked all the children to shut their eyes, and listen to the sound of the blocks being dropped in the box and to count in their heads the sounds they hear.  She then asked the children to show with their fingers the number of sounds they heard. Children were then encouraged to use two hands to make the same number - the activity is extended to find all the possible combinations of making the number with two hands, relating number bonds.

Ob 6
It was impressive to see such young children quickly make the connection between a number and how it could be broken into portions using their fingers as tools.

Count on

The teacher explained to the children they were going to start at number 4 and count on, she asked the children to show 4 fingers and add a finger everytime they heard a block drop in the box, 2 blocks fall in the box the children have 6 fingers showing.

The teacher reiterated  the four things the children has learnt and praised them for being so clever.

Discussion with EYFS Lead teacher

How do you introduce maths to the children?

“We begin learning through maths or literacy focused sessions on the carpet, these are supported by freeflow activities.  Adults support freeflow by adding language, like bigger, longer etc”.

How do you know they understand the meaning?

“We see evidence through the children's spoken words and actions in both short and long observations, never questioned by an adult, always from the child led play.  Regarding maths - the language is established first then the meaning and number writing. The whole concept of EYFS is to establish emotional self confidence in learning”

Ob 7

Establishing emotional self confidence in learning  - this statement is the basis of children being confident learners as they progress, being comfortable with their own strategies of problem solving.

What do you see children do in the way of maths mark making?

“Children lead in this activity they do it when its relevant to them - this could be water marking for example, or a recent example was when the children decided to do a show and thought they would need Tickets so they made them the action was spontaneous”.

How are pen holding skills taught or guided?

“When the child is ready I introduce the tripod flip, The aim is for the child to be able to write their name by the end of EYFS."


Do you use Subitizing or patterns?

The term was clarified when I pointed to a plaque in the garden and the Nursery teacher confirmed the use of domino cards

“She reiterated it is crucial to get the stages right; language first then you have a chance of children taking on more abstract concepts of maths”

Ob 8
Children learn through doing; they show each other, they try things out, they copy or model each other.
Children show understanding through language in freeplay, which is observed by adults and recorded.
Adults make meaning relating language to the task, match, fit together, size, shapes, bigger smaller.

How do you use digital tools like iPads and the Smart Screen?

“iPads are not used in class much but they are available; when we use them an egg timer is used to manage turn taking”

“Children use them at home and it's nice to do different things a school”

The teacher had strong concerns that the use of tablets can be negative, see points below:

  1.          Doesn’t help development of language
  2. Reduces peer interaction

  3. Kids get ‘locked in’

  4. Can get overly attached

  5. She felt they were not useful at this age

However they can be used as a calming aid

The teacher felt ICT goals are easily achieved from the experiences children have at home with devices

Literacy Focus Session - Carpet activity

Children listened to the story - “Dogs colourful day”, this was read to the children from a book during the story the teacher asked the children questions.  How many spots? Counting on from..., counting backwards and forwards building on the maths focus task earlier in the afternoon.

6 spots - show all the ways to make 6 spots - children respond holding up their fingers in various combinations 2 fingers plus 4 fingers, 1 + 5, 3 + 3

Teacher tests every child before they leave the carpet for a snack to clarify if they have understood the learning outcomes of the session.

Further discussion with EYFS Lead teacher

Do the children ever use tracing activities to help with their pencil control?

“Tracing goes in and out of fashion, white/wipe boards work well because children can wipe off their work, boys don’t like getting it wrong”


Ways to learn Maths

I now have a clear understanding from one setting how the teaching of Maths is conducted in EYFS.  It was clear at the date of the session (Spring term), that the school children understood the routine of the learning environment and were able to concentrate and engage, everything ran smoothly

I followed up the visit with a request to understand situations where Maths learning was difficult and what were the scenarios where children did not show understanding

Use of Digital

This school was confident with their approach, which did not include activities for children to engage with digital resources independently. They have tried to use iPads but have rejected them as a resource for a number of very valid reasons both practical and relating to learning.


  1. Doesn’t develop language
  2. Reduces peer interaction

  3. Kids get locked in

  4. Can get overly attached

  5. But can be used as a calming aid

  6. ICT goals are easily achieved from the experiences children have at home with devices

  7. iPads are not used much but they are available

    • “Children use them at home and it's nice to do different things a school”

    • Large Smart Screen is good for showing a concept or idea at carpet time. Videos or animations reaffirm a topic that has been introduced - the visual and audible nature of the animations and films are very engaging


  1. The large Smart Screen is not reliable for interaction as hotspots are not always where they should be and this can affect the affirmation of learning if the selection area is giving the wrong feedback.
  2. IPads, management of charging can be difficult, knowing before you need them if they are charged up?

  3. IPads are a shared resource with Nursery so not ‘to hand’ when setting up freeflow activities.

Moving forward

Identify a wider pool of settings to see if this is widespread belief