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Gallery 2

    © Copyright M. Worthington & E. Carruthers 2012

Case-studies of individual children from Early Excellence Centres in England.
 
The dimensions of each child's mathematical graphics in the case-studies below, are shown in the Taxonomy.

In Gallery 2 we are showcasing examples sent in by teachers who are working in this way. These case studies were written by teachers from 'Project 2003' who teach in Early Excellence centres throughout England.

Please scroll down for case studies


Junior, age: 3 years Wigan, Lancashire

Context: role play – ice-cream parlour

Observation: we had been talking about the seaside. Several children were playing freely with real coins and adopting the role of customer and ice-cream attendant. They used the play till and seemed naturally to exchange one coin for one ice-cream – so that if four ice creams were bought, four coins were handed to the attendant.

Junior chose to put something down on paper to show what he had been doing. He drew round five shapes to represent the pennies and told me he had bought four ice-creams: he explained that he had forgotten he’d given four pennies (rather than the five he’d drawn). He explained that the large rectangle he’d drawn was an ice-cream’. The remaining marks were ‘something off the T.V.’ – by this time his thoughts seemed to have moved away from playing ice-cream parlours!

The maths: counting to five. Marks based on one mark for one item, i.e. five circles to represent the five pennies.

(See the taxonomy) dimension: 4b - Representing quantities that are counted

   


Lauren – age: 3.6 years, Wakefield, Yorkshire

Context: snack time

Observation: On Friday I observed a new member of our Nursery group - Lauren - recording children at our snack table. Lauren was sitting at the table with a group of friends. She had found our snack register and was marking off children as they came to have a snack. She could not read their names, but was ‘ticking’ the names - in green felt-tip - that had already been marked off by an adult. I think I would have previously regarded this as literacy rather than mathematical mark-making, and am really pleased to have been enlightened by this research programme.

The maths: one-to-one counting; data handling

(See the taxonomy) dimension: 4b – representing quantities that are counted

 

   


   


Molly, age: 3 years 9 months Wigan, Lancashire

Context: birthdays

Observation: Molly was sitting with a group of friends at the graphics table. There were birthday cards with ages (numbers) on and pens and paper there. One child had just had his fourth birthday, so there had been talk of parties. Molly wrote on the card and told me “it says ‘Happy Birthday to Molly’” and said that she was 4. Molly is very keen to be four as many of her friends are already – it’s obviously very important to her.

The maths: measures (time/age) and number

(See the taxonomy) dimension: 1 – Early explorations with marks


   


Children: nursery, 3 & 4 year-olds Plymouth, Devon

Editor’s note: this example is valuable to show the range of forms (marks) that children use. The children read the seat number they had written.

Context: plane tickets

Observation: We had been looking at transport and journeys. The children had become keen on planes and would line up chairs to make several rows of seats. The driver (they didn’t take to the word ‘pilot’) always sat in the front and the children would pop on and off the plane rather like you would do if you were travelling on a bus.

We decided to make some 'tickets' and the children used them to write their own seat numbers, and they used a variety of marks. Interestingly we had two older children who could both represent standard numbers, but who chose to use tallies and dots – they counted and re-counted their marks just to check the number they'd represented. This play led to tickets being used in a variety of situations.

The maths: writing and using numbers for real purposes

(See the taxonomy) dimension: early written numerals; numerals as labels; representing quantities that are counted.

 

To see these examples in greater detail, please click on the images. Each image will open in a new window. Please close the window to return to this page.

First row - written forms:

Conor:
“number 13”

Jonathon: “3”

Sam: “8”

     
Second row –
Symbolic (Early written numerals):
Louis: “89” Sarah: “7” Joe: “7”
 

Third row – Iconic:

Abigail: “Number 5”
 

 Fourth row – Symbolic

Sarah: “4” Abigail: “Number 8” Elliot: “6”
Here Abigail has used a number she knows and can write, to stand for the number she wants to write - ‘8’.

Tim, age: 4.1 years, Haringey, London

Context: counting logs

Observation: Tim was in the garden, lifting old fence posts onto a trolley. He spent time transporting them to another area of the garden. His teacher asked if he knew how many he had moved. There were clipboards with paper and pencils outside and later in the play session Tim used these to help him think about what he’d done. He counted the marks as he wrote them (from left to right) and when he got to 8, he went back and checked, counting one to one and then continued to 25 (he missed a few). He then drew four long logs, saying “they were very lo-o-o-ong”. Tim then wrote a sign which he read as ‘This says “Do not move my logs and do not park here”’

The maths: counting beyond 10; counting one-to-one and self-checking; length (measurement)

(See the taxonomy) dimension: 2. early written numerals; 4b – representing quantities that are counted.
   


