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© Copyright M. Worthington & E. Carruthers 2010 |
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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
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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
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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
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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 |
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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.
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To see these examples in greater detail,
please click on the images. Each image will
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First
row - written forms: |
Conor:
“number 13” |
Jonathon:
“3” |
Sam: “8” |
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Second row –
Symbolic (Early written numerals): |
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Louis: “89” |
Sarah: “7” |
Joe: “7” |
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Third row – Iconic: |
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Abigail: “Number 5” |
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Fourth row – Symbolic |
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Sarah: “4” |
Abigail: “Number 8” |
Elliot: “6” |
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Here Abigail has used a
number she knows and can write, to stand for the number
she wants to write - ‘8’. |
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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.
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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
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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
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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 |
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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
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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 |
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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
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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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