Lara, age: 4.4 years Plymouth, Devon

Context: number lines

Observation: we had been using number lines as a group and had been counting and arranging numbers on our washing line. In the graphics area I had added a pot of paper numerals and several number lines. Several children were busy pasting and stamping – using everything that was available. Soon the idea that they were making number lines sprung up within the group. Lara then went on to ‘do numbers’, saying ‘I can do a 4, can do a 5, I can do a 1 and a 2’.

I do not recall Lara attempting to represent numerals of her own accord on any previous occasion.

The maths: number lines, exploring written numerals

(See the taxonomy) dimension: 2. Early written numerals
 


William age: 4.6 years, Greenwich, London

Context: Star Wars

Observation: William is very interested in 'Star Wars' and often plays out various scenes with his friend. He often chooses to draw pictures similar to this. The colours are important - red for Darth Maul etc!!

Each mark represents a ‘light sabre’; each has an owner (characters from Star Wars). William therefore had to work out how many to draw. He draws hundreds of these pictures at the moment – either of light sabres or bows and arrows from the Lord of the Rings – they seem to be linked to his fascination at the moment with counting or amounts and he will count all sorts of objects, again and again.

We've changed our policy to allow superhero play and let children make guns swords etc from construction and workshop materials. We all feel that this has helped us find a way of supporting some of our children especially boys. So that instead of saying no you can’t do that all the time we can extend their interests especially in areas like mark making and increase their self esteem.

The maths: one-to-one counting; abstraction; counting in his head (Super Heroes he recalls)

(See the taxonomy) dimension: 4b – representing quantities that are counted
   


Mark, age: 4.8 years Greenwich, London

Context: playing garages

Observation: We had a garage role- play area outside. Mark had been playing in the garage next to the Graphics area. He began drawing these crosses in a corner of the playground near the graphics area and told everyone who approached that it was a no entry area!

Lots of children (mainly boys) were busy mending cars and writing on clip boards. Mark does not often choose to mark make.

The maths: exploring abstract symbols for a purpose

(See the taxonomy) dimension: 1 – Early explorations with marks


   


John, age: 4. 9 years Greenwich, London

Context: phone numbers

Observation: I was with a group of children in the Graphics area when John approached me, with a brief case in one hand. Looking at the phone on the table, he told me he’d just dial his number. He then took a piece of card (an old birthday card) and said “I’ll write my phone number down for you”. He wrote on the reverse, and then handed the card to me and asked me to write my number down too.

John is very interested in writing information at the moment. He particularly enjoys writing messages.

The maths: using numbers for his own purpose and to convey meaning to others

(See the taxonomy) dimension: 3 – numerals as labels
   


Lucy, age: 4. 9 years Greenwich, London

Context: triggered by play with raffle tickets

Observation: Lucy and Sue are playing together with some raffle tickets. Lucy has picked up a little book with blank pages and filled it with numbers, repeating '5, 6 and 7'. When I join them, Lucy is copying her friend in writing the letter ‘S’ inside the book cover, and next to a '5'.

The maths: writing numbers for her own purpose

(See the taxonomy) dimension: 3 – Numerals as labels


   


Callum, age: 5.0 years Wakefield, Yorkshire

Context: drinks list

Observation: Callum was in our holiday club playing in the role play area. He decided to write a drinks list for the staff. In addition to the drinks he wanted to know how many biscuits each person wanted and this is the way he recorded it.

During his time with us in Nursery, Callum was a reluctant writer, often saying” I can't write, I can't do it" even though we provided plenty of opportunities for him to make marks in play situation. He now attends a local infant school and it was noticeable how much more interested he had become (when we saw him at the Holiday Club) - in recording numbers and information.

The Maths: counting, collecting data

(See the taxonomy) dimension: 3 – Numerals as labels; 4b – Representing quantities that are counted
   


Chloë, age: 5 years – (child with special learning needs) Bath, Avon

Context: register

Observation: Chloë had brought her own exercise book from home to play with in the graphics area. She said she was “making register”. She wrote the names down (as squiggles) for the children in the class and then counted them to see if she’d made the right number of marks. She counted to 4 and then counted random numbers to 20. She used number strips to check and count how many children were in the class. She chose to use tallies to represent the number of children who were away.

Chloë has a statement of special needs and finds articulating language difficult. I have found it interesting to observe how the children have responded to an increase in the variety of equipment that I have put in my graphics area. Although in the past we have used number lines I have now included counters, number tape and a variety of dice in the graphics area. Chloë has never before shown any interest in the graphics area.

The mathematics: counting and relating names of numbers to children.

(See the taxonomy) dimension: 4b – representing quantities that are counted
   


 

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